Graph edit distance determination in pharmacochemical-like space

Abstract

Systems and methods for estimating a graph edit distance (GED) between compounds are provided. A first graph representing a first compound includes a plurality of nodes and a plurality of edges. An atom of the first compound is represented by the node of the first graph, and a bond of the first compound is represented by the edge of the first graph. A second graph representing a second compound also includes a plurality of nodes and a plurality of edges. Atoms of the second compound are represented by the nodes of the second graph, and bonds of the second compound are represented by edges of the second graph. The first graph is input into a model to generate a first potential embedding. The second graph is input into the model to generate a second potential embedding. An estimated value (GED) between the two compounds is determined from a difference between the two potential embeddings.

Description

[0001] Cross-references to related applications

[0002] This application claims priority to U.S. Provisional Patent Application No. 63 / 492,200, filed March 24, 2023, entitled “Graph Edit Distance Determination in Medicinal Chemical Spaces,” which is hereby incorporated by reference.

[0003] This application also claims priority to U.S. Provisional Patent Application No. 63 / 492,208, filed March 24, 2023, entitled “Improved Binding Site Models,” which is hereby incorporated by reference. Technical Field

[0004] This application relates to determining an estimate of the graph editing distance between compounds. Background Technology

[0005] Figure 3A illustrates the graph edit distance and how it measures chemical similarity. Molecules can be represented as graphs, where the atoms of a molecule are represented as nodes in the graph, and the bonds of a molecule are represented as edges in the graph. Graph editing comprises six basic operations: (i) node addition, (ii) node deletion, (iii) node substitution or relabeling, (iv) edge addition, (v) edge deletion, and (vi) edge substitution or relabeling. Each of these six basic operations can be associated with a cost. A path defines a set of basic operations that transform one graph into another. The sum of the costs of each basic operation in a path defines the cost of the path. The graph edit distance is the path with the lowest cost. Therefore, if there are two or more (sets of basic operations) that can transform one graph into another, the graph edit distance is defined as the path with the lowest cost. An example is shown in Figure 3A where pyridine is transformed into aniline. While there may be multiple paths that can be used to perform the transformation, the path with the lowest cost is the graph edit distance. For the transformation from pyridine to aniline, the path with the lowest cost is the substitution of N to C, the addition of an N atom, and the addition of a CN bond. This transforms the graph of pyridine into the graph of aniline. If the cost of each of these three basic operations is one, the total cost of the transformation from pyridine to aniline (i.e., the graph edit distance) will be 3.

[0006] Graph edit distance (GED) can be compared with other molecular similarity metrics, such as fingerprinting methods and methods based on maximum common substructures (MCS). See Zhang et al., 2015, “Design of chemical space networks using a Tanimoto similarity variant based upon maximum common substructures,” *J. Comput. Aided Des.*, 29, 937, which is hereby incorporated by reference. Fingerprinting methods can be overly sensitive to small changes within a molecule, especially when the change occurs in the middle of the molecule. Therefore, small changes in the middle of the molecule can result in a large fingerprint metric, while the same change at the periphery of the molecule will not. In contrast, moving a small change from the periphery to the middle of the molecule can reduce the MCS metric by fifty percent. GED is sensitive to molecular changes regardless of where the change occurs. Therefore, GED yields similar values ​​for small changes in the middle and periphery of the molecule. For example, if carbon is changed to nitrogen, the GED value will always be 1, regardless of where the change occurs in the molecule.

[0007] GED and MCS metrics are chemically intuitive because they track well the actual chemical changes required to transform one molecule into another, which fingerprinting methods typically cannot. From the perspective of defining the transformation from one molecule to another, GED is chemically intuitive. From a different perspective, MCS is chemically intuitive. MCS indicates how much of the two molecules are common.

[0008] The drawback of GED is its extremely high computational cost. In fact, exact GED calculations have been characterized as an NP-complete computational task. The computational cost increases unfavorably with the molecular weight of the compounds being compared. For example, for compounds with molecular weights from 350 to 500 Daltons, the cost of GED calculations is prohibitively high when used on a large scale in most drug discovery applications (such as QSAR modeling of compounds, identification of chemically related analogs, etc.). Due to the high computational cost, substitutes for approximating or estimating exact GEDs have been developed to replace exact GED calculations. One such GED approximation algorithm is called the Hungarian algorithm. See Bougleux et al., 2017, “A Hungarian Algorithm for Error-Correcting Graph Matching”, Lecture Notes in Computer Science, International Workshop on Graph-Based Representations in Pattern Recognition (GbR), Anacapri, Italy, LNCS10310, which is hereby incorporated by reference. The Hungarian algorithm suffers from adverse scaling with molecular weight. However, the mean square error of the GED approximation produced by the Hungarian algorithm is unsatisfactory compared to the true GED.

[0009] Another GED approximation method is SimGNN. See Bai et al., 2019, ACM International Conference on Web Search and Data Mining, which is hereby incorporated by reference. SimGNN is a general-purpose program for computing graph similarity (including similarity between compound graphs). SimGNN is trained on the AIDS, LINUX program dependency graph, and IMDB self-network datasets. Of these three datasets, only the AIDS dataset relates to drug-like systems. Therefore, SimGNN solves the general graph editing problem and can be used for graphs much larger than molecules. Furthermore, much of what SimGNN is trained on does not represent the drug-like chemical space. As discussed in further detail below, the mean squared error of the SimGNN GED approximation (such as the approximation produced by the Hungarian algorithm) is unsatisfactory when applied to drug-like applications.

[0010] Therefore, given the above background, what is needed in the art is a computer system and method for performing the improved GED approximation. Summary of the Invention

[0011] This disclosure addresses the identification problems in the prior art. A system and method for estimating the graph edit distance (GED) between compounds are provided. A first graph representing a first compound comprises multiple nodes and multiple edges. Atoms of the first compound are represented by the nodes of the first graph, and bonds of the first compound are represented by the edges of the first graph. A second graph representing a second compound also comprises multiple nodes and multiple edges. Atoms of the second compound are represented by the nodes of the second graph, and bonds of the second compound are represented by the edges of the second graph. The first graph is input into a model to generate a first isometric preserving latent embedding. The second graph is input into a second model to generate a second isometric preserving latent embedding. An estimate (GED) between the two compounds is provided using the difference between the first and second isometric preserving latent embeddings.

[0012] A. Graph-based embodiments. Therefore, one aspect of this disclosure provides a system and method for estimating the graph editing distance between a first compound and a second compound.

[0013] A first graph representing the first compound is obtained. The first graph contains a first plurality of nodes and a first plurality of edges. Each atom of the first compound is represented by one of the first plurality of nodes. Each bond of the first compound is represented by one of the first plurality of edges.

[0014] In some embodiments, a second graph representing the second compound is obtained. The second graph includes a second plurality of nodes and a second plurality of edges. Each atom of the second compound is represented by one of the second plurality of nodes. Each bond of the second compound is represented by one of the second plurality of edges.

[0015] In some such embodiments, the exact graph edit distance between the first compound and the second compound is between 1 and 10.

[0016] In some such embodiments, the exact graph edit distance between the first compound and the second compound is between 1 and 15.

[0017] In some embodiments, the first compound and the second compound are each organic compounds with a molecular weight of less than 500 Daltons, less than 1000 Daltons, less than 2000 Daltons, less than 4000 Daltons, less than 6000 Daltons, less than 8000 Daltons, less than 10000 Daltons, or less than 20000 Daltons.

[0018] In some embodiments, the first compound and the second compound are each organic compounds with a molecular weight between 400 Daltons and 10,000 Daltons.

[0019] The first graph is input into a model containing multiple parameters. The model (e.g., through at least 10,000 computations, such as processor instructions) applies the multiple parameters of the model to the first graph to generate a first isometric latent embedding representing the first compound as the first output of the model.

[0020] The second graph is input into the model. The second model (e.g., through at least 10,000 computations, such as processor instructions) applies multiple parameters to the second graph to generate a second isometric latent embedding representing the second compound as the second output of the model.

[0021] In some embodiments, the model is a messaging network.

[0022] In some embodiments, the model is a graph neural network.

[0023] In some embodiments, the model is a message-passing graph neural network with 3 to 8 layers.

[0024] In some embodiments, the model is a message-passing graph neural network consisting of 5 layers.

[0025] In some embodiments, the model contains 500,000 or more parameters, or 1 × 102 6 One or more parameters.

[0026] In some embodiments, the model performs at least 100,000 computations to compute a first isometric preserving latent embedding, and the model performs at least 100,000 computations to compute a second isometric preserving latent embedding.

[0027] An estimate of the graph editing distance between the first and second compounds is provided by using the difference between the first and second isometric latent embeddings.

[0028] In some embodiments, the difference is the L2 norm difference between the first isometric latent embedding and the second isometric latent embedding. In some embodiments, the first latent space is a first vector containing a first plurality of vector values, the second latent space is a second vector containing a second plurality of vector values, and the L2 norm difference between the first vector and the second vector is considered as the square root of the sum of the squared differences of the corresponding vector values ​​between the first vector and the second vector.

[0029] In some embodiments, when the estimated graph editing distance is below a threshold (e.g., less than 5, less than 4, less than 3, or less than 2), it is determined whether the second compound is a chemically related analog of the first compound.

[0030] In some embodiments, for each corresponding unique compound pair in the compound database, the process of obtaining a first graph, obtaining a second graph, inputting the first graph, inputting the second graph, and providing an approximate GED is repeated to form multiple estimated graph edit distances, wherein the first compound in the corresponding unique compound pair is the first compound, and the second compound in the corresponding unique compound pair is the second compound. The multiple estimated graph edit distances are then clustered into multiple clusters by evaluating the multiple distances using a criterion function. Compounds are then selected from one or more of the multiple clusters for evaluation in a drug discovery procedure.

[0031] In some embodiments, an estimate of the graph editing distance is used to establish a quantitative structure-activity relationship model that includes a first compound and a second compound.

[0032] In some embodiments, an estimate of the graph editing distance is used to determine the activity cliff relative to the drug target.

[0033] Another aspect of this disclosure provides a method for estimating a graph editing distance between a first compound and a second compound. The method includes (A) obtaining a first graph representing the first compound, the first graph including a first plurality of nodes and a first plurality of edges. Each atom of the first compound is represented by one of the first plurality of nodes, and each bond of the first compound is represented by one of the first plurality of edges. The method further includes (B) obtaining a second graph representing the second compound. The second graph includes a second plurality of nodes and a second plurality of edges. Each atom of the second compound is represented by one of the second plurality of nodes, and each bond of the second compound is represented by one of the second plurality of edges. The method further includes (C) inputting the first graph into a model including a plurality of parameters. The model (e.g., through at least 10,000 computations, such as processor instructions) applies the plurality of parameters to the first graph to generate a first isometric latent embedding representing the first compound as a first output of the model. The method further includes (D) inputting the second graph into the model. The model (e.g., through at least 10,000 computations) applies the plurality of parameters to the second graph to generate a second isometric latent embedding representing the second compound as a second output of the model. The method further includes (E) providing an estimate of the graph editing distance between the first compound and the second compound using the difference between the first isometric latent embedding and the second isometric latent embedding.

[0034] Another aspect of this disclosure provides a non-transitory computer-readable storage medium. The non-transitory computer-readable storage medium stores instructions that, when executed by a computer system, cause the computer system to perform a method for estimating a graph editing distance between a first compound and a second compound. The method includes (A) obtaining a first graph representing the first compound. The first graph includes a first plurality of nodes and a first plurality of edges. Each atom of the first compound is represented by one node of the first plurality of nodes, and each bond of the first compound is represented by one edge of the first plurality of edges. The method further includes (B) obtaining a second graph representing the second compound. The second graph includes a second plurality of nodes and a second plurality of edges. Each atom of the second compound is represented by one node of the second plurality of nodes, and each bond of the second compound is represented by one edge of the second plurality of edges. The method further includes (C) inputting the first graph into a model containing a plurality of parameters. The model (e.g., through at least 10,000 calculations) applies the plurality of parameters to the first graph to generate a first isometric preserving latent embedding representing the first compound as a first output of the model. The method further includes (D) inputting the second graph into the model. The model (e.g., through at least 10,000 computations) applies multiple parameters to a second graph to generate a second isometric preserving latent embedding representing the second compound as a second output of the model. The method further includes (E) providing an estimate of the graph editing distance between the first and second compounds using the difference between the first and second isometric preserving latent embeddings.

[0035] B. Compound Representation Example. Another aspect of this disclosure provides a computer system for estimating a graph edit distance between a first compound and a second compound. The computer system includes one or more processors and a memory addressable by the one or more processors. The memory stores at least one program for execution by the one or more processors. The at least one program includes the following instructions: (A) inputting a first representation of the first compound into a model containing multiple parameters. The model applies the multiple parameters to the first representation of the first compound to generate a first isometric preserving latent embedding representing the first compound as a first output of the model. The at least one program further includes the following instructions: (B) inputting a second representation of the second compound into the model. The model applies the multiple parameters to the second representation of the second compound to generate a second isometric preserving latent embedding representing the second compound as a second output of the model. The at least one program further includes the following instructions: (C) providing an estimate of the graph edit distance between the first compound and the second compound using the difference between the first isometric preserving latent embedding and the second isometric preserving latent embedding.

[0036] In some embodiments, the difference is the L2 norm difference between a first isometric preserving latent embedding and a second isometric preserving latent embedding. In some such embodiments, the first isometric preserving latent embedding is a first vector containing a first plurality of vector values, the second isometric preserving latent embedding is a second vector containing a second plurality of vector values, and the L2 norm difference between the first and second vectors is considered as the square root of the sum of the squared differences of the corresponding vector values ​​between the first and second vectors, wherein the model is trained such that the L2 norm of the difference between the first and second vectors is an estimate of the GED between the first and second vectors.

[0037] In some embodiments, the at least one procedure further includes instructions for determining that the second compound is a chemically related analog of the first compound when the estimated graph editing distance is below a threshold.

[0038] In some embodiments, the at least one procedure further includes instructions for repeatedly performing input (A), input (B), and provide (C) for each corresponding unique compound pair in the compound database, thereby forming multiple graph edit distances, wherein a first compound in the corresponding unique compound pair is the first compound, and a second compound in the corresponding unique compound pair is the second compound. In some such embodiments, the multiple graph edit distances are clustered into multiple clusters by evaluating multiple distances using a criterion function, and compounds are selected from one or more of the multiple clusters for evaluation in a drug discovery procedure.

[0039] In some embodiments, the at least one program further includes instructions for using an estimate of the graph editing distance to establish a quantitative structure-activity relationship model including a first compound and a second compound.

[0040] In some embodiments, the at least one procedure further includes instructions for determining the activity cliff relative to the drug target using an estimate of the graph editing distance.

[0041] In some embodiments, the model is a graph convolutional neural network.

[0042] In some embodiments, the model is a graph neural network (message passing network).

[0043] In some embodiments, the model is a message-passing graph neural network consisting of 3 to 8 layers.

[0044] In some embodiments, the model is a message-passing graph neural network consisting of 5 layers.

[0045] In some embodiments, the model is an autoencoder. In some embodiments, the autoencoder is a variational autoencoder, an adversarial autoencoder, a regularized autoencoder, a sparse autoencoder, or a metric learning autoencoder.

[0046] In some embodiments, the first represents a first fingerprint of a first compound, and the second represents a second fingerprint of a second compound.

[0047] In some embodiments, "first" represents a first plurality of descriptors of a first compound, and "second" represents a second plurality of descriptors of a second compound.

[0048] In some embodiments, the first representation is a first three-dimensional structural representation of the first compound, and the second representation is a second three-dimensional structural representation of the second compound.

[0049] In some embodiments, the first representation is a first tensor-based representation of the first compound, and the second representation is a second tensor-based representation of the second compound.

[0050] In some embodiments, the first representation is a first string representation of the first compound, and the second representation is a second string representation of the second compound.

[0051] In some embodiments, the model contains 500,000 or more parameters. In some embodiments, the model contains 1×10 6 One or more parameters.

[0052] In some embodiments, the first compound and the second compound each satisfy two or more, three or more, or all four of the Lipinski Five Rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

[0053] In some embodiments, the exact image edit distance between the first compound and the second compound is between 1 and 10. In some embodiments, the exact image edit distance between the first compound and the second compound is between 1 and 15.

[0054] In some embodiments, the first compound and the second compound are each organic compounds with a molecular weight of less than 500 Daltons. In some embodiments, the first compound and the second compound are each organic compounds with a molecular weight of less than 1000 Daltons. In some embodiments, the first compound and the second compound are each organic compounds with a molecular weight of less than 2000 Daltons. In some embodiments, the first compound and the second compound are each organic compounds with a molecular weight of less than 4000 Daltons, less than 6000 Daltons, less than 8000 Daltons, less than 10000 Daltons, or less than 20000 Daltons. In some embodiments, the first compound and the second compound are each organic compounds with a molecular weight between 300 Daltons and 1500 Daltons.

[0055] In some embodiments, the model performs at least 100,000 computations to compute a first isometric preserving latent embedding, and the model performs at least 100,000 computations to compute a second isometric preserving latent embedding.

[0056] Another aspect of this disclosure provides a method for estimating a graph edit distance between a first compound and a second compound. The method includes (e.g., at a computer system including one or more processors and memory addressable by the one or more processors) (A) inputting a first representation of the first compound into a model including a plurality of parameters, wherein the model applies the plurality of parameters to the first representation of the first compound to generate a first isometric preserving latent embedding representing the first compound as a first output of the model. The method further includes (e.g., at a computer system including one or more processors and memory addressable by the one or more processors) (B) inputting a second representation of the second compound into the model, wherein the model applies the plurality of parameters to the second representation of the second compound to generate a second isometric preserving latent embedding representing the second compound as a second output of the model. The method further includes (e.g., at a computer system including one or more processors and memory addressable by the one or more processors) (C) providing an estimate of the graph edit distance between the first compound and the second compound using the difference between the first isometric preserving latent embedding and the second isometric preserving latent embedding.

[0057] Another aspect of this disclosure provides a non-transitory computer-readable storage medium. The non-transitory computer-readable storage medium stores instructions that, when executed by a computer system, cause the computer system to perform a method for estimating a graph edit distance between a first compound and a second compound. The method includes (A) inputting a first representation of the first compound into a model comprising a plurality of parameters. The model applies the plurality of parameters to the first representation of the first compound to generate a first isometric preserving latent embedding representing the first compound as a first output of the model. The method further includes (B) inputting a second representation of the second compound into the model. The model applies the plurality of parameters to the second representation of the second compound to generate a second isometric preserving latent embedding representing the second compound as a second output of the model. The method further includes (C) providing an estimate of the graph edit distance between the first compound and the second compound using the difference between the first isometric preserving latent embedding and the second isometric preserving latent embedding. Attached Figure Description

[0058] The accompanying drawings illustrate embodiments of the systems and methods of this disclosure by way of example. It should be clearly understood that the specification and drawings are for illustrative purposes and to aid understanding only, and are not intended to be defined as limitations on the systems and methods of this disclosure.

[0059] Figure 1 Computer systems according to some embodiments of the present disclosure are shown.

[0060] Figure 2A , 2B Images 2C and 2D illustrate methods for estimating the graph editing distance between a first compound and a second compound according to some embodiments of the present disclosure, wherein optional elements are indicated by dashed boxes.

[0061] Figure 3A illustrates graph editing distance according to existing technology and how it measures chemical similarity.

[0062] Figure 3B The desired properties of a training set for training a model to approximate graph edit distances, according to some embodiments of the present disclosure, are shown.

[0063] Figure 4 Statistics on training and testing class drug datasets and training and testing fragment datasets for training models to approximate graph-edited distances according to some embodiments of the present disclosure are shown.

[0064] Figure 5 The performance of the prior art model SimGNN, trained on fragment datasets and drug-like datasets according to some embodiments of this disclosure, is shown.

[0065] Figure 6The expected formal properties of the model used for approximating graph editing distance are shown, and how the existing model SimGNN does not possess some of these formal properties.

[0066] Figure 7 This is a schematic diagram of a system for approximate graph editing distance according to some embodiments of the present disclosure.

[0067] Figure 8 This demonstrates the system MolGEDNet according to this disclosure in targeting Figure 4 The performance of the approximate graph editing distance on the test dataset is compared with the existing technology model SimGNN in terms of mean squared error.

[0068] Figure 9 This demonstrates how the system MolGEDNet, according to this disclosure, sorts and uses graph edit distances using approximate graph edit distances. Figure 4 When ranking graph edit distances on the test dataset, the model performs better than existing technology models like SimGNN in Spearman's p and Kendall's τ. Β (Kendall's) performance.

[0069] Figure 10 Some embodiments according to this disclosure are shown, by... Figure 4 On the test dataset, mean squared error, Spearman p, and Kendall τ were used. Β The system according to this disclosure optimizes the model by determining the model dimension relative to the graph embedding size based on the edge embedding size and the node embedding size.

[0070] Figure 11 Some embodiments of the present disclosure are shown, in which the system according to the present disclosure is optimized by optimizing the exit between layers of the model during model hyperparameter training.

[0071] Figure 12 Some embodiments of the present disclosure are shown, in which the system according to the present disclosure is optimized by optimizing the number of layers in the model.

[0072] Figure 13 This demonstrates the performance of the MolGEDNet model according to this disclosure. Figure 4 After training the hyperparameters on the test dataset, the mean squared error Spearman p and Kendall τ were used. Β Performance in this aspect.

[0073] Figure 14 According to embodiments of this disclosure, in Figure 4 The distance pairs on the drug testing dataset are edited based on the real graph. Figure 13 The graph editing distance error generated by the hyperparameter optimization model is stratified.

[0074] Figure 15 Showing Figure 4 Example compound pairs in a drug testing dataset, each compound pair having a ground truth graph edit distance of one, and by... Figure 13 The hyperparameter optimization system is used to calculate the absolute error of the approximate graph editing distance for these compounds.

[0075] Figure 16 Specify in Figure 15 The betweenness centrality of each distinct node in the graph for example compound pairs.

[0076] Figure 17 This demonstrates an embodiment of the present disclosure, compared to the Hungarian algorithm. Figure 13 The runtime performance of the hyperparameter optimization model varies with... Figure 14 The changes in the average molecular weight of compounds compared in the drug testing set.

[0077] Figure 18 Some embodiments according to this disclosure are illustrated. Figure 7 The details of the system.

