Physics-based guidance for molecular structure prediction using generative diffusion models

Abstract

Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for determining a predicted 3D structure of a molecular system In one aspect, a method comprises using a generative diffusion model to generate the predicted 3D structure of the molecular system by denoising 3D structure data for the molecular system over a sequence of denoising iterations, comprising, at each of a plurality of denoising iterations: processing current structure data for the molecular system using a physics scoring model to generate a physics score that characterizes a degree to which the current structure data satisfies one or more physical constraints on the 3D structure of the molecular system; and generating a respective physics adjustment to the spatial position for each of the plurality of atoms based on the physics score.

Description

Isomorphic Labs Limited F&R Ref.: 53672-0025W01 PCT ApplicationPHYSICS-BASED GUIDANCE FOR MOLECULAR STRUCTURE PREDICTIONUSING GENERATIVE DIFFUSION MODELSBACKGROUND

[0001] This specification relates to processing data using machine learning models.

[0002] Machine learning models receive an input and generate an output, e.g., a predicted output, based on the received input. Some machine learning models are parametric models and generate the output based on the received input and on values of the parameters of the model.

[0003] Some machine learning models are deep models that employ multiple layers of models to generate an output for a received input. For example, a deep neural network is a deep machine learning model that includes an output layer and one or more hidden layers that each apply a non-linear transformation to a received input to generate an output.SUMMARY

[0004] This specification describes a system implemented as computer programs on one or more computers in one or more locations that can generate and apply a physics adjustment as part of denoising a predicted three-dimensional (3D) structure of a molecular system using a generative diffusion model. In particular, the predicted 3D molecular structure can be a joint 3D structure of a protein and one or more ligands.

[0005] The system can provide for physics-based guidance to improve the output quality of the generative diffusion model by integrating a physics-scoring subsystem to influence the diffusion process. In particular, the physics adjustment can be determined based on a physics score, e.g., the system can evaluate one or more of a chirality criterion that characterizes the handedness of the molecular structure, a minimum distance criterion between atoms in the chemical structure, a bond length criterion, and a bond angle criterion. The system can then generate gradients of the physics score and use these gradients to guide the diffusion process toward physically-viable molecular structures, e.g., predicted 3D structures that are governed by biophysical and biochemical considerations.

[0006] In an example implementation of this specification, the system can apply the physicsbased guidance to a generative diffusion model, e.g., a neural network configured to transform an initial state representing a random arrangement of atoms in the molecular structure through a sequence of denoising transformations to generate the predicted 3D structure.

[0007] In particular, the physics-scoring subsystem can be used to evaluate and guide the output molecular system structure generated by the generative diffusion model, e.g., as theIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application generative diffusion model produces candidate structures which are then assessed for physical feasibility. Based on the physics scores, the generative diffusion model can adjust its output generation process in order to generate physically-viable chemical structures.

[0008] A “protein” can be understood to refer to any biological molecule that is specified by one or more sequences (or “chains”) of amino acids. For example, the term protein can refer to a protein domain, e.g., a portion of an amino acid chain of a protein that can undergo protein folding nearly independently of the rest of the protein. As another example, the term protein can refer to a protein complex, i.e., that includes multiple amino acid chains that jointly fold into a protein structure.

[0009] A “ligand” can refer to a molecule or compound that binds to a target molecule, e.g., a protein. Ligands can include, e.g., small organic molecules, complex organic molecules, proteins, biomolecules, and so forth.

[0010] A “multiple sequence alignment” (MSA) for an amino acid chain in a protein specifies a sequence alignment of the amino acid chain with multiple additional amino acid chains, e.g., from other proteins, e.g., homologous proteins. More specifically, the MSA can define a correspondence between the positions in the amino acid chain and corresponding positions in multiple additional amino acid chains. A MSA for an amino acid chain can be generated, e.g., by processing a database of amino acid chains using any appropriate computational sequence alignment technique, e.g., progressive alignment construction. The amino acid chains in the MSA can be understood as having an evolutionary relationship, e.g., where each amino acid chain in the MSA may share a common ancestor. The correlations between the amino acids in the amino acid chains in a MSA for an amino acid chain can encode information that is relevant to predicting the structure of the amino acid chain.

[0011] A “binding pocket” on a protein can refer to a specific three-dimensional cavity or crevice within the structure of the protein where a ligand can bind to the protein. The binding pocket can, in some cases, be understood as a "lock" that fits the shape and chemical properties of ligands that act as "keys" for the lock. In other cases, the ligand may initially not fit perfectly into the binding pocket, e.g., due to structural differences or slight mismatches in shape or chemical groups, but conformational changes during binding can cause the interaction between the ligand and the binding pocket to become more complementary and specific, e.g., as in induced-fit binding. Examples of binding pockets include, e.g., orthosteric binding pockets, allosteric binding pockets, and cryptic binding pockets.

[0012] A “block” (e.g., a “self-attention block”) in a neural network can refer to a group of one or more neural network layers in the neural network.Isomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application

[0013] A “binding affinity” of a ligand for a protein refers to the strength or degree of attraction between the ligand and the protein when they interact to form a complex.

[0014] A 3D spatial position of an atom can be represented by a set of coordinates in an appropriate coordinate system, e.g., a 3D Cartesian coordinate system or a spherical coordinate system.

[0015] Particular embodiments of the subject matter described in this specification can be implemented so as to realize one or more of the following advantages.