[0078] Figure 19 Showing according to Figure 13 How optimized hyperparameters are used in message-passing graph neural networks to perform node, edge, and graph updates according to embodiments of this disclosure.

[0079] Figure 20 Details of a message-passing graph neural network according to embodiments of the present disclosure are shown.

[0080] Figure 21 illustrates the difference between the chemical distance and the exact map editing distance based on prior art.

[0081] Figure 22 Computer systems according to some embodiments of the present disclosure are shown.

[0082] Figure 23A , 23B 23C illustrates methods for training models to predict the potency of test compounds against orthogenic sites of target proteins according to some embodiments of the present disclosure.

[0083] Figure 24 The compound selection process is demonstrated.

[0084] Figure 25 It shows the timeline and phases for releasing training data from pre-trained structures as binding site models.

[0085] Figure 26 The benchmarks used to ensure that the binding model learns real protein binding characteristics are demonstrated.

[0086] Figure 27 This further demonstrates the benchmarks used to ensure that the binding model learns real protein binding characteristics.

[0087] Figure 28 A model using AlphaFold2 to obtain underrepresented treatment-related protein classes is demonstrated.

[0088] Figure 29A This demonstrates the predicament that most compound activity measurements on a target cannot be reliably mapped to specific binding sites on the target.

[0089] Figure 29B This demonstrates a method to determine which binding site on the target a compound binds to by first clustering compounds that bind to a given target into multiple clusters.

[0090] Figure 30 This demonstrates the mapping of compounds with known binding sites to a given target to... Figure 29A and 29B Clusters were identified, and clusters with consistency were determined, meaning that all compounds mapped to such clusters mapped to the same binding site on a given target.

[0091] Figure 31A and 31B This demonstrates how to use known target structures to select target models whose structures have not yet been resolved, and how to determine the binding sites of specific compounds on such targets.

[0092] Figure 32 This demonstrates how using compound-labeled multi-site markers of targets to train binding site models, according to embodiments of the present disclosure, deconvolve structure-activity relationship data.

[0093] Figure 33A and 33B This demonstrates how using compound-labeled multi-site markers of targets to train binding site models, according to embodiments of the present disclosure, deconvolve structure-activity relationship data.

[0094] Throughout the various views in the accompanying drawings, the same reference numerals refer to the corresponding parts. Detailed Implementation

[0095] Introduction. This disclosure provides a system and method for estimating the graph edit distance (GED) between compounds. A first graph representing a first compound contains multiple nodes and multiple edges. Atoms of the first compound are represented by the nodes of the first graph, and bonds of the first compound are represented by the edges of the first graph. A second graph representing a second compound also contains multiple nodes and multiple edges. Atoms of the second compound are represented by the nodes of the second graph, and bonds of the second compound are represented by the edges of the second graph. The first graph is input into a model to generate a first isometric preserving latent embedding. The second graph is input into a model to generate a second isometric preserving latent embedding. An estimate (GED) between the two compounds is provided using the difference between the first and second isometric preserving latent embeddings.

[0096] Detailed reference will now be made to embodiments, examples of which are illustrated in the accompanying drawings. Numerous specific details are set forth in the following detailed description to provide a thorough understanding of this disclosure. However, it will be apparent to those skilled in the art that this disclosure can be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits, and networks have not been described in detail so as not to unnecessarily obscure aspects of the embodiments.

[0097] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains. All patents and publications referenced herein are incorporated herein by reference in their entirety.

[0098] Multiple instances can be provided for the components, operations, or structures described herein as a single instance. Finally, the boundaries between individual components, operations, and data stores are somewhat arbitrary and specific operations are described within the context of a particular illustrative configuration. Other forms of functionality are envisioned, and they may fall within the scope of the implementation. Generally, structures and functions presented as separate components in the example configuration can be implemented as composite structures or components. Similarly, structures and functions presented as single components can be implemented as separate components. These structures and functions, as well as other variations, modifications, additions, and improvements, fall within the scope of the implementation.

[0099] It will also be understood that while the terms first, second, etc., may be used herein to describe various elements, these elements should not be limited by these terms. These terms are used only to distinguish one element from another. For example, without departing from the scope of this disclosure, a first subject may be referred to as a second subject, and similarly, a second subject may be referred to as a first subject. Although both the first and second subjects are subjects, they are not the same subject.

[0100] The terminology used in this disclosure is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in the specification and appended claims of this invention, unless the context clearly indicates otherwise, the singular forms “a,” “an,” and “the” are intended to equally include the plural forms. It will also be understood that the term “and / or,” as used herein, refers to and covers any and all possible combinations of one or more of the associated enumerated items. It will be further understood that, when used in this specification, the terms “comprises” and / or “comprising” specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0101] As used herein, depending on the context, the term "if" can be interpreted as "when the prerequisite is true" or "when the prerequisite is true" or "in response to determining that the prerequisite is true" or "based on the determination that the prerequisite is true" or "in response to detecting that the prerequisite is true". Similarly, depending on the context, the phrases "if it is determined (that the prerequisite is true)" or "if (that the prerequisite is true)" or "when (that the prerequisite is true)" can be interpreted as "when it is determined that the prerequisite is true" or "in response to determining that the prerequisite is true" or "based on the determination that the prerequisite is true" or "in response to detecting that the prerequisite is true".

[0102] Furthermore, when reference numerals are assigned the designation "i," they refer to general components, sets, or embodiments. For example, a cell component referred to as "cell component i" refers to the i-th cell component among a plurality of cell components.

[0103] The foregoing description includes example systems, methods, techniques, instruction sequences, and computer program products embodying illustrative embodiments. Numerous specific details have been set forth for purposes of explanation in order to provide an understanding of various embodiments of the subject matter of the invention. However, it will be apparent to those skilled in the art that embodiments of the subject matter of the invention can be practiced without these specific details. Generally, well-known illustrative examples, protocols, structures, and techniques have not been shown in detail.

[0104] For purposes of explanation, the foregoing description has been made with reference to specific embodiments. However, the illustrative discussion below is not intended to be exhaustive or to limit the embodiments to the precise forms disclosed. Many modifications and variations are possible in light of the above teachings. The embodiments were chosen and described in order to best explain the principles and their practical application, thereby enabling others skilled in the art to best utilize the embodiments and various embodiments with various modifications suited to the intended particular use.

[0105] For clarity, not all conventional features of the embodiments described herein are shown or described. It will be understood that in the development of any such practical embodiment, numerous implementation-specific decisions are made to achieve the designer's specific goals, such as compliance with constraints related to use cases and business, and these specific goals will vary from implementation to implementation and designer to designer. Furthermore, it will be understood that such design work can be complex and time-consuming, but remains a routine engineering task for those skilled in the art who benefit from this disclosure.

[0106] Some portions of this specification describe embodiments of the invention based on algorithms and symbolic representations of information operations. These algorithmic descriptions and representations are typically used by those skilled in the art of data processing to effectively convey the essence of their work to others skilled in the art. While these operations are described functionally, computationally, or logically, they should be understood to be implemented via computer programs or equivalent circuits, microcode, etc.

[0107] The language used in this specification has been chosen primarily for readability and guidance purposes, and not for describing or limiting the subject matter of the invention. Therefore, the scope of the invention is intended to be limited not by this specific embodiment, but by any of the claims published in the application based thereon. Consequently, the disclosure of embodiments of the invention is intended to be illustrative and not to limit the scope of the invention.

[0108] Generally, the terms used in the claims and specification are intended to be understood in their ordinary meaning as would be understood by one of ordinary skill in the art. Certain terms are defined below to make this clearer. If any ordinary meaning conflicts with the provided definitions, the provided definitions will prevail.

[0109] Any term not directly defined herein shall be understood to have the meaning generally associated with it as understood within the art of this invention. Certain terms are discussed herein to provide additional guidance to those skilled in the art in describing compositions, apparatuses, methods, etc., and how to manufacture or use these compositions, apparatuses, methods, etc., of various aspects of the invention. It will be understood that the same thing can be described in more than one way. Therefore, alternative language and synonyms may be used to represent any one or more terms discussed herein. It is not important whether a particular term is elaborated or discussed exhaustively herein. Several synonyms or alternative methods, materials, etc., are provided. Unless expressly stated, the statement of one or more synonyms or equivalents does not preclude the use of other synonyms or equivalents. Examples (including examples of terms) are for illustrative purposes only and do not limit the scope and meaning of the various aspects of the invention herein.

[0110] For the avoidance of doubt, it is intended that specific features (e.g., integers, properties, values, uses, diseases, molecular formulas, compounds, or groups) described in connection with a particular aspect, embodiment, or example of this disclosure be understood to be applicable to any other aspect, embodiment, or example described herein, unless incompatible with it. Therefore, such features may be used in conjunction with any definition, claim, or embodiment defined herein, where appropriate. All features disclosed in this specification (including any appended claims, abstract, and drawings) and / or all steps of any method or process so disclosed may be combined in any combination, except where at least some features and / or steps are mutually exclusive combinations. This disclosure is not limited to any details of any disclosed embodiment. This disclosure extends to any novel feature or any novel combination of said features disclosed in this specification (including any appended claims, abstract, and drawings), or to any novel step or any novel combination of said steps in any method or process so disclosed.

[0111] definition.

[0112] As used herein, the terms “compound” and “molecule” are used interchangeably.

[0113] As used herein, the term "about" means that dimensions, sizes, formulations, parameters, shapes, and other quantities and characteristics are not and need not be exact, but may be approximate and / or larger or smaller as needed, reflecting tolerances, conversion factors, rounding, measurement errors, and other factors known to those skilled in the art. Generally, dimensions, sizes, formulations, parameters, shapes, or other quantities or characteristics are "about" or "approximately," whether or not explicitly stated. It should be noted that embodiments of distinctly different sizes, shapes, and dimensions may be adopted using the described arrangements.

[0114] As used herein, the term "fingerprint" in the context of compound fingerprinting refers to a digital summary of the compound. Non-limiting examples of such digital summaries include sunlight fingerprints, BCI fingerprints, ECFC4 fingerprints, ECFP4 fingerprints, EcFC fingerprints, MDL fingerprints, atom-pair fingerprints (APFP fingerprints), topological torsion fingerprints (TTFP), UNITY 2D fingerprints, RNNS2S fingerprints, and GraphConv fingerprints. See Franco, 2014, “The Use of 2D fingerprint methods to support the assessment of structural similarity in orphan drug legislation,” *Journal of Cheminformatics*, 6, p. 5; and Rensi and Altman, 2017, “Flexible Analog Search with Kernel PCA Embedded Molecule Vectors,” *Computational and Structural Biotechnology Journal*, doi:10.1016 / j.csbj.2017.03.003, each of which is hereby incorporated by reference. See also Raymond and Willett, 2002, “Effectiveness of graph-based and fingerprint-based similarity measures for virtual screening of 2D chemical structure databases”, Journal of Computer-Aided Molecular Design (Computer-Aided) 16, 59-71, and Franco et al., 2014, “Using 2D fingerprinting methods to support the assessment of structural similarity in orphan drug legislation”, Journal of Cheminformatics 6(5), each of which is hereby incorporated by reference.

[0115] As used interchangeably herein, the terms “classifier,” “model,” “algorithm,” “regressor,” and / or “classifier” refer to a machine learning model or algorithm. In some embodiments, the model is unsupervised learning. In some embodiments, the model is supervised machine learning. Non-limiting examples of supervised learning include, but are not limited to, logistic regression, neural networks, support vector machines, Naive Bayes algorithm, nearest neighbor algorithm, random forest algorithm, decision tree, boosting tree, multinomial logistic regression, linear models, linear regression, gradient boosting, mixture models, hidden Markov models, Gaussian NB algorithm, linear discriminant analysis, or any combination thereof. In some embodiments, the model is a multinomial classifier algorithm. In some embodiments, the model is a 2-stage stochastic gradient descent (SGD) model. In some embodiments, the model is a deep neural network (e.g., a deep and breadth sample-level model). In some embodiments, the classifier or model of this disclosure has 25 or more, 100 or more, 1000 or more, 10,000 or more, 100,000 or more, or 1 × 10 6 It has one or more parameters, and therefore cannot be calculated by the brain.

[0116] Furthermore, as used herein, the term "parameter" refers to any coefficient or similarly internal or external element (e.g., weights and / or hyperparameters) in an algorithm, model, regressor, and / or classifier that may affect (e.g., modify, customize, and / or adjust) one or more inputs, outputs, and / or functions of the algorithm, model, regressor, and / or classifier. For example, in some embodiments, a parameter refers to any coefficient, weight, and / or hyperparameter that can be used to control, modify, customize, and / or adjust the behavior, learning, and / or performance of an algorithm, model, regressor, and / or classifier. In some cases, parameters are used to increase or decrease the influence of inputs (e.g., features) on an algorithm, model, regressor, and / or classifier. As a non-limiting example, in some embodiments, parameters are used to increase or decrease the influence of nodes (e.g., nodes in a neural network), where nodes include one or more activation functions. Assigning parameters to specific inputs, outputs, and / or functions for a given algorithm, model, regressor, and / or classifier is not limited to any particular paradigm and can be used for any suitable algorithm, model, regressor, and / or classifier architecture to achieve the desired performance. In some embodiments, parameters have fixed values. In some embodiments, the values ​​of the parameters may be adjusted manually and / or automatically. In some embodiments, the values ​​of the parameters are modified through the validation and / or training process of the algorithm, model, regressor, and / or classifier (e.g., through error minimization and / or backpropagation methods). In some embodiments, the algorithms, models, regressors, and / or classifiers of this disclosure include multiple parameters. In some embodiments, the plurality of parameters is n parameters, wherein: n≥2; n≥5; n≥10; n≥25; n≥40; n≥50; n≥75; n≥100; n≥125; n≥150; n≥200; n≥225; n≥250; n≥350; n≥500; n≥600; n≥750; n≥1,000; n≥2,000; n≥4,000; n≥5,000; n≥7,500; n≥10,000; n≥20,000; n≥40,000; n≥75,000; n≥100,000; n≥200,000; n≥500,000; n≥1×10 6 n≥5×10 6 ; or n≥1×10 7 Therefore, the algorithms, models, regressors, and / or classifiers of this disclosure cannot be performed by the brain. In some embodiments, n is 10,000 with 1 × 10 7 Between, 100,000 and 5×10 6 Between 500,000 and 1×10 6In some embodiments, the algorithms, models, regressors, and / or classifiers of this disclosure operate in a k-dimensional space, where k is a positive integer of 5 or greater (e.g., 5, 6, 7, 8, 9, 10, etc.). Therefore, the algorithms, models, regressors, and / or classifiers of this disclosure cannot be generated by the brain.

[0117] Neural Networks. In some embodiments, the model is a neural network (e.g., a convolutional neural network and / or a residual neural network). Neural networks are also called artificial neural networks (ANNs), including convolutional and / or residual neural networks (deep learning models). In some embodiments, a neural network is a machine learning model trained to map an input dataset to an output dataset, wherein the neural network includes a set of interconnected nodes organized into multiple layers. For example, in some embodiments, a neural network architecture includes at least an input layer, one or more hidden layers, and an output layer. In some embodiments, a neural network includes any total number of layers and any number of hidden layers, wherein the hidden layers act as trainable feature extractors that allow mapping a set of input data to output values ​​or a set of output values. In some embodiments, a deep learning model is a neural network that includes multiple hidden layers, such as two or more hidden layers. In some cases, each layer of a neural network includes multiple nodes (or "neurons"). In some embodiments, a node receives input directly from the input data or the output of nodes in previous layers and performs a specific operation, such as a summation operation. In some embodiments, the connection from the input to the node is associated with parameters (e.g., weights and / or weighting factors). In some embodiments, a node pairs all inputs with x i The product of the weighted sum and its associated parameters is added. In some embodiments, the weighted sum cancels out the bias b. In some embodiments, the output of a node or neuron is gated using a threshold or activation function f, which in some cases is a linear or nonlinear function. In some embodiments, the activation function is, for example, a modified linear unit (ReLU) activation function, a leaky ReLU activation function, or other functions such as a saturated hyperbolic tangent function, an identity function, a binary step function, a logic function, an arcTan function, a softsign function, a parameter-modified linear unit function, an exponential linear unit function, a softPlus function, a curved identity function, a softExponential function, a Sinusoid function, a Sine function, a Gaussian function, or a sigmoid function, or any combination thereof.

[0118] In some implementations, the parameters of the neural network (weighting factors, biases, and / or thresholds or other computed parameters) are "taught" or "learned" during the training phase using one or more sets of training data. For example, in some implementations, the parameters are trained using input data from the training dataset and gradient descent or backpropagation methods so that the output values ​​computed by the ANN are consistent with the instances included in the training dataset. In some embodiments, the parameters are obtained from the backpropagation neural network training process.

[0119] According to this disclosure, any of a variety of neural networks is suitable for use. Examples include, but are not limited to, feedforward neural networks, radial basis function networks, recurrent neural networks, residual neural networks, convolutional neural networks, residual convolutional neural networks, and any combination thereof. In some embodiments, machine learning utilizes pre-trained and / or transfer learning ANN or deep learning architectures. In some implementations, convolutional neural networks and / or residual neural networks are used according to this disclosure.

[0120] For example, a deep neural network model includes an input layer, multiple individually parameterized (e.g., weighted) convolutional layers, and an output scorer. The parameters (e.g., weights) of each of the convolutional layers and the input layer contribute to a plurality of parameters (e.g., weights) associated with the deep neural network model. In some embodiments, at least 50 parameters, at least 100 parameters, at least 1000 parameters, at least 2000 parameters, or at least 5000 parameters are associated with the deep neural network model. Therefore, deep neural network models require a computer to operate because they cannot be solved by the brain. In other words, given the model's input, the model's output needs to be determined using a computer, not by the brain in such embodiments. See, for example, Krizhevsky et al., 2012, “Imagenet classification with deep convolutional neural networks”, Advances in Neural Information Processing Systems, 2, edited by Pereira, Burges, Bottou, and Weinberger, pp. 1097-1105, Curran Associates, Inc.; Zeiler, 2012, “ADADELTA: an adaptive learning rate method”, CoRR, Vol. 1212.5701; and Rumelhart et al., 1988, “Neurocomputing: Foundations of research”, chapter “Learning Representations by Back-propagating Errors”, pp. 696-699, Cambridge, MIT Press, Massachusetts, USA. Each of these references is hereby incorporated by reference.

[0121] Neural networks (including convolutional neural networks) suitable for use as models are disclosed in the following literature: for example, Vincent et al., 2010, “Stacked denoising autoencoders: Learning useful representations in deep network with a local denoising criterion”, Journal of Machine Learning Research, 11, pp. 3371-3408; Larochelle et al., 2009, “Exploring strategies for training deep neural networks”, Journal of Machine Learning Research, 10, pp. 1-40; and Hassoun, 1995, Fundamentals of Artificial Neural Networks, Massachusetts Institute of Technology, each of which is hereby incorporated by reference. Other example neural networks suitable for use as models are disclosed in the following literature: Duda et al., 2001, Pattern Classification, 2nd ed., John Wiley & Sons, Inc., New York; and Hastie et al., 2001, The Elements of Statistical Learning, Springer-Verlag, New York, each of which is hereby incorporated in its entirety by reference.Other example neural networks suitable for use as models are described in the following literature: Draghici, 2003, Data Analysis Tools for DNA Microarrays, Chapman & Hall / CRC; and Mount, 2001, Bioinformatics: sequence and genome analysis, Cold Spring Harbor Laboratory Press, Cold Spring Harbor, New York, each of which is hereby incorporated in its entirety by reference.

[0122] Support Vector Machine. In some embodiments, the model is a Support Vector Machine (SVM). Suitable SVMs for use as models are described, for example, in the following literature: Cristianini and Shaw-Taylor, 2000, "An Introduction to Support Vector Machines," Cambridge University Press, Cambridge; Boser et al., 1992, "A training algorithm for optimal margin classifiers," Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory, ACM Press, Pittsburgh, PAN, pp. 142-152; Vapnik, 1998, "Statistical Learning Theory." Theory), Wiley & Co., New York; Mount, 2001, Bioinformatics: Sequence and Genome Analysis, Cold Spring Harbor Laboratory Press, Cold Spring Harbor, New York; Duda, Pattern Classification, 2nd Edition, 2001, John Wiley & Co., pp. 259, 262-265; and Hastie, 2001, Elements of Statistical Learning, Springer, New York; and Furey et al., 2000, Bioinformatics 16, 906-914, each of which is hereby incorporated in its entirety by reference. When used for classification, SVM separates a given binary-labeled dataset from a hyperplane that is maximally farthest from the labeled data. For some cases where there is no linear separation, SVM operates in conjunction with a “kernel” technique that automatically implements a nonlinear mapping to the feature space. In some cases, the hyperplane discovered by SVM in the feature space corresponds to a nonlinear decision boundary in the input space. In some embodiments, multiple parameters (e.g., weights) associated with SVM define the hyperplane. In some embodiments, the hyperplane is defined by at least 10, at least 20, at least 50, or at least 100 parameters, and the SVM model requires a computer to compute because it cannot be solved by the brain.

[0123] Naive Bayes Model. In some embodiments, the model is a Naive Bayes model. Suitable Naive Bayes models for use as models are disclosed in the following literature: e.g., Ng et al., 2002, “On discriminative vs. generative classifiers: A comparison of logistic regression and naive Bayes”, Advances in Neural Information Processing Systems, 14, which is hereby incorporated by reference. Naive Bayes models are any models in the family of “probabilistic models” that apply the Bayes theorem and the strong (naive) independence assumption between features. In some embodiments, they are combined with kernel density estimation. See, for example, Hastie et al., 2001, The elements of statistical learning: data mining, inference, and prediction (edited by Tibshirani and Friedman, Springer, New York), which is hereby incorporated by reference.

[0124] Nearest Neighbor. In some embodiments, the model is a nearest neighbor model. In some implementations, the nearest neighbor model is memory-based and does not include the model to be fitted. For nearest neighbors, given a query point x0 (the test object), the k nearest training points x0 can be identified. (r) ,r,...,k (here, the training objects), and then classify using the k nearest neighbor pairs x0. In some embodiments, the distance is determined as d using the Euclidean distance in the feature space. (i) =‖x (i) -x (O) Typically, when using nearest neighbor models, the abundance data used to compute linear discriminants is standardized to have a mean of zero and a variance of 1. In some embodiments, the nearest neighbor rule is refined to address issues of unequal classification priors, differential misclassification costs, and feature selection. Many of these refinements involve some form of weighted voting on neighbors. For more information on nearest neighbor analysis, see Duda, Pattern Classification, 2nd Edition, 2001, John Wiley & Sons; and Hastie, Elements of Statistical Learning, 2001, Springer, New York, each of which is hereby incorporated by reference.

[0125] The k-nearest neighbor model is a nonparametric machine learning method where the input consists of the k nearest training instances in the feature space. The output is a class membership. An object is classified by multiple votes from its neighbors, whereby the object is assigned to the most common class among its k nearest neighbors (k is a positive integer, typically small). If k = 1, the object is simply assigned to the class of a single nearest neighbor. See Duda et al., 2001, Pattern Classification, 2nd Edition, John Willie & Sons, which is hereby incorporated by reference. In some embodiments, the amount of distance computation required to solve the k-nearest neighbor model makes it necessary to use a computer to solve the model for a given input, as it cannot be done by the brain.

[0126] Random forests, decision trees, and boosting trees. In some embodiments, the model is a decision tree. Decision trees suitable for use as models are described in: Duda, 2001, Pattern Classification, John Willie & Sons, New York, pp. 395-396, which is hereby incorporated by reference. Tree-based methods divide the feature space into a set of rectangles and then fit a model (e.g., a constant) to each rectangle. In some embodiments, the decision tree is a random forest regression. For example, a specific model is the Classification and Regression Tree (CART). Other specific decision tree models include, but are not limited to, ID3, C4.5, MART, and random forests. CART, ID3, and C4.5 are described in: Duda, 2001, Pattern Classification, John Willie & Sons, New York, pp. 396-408 and 411-412, which is hereby incorporated by reference. CART, MART, and C4.5 are described in: Hastie et al., 2001, Elements of Statistical Learning, Springer, New York, Chapter 9, which is hereby incorporated by reference in its entirety. Random forests are described in: Breiman, 1999, “Random Forests – Random Features,” Technical Report 567, Statistics Department, UC Berkeley, September 1999, which is hereby incorporated by reference in its entirety. In some embodiments, decision tree models include at least 10, at least 20, at least 50, or at least 100 parameters (e.g., weights and / or decisions) and require computation by a computer, as they cannot be solved by the brain.

[0127] Regression. In some embodiments, the model uses a regression formula. In some embodiments, the regression formula is determined using any type of regression. For example, in some embodiments, the regression is logistic regression. In some embodiments, the regression is logistic regression regularized using lasso, L2, or elastic net regularization. In some embodiments, extracted features with corresponding regression coefficients that do not meet a threshold are removed (not considered). In some embodiments, a generalization of a logistic regression model that handles multi-class responses is used as the model. Logistic regression is disclosed in: Agresti, An Introduction to Categorical Data Analysis, 1996, Chapter 5, pp. 103-144, John Willie & Sons, New York, which is hereby incorporated by reference. In some embodiments, the model utilizes a regression model disclosed in: Hastie et al., Elements of Statistical Learning, Springer, New York, 2001. In some embodiments, the logistic regression model includes at least 10, at least 20, at least 50, at least 100, or at least 1000 parameters (e.g., weights) and requires a computer to compute because it cannot be solved by the brain.

[0128] Linear discriminant analysis models. In some embodiments, the model is linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis. In some embodiments, such models are generalizations of Fisher's linear discriminant, a method used in statistics, pattern recognition, and machine learning to find linear combinations of features that characterize or distinguish two or more classes of objects or events. In some embodiments, the resulting combinations are used as models (linear models) in some embodiments of this disclosure.

[0129] Hybrid models and Hidden Markov models. In some embodiments, the model is a hybrid model, such as the model described in McLachlan et al., Bioinformatics 18(3):413-422, 2002. In some embodiments, particularly those including a time component, the model is a Hidden Markov model, such as the model described in Schliep et al., Bioinformatics 19(1):i255-i263, 2003.

[0130] Model ensembles and boosting. In some embodiments, a model ensemble (two or more models) is used. In some embodiments, boosting techniques such as AdaBoost are combined with many other types of learning algorithms to improve model performance. In this approach, the outputs of any model disclosed herein, or their equivalents, are combined into a weighted sum representing the final output of the boosted model. In some embodiments, any measure of central tendency known in the art is used to combine multiple outputs from the models, including but not limited to mean, median, mode, weighted mean, weighted median, weighted mode, etc. In some embodiments, voting is used to combine multiple outputs. In some embodiments, the respective models in the model ensemble are weighted or unweighted.

[0131] As used in this paper, the term "latent space" refers to a multidimensional space in which data points are represented after being encoded by the model. Although such data points are multidimensional, their dimensionality is lower than that of the model input. As used in this paper, the latent space has a lower dimensionality compared to the original input space of the pattern, thus making storage and computation more efficient.

[0132] As used in this paper, the term "latent embedding" refers to embedding data points into a low-dimensional space through a model.

[0133] As used herein, the term "vector" is an enumerated list of elements, such as an array of elements, where each element has an assigned meaning. Therefore, the term "vector" as used in this disclosure is interchangeable with the term "tensor." As an example, if a vector contains abundance counts of corresponding unit components in multiple units, then the vector contains predetermined elements for each unit in the multiple units. For ease of presentation, in some cases, a vector may be described as one-dimensional. However, this disclosure is not limited thereto. Vectors of any dimension may be used in this disclosure, provided that a description of what each element in the vector represents is defined (e.g., element 1 represents the abundance count of unit 1 in the multiple units, etc.).

[0134] Example computer system

[0135] Figure 1 A computer system 100 for estimating the graph editing distance between a first compound and a second compound is shown.

[0136] refer to Figure 1 In a typical embodiment, computer system 100 includes one or more computers. Figure 1For ease of illustration, computer system 100 is referred to as a computer including all the functions of the disclosed computer system 100. However, this disclosure is not limited thereto. The functions of computer system 100 can be distributed across any number of networked computers and / or reside on each of several networked computers and / or virtual machines. Those skilled in the art will understand that computer system 100 can employ a variety of different computer topologies, and all such topologies are within the scope of this disclosure.

[0137] Considering the foregoing, let's turn to... Figure 1 The computer system 100 includes one or more processing units (CPU and / or GPU) 59, a network or other communication interface 84, a user interface 78 (e.g., including an optional display 82 and an optional keyboard 80 or other form of input device), memory 92 (e.g., random access memory, persistent memory, or a combination thereof), one or more disk storage devices and / or persistent devices 90 optionally accessed by one or more controllers 88, one or more communication buses 12 for interconnecting the aforementioned components, and a power supply 79 for powering the aforementioned components. Where components of memory 92 are not persistent, known computing techniques such as caching can be used to seamlessly share data in memory 92 with non-volatile memory 90 or non-volatile / persistent portions of memory 92. Memory 92 and / or memory 90 may include large-capacity storage devices remotely located relative to the central processing unit 59. In other words, some data stored in memory 92 and / or memory 90 may actually be hosted on a computer external to computer system 100, but can be accessed electronically by computer system 100 using network interface 84 via the Internet, intranet, or other forms of network or cable. In some embodiments, computer system 100 utilizes a model running from memory associated with one or more graphics processing units to improve system speed and performance. In some alternative embodiments, computer system 100 utilizes a model running from memory 92 instead of memory associated with the graphics processing unit.

[0138] In some embodiments, computer system 100 presents media to a user via display 82. Examples of media presented by display 82 include one or more images, videos, audio (e.g., waveforms of audio samples), or combinations thereof. In a typical embodiment, display 82 presents the one or more images, videos, audio, or combinations thereof via a client application (e.g., a client application hosted by computer system 100, a client application accessible through computer system 100, etc.). In some embodiments, audio is presented via an external device (e.g., a speaker, headphones, an input / output (I / O) subsystem, etc.) that receives audio information from computer system 100 and presents audio data based on that audio information. In some embodiments, user interface 78 also includes an audio output device, such as a speaker or an audio output device for connecting a speaker, headphones, or headphones.

[0139] Memory 92 includes high-speed random access memory, such as DRAM, SRAM, DDR RAM, or other random access solid-state memory devices, and optionally includes non-volatile memory, such as one or more disk storage devices, optical disk storage devices, flash memory devices, or other non-volatile solid-state memory devices. Memory 92 may optionally include one or more storage devices located remotely from CPU 59. The non-volatile memory devices within memory 92, or alternatively, include non-transitory computer-readable storage media. Access to memory 92 by other components of computer system 100 (such as CPU 59) may optionally be controlled by controller 88. In some embodiments, memory 92 includes a large-capacity memory located remotely relative to CPU 59. In other words, some data stored in memory 93 may actually be hosted on a device external to computer system 100, but may be accessed electronically by computer system 100 using network interface 84 via the Internet, intranet, or other forms of network or cable.

[0140] The memory 92 of computer system 100 stores:

[0141] ● Optional operating system 30 (e.g., ANDROID, iOS, DARWIN, RTXC, LINUX, UNIX, OS X, WINDOWS, or embedded operating systems such as VxWorks), which includes programs for handling various basic system services;

[0142] ● The approximate graph edit distance (GED) calculation module 32 of the spatial data evaluation module 36 is used to estimate the graph edit distance between the first compound and the second compound;

[0143] ●The identity of the first compound 34;

[0144] ● Figure 36 of the first compound 34, the graph comprising a plurality of nodes (38-1, ..., 38-N, where N is a positive integer of 2 or greater) and a plurality of edges (40-1, ..., 40-M, where M is a positive integer of 2 or greater), each edge 40 identifying a source node (e.g., 42-1-1) and a destination node (42-1-2) among the plurality of nodes, wherein each atom of the first compound 36 is represented by a node 38 among the plurality of nodes, and each bond of the first compound is represented by an edge 40 among the plurality of edges;

[0145] ●The identity of the second compound 44;

[0146] ● Figure 46 of the second compound 44, comprising multiple nodes (48-1, ..., 48-X, where X is a positive integer of 2 or greater) and multiple edges (50-1, ..., 50-Y, where Y is a positive integer of 2 or greater), each edge 50 identifying a source node (e.g., 52-1-1) and a destination node (52-1-2) among the multiple nodes, wherein each atom of the second compound 46 is represented by node 48 among the multiple nodes, and each bond of the second compound is represented by edge 50 among the multiple edges; and

[0147] ● Training library 56, which contains training compound pairs 58-1, ..., 58-Q, where Q is a positive integer of 2 or greater, and each pair of training compounds is associated with a ground truth graph edit distance of 60.

[0148] In some embodiments, one or more identified data elements or modules of computer system 100 are stored in one or more of the aforementioned memory devices and correspond to a set of instructions for performing the functions described above. The identified data, modules, or programs (e.g., instruction sets) do not need to be implemented as separate software programs, programs, or modules, and therefore various subsets of these modules can be combined or otherwise rearranged in different embodiments. In some embodiments, memories 92 and / or 90 (and optionally 52) optionally store subsets of the identified modules and data structures. Furthermore, in some embodiments, memories 92 and / or 90 (and optionally 52) store other modules and data structures not described above.

[0149] Example Method

[0150] Given that a system for estimating the graph editing distance between the first and second compounds has been disclosed, a method for performing such characterization is described in detail with reference to Figure 2 and discussed below.

[0151] Box 200. Reference box 200 provides a system and method for estimating the graph editing distance between a first compound 34 and a second compound 44.

[0152] Box 202. Referring to box 202, optionally a first graph 36 representing the first compound is obtained. The first graph contains a first plurality of nodes and a first plurality of edges. Each atom of the first compound is represented by node 38 of the first plurality of nodes. Each bond of the first compound is represented by edge 40 of the first plurality of edges.

[0153] Box 204. Referring to box 204, a second figure 46 representing the second compound 44 is optionally obtained. The second figure 46 includes a second plurality of nodes and a second plurality of edges. Each atom of the second compound is represented by node 48 in the second plurality of nodes. Each bond of the second compound is represented by edge 50 in the second plurality of edges.

[0154] Referring to box 206, in some embodiments, the first compound and the second compound each satisfy two or more, three or more, or all four of the Lipinski Five Rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5. See Lipinski, 1997, *Advanced Drug Delivery Review*, pp. 23, 3, which is hereby incorporated herein by reference in its entirety. In some embodiments, the first compound and the second compound each satisfy one or more criteria in addition to the Lipinski Five Rules. For example, in some embodiments, the first compound and the second compound each have five or fewer aromatic rings, four or fewer aromatic rings, three or fewer aromatic rings, or two or fewer aromatic rings.

[0155] Boxes 208-210. Referring to box 208, in some embodiments, the exact image edit distance between the first compound and the second compound is between 1 and 10. Referring to box 210, in some embodiments, the exact image edit distance between the first compound and the second compound is between 1 and 15. In some embodiments, the exact image edit distance between the first compound and the second compound is unknown.

[0156] Referring to boxes 212-214, in some embodiments, the first compound and the second compound are each organic compounds with a molecular weight of less than 500 Daltons, less than 1000 Daltons, less than 2000 Daltons, less than 4000 Daltons, less than 6000 Daltons, less than 8000 Daltons, less than 10000 Daltons, or less than 20000 Daltons. Referring to box 214, in some embodiments, the first compound and the second compound are each organic compounds with a molecular weight between 400 Daltons and 10000 Daltons.

[0157] In some embodiments, the molecular weights of the first compound and the second compound are at least 10 Da, at least 20 Da, at least 50 Da, at least 100 Da, at least 200 Da, at least 500 Da, at least 1 kDa, at least 2 kDa, at least 3 kDa, at least 5 kDa, at least 10 kDa, at least 20 kDa, at least 30 kDa, at least 50 kDa, at least 100 kDa, or at least 500 kDa. In some embodiments, the molecular weights of the first compound and the second compound are each not exceeding 1000 kDa, not exceeding 500 kDa, not exceeding 100 kDa, not exceeding 50 kDa, not exceeding 10 kDa, not exceeding 5 kDa, not exceeding 2 kDa, not exceeding 1 kDa, not exceeding 500 Da, not exceeding 300 Da, not exceeding 100 Da, or not exceeding 50 Da. In some embodiments, the molecular weights of the first compound and the second compound are 10 Da to 900 Da, 50 Da to 1000 Da, 100 Da to 2000 Da, 1 kDa to 10 kDa, 5 kDa to 500 kDa, or 100 kDa to 1000 kDa, respectively. In some embodiments, the molecular weights of the first compound and the second compound each fall into another range that begins at a value not less than 10 Daltons and ends at a value not more than 1000 kDa.

[0158] In some embodiments, the first compound and the second compound are each small molecules. For example, in some embodiments, the first compound and the second compound are each organic compounds with a molecular weight of less than about 1,000 Daltons (e.g., less than 900 Daltons).

[0159] Box 216. Referring to box 216, the first graph or other representation of the first compound is input into a model containing multiple parameters. The model (e.g., through at least 10,000 calculations) applies the multiple parameters to the first graph to generate a first isometric latent embedding representing the first compound as the first output of the model.

[0160] like Figure 10 As shown, in some embodiments, the first isometric preserving latent embedding has 64, 96, 128, 192, or 256 dimensions. In some embodiments, the dimensions of the first isometric preserving latent embedding are between 64 and 1024. In some embodiments, the dimensions of the first isometric preserving latent embedding are between 64 and 512.

[0161] In some embodiments, the model (e.g., Figure 7 Model 702 contains more than 400 parameters, more than 1,000 parameters, more than 2,000 parameters, more than 5,000 parameters, more than 10,000 parameters, more than 100,000 parameters, or more than 1×10⁻⁶ parameters. 6 One parameter.

[0162] In some embodiments, the model includes 10,000 or more parameters, 100,000 or more parameters, or 1×102 parameters. 6 One or more parameters. In some embodiments, the model contains 1,000 parameters. In some embodiments, the model consists of 10 to 10 million parameters. In some embodiments, the model contains at least 10, at least 50, at least 100, at least 500, at least 1,000, at least 2,000, at least 5,000, at least 10,000, at least 20,000, at least 50,000, at least 100,000, at least 200,000, at least 500,000, at least 1 million, at least 2 million, at least 3 million, at least 4 million, or at least 5 million parameters. In some embodiments, the model comprises no more than 8 million, no more than 5 million, no more than 4 million, no more than 1 million, no more than 500,000, no more than 100,000, no more than 50,000, no more than 10,000, no more than 5,000, no more than 1,000, or no more than 500. In some embodiments, the first model comprises 10 to 5,000, 500 to 10,000, 10,000 to 500,000, 20,000 to 1 million, or 1 million to 5 million parameters. In some embodiments, the number of parameters in the model falls into another range that begins with no fewer than 10 parameters and ends with no more than 8 million parameters.

[0163] In some embodiments, the amount of information input into the first graph or other representation of the first compound into model 702, combined with the number of parameters of the model, results in more than 10,000 calculations, more than 100,000 calculations, or more than 1 × 10⁻⁶ calculations. 6 Calculations exceeding 5 × 10 6 The calculation or more than 1×10 7 The first isometric preserving potential embedding is computed using the next computation.

[0164] In some embodiments, compounds may be represented in a form other than a diagram for input into the model of this disclosure. For example, in some embodiments, compounds are represented as fingerprints, and the fingerprints of compounds are input into the model to generate isospaced preserving potential embeddings of molecules. Non-limiting examples of fingerprint representations of compounds have been given in the definitions section above.

[0165] In some embodiments, the compound is represented as a descriptor, and the descriptor of the compound is input into the model to generate isometric latent embeddings of the compound. Descriptors include, but are not limited to, physicochemical descriptors, topological descriptors, electronic descriptors, geometric descriptors, functional group counts, toxicological and environmental descriptors, and any combination thereof.

[0166] Physicochemical descriptors include, but are not limited to, molecular weight (the sum of the atomic weights of all atoms in a compound), LogP, penalized logP, compound acid dissociation constant (pKA), compound acid dissociation constant (kA), compound topological polar surface area (TPSA), polar surface area (PSA) (the molecular surface area occupied by polar atoms and functional groups, commonly used to predict membrane permeability and bioavailability), solubility (predicting the solubility of a compound in different solvents or aqueous solutions), and drug similarity. See, for example, Prasanna and Doerksen et al., 2009, “Topological Polar Surface Area: AUseful Descriptor in 2D-QSAR” 16(1), pp. 21-41, which is hereby incorporated by reference.

[0167] LogD is the distribution constant of a compound's lipophilicity. In some embodiments, LogD is calculated based on the compound's chemical structure (cLogD). Generally, cLogD refers to the calculated distribution constant of a molecule's lipophilicity. This is typically determined for compounds in an aqueous phase, which may be adjusted to a specific pH using a buffer solution. This parameter can be used as an estimate of a compound's overall lipophilicity, which affects the compound's performance in a range of biological processes related to drug discovery, such as solubility, biomembrane permeability, hepatic clearance, lack of selectivity, and / or nonspecific toxicity. In some cases, lipophilicity can be used as an estimate of drug similarity. See Cambridge MedChemConsulting, 2019, "Lipophilicity," available online at cambridgemedchemconsulting.com / resources / physiochem / logD.html, which is hereby incorporated herein by reference in its entirety.

[0168] logP is a measure of the hydrophilicity of a compound. The partition coefficient (abbreviated as P) is defined as a specific ratio of the solute concentrations between two solvents (two liquid phases), particularly for non-ionized solutes, and therefore the logarithm of this ratio is log P. As used herein, by convention, the numerator of this ratio is the concentration of the compound in octanol, and the denominator is the concentration of the compound in water.

[0169] The penalized logP is the logP score, which also takes into account ring size and synthetic accessibility. See, for example, Ertl, 2009, “Estimation of synthetic accessibility score of drug-like molecules”, J. Cheminform, which is hereby incorporated by reference.

[0170] In some embodiments, pKA is estimated using the structure of the compound. See, for example, Seybold and Shields, 2015, “Computational estimation of pKa values”, WIREs Comput Mol Sci, 5, pp. 290-297, which is hereby incorporated by reference.

[0171] Compound topological polar surface area (TPSA) is a measure of the polar surface area of ​​a compound that utilizes functional group contributions based on large structural databases without requiring calculation of the compound's three-dimensional structure or determination of which or which are relevant biological conformations. See, for example, Prasanna and Doerksen et al., 2009, "Topological Polar Surface Area: A Useful Descriptor in 2D-QSAR" 16(1), pp. 21-41, which is hereby incorporated by reference.

[0172] Topological descriptors include, but are not limited to, atom and bond counts (the number of atoms and bonds in a compound), molecular connectivity indices (graph-based indices representing structural connectivity, such as the Wiener index, Balaban index, and Zagreb index), and molecular diameters (a measure of molecular size or compactness, typically calculated as the maximum distance between any two atoms in a molecule). See Balaban and Ivanciuc, 1999, *Historical Development of Topological Indices*, CRC Press, 1st edition, which is hereby incorporated by reference.

[0173] Electronic descriptors include, but are not limited to, electronegativity (a measure of an atom’s tendency to attract electrons in a chemical bond), ionization potential (the energy required to remove an electron from an atom or molecule), and electron density (the distribution of electron charge within a molecule, usually represented by a molecular orbital or electron density map).

[0174] Geometric descriptors include, but are not limited to, bond lengths and bond angles (measurements of the lengths and angles between atoms in a molecule), twist angles (measurements of the rotation around a single bond in a molecule), and surface area and volume (geometric properties characterizing the shape and size of a molecule).

[0175] Functional group counting descriptors include, but are not limited to, counting of specific functional groups or substructures within a compound, such as hydroxyl groups, aromatic rings, or carboxylic acid groups.

[0176] Toxicological and environmental descriptors include, but are not limited to, toxicity carriers (substructural features associated with toxicity or adverse effects in a compound) and environmental fate descriptors (predictions of a compound’s performance in the environment, including biodegradability, persistence, and bioaccumulation potential).

[0177] The QED score is described in the following literature: Bickerton et al., 2012, “Quantifying the chemical beauty of drugs”, Nature Chemistry 4(2), pp. 90-98, which is hereby incorporated by reference.

[0178] Non-limiting examples of descriptors for compounds are described in the following literature: Seko, 2017, “Representation of compounds for machine-learning prediction of physical properties”, Physical Review B95, 144110, which is hereby incorporated by reference.

[0179] In some embodiments, the compound is represented as a three-dimensional structural representation, and this three-dimensional structural representation is input into a model to generate isospaced preserving potential embeddings of the molecule. Non-limiting examples of three-dimensional structural representations of compounds include, but are not limited to, pharmacophore models (hypothetical representations of the spatial arrangement of chemical features, such as hydrogen bond donors, acceptors, aromatic rings, etc. of a compound), conformational sets (representations of multiple conformations or energy-accessible states of a compound), and quantum mechanical calculations, such as ab initio calculations and density functional theory (DFT) methods, that can inform the 3D geometry of the compound.

[0180] In some embodiments, the compound is represented as a tensor-based representation, and this tensor-based representation is input into the model to generate iso-preserving potential embeddings of the molecules. Non-limiting examples of tensor-based representations of compounds are disclosed in: Huo and Rupp, 2022, “Unified representation of molecules and crystals for machine learning”, Machine Learning, 3, 045017, which is hereby incorporated by reference.

[0181] In some embodiments, the compound is represented as a string representation, and the string representation of the compound is input into the model to generate isometric preserving potential embeddings of the molecule. Non-limiting examples of string representations of compounds include, but are not limited to, Simplified Molecular Input Line Input Systems (SMILES; see, for example, Honda et al., 2019, “SMILES Transformer: Pre-trained Molecular Fingerprint for Low Data Drug Discovery”, arXiv:1911.04738), SMILES Arbitrary Target Specification (SMARTS; see, for example, “SMARTS-ALanguage for Describing Molecular Patterns”, 2022, published online at daylight.com / dayhtml / doc / theory / theory.smarts.html (accessed December 2020)), and DeepSMILES (see, for example, O'Boyle and Dalke, 2018, “DeepSMILES: an adaptation of SMILES for use in machine learning of chemical structures”). Machine-learning of chemical structures, ChemRxiv preprint (https: / / doi.org / 10.26434 / chemrxiv.7097960.v1.) and self-referenced embedded strings (SELFIES) (Krenn et al., 2022, “SELFIES and the future of molecular string representations”, Patterns 3(10), pp. 1-27), the references of which are hereby incorporated by reference.

[0182] Box 218. Refer to box 218 to input the second figure or other representations of the first compound into the model. Although Figure 7Two models, 702 and 704, are shown, but in a typical embodiment, models 702 and 704 are in fact the same model. That is, a first graph (or other representation) of a first compound is input into model 702 to obtain a first isometric latent embedding, and then a second graph (or other representation) of a second compound is input into model 702 to obtain a second isometric latent embedding. Figure 7 Two models, 702 / 704, are depicted to better illustrate the comparison of model outputs. In some embodiments, the amount of information in the second graph (or other representation of the second compound) input into the model, combined with the number of model parameters, results in more than 10,000 calculations, more than 100,000 calculations, or more than 1 × 10⁻⁶ calculations. 6 Calculations exceeding 5 × 10 6 The calculation or more than 1×10 7 The second isometric preserving potential embedding is computed.

[0183] As used herein, in some embodiments, the first and second isometric latent embeddings refer to latent embeddings generated by a model that conforms to a threshold range. Figure 6 The symmetry and self-distance requirements are shown.

[0184] As used herein, in some embodiments, the first and second isometric latent embeddings refer to latent embeddings generated by a model that, within a threshold range, fits within the compound's test dataset (e.g., used for computation). Figure 6 The dataset containing the statistics shown conforms to Figure 6 The symmetry properties shown In some embodiments, the threshold is 0.5 or less, 0.4 or less, 0.3 or less, or 0.2 or less. In some embodiments, the threshold is a value between 0.1 and 0.5.

[0185] As used herein, in some embodiments, the first and second isometric latent embeddings refer to latent embeddings generated by a model that, within a threshold range, fits within the compound's test dataset (e.g., used for computation). Figure 6 The dataset containing the statistics shown conforms to Figure 6 The displayed self-distance attribute In some embodiments, the threshold is 1.4 or less, 1.3 or less, 1.2 or less, 1.1 or less, 1.0 or less, 0.9 or less, 0.8 or less, 0.7 or less, 0.6 or less, or 0.5 or less. In some embodiments, the threshold is a value between 0.1 and 1.5.

[0186] Boxes 220-222. Referring to box 220, in some embodiments, the model is a message passing network. Referring to box 222, in some embodiments, the model is a graph neural network.

[0187] In some embodiments, the model is any model that takes a representation of a compound and outputs an isometric representation of the compound that preserves the potential embedding.

[0188] An isometric preserving latent embedding is an embedding that preserves the geometric properties of the input space in the latent space. In some embodiments, the model used to generate such isometric preserving latent embeddings is an autoencoder.

[0189] In some embodiments, the model is a variational autoencoder (VAE). A VAE is a generative model that learns to probabilistically encode and decode data points. It is trained to maximize the probability of generating input data while minimizing the discrepancy between the learned latent distribution and the prior distribution (typically Gaussian). By encouraging the latent space to follow a specific distribution (e.g., Gaussian), a VAE implicitly aims to preserve local structure and distance relationships in the input space, which to some extent makes it equidistant. See, for example, Kingma and Max, 2019, Foundations and Trends in Machine Learning, 12(4), ISSN 1935-8237, which is hereby incorporated by reference.

[0190] In some embodiments, the model is an adversarial autoencoder (AAE). AAEs combine the principles of variational autoencoders with adversarial training. In addition to accurately reconstructing the input data, they train a discriminator to distinguish samples from the true latent distribution from samples from the encoder distribution. The adversarial training component encourages the encoder to generate latent embeddings that are indistinguishable from samples drawn from the prior distribution, which can improve isometric preservation.

[0191] In some embodiments, the model is a regularized autoencoder. Various regularization techniques can be applied to a standard autoencoder to encourage isometry in the latent space. For example, adding a penalty term to the loss function penalizes deviations from the desired structure or distribution in the latent space. In some embodiments, as described in the Examples section, L2 norm regularization is applied to the autoencoder to maintain isometry.

[0192] In some embodiments, the model is a sparse autoencoder, a denoising autoencoder (see, for example, Zheng, 2019, "Stacked Denoising Auto-Encoder for Short-Term Load Forecasting: Deep Learning with Stacked Denoising Auto-Encoder Algorithm"), or a shrinking autoencoder. In some embodiments, such autoencoders indirectly encourage isometric preservation by facilitating robust representations that capture salient features of the input data.

[0193] In some embodiments, the model is a metric learning autoencoder. As used herein, metric learning autoencoders are explicitly designed to learn embeddings to preserve specific distance metrics or relationships in the input space. These models incorporate loss functions that directly encourage isometry preservation, such as triple loss or contrastive loss. By optimizing these loss functions during training, the autoencoder learns to map similar input samples to nearby points in the latent space, thereby preserving local distances and geometry.

[0194] In some embodiments, the model is a graph neural network (GNN), also known as a message passing network. See Baskin et al., 1997, “A neural device for searching direct correlations between structures and properties of chemical compounds”, Journal of Chemical Information and Computer Science, 37(4):715-721; Sperduti and Starita, 1997, “Supervised neural networks for the classification of structures”, IEEE Transactions on Neural Networks, 8(3), pp.714-735; Scarselli et al., 2008, “The graph neural network model”, IEEE Transactions on Neural Networks, 20(1), pp.61-80; and Gilmer et al., 2017, “Message Passing Neural Networks”, published in: Schütt et al. (eds.), Machine Learning Meets Quantum Physics), Lecture Notes in Physics, 968, Springer, Cham, with each reference hereby incorporated by way of citation.

[0195] In some embodiments, the model is a Graph Convolutional Neural Network (GCN). Generally, message passing in GNNs is computed using nonlinear neural networks, which can be computationally expensive. In contrast, GCN (Kipf and Welling, 2017) is a significant simplification of GNNs, using a linear message passing scheme, represented as...

[0196]

[0197] Where H in (H out ) is the input (output) feature of the l-th layer. It is a renormalized adjacency matrix with self-looping, and W is the trainable weights. GCN, a variant of GNN, is computationally efficient compared to message passing in GNNs computed using nonlinear neural networks. In some embodiments, the graph representation of GCN remains unchanged as long as the initialization is carefully designed. It is also inductive, because the node embeddings after the GCN operation can be computed for any unseen graph. GCN is a node embedding model belonging to the family of models based on neighbor aggregation. Its core operation, graph convolution, operates on the node representation, which is represented as...

[0198]

[0199] in d is the set of first-order neighbors of node n plus n itself. n It is the degree of node n plus 1. It is the weight matrix associated with the l-th GCN layer. It is a bias, and f1(·) is an activation function, such as ReLU(x) = max(0,x). Intuitively, graph convolution operations aggregate features from the first-order neighbors of a node. See Bai et al., 2019, “ACM International Internet Search and Data Mining Conference”, February 11-15, 2019, Melbourne, Victoria, Australia, which is hereby incorporated by reference. In some embodiments, the graph of the compound is encoded using single-encoding based on node type (e.g., nodes of all carbon types share the same single-encoding vector), so the aggregation result is the same even if the node ID is permuted. For graphs with unlabeled nodes, each node has the same label, resulting in the same constants as the initial representation. In some embodiments, the GCN has 2, 3, 4, 5, 6 or more layers.

[0200] Non-restricted examples of GCNs are disclosed in the following literature: Behler Parrinello, 2007, “Generalized Neural-Network Representation of HighDimensional Potential-Energy Surfaces”, Physical Review Letters 98, 146401; Chmiela et al., 2017, “Machine learning of accurate energy-conserving molecular force fields”, Science Advances 3(5):e1603015; Schütt et al., 2017, “SchNet: A continuous-filter convolutional neural network for modeling quantum interactions”, Advances in Neural Information Processing Systems 30, pp. 992-1002; Feinberg et al., 2018, “PotentialNet for molecular property prediction”. “Molecular Property Prediction”, ACS Cent. Sci. 4, 11, 1520-1530; and Stafford et al., 2022, “AtomNet PoseRanker: Enriching Ligand Pose Quality for Dynamic Proteins in Virtual High Throughput Screens”, J. CHEM INF MODEL 62, pp. 1178-1189, each of which is hereby incorporated by reference.

[0201] In some embodiments, such as Figure 18 The model shown uses a messaging network instead of a GCN. In some embodiments, such as Figure 19 The model shown uses a messaging network instead of a GCN. In some embodiments, such as Figure 20The model shown uses a message passing network instead of a GCN.

[0202] In some embodiments, the model is any encoder that takes a graph of the compound or other representation of the compound and outputs a vector representing the compound.

[0203] Boxes 224-228. Referring to box 224, in some embodiments, the model is a message-passing graph neural network with 3 to 8 layers. Referring to box 226, in some embodiments, the model is a message-passing graph neural network consisting of 5 layers. Referring to box 228, in some embodiments, the model contains 500,000 or more parameters, or 1 × 10⁻⁶ parameters. 6 One or more parameters.

[0204] Box 230. Referring to box 230, in some embodiments, the model performs at least 100,000 computations to compute a first isometric preserving latent embedding, and the model performs at least 100,000 computations to compute a second isometric preserving latent embedding.

[0205] Boxes 232-234. Referring to box 232, in some embodiments, an estimate of the graph editing distance between the first compound and the second compound is provided as the L2 norm difference between the first and second isometric latent embeddings. Referring to box 234, in some embodiments, the first isometric latent embedding is a first vector containing a first plurality of vector values, the second isometric latent embedding is a second vector containing a second plurality of vector values, and the L2 norm difference between the first and second vectors is considered as the square root of the sum of the squared differences of the corresponding vector values ​​between the first and second vectors.

[0206] Advantageously, by using the L2 norm difference between the model's first and second outputs as the GED estimate, in addition to the positive aspect, Figure 6 All properties of the distance metric outlined at the top are satisfied.

[0207] Box 236. One practical application / technical effect of GED is finding chemically related analogs. For example, in drug discovery work, consider the case where the first compound is a known lead compound. In this case, compounds that are chemically related analogs can be searched in one or more compound databases by calculating the GED distance between the first compound and each compound in one or more compound databases. An example of such a compound database is the PubChem database (see Kim et al., 2021, “PubChem 2021: new data content and improved web interfaces”, Nucleic Acids Research 8(49)(D1), pp. D1388-D1395, which is hereby incorporated by reference). Another example of such databases is the ZINC database (see Irwin et al., 2020, “ZINC20—A Free Ultralarge-Scale Chemical Database for LigandDiscovery”, *Journal of Chemical Information and Modeling*, 60(12), 6065-6073, which is hereby incorporated by reference). Another example of such databases is the ChEMBL database. ChEMBL is an artificially curated database of bioactive molecules with drug-like properties. See Gaulton et al., 2019, “ChEMBL: towards direct deposition of bioassay data”, *Nucleic Acid Research*, 47(D1), D930-D940, which is hereby incorporated by reference. Other examples of such databases include those containing commercially available molecules, such as MCULE (Kiss et al., 2012, “Http: / / Mcule.Com: A Public Web Service for Drug Discovery”, Journal of Cheminformatics 4(1), p. 17) and ENAMINE (Irwin et al., 2016, “Docking Screens for Novel Ligands Conferring New Biology”, J. Med. Chem. 59(9), pp. 4103-4120), each of which is hereby incorporated by reference.

[0208] In some embodiments, the GED distance between the first compound and each of 10 or more compounds in one or more compound databases is calculated in this manner.

[0209] In some embodiments, the GED distance between the first compound and each of 100 or more compounds in one or more compound databases is calculated in this manner.

[0210] In some embodiments, the GED distance between the first compound and each of 1,000 or more compounds in one or more compound databases is calculated in this manner.

[0211] In some embodiments, the GED distance between the first compound and each of 10,000 or more compounds in one or more compound databases is calculated in such a manner.

[0212] In some embodiments, the GED distance between the first compound and each of 100,000 or more compounds in one or more compound databases is calculated in this manner.

[0213] In some embodiments, the first compound is calculated in this manner in relation to one or more compound databases at a ratio of 1×10⁻⁶. 6 1, 2×10 6 1, 3×10 6 1, 4×10 6 5×10 6 6×10 6 7×10 6 8×10 6 One or 9×10 6 GED distance between each of one or more compounds.

[0214] In some embodiments, the first compound is calculated in this manner in relation to one or more compound databases at a ratio of 1×10⁻⁶. 7 1, 2×10 7 1, 3×10 7 1, 4×10 7 5×10 7 6×10 7 7×10 7 8×10 7 One or 9×10 7 GED distance between each of one or more compounds.

[0215] In drug discovery, a lead compound is a biologically active molecule that may be useful but may require modification to better suit a target or have better pharmacological properties. Compounds whose estimated GED is less than a threshold (e.g., less than 10, less than 9, less than 8, less than 7, less than 6, less than 5, less than 4, less than 3, or less than 2) can then be evaluated as chemically related analogs of the first compound, and thus their suitability for the target or their ability to have better pharmacological properties can be assessed. Therefore, referring to box 236, in some embodiments, when the estimated GED is less than a threshold, it is determined whether a second compound is a chemically related analog of the first compound. In some embodiments, the threshold is any real number between 2 and 10 (inclusive). In some embodiments, the threshold is 2, 3, 4, 5, 6, 7, 8, 9, or 10. In some embodiments, the threshold is 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, or 9.5.

[0216] Box 238. Another practical application / technical effect of GED is to ensure the diversity of chemical libraries, or the diversity of chemicals selected for drug discovery procedures. For example, GED can be used as a distance metric to cluster one or more compound databases into clusters, and compounds can then be selected from each of the resulting clusters for evaluation in drug discovery procedures.

[0217] One example of such compound databases is the PubChem database (see Kim et al., 2021, “PubChem 2021: New Data Content and Improved Web Interfaces”, Nucleic Acid Research 8(49)(D1), pp. D1388-D1395, which is hereby incorporated by reference). Another example of such databases is the ZINC database (see Irwin et al., 2020, “ZINC20—A Free, Large-Scale Chemical Database for Ligand Discovery”, Journal of Chemical Information and Modeling 60(12), 6065-6073, which is hereby incorporated by reference). Another example of such databases is the ChEMBL database. ChEMBL is an artificially curated database of bioactive molecules with drug-like properties. See Gaulton et al., 2019, “ChEMBL: Towards Direct Deposition of Bioassay Data”, Nucleic Acid Research 47(D1), D930-D940, which is hereby incorporated by reference. Other examples of such databases include those that are commercially available molecules, such as MCULE (Kiss et al., 2012, “Http: / / Mcule.com: A public web service for drug discovery”, Journal of Cheminformatics 4(1), p. 17) and ENAMINE (Irwin et al., 2016, “Docking screening of novel ligands for new biology”, Journal of Medicinal Chemistry 59(9), pp. 4103-4120), each of which is hereby incorporated by reference.

[0218] Therefore, referring to block 238, in some embodiments, for each corresponding unique compound pair in the compound database, the optional process of obtaining a first graph (block 202), optionally obtaining a second graph (block 204), inputting the first graph or other representation of the first compound (block 216), inputting the second graph or other representation of the second compound (block 218), and providing an approximate GED is repeated to form multiple graph edit distances, wherein the first compound in the corresponding unique compound pair is the first compound, and the second compound in the corresponding unique compound pair is the second compound. The multiple graph edit distances are then clustered into multiple clusters by evaluating the multiple distances using a criterion function. Compounds are then selected from one or more of the multiple clusters for evaluation in a drug discovery procedure. In some embodiments, the compounds are selected from 2, 3, 4, 5, 6, 7, 8, 9, or 10 or more different clusters in the drug discovery procedure. In some embodiments, 10 or more, 100 or more, 1000 or more, 10,000 or more, 100,000 or more, or 1×10 are selected from each of one or more clusters. 6 One or more compounds.

[0219] In some embodiments, 100 or more unique compound pairs are evaluated for box 238. In some embodiments, 1000 or more unique compound pairs are evaluated for box 238. In some embodiments, 10,000 or more unique compound pairs are evaluated for box 238. In some embodiments, 100,000 or more unique compound pairs are evaluated for box 238. In some embodiments, 1×10 6 One or more unique pairs of compounds.

[0220] In some embodiments, 1×10 is evaluated for block 238. 6 1, 2×10 6 1, 3×10 6 1, 4×10 6 5×10 6 6×10 6 7×10 6 8×10 6 One or 9×10 6 One or more unique compound pairs. In some embodiments, 1×10⁻⁶ is evaluated for box 238. 7 1, 2×10 7 1, 3×10 7 1, 4×10 7 5×10 7 6×10 7 7×10 7 8×10 7 One or 9×10 7 One or more unique compound pairs. In some embodiments, 1×10⁻⁶ is evaluated for box 238. 8 1, 2×10 8 1, 3×10 8 1, 4×10 8 5×10 8 6×10 8 7×10 8 8×10 8 One or 9×10 8 One or more unique pairs of compounds.

[0221] In some embodiments, clustering is unsupervised clustering. In some embodiments, clustering is supervised clustering. Clustering algorithms suitable for use according to box 348 are described in the following literature: e.g., Duda and Hart, Pattern Classification and Scene Analysis, 1973, pp. 211-256, John Willie & Sons, New York (hereinafter referred to as "Duda 1973"), which is hereby incorporated in its entirety by reference. As an illustrative example, in some embodiments, the clustering problem is described as the problem of finding natural groupings in a dataset. To identify natural groupings, two problems need to be solved. First, a method for measuring the similarity (or dissimilarity) between two samples must be determined. This measure (e.g., a similarity metric) is used to ensure that samples in one cluster are more similar to each other than samples in other clusters. Second, a mechanism for partitioning the data into clusters using the similarity metric must be determined. One way to begin clustering research is to define a distance function and compute a distance matrix between all pairs of samples in the training set. If distance is a good measure of similarity, then the distance between reference entities in the same cluster is significantly smaller than the distance between reference entities in different clusters. However, in some implementations, clustering does not use a distance metric. For example, in some embodiments, a non-metric similarity function s(x,x') is used to compare two latent embeddings x and x'. In some such embodiments, s(x,x') is a symmetric function with a large value when x and x' are somewhat "similar". Once a method for determining the "similarity" or "dissimilarity" between latent embeddings is selected, clustering uses a criterion function to measure the clustering quality of any partition of the data. The data is clustered using partitions of multiple compound pairs that extremum the criterion function. Specific exemplary clustering techniques considered for use in this disclosure include, but are not limited to, hierarchical clustering (aggregate clustering using nearest neighbor, farthest neighbor, average connectivity, centroid, or sum of squares algorithms), k-means clustering, fuzzy k-means clustering, and Jarvis-Patrick clustering. In some embodiments, clustering includes unsupervised clustering (e.g., without pre-planning the number of clusters and / or pre-determining the cluster allocation).

[0222] Box 240. Another practical application / technical effect of GED is the establishment of quantitative structure-activity relationship (QSAR) models. QSAR models are computational or mathematical models that attempt to identify significant correlations between molecular structure and molecular activity. Due to the vast amount of available data on chemical compounds and their reactivity, computational tools are needed to shorten drug synthesis and testing cycle times. These tools are crucial if activity data is to be analyzed and new models created for virtual screening techniques. For QSAR models, the GED distance is used as the basis for quantifying differences in molecular structure. See, for example, Garcia-Hernandez, 2020, “Learning the Edit Costs of Graph Edit Distance Applied to Ligand-Based Virtual Screening,” Current Topics in Medicinal Chemistry, 20, 1582-1592, which is hereby incorporated by reference. Therefore, referring to box 240, in some embodiments, estimates of GED are used to establish quantitative structure-activity relationship models including a first and a second compound.

[0223] In some embodiments, the QSAR is established in relation to a first compound, which is a known lead compound in drug discovery work. In this case, compounds associated with a predetermined GED of the first compound can be searched in one or more compound databases, and then QSARs can be established using these compounds.

[0224] One example of such compound databases is the PubChem database (see Kim et al., 2021, “PubChem 2021: New Data Content and Improved Web Interfaces”, Nucleic Acid Research 8(49)(D1), pp. D1388-D1395, which is hereby incorporated by reference). Another example of such databases is the ZINC database (see Irwin et al., 2020, “ZINC20—A Free, Large-Scale Chemical Database for Ligand Discovery”, Journal of Chemical Information and Modeling 60(12), 6065-6073, which is hereby incorporated by reference). Another example of such databases is the ChEMBL database. ChEMBL is an artificially curated database of bioactive molecules with drug-like properties. See Gaulton et al., 2019, “ChEMBL: Towards Direct Deposition of Bioassay Data”, Nucleic Acid Research 47(D1), D930-D940, which is hereby incorporated by reference. Other examples of such databases include those that are commercially available molecules, such as MCULE (Kiss et al., 2012, “Http: / / Mcule.com: A public web service for drug discovery”, Journal of Cheminformatics 4(1), p. 17) and ENAMINE (Irwin et al., 2016, “Docking screening of novel ligands for new biology”, Journal of Medicinal Chemistry 59(9), pp. 4103-4120), each of which is hereby incorporated by reference.

[0225] Therefore, in some embodiments, the first compound is calculated in relation to 10, 100, 1,000, 10,000, 100,000, or 1×10⁻⁶ compounds from a compound database. 6 One or 1×10 7The GED distance between each of one or more compounds is used to determine QSAR, and those compounds within the estimated GED threshold of the first compound are used. In some embodiments, the estimated GED threshold is less than 10, less than 9, less than 8, less than 7, less than 6, less than 5, less than 4, less than 3, or less than 2. In some embodiments, the estimated GED threshold is any real number between 2 and 10 (inclusive). In some embodiments, the estimated GED threshold is 2, 3, 4, 5, 6, 7, 8, 9, or 10. In some embodiments, the estimated GED threshold is 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, or 9.5. In some embodiments, 10% to 90% of the compounds for which the estimated GED is evaluated relative to the first compound in one or more databases are within the estimated GED threshold. In some embodiments, 20% to 80% of the compounds for which the estimated GED is evaluated relative to the first compound in one or more databases are within the estimated GED threshold. In some embodiments, at least 20%, 30%, 40%, 50%, or 60% of the compounds for which GED is estimated relative to a first compound in one or more databases are within the estimated GED threshold. In some embodiments, less than 90%, 80%, 70%, 60%, or 50% of the compounds for which GED is estimated relative to a first compound in one or more databases are within the estimated GED threshold.

[0226] Box 242. Another practical application / technical effect of GED is defining the activity cliff. An activity cliff occurs when a molecule undergoes a finite number of changes (such as one or two small changes) and the activity of the derived molecule decreases by an order of magnitude relative to the original molecule. Knowledge of the activity cliff is an important aspect of structure-activity analysis. See, for example, Wassermann et al., 2010, “Activity Landscape Representations for Structure-Activity Relationship Analysis,” *Journal of Medicinal Chemistry*, 53, 8209-8233, which is hereby incorporated by reference. Therefore, referring to box 242, in some embodiments, estimates from GED are used to determine the activity cliff relative to a drug discovery procedure.

[0227] Other embodiments

[0228] Another aspect of this disclosure provides a computer system for estimating a graph edit distance between a first compound and a second compound. The computer system includes one or more processors and a memory addressable by the one or more processors. The memory stores at least one program for execution by the one or more processors. The at least one program includes the following instructions: (A) inputting a first representation of the first compound into a model containing multiple parameters. The model applies the multiple parameters to the first representation of the first compound to generate a first latent embedding representing the first compound as a first output of the model. The at least one program further includes the following instructions: (B) inputting a second representation of the second compound into the model. The model applies the multiple parameters to the second representation of the second compound to generate a second latent embedding representing the second compound as a second output of the model. The at least one program further includes the following instructions: (C) providing an estimate of the graph edit distance between the first compound and the second compound using the difference between the first latent embedding and the second latent embedding.

[0229] In some embodiments, the difference is the L2 norm difference between the first latent embedding and the second latent embedding. In some such embodiments, the first latent embedding is a first vector containing a first plurality of vector values, the second latent embedding is a second vector containing a second plurality of vector values, and the L2 norm difference between the first and second vectors is considered as the square root of the sum of the squared differences of the corresponding vector values ​​between the first and second vectors. In some such embodiments, the model is trained such that the L2 norm of the difference between the first and second vectors is an estimate of the GED between the first and second vectors.

[0230] In some embodiments, the at least one procedure further includes instructions for determining that the second compound is a chemically related analog of the first compound when the estimated graph editing distance is below a threshold.

[0231] In some embodiments, the at least one procedure further includes instructions for repeatedly performing input (A), input (B), and provide (C) for each corresponding unique compound pair in the compound database, thereby forming multiple graph edit distances, wherein a first compound in the corresponding unique compound pair is the first compound, and a second compound in the corresponding unique compound pair is the second compound. In some such embodiments, the multiple graph edit distances are clustered into multiple clusters by evaluating multiple distances using a criterion function, and compounds are selected from one or more of the multiple clusters for evaluation in a drug discovery procedure.

[0232] In some embodiments, the at least one program further includes instructions for using an estimate of the graph editing distance to establish a quantitative structure-activity relationship model including a first compound and a second compound.

[0233] In some embodiments, the at least one procedure further includes instructions for determining the activity cliff relative to the drug target using an estimate of the graph editing distance.

[0234] In some embodiments, the model is a graph convolutional neural network.

[0235] In some embodiments, the model is a graph neural network (message passing network).

[0236] In some embodiments, the model is a message-passing graph neural network consisting of 3 to 8 layers.

[0237] In some embodiments, the model is a message-passing graph neural network consisting of 5 layers.

[0238] In some embodiments, the model is an autoencoder. In some embodiments, the autoencoder is a variational autoencoder, an adversarial autoencoder, a regularized autoencoder, a sparse autoencoder, or a metric learning autoencoder.

[0239] In some embodiments, the first represents a first fingerprint of a first compound, and the second represents a second fingerprint of a second compound.

[0240] In some embodiments, "first" represents a first plurality of descriptors of a first compound, and "second" represents a second plurality of descriptors of a second compound.

[0241] In some embodiments, the first representation is a first three-dimensional structural representation of the first compound, and the second representation is a second three-dimensional structural representation of the second compound.

[0242] In some embodiments, the first representation is a first tensor-based representation of the first compound, and the second representation is a second tensor-based representation of the second compound.

[0243] In some embodiments, the first representation is a first string representation of the first compound, and the second representation is a second string representation of the second compound.

[0244] In some embodiments, the model contains 500,000 or more parameters. In some embodiments, the model contains 1×10 6 One or more parameters.

[0245] In some embodiments, the first compound and the second compound each satisfy two or more, three or more, or all four of the Lipinski Five Rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

[0246] In some embodiments, the exact image edit distance between the first compound and the second compound is between 1 and 10. In some embodiments, the exact image edit distance between the first compound and the second compound is between 1 and 15.

[0247] In some embodiments, the first compound and the second compound are each organic compounds with a molecular weight of less than 500 Daltons. In some embodiments, the first compound and the second compound are each organic compounds with a molecular weight of less than 1000 Daltons. In some embodiments, the first compound and the second compound are each organic compounds with a molecular weight of less than 2000 Daltons. In some embodiments, the first compound and the second compound are each organic compounds with a molecular weight of less than 4000 Daltons, less than 6000 Daltons, less than 8000 Daltons, less than 10000 Daltons, or less than 20000 Daltons. In some embodiments, the first compound and the second compound are each organic compounds with a molecular weight between 300 Daltons and 1500 Daltons.

[0248] In some embodiments, the model performs at least 100,000 computations to compute the first latent embedding, and the model performs at least 100,000 computations to compute the second latent embedding.

[0249] In some embodiments, the first potential embedding is a first isometric preserving potential embedding. In some embodiments, the second potential embedding is a second isometric preserving potential embedding.

[0250] Another aspect of this disclosure provides a method for estimating a graph edit distance between a first compound and a second compound. The method includes (e.g., at a computer system including one or more processors and memory addressable by said one or more processors) (A) inputting a first representation of the first compound into a model including multiple parameters. The model applies the multiple parameters to the first representation of the first compound to generate a first latent embedding representing the first compound as a first output of the model. The method further includes (e.g., at a computer system including one or more processors and memory addressable by said one or more processors) (B) inputting a second representation of the second compound into the model. The model applies multiple parameters to the second representation of the second compound to generate a second latent embedding representing the second compound as a second output of the model. The method further includes (e.g., at a computer system including one or more processors and memory addressable by said one or more processors) (C) providing an estimate of the graph edit distance between the first compound and the second compound using the difference between the first latent embedding and the second latent embedding. In some embodiments, the first latent embedding is a first isometric latent embedding. In some embodiments, the second latent embedding is a second isometric latent embedding. In some embodiments, the difference is the L2 norm difference between the first latent embedding and the second latent embedding.

[0251] Another aspect of this disclosure provides a non-transitory computer-readable storage medium. The non-transitory computer-readable storage medium stores instructions that, when executed by a computer system, cause the computer system to perform a method for estimating a graph edit distance between a first compound and a second compound. The method includes (A) inputting a first representation of the first compound into a model comprising a plurality of parameters. The model applies the plurality of parameters to the first representation of the first compound to generate a first latent embedding representing the first compound as a first output of the model. The method further includes (B) inputting a second representation of the second compound into the model. The model applies the plurality of parameters to the second representation of the second compound to generate a second latent embedding representing the second compound as a second output of the model. The method further includes (C) providing an estimate of the graph edit distance between the first compound and the second compound using the difference between the first latent embedding and the second latent embedding. In some embodiments, the first latent embedding is a first isometric latent embedding. In some embodiments, the second latent embedding is a second isometric latent embedding. In some embodiments, the difference is an L2 norm difference between the first latent embedding and the second latent embedding.

[0252] The model is trained to predict the potency of the test compound against the target protein.

[0253] Successful drug discovery relies on identifying biologically active lead molecules that are chemically distinct from known compounds targeting disease targets. This is particularly challenging when available data on nearby ligands is scarce or nonexistent (as is the case with novel targets), or when novel scaffolds are far apart in chemical space. Structure-based virtual high-throughput screening (vHTS) methods are designed to overcome this challenge by identifying novel compounds with predicted activity from a vast library of chemistry, such as MCULE (Kiss et al., http: / / Mcule.com: Journal of Cheminformatics 2012, 4(1), p. 17) or ENAMINE (Irwin and Shoichet, 2016, docking screening of novel ligands conferring new biology, Journal of Medicinal Chemistry 59(9), 4103-4120).

[0254] Therefore, virtual screening is a tool for identifying novel inhibitors of proteins with known structures. See, for example, Wallach et al., 2015, “AtomNet: A Deep Convolutional Neural Network for Bioactivity Prediction in Structure-based Drug Discovery”, doi:2910.48550 / arxiv.1510.02855; Lyu et al., 2019, “Ultra large library docking for discovering new chemotypes”, Nature 566:7743566,20224-229. doi:10.1038 / s41586-019-0917-9; and Bender et al., 2021, “Apractical guide to large-scale docking”, Nature Protocols. Protocols) 16:1016, 394799-4832, each of which is incorporated by reference. Conventional, structure-based virtual high-throughput screening methods use empirical or force-field-based scoring functions to dock ligands with most rigid acceptors and rank compounds. See Trott and Olson, 2010, “AutoDock Vina: Improving the speed and accuracy of docking with a new scoring function, efficient optimization, and multithreading”, J ComputChem 31, 455-461, which is hereby incorporated by reference. Docking with structures that deviate from the ligand-bound state can lead to inaccurate predictions of bound complexes and poor compound ranking. For example, it is often difficult to find active compounds when docking with experimental structures that do not contain ligands (e.g., apo state) or when homologous ligands are very small.See, for example, Abagyan et al., 2010, “Recipes for the selection of experimental protein conformations for virtual screening,” *Journal of Chemical Information and Modeling*, 50, 32186-193, which is hereby incorporated by reference. Another obstacle is that many protein targets with disordered or flexible domains cannot be experimentally structured. AlphaFold (AF) has the potential to accelerate drug discovery thanks to its accurate structural predictions of such proteins. See Jumper et al., 2024, “Highly accurate protein structure prediction with AlphaFold,” *Nature*, doi:4110.1038 / s41586-021-03819-2, which is hereby incorporated by reference. However, these are still only rigid structures, and their utility will be limited if they do not represent similarly bound structures. References include, for example, Vijayan et al., 2015, “Conformational analysis of the DFG-out kinase motif and biochemical profiling of structurally validated type II inhibitors,” *Journal of Medicinal Chemistry*, 58, 466-479; and Wankowicz et al., 2022, “Ligand binding remodels protein side chain conformational heterogeneity,” *Elife*, 11. Doi:10.7554 / ELIFE.74114, each of which is hereby incorporated by reference.

[0255] The vHTS approach, which applies deep learning to structure-based drug discovery, offers pharmaceutical companies a pathway to identify promising new compounds. These approaches have the potential to have a greater impact on challenging research areas for pharmaceutical companies, such as those focused on identifying compounds for target proteins with multiple binding sites. However, using these computational methods requires extensive, well-annotated data on compounds and the protein sites they bind to. This problem is further complicated by the presence of allosteric sites in many protein targets. Allosteric sites are alternative locations on a protein outside its ortho-(active) site, which can modulate the protein's function in some way. Compounds and proteins are typically matched using measurements of binding activity. While this works well for most tested compounds that bind to a single protein site, there are also many diverse protein targets that can bind to one of several possible sites. In such cases, incorrect binding site information used in training predictive models can lead to poor model performance. Unfortunately, because most compound activity measurements do not directly map to exact binding sites on proteins, there is insufficient site-level annotated data in public databases such as the Protein Database (PDB) or ChEMBL for training models targeting alternative sites.

[0256] In view of the above, there is a need for improved methods for training models to predict the potency of target compounds. One aspect of this disclosure addresses this shortcoming by assigning binding sites to such compounds by comparing training compounds known to bind to target proteins having orthostatic and one or more allosteric sites with reference compounds having known binding sites. In this way, a more accurate posture of such training compounds is achieved because the training compounds are now placed at the binding sites based on the chemical intuition provided by the reference compounds. Using this type of training data to train binding models, it has been found that such binding models trained on this type of multi-site data provide improved potency predictions.

[0257] Figure 22 A computer system 2200 for predicting the potency of a test compound against a target protein is shown. (Reference) Figure 22 In a typical embodiment, computer system 2200 includes one or more computers. Figure 22 For ease of illustration, computer system 2200 is referred to as a computer including all the functions of the disclosed computer system 2200. However, this disclosure is not limited thereto. The functions of computer system 2200 can be distributed across any number of networked computers and / or reside on each of several networked computers and / or virtual machines. Those skilled in the art will understand that computer system 2200 can adopt a variety of different computer topologies, and all such topologies are within the scope of this disclosure.

[0258] Considering the foregoing, let's turn to... Figure 22 The computer system 2200 includes one or more processing units (CPUs) 2259, a network or other communication interface 2284, a user interface 2278 (e.g., including an optional display 2282 and an optional keyboard 2280 or other form of input device), memory 2292 (e.g., random access memory, persistent memory, or a combination thereof), one or more disk storage devices and / or persistent devices 2290 optionally accessed by one or more controllers 2288, one or more communication buses 2212 for interconnecting the above components, and a power supply 2279 for powering the above components. Where components of memory 2292 are not persistent, known computing techniques such as caching can be used to seamlessly share data in memory 2292 with non-volatile memory 2290 or non-volatile / persistent portions of memory 2292. Memory 2292 and / or memory 2290 may include large-capacity storage devices remotely located relative to the central processing unit 2259. In other words, some data stored in memory 2292 and / or memory 2290 can actually be hosted on a computer external to computer system 2200, but accessible electronically by computer system 2200 via network interface 2284 through the Internet, intranet, or other forms of network or cable. In some embodiments, computer system 2200 utilizes model 2248, which runs from memory associated with one or more graphics processing units, to improve system speed and performance. In some alternative embodiments, computer system 2200 utilizes model 2248, which runs from memory 2292 instead of memory associated with a graphics processing unit.

[0259] The memory 2292 of the computer system 2200 stores:

[0260] ●Optional operating system 2230, which includes programs for handling various basic system services;

[0261] ●Efficacy prediction calculation module 2232, which is used to train model 2248 to predict the efficacy of the test compound against the target protein;

[0262] ● Training data 2234, which includes data on a plurality of training compounds, wherein each corresponding training compound 2236 among the plurality of training compounds is labeled with: (i) a corresponding protein target 2240 among a plurality of protein targets; (ii) a binding site of a corresponding protein target 2242; and (iii) efficacy against protein target 2238;

[0263] ● The atomic structure of each target protein 2246 in multiple proteins; and

[0264] ● and binding site model 2248, which is used to predict the potency of test compounds on target proteins.

[0265] In some embodiments, one or more of the identified data elements or modules of the computer system 2200 are stored in one or more of the aforementioned memory devices and correspond to a set of instructions for performing the functions described above. The identified data, modules, or programs (e.g., instruction sets) do not need to be implemented as separate software programs, programs, or modules, and therefore various subsets of these modules can be combined or otherwise rearranged in different embodiments. In some embodiments, memories 2292 and / or 2290 optionally store a subset of the modules and data structures identified above. Furthermore, in some embodiments, memories 2292 and / or 2290 store additional modules and data structures not described above.

[0266] Given that a system for training model 2248 to predict the potency of test compounds against target proteins has been disclosed, the method for performing such characterization is described in detail with reference to Figure 23 and discussed below.

[0267] Referring to box 2300, in some embodiments, systems and methods are provided for training a model to predict the potency of a test compound against a target protein. In some embodiments, the model is part of a compound selection workflow. As a non-limiting example, in some embodiments, the systems and methods of this disclosure are used for training... Figure 24 Model 2402 of the compound selection workflow.

[0268] Box 2302. Referring to box 2302, a dataset containing data from multiple training compounds is obtained. Each training compound is labeled with a corresponding protein target, a binding site for the corresponding protein target, and its potency against the protein target. In some embodiments, the potency is represented by the model as a calculated pKi. In some embodiments, the potency is represented by the model as a calculated IC50, EC50, Kd, ​​KI, or pKI of the corresponding compound against the target protein. Such power measures are called binding coefficients and are typically described in the following literature: Huuser (ed.), 2006, “High-Throughput-Screening in Drug Discovery,” Methods and Principles in Medicinal Chemistry, 35; and Chen (ed.), 2019, A Practical Guide to Assay Development and High-Throughput Screening in Drug Discovery, CRC Press, Berklee, each of which is hereby incorporated by reference.

[0269] One non-limiting source of such compounds is ChEMBL. ChEMBL is an artificially curated database of bioactive molecules with drug-like properties. See Gaulton et al., 2019, “ChEMBL: Towards Direct Deposition of Bioassay Data”, Nucleic Acid Research 47(D1), D930-D940, which is hereby incorporated by reference.

[0270] Referring to box 2304, in some embodiments, each training compound satisfies two or more, three or more, or all four of the Lipinski Five Rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5. See Lipinski, 1997, Review of Advanced Drug Delivery, 23, 3, which is hereby incorporated herein by reference in its entirety. In some embodiments, in addition to the Lipinski Five Rules, the training compound also satisfies one or more criteria. For example, in some embodiments, the training compound has five or fewer aromatic rings, four or fewer aromatic rings, three or fewer aromatic rings, or two or fewer aromatic rings.

[0271] Boxes 2306-2308. Referring to box 2306, in some embodiments, each training compound is an organic compound with a molecular weight less than 500 Daltons, less than 1000 Daltons, less than 2000 Daltons, less than 4000 Daltons, less than 6000 Daltons, less than 8000 Daltons, less than 10000 Daltons, or less than 20000 Daltons. Referring to box 208, in some embodiments, each training compound is an organic compound with a molecular weight between 400 Daltons and 10000 Daltons.

[0272] In some embodiments, the molecular weight of each training compound is at least 10 Da, at least 20 Da, at least 50 Da, at least 100 Da, at least 200 Da, at least 500 Da, at least 1 kDa, at least 2 kDa, at least 3 kDa, at least 5 kDa, at least 10 kDa, at least 20 kDa, at least 30 kDa, at least 50 kDa, at least 100 kDa, or at least 500 kDa. In some embodiments, the molecular weight of each training compound is no more than 1000 kDa, no more than 500 kDa, no more than 100 kDa, no more than 50 kDa, no more than 10 kDa, no more than 5 kDa, no more than 2 kDa, no more than 1 kDa, no more than 500 Da, no more than 300 Da, no more than 100 Da, or no more than 50 Da. In some embodiments, the molecular weight of each training compound is 10 Da to 900 Da, 50 Da to 1000 Da, 100 Da to 2000 Da, 1 kDa to 10 kDa, 5 kDa to 500 kDa, or 100 kDa to 1000 kDa. In some embodiments, the molecular weight of each training compound falls into another range that begins at a value not less than 10 Daltons and ends at a value not more than 1000 kDa.

[0273] In some embodiments, each training compound is a small molecule. For example, in some embodiments, each training compound is an organic compound with a molecular weight of less than about 1,000 Daltons (e.g., less than 900 Daltons).

[0274] Box 2310. Referring to box 2310, in some embodiments, the plurality of training compounds comprises 100 or more, 1000 or more, 2000 or more, 10,000 or more, 100,000 or more, or 1 × 10⁻⁶. 6 One or more training compounds. In some embodiments, the number of training compounds is between 500 and 1×10⁻⁶. 7 Between 1000 training compounds. In some embodiments, the number of training compounds is between 1000 training compounds and 1×10⁻⁶. 6Between 10,000 and 100,000 training compounds. In some embodiments, the number of training compounds is between 10,000 and 100,000.

[0275] Referring to box 2312, in some embodiments, each of the plurality of protein targets is represented by one or more training compounds, and the plurality of protein targets includes 10 or more protein targets or 100 or more protein targets. In other words, in some embodiments, for each of the plurality of protein targets, at least one training compound is docked to the protein target to generate a pose for training the model.

[0276] In some embodiments, each of the plurality of protein targets is represented by five or more compounds, and the plurality of protein targets comprises ten or more protein targets or one hundred or more protein targets. In other words, in some embodiments, for each corresponding protein target among the plurality of protein targets, at least a given training compound is docked with the protein target to generate five or more poses for training the model.

[0277] In some embodiments, each of the plurality of protein targets is represented by 50 or more compounds, and the plurality of protein targets includes 10 or more protein targets or 100 or more protein targets.

[0278] In some embodiments, each of the plurality of protein targets is represented by 100 or more compounds, and the plurality of protein targets includes 10 or more protein targets or 100 or more protein targets.

[0279] In some embodiments, each of the plurality of protein targets is represented by 500 or more compounds, and the plurality of protein targets includes 10 or more protein targets or 100 or more protein targets.

[0280] In some embodiments, each of the plurality of protein targets is represented by 1,000, 10,000, or 100,000 or more compounds, and the plurality of protein targets includes 10 or more protein targets or 100 or more protein targets.

[0281] Box 2314. Referring to box 2314, in some embodiments, at least 5%, 10%, or 15% of the multiple protein targets contain multiple binding sites. To obtain correct posture information for such training compounds docking with the target proteins, it is important to identify the binding sites of the training compounds that bind to the proteins. For example, referring to… Figure 29A If the training compound docks with the binding site depicted on the left side of the attached figure, the attitude data of the training compound provided to the model for training purposes will be incorrect when the training compound actually binds with the binding site depicted on the right side of the attached figure. Figure 29B As shown, one way to determine the true binding sites of such training compounds is to cluster them with compounds that have known binding sites based on their compound fingerprints (such as ECFP4). Figure 29B and 30 The description suggests that when each of the compounds in each cluster with a known binding site maps to the same binding site, it can be assured that the remaining compounds in the cluster also bind to the same binding site, even if no structural data shows that this is the case.

[0282] like Figure 31A Tools such as AF2, as demonstrated, can extend the mapping task to protein targets for which experimental structural data (e.g., X-ray crystallography data) have not yet elucidated the protein targets. AF2 is described in the following references: Jumper et al., 2021, “Highly accurate protein structure prediction for the human proteome”, Nature 596, pp. 583-589; and Tunyasuvunakool et al., 2021, “Highly accurate protein structure prediction for the human proteome”, Nature 596, 590-596, each of which is hereby incorporated by reference. References Figure 31A Protein targets that bind to the test or training compound are called ligand-bound or HOLO conformations, while protein targets that do not bind to the test or training compound are called ligandless or APO conformations. Figure 31AAs indicated, in the method of expanding the number of target proteins that can be used to train the model, the AF2 structure is generated by the UniProt protein identifier, except for those whose structures have been experimentally determined by means such as X-ray crystallography or nuclear magnetic resonance and indexed in the protein database (PDB) accessed via BLASTp. In some embodiments, structures that generate a structure with less than 30% sequence identity to the highest BLASTp hit in the BLASTp search of the protein database or without HOLO homologs or structures are discarded. Blastp is described in the following references: Altschul et al., 1997, “Gapped BLAST and PSI-BLAST: a new generation of protein database search programs”, Nucleic Acid Research 25(17), pp. 3389-402; and Zhang and Freddolino, 2023, “A large-scale assessment of sequence database search tools for homology-based protein function prediction”, https: / / doi.org / 10.1101 / 2023.11.14.567021, each of which is hereby incorporated by reference. UniProt is described in the following reference: UniProt: the Universal Protein Knowledgebase in 2023, *Nucleic Acid Research* 51:D523-D531 (2023), which is hereby incorporated by reference. The PDB database is described in the following reference: Berman et al., 2000, “The Protein Data Bank (2000)”, *Nucleic Acid Research* 28:235-242, which is hereby incorporated by reference. References Figure 31AIn some embodiments, the template is considered average when the HOLO template of the target protein generated by AF2 has 30% to 70% sequence identity with the highest BLASTp hit of the UniProt sequence containing the target protein from a query in the PDB database. In some embodiments, the template is considered good when the HOLO template of the target protein generated by AF2 has 70% to 95% sequence identity with the highest BLASTp hit of the UniProt sequence containing the target protein from a query in the PDB database. In some embodiments, the template is considered resolved when the HOLO template of the target protein generated by AF2 has greater than 95% sequence identity with the highest BLASTp hit of the UniProt sequence containing the target protein from a query in the PDB database.

[0283] Box 2315. Referring to Box 2315, the model is trained using the training dataset. For each corresponding training compound among a plurality of training compounds, one or more postures of the corresponding training compound at the binding sites of the target proteins identified for the training compound in the dataset are each input into the model, and the actual known potency of the corresponding training compound is evaluated.

[0284] In some embodiments, this is accomplished via command-line arguments --exhaustiveness 384 --energy_range99999 --num_modes 64 --mc_steps 3 --minimize_iters 40 --accurate_line --approximation linear --autobox_add 2.0 --seed 42, as described in: Stafford et al., 2022, “AtomNet PoseRanker: Enriching Ligand Pose Quality of Dynamic Proteins in Virtual High-Throughput Screening”, Journal of Chemical Information and Modeling 62, pp. 1178-1189, which is hereby incorporated by reference. In such methods, a bounding box is drawn around a specified binding site in the target protein, and then the training compound is docked to the portion of the target protein contained within that bounding box. Figure 8A shows the bounding boxes of two different binding sites of the target protein. In some embodiments, the conformation of the training compound is obtained using a program such as RDKit. See Landrum, G. RDKit: Open-Source Cheminformatics. In some such embodiments, RDKit is used to perform UFF energy minimization on the SMILES description of the training compound to obtain the conformation of the training compound at the binding site. See also Meller et al., 2023, “Discovery of a cryptic pocket in the AI-predicted structure of PPM1D phosphatase explains the binding site and potency of its allosteric inhibitors”, bioRxiv [preprint], March 24, 2023: 2023.03.22.533829.doi:10.1101 / 2023.03.22.533829, for information on how the attitude of the compound at the protein binding site is constructed in some embodiments.

[0285] In some embodiments, multiple descriptors are generated for each posture of the corresponding training compound at the binding site and input into the model. In some embodiments, each heavy atom (non-hydrogen atom) is described with its corresponding SYBYL atom type, thereby indicating its chemical environment, for example, generated by converting to Mol2 format using OpenBabel. See O'Boyle et al., 2011, "Open Babel: An Open Chemical Toolbox," *Journal of Cheminformatics*, 3, 33, which is hereby incorporated by reference. In some embodiments, protons are not explicitly represented in the descriptor set, and all metals are of a single type. In some embodiments, the target protein binding site and the training compound are kept as distinct entities, and their atom types are encoded separately.

[0286] The error in the predictive power of the corresponding training compounds is obtained through the model of the system disclosed herein (e.g., Figure 22 Model 2248 and Figure 24The parameters of model 2402 are backpropagated. In some embodiments, the model is trained against the error of the power estimated by the model, based on the actual power of the training compound. One approach to performing such training is to use stochastic gradient descent and the AdaDelta adaptive learning method (Zeiler, 2012, “ADADELTA: An Adaptive Learning Rate Approach”, CoRR, Vol. 1212.5701, which is hereby incorporated by reference), and the backpropagation algorithm provided in Rumelhart et al., 1988, “Neural Computation: Foundations of Research”, Chapter: Learning Representations by Backpropagation Error, pp. 696-699, Cambridge, MIT Press, Massachusetts, USA, which is hereby incorporated by reference. However, any backpropagation method can be used for training.

[0287] Box 2316. Refer to box 2316 to obtain the test chemical compound.

[0288] Referring to box 2318, in some embodiments, the test compound satisfies two or more, three or more, or all four of the Lipinski Five Rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight less than 500 Daltons, and (iv) a LogP less than 5. See Lipinski, 1997, Review of Advanced Drug Delivery, 23, 3, which is hereby incorporated herein by reference in its entirety. In some embodiments, in addition to the Lipinski Five Rules, the test compound also satisfies one or more criteria. For example, in some embodiments, the test compound has five or fewer aromatic rings, four or fewer aromatic rings, three or fewer aromatic rings, or two or fewer aromatic rings.

[0289] Boxes 2320-2322. Referring to box 2320, in some embodiments, the test compound is an organic compound with a molecular weight less than 500 Daltons, less than 1000 Daltons, less than 2000 Daltons, less than 4000 Daltons, less than 6000 Daltons, less than 8000 Daltons, less than 10000 Daltons, or less than 20000 Daltons. Referring to box 2322, in some embodiments, the test compound is an organic compound with a molecular weight between 400 Daltons and 10000 Daltons.

[0290] Box 2324. Referring to box 2324, the test chemical compound is placed close to the binding site of the target protein to obtain the test posture. The posture has been described above in conjunction with the training compound. Further examples of postures are described in U.S. Patent Nos. 11,080,570, 10,546,237, 10,482,355, 10,002,312, and 9,379,059, and U.S. Provisional Patent Application No. 63 / 336,841, filed April 29, 2022, entitled “Characterization of Interactions Between Compounds and Polymers Using PoseEnsembles,” each of which is hereby incorporated by reference.

[0291] Box 2325. Referring to box 2325, the test orientation is input into the model to predict the effectiveness of the test compound at the binding site. For example... Figure 32 , 33A As demonstrated in 33B, advantageously, the model trained on the multi-site data of this disclosure exhibits improved performance in predicting the potency of compounds against target proteins. In particular, Figure 32 This indicates that the area under the receiver operating characteristic (ROC) curve (AUC) of the model trained using the binding site-specific data of this disclosure is an improvement relative to the static assumption that each training compound binds to the orthogenic site of the target protein. This is even true for the major binding site (…). Figure 32 This improvement was also observed at the orthogenetic site, active site, and binding site 1). Figure 33A This demonstrates the use of the references in this article. Figure 31A The protein target generated by AF2 ( Figure 33A Training multiple protein targets enhanced with AF2_holo on the Y-axis compared to protein targets not generated with AF2 ( Figure 33A Improvement of the mean squared error of the model during training with multiple protein targets enhanced by holo on the Y-axis. Figure 33B This demonstrates the use of the references in this article. Figure 31A The protein target generated by AF2 ( Figure 33B Training multiple protein targets enhanced with AF2_holo on the Y-axis compared to protein targets not generated with AF2 ( Figure 33B TauB improves training on multiple protein targets with enhanced holo on the Y-axis.

[0292] Referring to box 2326, in some embodiments, the model includes a plurality of parameters. In some embodiments, the model applies the plurality of parameters to the pose through at least 10,000 computations to generate predictive power. In some embodiments, the model performs at least 100,000 computations or at least 1 × 10⁻⁶ computations. 6 This calculation applies multiple parameters to the attitude to generate predictive power.

[0293] Box 2328. Referring to box 2328, in some embodiments, the model is a graph neural network. In some embodiments, the model is an SE(3)-equal-variable graph attention transformer. In some embodiments, the model is a message-passing neural network. Message-passing neural networks are described, for example, in Gilmer et al., 2020, “Message-Passing Neural Networks”, published in: Schütt et al. (eds.), Machine Learning Meets Quantum Physics, Lectures in Physics 968, Springer, Kam, and each of the aforementioned references is hereby incorporated by reference.

[0294] In some embodiments, the model is a graph convolutional neural network. Non-limiting examples of graph convolutional neural networks are disclosed in the following literature: Behler Parrinello, 2007, "Generalized Neural Network Representation of High-Dimensional Potential Energy Surfaces", Physical Review Letters 98, 146401; Chmiela et al., 2017, "Machine Learning for Accurate Energy-Conserving Molecular Force Fields", Science Advances 3(5):e1603015; Schütt et al., 2017, "SchNet: A Continuous Filtering Convolutional Neural Network for Simulating Quantum Interactions", Advances in Neural Information Processing Systems 30, pp. 992-1002; Feinberg et al., 2018, "Learning Networks for Predicting Molecular Properties", ACS Central Science 4, 11, 1520-1530; and Stafford et al., 2022, "AtomNet PoseRanker: Enriching Ligand Pose Quality of Dynamic Proteins in Virtual High-Throughput Screening", Journal of Chemical Information and Modeling 62, pp. 1178-1189. Each of these references is hereby incorporated by reference.

[0295] In some embodiments, the model’s final readout layer independently extracts relevant features from the training compound and protein target embeddings and passes them through the final multilayer perceptron.

[0296] In some embodiments, the model is or is similar to the GRAPHite architecture described in the following literature: Stafford et al., 2022, “AtomNet PoseRanker: Enriching Ligand Pose Quality of Dynamic Proteins in Virtual High-Throughput Screening”, *Journal of Chemical Information and Modeling*, 62, pp. 1178-1189. The GRAPHite architecture is a directional graph convolutional network (GCN) consisting of four graph convolutional layers. In some embodiments, the first two layers include ligand and receptor features, while the last two layers are simply ligands. In some embodiments, nodes in the graph represent ligand and receptor atoms. In some embodiments, only any ligand atom is represented. Only acceptor atoms within a certain range are used as part of the graph. In some embodiments, edges are formed by distances between them. The atoms are defined within the range, and the edge weights are distance-dependent. In some embodiments, the last layer is aggregated into an embedding. In some embodiments, the embedding is passed through two (independent) multilayer perceptrons to predict two outputs: an ANPR pose quality score and a Vina docking score. In some embodiments, those outputs are then concatenated with the embedding and passed through a third multilayer perceptron, which outputs the predictive power in the form of pKi.

[0297] Box 2330. Reference box 2330, in some embodiments, the model contains 500,000 or more parameters, or 1 × 10 6 One or more parameters. In some embodiments, the model contains more than 400 parameters, more than 1,000 parameters, more than 2,000 parameters, more than 5,000 parameters, more than 10,000 parameters, more than 100,000 parameters, or more than 1 × 10⁻⁶ parameters. 6 The number of parameters. In some embodiments, the amount of information in the pose input to the model is combined with the number of parameters of the model, resulting in more than 10,000 calculations, more than 100,000 calculations, or more than 1 × 10⁻⁶ calculations. 6 Calculations exceeding 5 × 10 6 The calculation or more than 1×10 7 This calculation is used to determine the predictive power.

[0298] Example

[0299] Example 1: Creating training and testing datasets. (Reference) Figure 3BTo provide a method for identifying GED approximations, training and test datasets were created. One desired property of the training / test split is to create training / test splits with a GED-like distribution of drug-like molecules / fragments. Another desired property is that the training / test pairs must be sufficiently dissimilar to ensure performance generalizes to the unseen chemical space (rather than model overlearning). To create training and test datasets with these properties, compounds were randomly selected from ChEMBL 30. ChEMBL is an artificially curated database of bioactive molecules with drug-like properties. See Gaulton et al., 2019, “ChEMBL: Towards Direct Deposition of Bioassay Data”, Nucleic Acid Research 47(D1), D930-D940, which is hereby incorporated by reference. The randomly selected compounds were then filtered for drug similarity. One method used to calculate the drug similarity score is Quantitative Drug Similarity Estimation (QED), Bickerton et al., 2012, “Quantifying the Chemical Beauty of Drugs”, Nature Chemistry 4, pp. 90-98, which is hereby incorporated by reference. Compounds with a QED drug similarity score of 0.5 or higher were selected. Further, the graph edit distance of the compounds was limited to less than 10. Going further, compounds were stratified according to GED to uniformly sample all GED values ​​between 0 and 10. Finally, Taylor-Butina clustering was used to segment the compounds into training / test sets using extended connectivity fingerprints, with at most four bonds (ECFP4) for each compound. Figure 3B As shown, all pairs in a given cluster are placed in the training or test set to ensure that no compound pair in the test set is sufficiently similar to the compound pairs in the training set, so that the model can simply memorize the pairs in the training set and extend this memory to the pairs in the test set, rather than learning a true approximation of the GED distance, even for chemical pairs not seen by the model.

[0300] The above describes the construction of the drug-like training / test dataset. (References) Figure 4The training dataset for drug classes contains 45,000 compounds, while the test dataset contains 4,500 compounds. The GED of the compounds was calculated using commercial software based on chemical GED. Figure 21 shows the difference between the chemical distance and the exact graph edit distance. As seen in Figure 21, the chemical graph edit distance considers chemical changes, while the exact GED considers the number of times these fundamental changes occur. The fragment dataset was created by randomly acquiring drug-class molecules and cutting them into fragments. The fragments were then filtered using the same criteria used for filtering the chemical dataset (QED > 0.5, GED < 10, stratified by GED), but the exact GED of the fragments was calculated using depth-first GED instead of chemical GED. Depth-first GED is described in: Abu-Aisheh et al., 2015, 4th International Conference on Applications and Methods of Pattern Recognition (4 th The International Conference on Pattern Recognition Applications and Methods, Lisbon, Portugal, is cited in this paper and is hereby incorporated by reference. Figure 4 This further demonstrates how the distribution of compounds varies with the number of heavy atoms in the training and test datasets. Figure 4 The training and testing datasets of the fragment dataset summarized in the text have training labels for each corresponding compound pair with the exact GED between the corresponding compound pairs. Figure 4 The training and testing datasets of the drug-like datasets summarized in the text have training labels for the chemical GEDs between the corresponding compound pairs.

[0301] Example 2: Testing SimGnn on the test and training datasets. (Reference) Figure 5 Based on the performance of existing technology models (SimGNN, Bai et al. 2019, ACM International Internet Search and Data Mining Conference), respectively... Figure 4 After training on fragment datasets and drug-like datasets, based on MSE, Spearman p, and Kendall τ... Β This will be explained. Here, Spearman P and Kendall T... Β This is based on the ability of the estimated GED to rank compound pairs in the test dataset, making the ranking match the ranking of the test dataset based on the real GED. Unfortunately, Figure 5 Performance statistics show that even in Figure 4 Even when trained on highly selected datasets, SimGNN's performance is still unsatisfactory. Figure 6 This explains the reasons for the shortcomings of SimGNN. For example... Figure 6As shown, GED is a distance metric, and therefore any model approximating GED should strive to satisfy the properties of the distance metric. Specifically, the distance to itself should be zero. Therefore, the GED value of a model estimating the distance between two identical molecules should return to zero. Furthermore, there should exist a symmetry such that the GED in the graph from molecule A to molecule B should be equal to the GED in the graph from molecule B to molecule A. Further, when the two graphs being compared (two compounds) are different, the estimated GED should be a positive value greater than zero. Finally, the model should obey the triangle inequality theorem. Figure 4 After training on a drug-like training set, the SimGNN model was used to evaluate compounds on the drug-like test set. It can be seen that the SimGNN's symmetry violation is 0.67, and the distance to self-violation is 1.52. In other words, on... Figure 4 In the drug-like test set, the GED approximation from molecule A to molecule B deviates from that from molecule B to molecule A by 0.67, while in the drug-like test set, the distance to itself should be zero, but in fact it is 1.52.

[0302] Example 3: Establishing an improved approximate GED calculation module 32. To solve... Figure 6 The shortcomings of the identification process were addressed, and a system was established. Figure 7 The system summarized in [the text]. Figure 7 This demonstrates how to obtain the first diagram G representing the first compound. i 36. The first graph contains a first plurality of nodes and a first plurality of edges. Each atom of the first compound is represented by node 38 of the first plurality of nodes, and each bond of the first compound is represented by edge 40 of the first plurality of edges. Further, a second graph G representing the second compound 44 is obtained. j 46. ​​The second graph contains a second plurality of nodes and a second plurality of edges. Each atom of the second compound is represented by node 48 in the second plurality of nodes, and each bond of the second compound is represented by edge 50 in the second plurality of edges. The first graph is input into a model 702 containing multiple parameters. Model 702 applies the multiple parameters to the first graph to generate a first latent embedding h representing the first compound. i As the first output of model 702, the second graph is input into model 704 (which is in fact model 702, but is shown separately for illustration). Model 704 applies multiple parameters to the second graph to generate a second potential embedding h representing the second compound. jAs the second output of model 704, the estimated graph editing distance between the first and second compounds is then determined as the L2 norm difference between the first and second latent embeddings. In the case where the first latent embedding is a first vector and the second latent embedding is a second vector, the L2 norm difference (between the first and second vectors) is considered as the square root of the sum of the squared differences between the corresponding vector element values ​​in the first and second vectors. Figure 18 Showing Figure 7 The mathematical explanation.

[0303] In this example, model 702 / 704 is a message-passing neural network. Message-passing neural networks are described, for example, in: Gilmer et al., 2020, “Message-passing Neural Networks”, published in: Schütt et al. (eds.), Machine Learning Meets Quantum Physics, Lectures in Physics 968, Springer Kamm, each of which is hereby incorporated by reference.

[0304] Example 4: Training system according to this disclosure. By training model 702 / 704 such that the L2 norm difference between the first and second outputs of the model equals the trained GED estimate, in addition to being positive, Figure 6 All properties of the distance metric outlined at the top are satisfied. In some embodiments, the positivity axiom fails when models 702 / 704 cannot distinguish between the two graphs.

[0305] Figure 7 The system 700 shown outputs the estimated graph edit distance (e.g., the L2 norm difference of the outputs of models 702 / 704). Then, the system of this disclosure is... Figure 4 The estimated GED for each corresponding training compound pair in the summarized fragment dataset or drug-like dataset is compared with the actual GED of the compound pair. In the case of fragmented datasets, the actual GED is... Figure 4 The exact GED summarized in [the text]. In the case of drug-like datasets, the actual GED is considered as follows: Figure 4The chemical GED summarized in this paper. The difference between the estimated GED generated by model 700 and the actual GED of the training set is considered as the error generated by the system (e.g., model 700) of this disclosure. To further train model 700, these errors are backpropagated through the parameters of models 702 / 704. In some embodiments, system 700 is trained on the error of the GED estimated by system 700 based on the actual GED of the training set. One approach to performing such training is to use stochastic gradient descent and the AdaDelta adaptive learning method (Zeiler, 2012 "ADADELTA: An Adaptive Learning Rate Approach", CoRR, Vol. 1212.5701, which is hereby incorporated by reference), and the backpropagation algorithm provided in Rumelhart et al., 1988, "Neural Computation: Foundations of Research", Chapter: Learning Representations by Backpropagation Error, pp. 696-699, Cambridge, MIT Press, which is hereby incorporated by reference. However, any backpropagation method can be used for training.

[0306] Figure 8 It shows Figure 7 The system known as MolGEDNet has a performance of 700. From Figure 8 As can be seen from this, MolGEDNet in Figure 4 It significantly outperforms SimGNN in terms of mean squared error on fragment datasets and drug-like datasets. Figure 9 It shows Figure 7 The system known as MolGEDNet achieved a performance of 700. From... Figure 9 As can be seen from this, MolGEDNet in Figure 4 Spearman p and Kendall τ on fragment datasets and drug-like datasets Β It significantly outperforms SimGNN.

[0307] Example 5: Adjusting the system's hyperparameters according to this disclosure. Utilizing, for example... Figure 8 and 9 The superiority metrics of MolGEDNet over SimGNN, as demonstrated and discussed in Example 4, involved adjusting the hyperparameters of MolGEDNet, such as... Figure 10 As shown. For Figure 10 ,and Figure 8 and 9 Similarly, models 702 / 704 are message-passing graph neural networks. For example... Figure 10 As shown, determining the dimensions of model 702 / 704 based on edge embedding size and node embedding size relative to the latent embedding size is optimal when using a size of 128. To obtain... Figure 10 The results shown are in Figure 4 The system was trained on a drug-like training dataset with 700 units, and then... Figure 4 Calculate the mean squared error, Spearman p, and Kendall τ on the drug testing dataset. Β .like Figure 10 The results show that the dimensions of model 702 / 704 are determined based on the edge embedding size and node embedding size relative to the latent embedding size, according to Spearman's p and Kendall's τ values ​​across all tested dimensions (64 to 256). Β This aspect did not have a significant impact on performance.

[0308] Figure 11 This demonstrates the model performance of MolGEDNet when considering different dropout percentages. Here, dropout refers to the percentage of output from each layer (the connection between layer i and layer i+1) that is discarded during model training. Therefore, for a dropout of 0.1, ten percent of the output from each layer is randomly selected and discarded during training, instead of being passed to subsequent layers within models 702 and 704. Figure 11 As shown, adding missing values ​​did not improve model performance (measured here by mean squared error). To obtain... Figure 11 The results shown are in Figure 4 On the drug training dataset Figure 11 The different dropout values ​​shown were used to train system 700, and then... Figure 4 The mean squared error is calculated on a drug-like test dataset with no dropouts (regardless of the amount of dropouts used during training).

[0309] Figure 12 This demonstrates the performance of MolGEDNet when the number of layers in models 702 and 704 differs. For Figure 12 Models 702 / 704 are message-passing graph neural networks, and the variation lies in the number of layers (4, 5, 6, or 7). For example... Figure 12 What is shown is for Figure 4 Using the test dataset, we found that the five-layer model 702 / 704 is optimal. To obtain... Figure 12 The results shown are in Figure 4 The system was trained on a drug-like training dataset with 700 units, and then... Figure 4 Calculate the mean squared error, Spearman's rho, and Kendall's τ on the drug testing dataset. Β .like Figure 12 The results presented by Spearman Rho and Kendall Rho show that the dimensionality of model 702 / 704 is determined relative to the number of layers in all test configurations (4 to 7 layers). Β This aspect does not have a significant impact on performance.

[0310] refer to Figure 13 Using a message-passing graph neural network 702 / 704, the optimal hyperparameters are 128 variable dimensions, 5 layers, and no dropouts. Figure 4 The training system was trained on a dataset of 700 drug-like training data. Figure 19 This demonstrates how models 702 / 704 utilize these optimal hyperparameters for node, edge, and graph updates. Figure 20 Demonstrates the generation Figure 13 The details of the message passing neural network for performance data. Then, in Figure 4 In a dataset of drug-like tests, a trained system was used to calculate the mean squared error, Spearman's p-value, and Kendall's τ-value. Β For example, in Figure 13 As observed, using these optimal hyperparameters, the mean square error of system 700 is 1.27, Spearman's rho is 0.94, and Kendall's τ... Β It is 0.81.

[0311] Example 6: Examine the error sources of the hyperparameter optimization system of this disclosure. Figure 14 Checked Figure 13 Error sources for the hyperparameter optimization system 700 in Example 5. Figure 14 This indicates that when the ground truth edit distance is less than five or six, the published model 702 / 704 tends to overestimate GED, while when the ground truth edit distance is greater than six, it tends to underestimate GED.

[0312] To determine where the error originated in the compounds, we examined compound pairs in the test set where the true GED was exactly 1. Figure 15 Examples of such pairs are shown, along with the estimated GED given by the disclosed model. Figure 15 The examples in the left box are pairs with larger errors, while Figure 15 The examples in the right-hand box are pairs with smaller errors. This shows that larger errors occur when the editor is at the center of the compound, while higher accuracy is achieved when the editor is at the periphery. Figure 16 In the middle, it is given Figure 15The betweenness centrality of the nodes that need to be changed in each pair. Betweenness centrality is a measure of centrality in a graph based on shortest paths. For each pair of vertices in a connected graph, there exists at least one shortest path between the vertices such that the number of edges traversed by the path (for an unweighted graph) or the sum of the edge weights (for a weighted graph) is minimized. The betweenness centrality of each vertex is the number of shortest paths that traverse these vertices. See Freeman, 1977, “A set of measures of centrality based on betweenness”, Sociometry 40(1):35-41, which is hereby incorporated by reference. Nodes with high betweenness centrality are closer to the center of the graph, while nodes on the periphery of the graph have low betweenness centrality. It can be seen that the GED estimate of the published model 702 / 704 has a high error when the betweenness centrality of the nodes that must be substituted in a given pair of compounds is high.

[0313] Example 7: Runtime of the hyperparameter optimization system disclosed in this paper. (Reference) Figure 17 The paper presents the average running time of the disclosed model 702 / 704 (MolGEDNet, with the optimal hyperparameters described in Example 5), the exact method, and the Hungarian algorithm as a function of the average molecular weight of the two compared compounds. It can be seen that MolGEDNet performs exceptionally well in terms of speed, being almost fifty times faster than the Hungarian approximation algorithm, while simultaneously being significantly more accurate.

[0314] in conclusion

[0315] For illustrative purposes, the foregoing description has been given with reference to specific embodiments. However, the illustrative discussion above is not intended to be exhaustive or to limit the embodiments to the precise forms disclosed. Many modifications and variations are possible in light of the above teachings. The embodiments were chosen and described in order to best explain the principles and their practical application, thereby enabling others skilled in the art to best utilize the embodiments and various embodiments with various modifications suited to the intended particular use.

Claims

1. A computer system for estimating a graph editing distance between a first compound and a second compound, the computer system comprising: One or more processors; as well as A memory addressable by the one or more processors, the memory storing at least one program for execution by the one or more processors, the at least one program containing instructions for performing the following operations: (A) Obtain a first graph representing the first compound, the first graph comprising a first plurality of nodes and a first plurality of edges, wherein each atom of the first compound is represented by one of the first plurality of nodes, and each bond of the first compound is represented by one of the first plurality of edges; (B) Obtain a second graph representing the second compound, the second graph comprising a second plurality of nodes and a second plurality of edges, wherein each atom of the second compound is represented by one of the second plurality of nodes, and each bond of the second compound is represented by one of the second plurality of edges; (C) The first graph is input into a model containing multiple parameters, wherein the model applies the multiple parameters to the first graph through at least 10,000 calculations to generate a first isometric latent embedding representing the first compound as the first output of the model; (D) The second graph is input into the model, wherein the model applies the plurality of parameters to the second graph through at least 10,000 calculations to generate a second isometric latent embedding representing the second compound as a second output of the model; as well as (E) Using the difference between the first equidistant preserving potential embedding and the second equidistant preserving potential embedding, an estimate of the graph editing distance between the first compound and the second compound is provided.

2. The computer system of claim 1, wherein the difference is the L2 norm difference between the first equidistant preserving latent embedding and the second equidistant preserving latent embedding.

3. The computer system according to claim 2, wherein The first equidistant preserving latent embedding is a first vector containing a first plurality of vector values; The second isometric preserving latent embedding is a second vector containing a second plurality of vector values; and The L2 norm difference between the first vector and the second vector is considered as the square root of the sum of the squared differences in the corresponding vector values ​​between the first vector and the second vector, wherein the model is trained such that the L2 norm of the difference between the first vector and the second vector is an estimate of the GED between the first molecule and the second molecule.

4. The computer system according to any one of claims 1 to 3, wherein the at least one program further comprises instructions for determining that the second compound is a chemically related analog of the first compound when the estimated value of the graph editing distance is below a threshold.

5. The computer system according to any one of claims 1 to 4, wherein the at least one program further comprises instructions for performing the following operations: For each corresponding unique compound pair in the compound database, the processes of obtaining (A), obtaining (B), inputting (C), inputting (D), and providing (E) are repeated to form multiple graph editing distances, wherein the first compound in the corresponding unique compound pair is the first compound, and the second compound in the corresponding unique compound pair is the second compound; By evaluating multiple distances using a criterion function, the multiple graph editing distances are clustered into multiple clusters; as well as Compounds are selected from one or more of the plurality of clusters for evaluation in a drug discovery process.

6. The computer system according to any one of claims 1 to 5, wherein the at least one program further comprises instructions for using the estimated value of the graph editing distance to establish a quantitative structure-activity relationship model including the first compound and the second compound.

7. The computer system according to any one of claims 1 to 6, wherein the at least one program further comprises instructions for determining an activity cliff relative to a drug target using the estimated value of the graph editing distance.

8. The computer system according to any one of claims 1 to 7, wherein the model is a graph convolutional neural network.

9. The computer system according to any one of claims 1 to 7, wherein the model is a graph neural network (message passing network).

10. The computer system according to any one of claims 1 to 7, wherein the model is a message-passing graph neural network consisting of 3 to 8 layers.

11. The computer system according to any one of claims 1 to 7, wherein the model is a message-passing graph neural network consisting of 5 layers.

12. The computer system according to any one of claims 1 to 7, wherein the model is an autoencoder.

13. The computer system of claim 12, wherein the autoencoder is a variational autoencoder, an adversarial autoencoder, a regularized autoencoder, a sparse autoencoder, or a metric learning autoencoder.

14. The computer system according to any one of claims 1 to 13, wherein the model comprises 500,000 or more parameters.

15. The computer system according to any one of claims 1 to 13, wherein the model comprises 1×10 6 One or more parameters.

16. The computer system according to any one of claims 1 to 15, wherein the first compound and the second compound each satisfy two or more, three or more, or all four of Lipinski's rule of Five: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

17. The computer system according to any one of claims 1 to 16, wherein the exact graph editing distance between the first compound and the second compound is between 1 and 10.

18. The computer system according to any one of claims 1 to 16, wherein the exact image editing distance between the first compound and the second compound is between 1 and 15.

19. The computer system according to any one of claims 1 to 18, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 500 Daltons.

20. The computer system according to any one of claims 1 to 18, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 1,000 Daltons.

21. The computer system according to any one of claims 1 to 18, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 2,000 Daltons.

22. The computer system according to any one of claims 1 to 18, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 4,000 Daltons, less than 6,000 Daltons, less than 8,000 Daltons, less than 10,000 Daltons, or less than 20,000 Daltons.

23. The computer system according to any one of claims 1 to 18, wherein the first compound and the second compound are each organic compounds with a molecular weight between 300 Daltons and 1500 Daltons.

24. The computer system according to any one of claims 1 to 23, wherein The model performs at least 100,000 computations to compute the first isometric preserving latent embedding, and The model performs at least 100,000 computations to compute the second isometric preserving potential embedding.

25. A method for estimating the graph editing distance between a first compound and a second compound, the method comprising: In a computer system that includes one or more processors and memory addressable by said one or more processors: (A) Obtain a first graph representing the first compound, the first graph comprising a first plurality of nodes and a first plurality of edges, wherein each atom of the first compound is represented by one of the first plurality of nodes, and each bond of the first compound is represented by one of the first plurality of edges; (B) Obtain a second graph representing the second compound, the second graph comprising a second plurality of nodes and a second plurality of edges, wherein each atom of the second compound is represented by one of the second plurality of nodes, and each bond of the second compound is represented by one of the second plurality of edges; (C) The first graph is input into a model containing multiple parameters, wherein the model applies the multiple parameters to the first graph through at least 10,000 calculations to generate a first isometric latent embedding representing the first compound as the first output of the model; (D) The second graph is input into the model, wherein the model applies the plurality of parameters to the second graph through at least 10,000 calculations to generate a second isometric latent embedding representing the second compound as a second output of the model; as well as (E) Using the difference between the first equidistant preserving potential embedding and the second equidistant preserving potential embedding, an estimate of the graph editing distance between the first compound and the second compound is provided.

26. The method of claim 25, wherein the difference is the L2 norm difference between the first latent embedding and the second latent embedding.

27. The method of claim 26, wherein The first equidistant preserving latent embedding is a first vector containing a first plurality of vector values; The second isometric preserving latent embedding is a second vector containing a second plurality of vector values; and The L2 norm difference between the first vector and the second vector is considered as the square root of the sum of the squared differences in the corresponding vector values ​​between the first vector and the second vector, wherein the model is trained such that the L2 norm of the difference between the first vector and the second vector is an estimate of the GED between the first molecule and the second molecule.

28. The method according to any one of claims 25 to 27, wherein the at least one procedure further comprises instructions for determining that the second compound is a chemically related analog of the first compound when the estimated value of the graph editing distance is below a threshold.

29. The method according to any one of claims 25 to 28, wherein the method further comprises: For each corresponding unique compound pair in the compound database, the processes of obtaining (A), obtaining (B), inputting (C), inputting (D), and providing (E) are repeated to form multiple graph editing distances, wherein the first compound in the corresponding unique compound pair is the first compound, and the second compound in the corresponding unique compound pair is the second compound; By evaluating multiple distances using a criterion function, the multiple graph editing distances are clustered into multiple clusters; as well as Compounds are selected from one or more of the plurality of clusters for evaluation in a drug discovery process.

30. The method according to any one of claims 25 to 29, the method further comprising using the estimated value of the graph editing distance to establish a quantitative structure-activity relationship model including the first compound and the second compound.

31. The method of any one of claims 25 to 30, wherein the method further comprises using the estimated value of the graph editing distance to determine the activity cliff relative to the drug target.

32. The method according to any one of claims 25 to 31, wherein the model is a graph convolutional neural network.

33. The method according to any one of claims 25 to 31, wherein the model is a graph neural network (message passing network).

34. The method according to any one of claims 25 to 31, wherein the model is a message-passing graph neural network consisting of 3 to 8 layers.

35. The method according to any one of claims 25 to 31, wherein the model is a message-passing graph neural network consisting of 5 layers.

36. The method according to any one of claims 25 to 31, wherein the model is an autoencoder.

37. The method of claim 36, wherein the autoencoder is a variational autoencoder, an adversarial autoencoder, a regularized autoencoder, a sparse autoencoder, or a metric learning autoencoder.

38. The method according to any one of claims 25 to 38, wherein the model comprises 500,000 or more parameters.

39. The method according to any one of claims 25 to 38, wherein the model comprises 1×10 6 One or more parameters.

40. The method according to any one of claims 25 to 39, wherein the first compound and the second compound each satisfy two or more, three or more, or all four of the Lipinski Five Rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

41. The method according to any one of claims 25 to 40, wherein the exact graph editing distance between the first compound and the second compound is between 1 and 10.

42. The method according to any one of claims 25 to 40, wherein the exact graph editing distance between the first compound and the second compound is between 1 and 15.

43. The method according to any one of claims 25 to 42, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 500 Daltons.

44. The method according to any one of claims 25 to 42, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 1,000 Daltons.

45. The method according to any one of claims 25 to 42, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 2,000 Daltons.

46. ​​The method according to any one of claims 25 to 42, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 4,000 Daltons, less than 6,000 Daltons, less than 8,000 Daltons, less than 10,000 Daltons, or less than 20,000 Daltons.

47. The method according to any one of claims 25 to 42, wherein the first compound and the second compound are each organic compounds with a molecular weight between 300 Daltons and 1500 Daltons.

48. The method according to any one of claims 25 to 47, wherein The model performs at least 100,000 computations to compute the first isometric preserving latent embedding, and The model performs at least 100,000 computations to compute the second isometric preserving potential embedding.

49. A non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium stores instructions, which, when executed by a computer system, cause the computer system to perform a method for estimating a graph editing distance between a first compound and a second compound, the method comprising: (A) Obtain a first graph representing the first compound, the first graph comprising a first plurality of nodes and a first plurality of edges, wherein each atom of the first compound is represented by one of the first plurality of nodes, and each bond of the first compound is represented by one of the first plurality of edges; (B) Obtain a second graph representing the second compound, the second graph comprising a second plurality of nodes and a second plurality of edges, wherein each atom of the second compound is represented by one of the second plurality of nodes, and each bond of the second compound is represented by one of the second plurality of edges; (C) The first graph is input into a model containing multiple parameters, wherein the model applies the multiple parameters to the first graph through at least 10,000 calculations to generate a first isometric latent embedding representing the first compound as the first output of the model; (D) The second graph is input into the model, wherein the model applies the plurality of parameters to the second graph through at least 10,000 calculations to generate a second isometric latent embedding representing the second compound as a second output of the model; as well as (E) Using the difference between the first equidistant preserving potential embedding and the second equidistant preserving potential embedding, an estimate of the graph editing distance between the first compound and the second compound is provided.

50. The non-transitory computer-readable storage medium of claim 45, wherein the difference is the L2 norm difference between the first equidistant preserving potential embedding and the second equidistant preserving potential embedding.

51. The non-transitory computer-readable storage medium according to claim 50, wherein... The first equidistant preserving latent embedding is a first vector containing a first plurality of vector values; The second isometric preserving latent embedding is a second vector containing a second plurality of vector values; and The L2 norm difference between the first vector and the second vector is considered as the square root of the sum of the squared differences in the corresponding vector values ​​between the first vector and the second vector, wherein the model is trained such that the L2 norm of the difference between the first vector and the second vector is an estimate of the GED between the first molecule and the second molecule.

52. The non-transitory computer-readable storage medium according to any one of claims 49 to 51, wherein the at least one program further comprises instructions for determining that the second compound is a chemically related analog of the first compound when the estimated value of the graph editing distance is below a threshold.

53. The non-transitory computer-readable storage medium according to any one of claims 49 to 52, wherein the method further comprises: For each corresponding unique compound pair in the compound database, the processes of obtaining (A), obtaining (B), inputting (C), inputting (D), and providing (E) are repeated to form multiple graph editing distances, wherein the first compound in the corresponding unique compound pair is the first compound, and the second compound in the corresponding unique compound pair is the second compound; By evaluating multiple distances using a criterion function, the multiple graph editing distances are clustered into multiple clusters; as well as Compounds are selected from one or more of the plurality of clusters for evaluation in a drug discovery process.

54. The non-transitory computer-readable storage medium according to any one of claims 49 to 53, the method further comprising using the estimated value of the graph editing distance to establish a quantitative structure-activity relationship model including the first compound and the second compound.

55. The non-transitory computer-readable storage medium according to any one of claims 49 to 54, wherein the method further comprises using the estimated value of the graph editing distance to determine the activity cliff relative to the drug target.

56. The non-transitory computer-readable storage medium according to any one of claims 49 to 55, wherein the model is a graph convolutional neural network.

57. The non-transitory computer-readable storage medium according to any one of claims 49 to 55, wherein the model is a graph neural network (messaging network).

58. The non-transitory computer-readable storage medium according to any one of claims 49 to 55, wherein the model is a message-passing graph neural network consisting of 3 to 8 layers.

59. The non-transitory computer-readable storage medium according to any one of claims 49 to 55, wherein the model is a message-passing graph neural network consisting of 5 layers.

60. The non-transitory computer-readable storage medium according to any one of claims 59 to 55, wherein the model is a self-encoder.

61. The non-transitory computer-readable storage medium of claim 60, wherein the autoencoder is a variational autoencoder, an adversarial autoencoder, a regularized autoencoder, a sparse autoencoder, or a metric learning autoencoder.

62. The non-transitory computer-readable storage medium according to any one of claims 49 to 61, wherein the model comprises 500,000 or more parameters.

63. The non-transitory computer-readable storage medium according to any one of claims 49 to 61, wherein the model comprises 1 × 10 6 One or more parameters.

64. The non-transitory computer-readable storage medium according to any one of claims 49 to 63, wherein the first compound and the second compound each satisfy two or more, three or more, or all four of the Lipinski Five Rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

65. The non-transitory computer-readable storage medium according to any one of claims 49 to 64, wherein the exact graph edit distance between the first compound and the second compound is between 1 and 10.

66. The non-transitory computer-readable storage medium according to any one of claims 49 to 64, wherein the exact graph edit distance between the first compound and the second compound is between 1 and 15.

67. The non-transitory computer-readable storage medium according to any one of claims 49 to 66, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 500 Daltons.

68. The non-transitory computer-readable storage medium according to any one of claims 49 to 66, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 1,000 Daltons.

69. The non-transitory computer-readable storage medium according to any one of claims 49 to 66, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 2,000 Daltons.

70. The non-transitory computer-readable storage medium according to any one of claims 49 to 66, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 4,000 Daltons, less than 6,000 Daltons, less than 8,000 Daltons, less than 10,000 Daltons, or less than 20,000 Daltons.

71. The non-transitory computer-readable storage medium according to any one of claims 49 to 66, wherein the first compound and the second compound are each organic compounds with a molecular weight between 300 Daltons and 1500 Daltons.

72. The non-transitory computer-readable storage medium according to any one of claims 49 to 71, wherein The model performs at least 100,000 computations to compute the first isometric preserving latent embedding, and The model performs at least 100,000 computations to compute the second isometric preserving potential embedding.

73. A computer system for estimating a graph editing distance between a first compound and a second compound, the computer system comprising: One or more processors; as well as A memory addressable by the one or more processors, the memory storing at least one program for execution by the one or more processors, the at least one program containing instructions for performing the following operations: (A) Inputting a first representation of the first compound into a model containing multiple parameters, wherein the model applies the multiple parameters to the first representation of the first compound to generate a first isometric latent embedding representing the first compound as a first output of the model; (B) Inputting a second representation of the second compound into the model, wherein the model applies the plurality of parameters to the second representation of the second compound to generate a second isometric latent embedding representing the second compound as a second output of the model; as well as (C) Using the difference between the first equidistant preserving potential embedding and the second equidistant preserving potential embedding, an estimate of the graph editing distance between the first compound and the second compound is provided.

74. The computer system of claim 73, wherein the difference is the L2 norm difference between the first equidistant latent embedding and the second equidistant latent embedding.

75. The computer system according to claim 73, wherein The first equidistant preserving latent embedding is a first vector containing a first plurality of vector values; The second potential isometric preserving embedding is a second vector containing a second plurality of vector values; and The L2 norm difference between the first vector and the second vector is considered as the square root of the sum of the squared differences in the corresponding vector values ​​between the first vector and the second vector, wherein the model is trained such that the L2 norm of the difference between the first vector and the second vector is an estimate of the GED between the first molecule and the second molecule.

76. The computer system according to any one of claims 73 to 75, wherein the at least one program further comprises instructions for determining that the second compound is a chemically related analog of the first compound when the estimated value of the graph editing distance is below a threshold.

77. The computer system according to any one of claims 73 to 76, wherein the at least one program further comprises instructions for performing the following operations: The input (A), input (B), and provision (C) are repeated for each corresponding unique compound pair in the compound database to form multiple graph edit distances, wherein the first compound in the corresponding unique compound pair is the first compound, and the second compound in the corresponding unique compound pair is the second compound; By evaluating multiple distances using a criterion function, the multiple graph editing distances are clustered into multiple clusters; as well as Compounds are selected from one or more of the plurality of clusters for evaluation in a drug discovery process.

78. The computer system according to any one of claims 73 to 77, wherein the at least one program further comprises instructions for using the estimated value of the graph editing distance to establish a quantitative structure-activity relationship model including the first compound and the second compound.

79. The computer system according to any one of claims 73 to 78, wherein the at least one program further comprises instructions for determining an activity cliff relative to a drug target using the estimated value of the graph editing distance.

80. The computer system according to any one of claims 73 to 79, wherein the model is a graph convolutional neural network.

81. The computer system according to any one of claims 73 to 79, wherein the model is a graph neural network (message passing network).

82. The computer system according to any one of claims 73 to 79, wherein the model is a message-passing graph neural network consisting of 3 to 8 layers.

83. The computer system according to any one of claims 73 to 79, wherein the model is a message-passing graph neural network consisting of 5 layers.

84. The computer system according to any one of claims 73 to 79, wherein the model is an autoencoder.

85. The computer system of claim 84, wherein the autoencoder is a variational autoencoder, an adversarial autoencoder, a regularized autoencoder, a sparse autoencoder, or a metric learning autoencoder.

86. The computer system according to any one of claims 73 to 85, wherein The first representation is the first fingerprint of the first compound, and The second representation is the second fingerprint of the second compound.

87. The computer system according to any one of claims 73 to 85, wherein The first representation is a first plurality of descriptors for the first compound, and The second representation is a second plurality of descriptors for the second compound.

88. The computer system according to any one of claims 73 to 85, wherein The first representation is a first three-dimensional structural representation of the first compound, and The second representation is a second three-dimensional structural representation of the second compound.

89. The computer system according to any one of claims 73 to 85, wherein The first representation is a first tensor-based representation of the first compound, and The second representation is a second tensor-based representation of the second compound.

90. The computer system according to any one of claims 73 to 85, wherein The first representation is a first string representation of the first compound, and The second representation is the second string representation of the second compound.

91. The computer system according to any one of claims 73 to 90, wherein the model comprises 500,000 or more parameters.

92. The computer system according to any one of claims 73 to 90, wherein the model comprises 1×10 6 One or more parameters.

93. The computer system according to any one of claims 73 to 92, wherein the first compound and the second compound each satisfy two or more, three or more, or all four of the Lipinski Five Rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

94. The computer system according to any one of claims 73 to 93, wherein the exact graph editing distance between the first compound and the second compound is between 1 and 10.

95. The computer system according to any one of claims 73 to 93, wherein the exact graph editing distance between the first compound and the second compound is between 1 and 15.

96. The computer system according to any one of claims 73 to 95, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 500 Daltons.

97. The computer system according to any one of claims 73 to 96, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 1,000 Daltons.

98. The computer system according to any one of claims 73 to 96, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 2,000 Daltons.

99. The computer system according to any one of claims 73 to 96, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 4,000 Daltons, less than 6,000 Daltons, less than 8,000 Daltons, less than 10,000 Daltons, or less than 20,000 Daltons.

100. The computer system according to any one of claims 73 to 96, wherein the first compound and the second compound are each organic compounds with a molecular weight between 300 Daltons and 1500 Daltons.

101. The computer system according to any one of claims 73 to 100, wherein The model performs at least 100,000 computations to compute the first isometric preserving latent embedding, and The model performs at least 100,000 computations to compute the second isometric preserving potential embedding.

102. A method for estimating the graph editing distance between a first compound and a second compound, the method comprising: In a computer system that includes one or more processors and memory addressable by said one or more processors: (A) Inputting a first representation of the first compound into a model containing multiple parameters, wherein the model applies the multiple parameters to the first representation of the first compound to generate a first isometric latent embedding representing the first compound as a first output of the model; (B) Inputting a second representation of the second compound into the model, wherein the model applies the plurality of parameters to the second representation of the second compound to generate a second isometric latent embedding representing the second compound as a second output of the model; as well as (C) Using the difference between the first equidistant preserving potential embedding and the second equidistant preserving potential embedding, an estimate of the graph editing distance between the first compound and the second compound is provided.

103. The method of claim 102, wherein the difference is the L2 norm difference between the first isometric latent embedding and the second isometric latent embedding.

104. The method of claim 103, wherein The first equidistant preserving latent embedding is a first vector containing a first plurality of vector values; The second isometric preserving latent embedding is a second vector containing a second plurality of vector values; and The L2 norm difference between the first vector and the second vector is considered as the square root of the sum of the squared differences in the corresponding vector values ​​between the first vector and the second vector, wherein the model is trained such that the L2 norm of the difference between the first vector and the second vector is an estimate of the GED between the first molecule and the second molecule.

105. The method according to any one of claims 102 to 104, wherein the method further comprises determining that the second compound is a chemically related analog of the first compound when the estimated value of the graph editing distance is below a threshold.

106. The method according to any one of claims 102 to 105, wherein the method further comprises: The input (A), input (B), and provision (C) are repeated for each corresponding unique compound pair in the compound database to form multiple graph edit distances, wherein the first compound in the corresponding unique compound pair is the first compound, and the second compound in the corresponding unique compound pair is the second compound; By evaluating multiple distances using a criterion function, the multiple graph editing distances are clustered into multiple clusters; as well as Compounds are selected from one or more of the plurality of clusters for evaluation in a drug discovery process.

107. The method according to any one of claims 102 to 106, wherein the method further comprises using the estimated value of the graph editing distance to establish a quantitative structure-activity relationship model including the first compound and the second compound.

108. The method of any one of claims 102 to 107, wherein the method further comprises using the estimated value of the graph editing distance to determine the activity cliff relative to the drug target.

109. The method according to any one of claims 102 to 108, wherein the model is a graph convolutional neural network.

110. The method according to any one of claims 102 to 108, wherein the model is a graph neural network (message passing network).

111. The method according to any one of claims 102 to 108, wherein the model is a message-passing graph neural network consisting of 3 to 8 layers.

112. The method according to any one of claims 102 to 111, wherein the model is a message-passing graph neural network consisting of 5 layers.

113. The method according to any one of claims 102 to 111, wherein the model is an autoencoder.

114. The method of claim 113, wherein the autoencoder is a variational autoencoder, an adversarial autoencoder, a regularized autoencoder, a sparse autoencoder, or a metric learning autoencoder.

115. The method according to any one of claims 102 to 114, wherein The first representation is the first fingerprint of the first compound, and The second representation is the second fingerprint of the second compound.

116. The method according to any one of claims 102 to 114, wherein The first representation is a first plurality of descriptors for the first compound, and The second representation is a second plurality of descriptors for the second compound.

117. The method according to any one of claims 102 to 114, wherein The first representation is a first three-dimensional structural representation of the first compound, and The second representation is a second three-dimensional structural representation of the second compound.

118. The method according to any one of claims 102 to 114, wherein The first representation is a first tensor-based representation of the first compound, and The second representation is a second tensor-based representation of the second compound.

119. The method according to any one of claims 102 to 114, wherein The first representation is a first string representation of the first compound, and The second representation is the second string representation of the second compound.

120. The method according to any one of claims 102 to 119, wherein the model comprises 500,000 or more parameters.

121. The method according to any one of claims 102 to 119, wherein the model comprises 1×10 6 One or more parameters.

122. The method according to any one of claims 102 to 121, wherein the first compound and the second compound each satisfy two or more, three or more, or all four of the Lipinski Five Rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

123. The method according to any one of claims 102 to 122, wherein the exact graph editing distance between the first compound and the second compound is between 1 and 10.

124. The method according to any one of claims 102 to 123, wherein the exact graph editing distance between the first compound and the second compound is between 1 and 15.

125. The method according to any one of claims 102 to 124, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 500 Daltons.

126. The method according to any one of claims 102 to 124, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 1,000 Daltons.

127. The method according to any one of claims 102 to 124, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 2000 Daltons.

128. The method according to any one of claims 102 to 124, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 4,000 Daltons, less than 6,000 Daltons, less than 8,000 Daltons, less than 10,000 Daltons, or less than 20,000 Daltons.

129. The method according to any one of claims 102 to 124, wherein the first compound and the second compound are each organic compounds with a molecular weight between 300 Daltons and 1500 Daltons.

130. The method according to any one of claims 102 to 129, wherein, The model performs at least 100,000 computations to compute the first latent embedding, and The model performs at least 100,000 computations to compute the second potential embedding.

131. A non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium stores instructions, which, when executed by a computer system, cause the computer system to perform a method for estimating a graph editing distance between a first compound and a second compound, the method comprising: (A) Inputting a first representation of the first compound into a model containing multiple parameters, wherein the model applies the multiple parameters to the first representation of the first compound to generate a first isometric latent embedding representing the first compound as a first output of the model; (B) Inputting a second representation of the second compound into the model, wherein the model applies the plurality of parameters to the second representation of the second compound to generate a second isometric latent embedding representing the second compound as a second output of the model; as well as (C) Using the difference between the first equidistant preserving potential embedding and the second equidistant preserving potential embedding, an estimate of the graph editing distance between the first compound and the second compound is provided.

132. The non-transitory computer-readable storage medium of claim 131, wherein the difference is the L2 norm difference between the first equidistant latent embedding and the second equidistant latent embedding.

133. The non-transitory computer-readable storage medium according to claim 132, wherein... The first equidistant preserving latent embedding is a first vector containing a first plurality of vector values; The second isometric preserving latent embedding is a second vector containing a second plurality of vector values; and The L2 norm difference between the first vector and the second vector is considered as the square root of the sum of the squared differences in the corresponding vector values ​​between the first vector and the second vector, wherein the model is trained such that the L2 norm of the difference between the first vector and the second vector is an estimate of the GED between the first molecule and the second molecule.

134. The non-transitory computer-readable storage medium according to any one of claims 131 to 133, wherein the method further comprises determining that the second compound is a chemically related analog of the first compound when the estimated value of the graph editing distance is below a threshold.

135. The non-transitory computer-readable storage medium according to any one of claims 131 to 134, wherein the method further comprises: The input (A), input (B), and provision (C) are repeated for each corresponding unique compound pair in the compound database to form multiple graph edit distances, wherein the first compound in the corresponding unique compound pair is the first compound, and the second compound in the corresponding unique compound pair is the second compound; By evaluating multiple distances using a criterion function, the multiple graph editing distances are clustered into multiple clusters; as well as Compounds are selected from one or more of the plurality of clusters for evaluation in a drug discovery process.

136. The non-transitory computer-readable storage medium according to any one of claims 131 to 135, wherein the method further comprises using the estimated value of the graph editing distance to establish a quantitative structure-activity relationship model including the first compound and the second compound.

137. The non-transitory computer-readable storage medium according to any one of claims 131 to 136, wherein the method further comprises using the estimated value of the graph editing distance to determine the activity cliff relative to the drug target.

138. The non-transitory computer-readable storage medium according to any one of claims 131 to 137, wherein the model is a graph convolutional neural network.

139. The non-transitory computer-readable storage medium according to any one of claims 131 to 137, wherein the model is a graph neural network (messaging network).

140. The non-transitory computer-readable storage medium according to any one of claims 131 to 137, wherein the model is a message-passing graph neural network consisting of 3 to 8 layers.

141. The non-transitory computer-readable storage medium according to any one of claims 131 to 137, wherein the model is a message-passing graph neural network consisting of 5 layers.

142. The non-transitory computer-readable storage medium according to any one of claims 131 to 137, wherein the model is a self-encoder.

143. The non-transitory computer-readable storage medium of claim 142, wherein the autoencoder is a variational autoencoder, an adversarial autoencoder, a regularized autoencoder, a sparse autoencoder, or a metric learning autoencoder.

144. The non-transitory computer-readable storage medium according to any one of claims 131 to 143, wherein The first representation is the first fingerprint of the first compound, and The second representation is the second fingerprint of the second compound.

145. The non-transitory computer-readable storage medium according to any one of claims 131 to 143, wherein The first representation is a first plurality of descriptors for the first compound, and The second representation is a second plurality of descriptors for the second compound.

146. The non-transitory computer-readable storage medium according to any one of claims 131 to 143, wherein The first representation is a first three-dimensional structural representation of the first compound, and The second representation is a second three-dimensional structural representation of the second compound.

147. The non-transitory computer-readable storage medium according to any one of claims 131 to 143, wherein The first representation is a first tensor-based representation of the first compound, and The second representation is a second tensor-based representation of the second compound.

148. The non-transitory computer-readable storage medium according to any one of claims 131 to 143, wherein The first representation is a first string representation of the first compound, and The second representation is the second string representation of the second compound.

149. The non-transitory computer-readable storage medium according to any one of claims 131 to 148, wherein the model comprises 500,000 or more parameters.

150. The non-transitory computer-readable storage medium according to any one of claims 131 to 148, wherein the model comprises 1 × 10 6 One or more parameters.

151. The non-transitory computer-readable storage medium according to any one of claims 131 to 150, wherein the first compound and the second compound each satisfy two or more, three or more, or all four of the Lipinski Five Rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

152. The non-transitory computer-readable storage medium according to any one of claims 131 to 151, wherein the exact graph editing distance between the first compound and the second compound is between 1 and 10.

153. The non-transitory computer-readable storage medium according to any one of claims 131 to 151, wherein the exact graph editing distance between the first compound and the second compound is between 1 and 15.

154. The non-transitory computer-readable storage medium according to any one of claims 131 to 153, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 500 Daltons.

155. The non-transitory computer-readable storage medium according to any one of claims 131 to 153, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 1,000 Daltons.

156. The non-transitory computer-readable storage medium according to any one of claims 131 to 153, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 2,000 Daltons.

157. The non-transitory computer-readable storage medium according to any one of claims 131 to 153, wherein the first compound and the second compound are each organic compounds with a molecular weight of less than 4,000 Daltons, less than 6,000 Daltons, less than 8,000 Daltons, less than 10,000 Daltons, or less than 20,000 Daltons.

158. The non-transitory computer-readable storage medium according to any one of claims 131 to 153, wherein the first compound and the second compound are each organic compounds with a molecular weight between 300 Daltons and 1500 Daltons.

159. The non-transitory computer-readable storage medium according to any one of claims 131 to 153, wherein The model performs at least 100,000 computations to compute the first latent embedding, and The model performs at least 100,000 computations to compute the second potential embedding.

160. A computer system for training a model to predict the potency of a test compound against a target protein, the computer system comprising: One or more processors; as well as A memory addressable by the one or more processors, the memory storing at least one program for execution by the one or more processors, the at least one program containing instructions for performing the following operations: Obtain a dataset containing data of multiple training compounds, wherein each of the multiple training compounds is labeled with: (i) a corresponding protein target among multiple protein targets, (ii) a binding site of the corresponding protein target, and (iii) efficacy against the protein target, wherein at least 5% of the multiple protein targets contain multiple binding sites, and wherein at least 5% of the multiple training compounds specify an allosteric site of a corresponding protein target among the multiple protein targets; as well as The model is trained using the dataset, wherein for each of the plurality of training compounds, the posture of the corresponding training compound at the binding site of the target protein identified for the training compound in the dataset is input into the model, and the potency of the corresponding training compound is evaluated.

161. The computer system of claim 160, wherein the at least one program further comprises instructions for performing the following operations: Obtain the test chemical compound; The test chemical compound is placed close to the binding site of the target protein to obtain the test posture; and The test posture is input into the model to obtain a prediction of the efficacy of the test compound against the target protein.

162. The computer system of claim 161, wherein the target protein is among the plurality of protein targets.

163. The computer system of claim 161, wherein the target protein is not any of the plurality of protein targets.

164. The computer system according to any one of claims 160 to 163, wherein each of the plurality of training compounds satisfies two or more of the Lipinski five rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

165. The computer system according to any one of claims 160 to 163, wherein each of the plurality of training compounds satisfies three or more of the Lipinski five rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

166. The computer system according to any one of claims 160 to 163, wherein each of the plurality of training compounds has: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

167. The computer system according to any one of claims 160 to 166, wherein each of the plurality of training compounds is an organic compound with a molecular weight of less than 500 Daltons.

168. The computer system according to any one of claims 160 to 166, wherein each of the plurality of training compounds is an organic compound with a molecular weight of less than 1,000 Daltons.

169. The computer system according to any one of claims 160 to 166, wherein each of the plurality of training compounds is an organic compound with a molecular weight of less than 2,000 Daltons.

170. The computer system according to any one of claims 160 to 166, wherein each of the plurality of training compounds is an organic compound with a molecular weight of less than 4,000 Daltons, less than 6,000 Daltons, less than 8,000 Daltons, less than 10,000 Daltons, or less than 20,000 Daltons.

171. The computer system according to any one of claims 160 to 166, wherein each of the plurality of training compounds is an organic compound with a molecular weight between 350 Daltons and 10,000 Daltons.

172. The computer system according to any one of claims 160 to 171, wherein the plurality of training compounds comprises 1,000 or more training compounds.

173. The computer system according to any one of claims 160 to 171, wherein the plurality of training compounds comprises 2000 or more training compounds.

174. The computer system according to any one of claims 160 to 171, wherein the plurality of training compounds comprises 10,000 or more training compounds.

175. The computer system according to any one of claims 160 to 174, wherein each of the plurality of protein targets is represented by one or more compounds of the plurality of compounds, and the plurality of protein targets comprises 10 or more protein targets.

176. The computer system according to any one of claims 160 to 174, wherein each of the plurality of protein targets is represented by one or more compounds of the plurality of compounds, and the plurality of protein targets comprises 100 or more protein targets.

177. The computer system according to any one of claims 160 to 174, wherein each of the plurality of protein targets is represented by 10 or more compounds of the plurality of compounds, and the plurality of protein targets comprises 10 or more protein targets.

178. The computer system according to any one of claims 160 to 177, wherein at least 10% of the plurality of protein targets contain a plurality of binding sites.

179. The computer system according to any one of claims 160 to 177, wherein at least 15% of the plurality of protein targets contain a plurality of binding sites.

180. The computer system of claim 161, wherein the test compound satisfies two or more of the Lipinski five rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

181. The computer system of claim 161, wherein the test compound satisfies three or more of the Lipinski five rules: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

182. The computer system of claim 161, wherein the test compound has: (i) no more than five hydrogen bond donors, (ii) no more than ten hydrogen bond acceptors, (iii) a molecular weight of less than 500 Daltons, and (iv) a LogP of less than 5.

183. The computer system of claim 161, wherein the test compound is an organic compound with a molecular weight of less than 500 Daltons.

184. The computer system of claim 161, wherein the test compound is an organic compound with a molecular weight of less than 1,000 Daltons.

185. The computer system of claim 161, wherein the test compound is an organic compound with a molecular weight of less than 2,000 Daltons, less than 4,000 Daltons, less than 6,000 Daltons, less than 8,000 Daltons, less than 10,000 Daltons, or less than 20,000 Daltons.

186. The computer system of claim 161, wherein the test compound is an organic compound with a molecular weight between 350 Daltons and 10,000 Daltons.

187. The computer system according to claim 161, wherein The model contains multiple parameters, and The model applies the plurality of parameters to the test posture through at least 10,000 calculations to generate the predictive power of the test compound.

188. The computer system according to any one of claims 160 to 187, wherein the model is a graph neural network.

189. The computer system according to any one of claims 160 to 188, wherein the model comprises 500,000 or more parameters.

190. The computer system according to any one of claims 160 to 189, wherein the model comprises 1×10 6 One or more parameters.

191. The computer system according to any one of claims 160 to 190, wherein the effectiveness against the protein target is pKi.

192. The computer system according to any one of claims 160 to 90, wherein the efficacy against the protein target is IC50, EC50, Kd, ​​or KI.

193. The computer system according to any one of claims 160 to 192, wherein the potency of the test compound against the target protein is pKi.

194. The computer system according to any one of claims 160 to 192, wherein the potency of the test compound against the target protein is IC50, EC50, Kd, ​​or KI.

195. A method for training a model to predict the potency of a test compound against a target protein, the method comprising: In a computer system that includes one or more processors and memory addressable by said one or more processors: Obtain a dataset containing data of multiple training compounds, wherein each corresponding training compound is labeled with: (i) a corresponding protein target among multiple protein targets, (ii) a binding site of the corresponding protein target, and (iii) potency against the protein target, wherein at least 5% of the multiple protein targets contain multiple binding sites, and wherein at least 5% of the multiple training compounds specify an allosteric site of a corresponding protein target among the multiple protein targets; and The model is trained using the dataset, wherein for each of the plurality of training compounds, the posture of the corresponding training compound at the binding site of the target protein identified for the training compound in the dataset is input into the model, and the potency of the corresponding training compound is evaluated.

196. The method of claim 195, further comprising: Obtain the test chemical compound; The test chemical compound is placed close to the binding site of the target protein to obtain the test posture; and The test posture is input into the model to obtain a prediction of the efficacy of the test compound against the target protein.

197. A non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium stores instructions, which, when executed by a computer system, cause the computer system to perform a method for training a model to predict the potency of a test compound against a target protein, the method comprising: Obtain a dataset containing data of multiple training compounds, wherein each corresponding training compound is labeled with: (i) a corresponding protein target among multiple protein targets, (ii) a binding site of the corresponding protein target, and (iii) potency against the protein target, wherein at least 5% of the multiple protein targets contain multiple binding sites, and wherein at least 5% of the multiple training compounds specify an allosteric site of a corresponding protein target among the multiple protein targets; and The model is trained using the dataset, wherein for each of the plurality of training compounds, the posture of the corresponding training compound at the binding site of the target protein identified for the training compound in the dataset is input into the model, and the potency of the corresponding training compound is evaluated.

198. The non-transitory computer-readable storage medium of claim 197, wherein the method further comprises: Obtain the test chemical compound; The test chemical compound is placed close to the binding site of the target protein to obtain the test posture; and The test posture is input into the model to obtain a prediction of the efficacy of the test compound against the target protein.

Images