[0016] The system of this specification can provide for the generation of physically-viable chemical structures by taking biophysical and biochemical considerations explicitly into account throughout the denoising process. By providing the physics adjustment to the denoising neural network, the model can be explicitly guided to generate physically-viable chemical structures.

[0017] The physics adjustment can decrease the use of computational resources necessary to generate a viable structure with respect to a generative diffusion model that only uses the denoising output as feedback for structure iteration. In particular, the system can both allow for the (i) the ability to generate a viable structure in fewer denoising attempts, e.g., in some cases, the system can be used to process the molecular system data multiple times to generate an ensemble of structures before selecting a viable structure, e.g., using a filtering step, and also (ii) for faster convergence, e.g., the generation of a physically viable structure in less denoising iterations in a single denoising attempt compared to a generative diffusion model that is not guided using the physics adjustment during the denoising process. For example, in the case that a user desires to generate a molecular structure with a particular chirality, the system can use the physics score to steer the generative diffusion model to generate the structure with the desired chirality in a single denoising attempt. In contrast, a conventional approach without the physics-based guidance can require the generation of an ensemble of predicted structures and an additional filtering step to select the structures with the desired chirality.

[0018] In the case that the physics scoring model is implemented as a rules-based evaluator, e.g., without machine learning, the physics guidance the system provides is deterministic. In particular, the system does not require the training of a large machine learning model for performing classifier guidance using a physical viability score. Since there are many factors to consider when assessing physical viability, training a single machine learning model to predict a physical viability score would require a large machine learning model suited to a complex task. Moreover, the system would have to process the current iteration data using the large machine learning model at a large number of denoising iterations. Furthermore, the system canIsomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT Application modularize the evaluation of certain biophysical and biochemical considerations into respective physics scoring models, e.g., respective rules-based evaluator models or computationally-lightweight machine learning models.

[0019] In contrast, by implementing a deterministic physics scoring model, or one or more respective rules-based evaluator models or computationally-lightweight machine learning models, the system can efficiently determine the physics score. More specifically, the system can enable a significant reduction of computational resources with a corresponding gain in computational efficiency at each denoising iteration compared to using a single large machine learning model to generate a physical viability score for classifier guidance.

[0020] The system can be used for any of a variety of drug discovery and drug repurposing tasks, as will be described in detail throughout this specification.

[0021] The details of one or more embodiments of the subject matter of this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0022] FIG. l is a system diagram of an example physics-based denoising system that includes a physics-scoring engine.

[0023] FIG. 2 illustrates a method for evaluating different physical constraints at a denoising iteration.

[0024] FIG. 3 illustrates a method for determining a chirality score using the determinant of three bond direction vectors in the current iteration structure data at a denoising iteration.

[0025] FIG. 4 is a flow diagram of an example process for using a physics adjustment to update a generated chemical structure for a molecular system at each of a number of denoising iterations.

[0026] FIG. 5 is a flow diagram of an example process for jointly training a denoising neural network and the physics scaling factors applied at a denoising iteration.

[0027] Like reference numbers and designations in the various drawings indicate like elements.DETAILED DESCRIPTION

[0028] FIG. 1 shows an example physics-based denoising system 100. The physics based denoising system 100 is an example of a system implemented as computer programs on one orIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application more computers in one or more locations in which the systems, components, and techniques described below are implemented.

[0029] The physics-based denoising system 100 can generate a predicted 3D structure of a molecular system by providing physics-based guidance to a generative diffusion model 115. In particular, the system 100 includes a physics scoring engine 140 that can evaluate the current output of a denoising iteration e.g., the current iteration structure data 130, using one or more biophysical or biochemical criteria to generate a physics score 145 characterizing the current output. The system 100 can then use the physics score 145 to determine a corresponding physics adjustment 150 to the output to guide the generative diffusion model 115 to generate physically-viable predicted structures.

[0030] The system 100 can receive and process data specifying a molecular system, e.g., molecular system data 105. As an example, the system 100 can receive the data characterizing the molecular system, e.g., by way of a user interface (e.g., a graphical user interface, GUI) or application programming interface (API) made available by the user, e.g., from the system 100 or from a separate upstream system.

[0031] In particular, the molecular system data 105 can include data that represents the chemical structure of one or more molecules, including data representing one or more of: the atomic composition of the molecule, the types of chemical bonds (e.g., single, double, or triple) between atoms and how these bonds connect the atoms to form the molecule, the spatial arrangement of the atoms (e.g., indicating the three-dimensional (3D) structure of the molecule, the types of functional groups present in the molecule (e.g., hydroxyl groups or carboxyl groups), and so forth.

[0032] As an example, the molecular system data 105 can include a Simplified Molecular Input Line Entry System (SMILES) string, e.g., which provides a representation of the chemical structure of the molecule in a one-dimensional string. As another example, the molecular system data 105 can include a molecular fingerprint of the molecule. As yet another example, the system 100 can receive a structural data file, e.g., a protein databank file, structure data file, chemical markup file, etc. as the molecular system data 105. As a further example, the molecular system data 105 can include an International Chemical Identifier (InChi) string defining the chemical structure of the molecular system.

[0033] In particular, the system 100 can receive molecular system data 105 specifying a protein and ligand for docking, e.g., in a complex. In this case, the physics-based denoising system 100 can process protein data and the ligand data using the generative diffusion model 115 to generate the predicted 3D structure 160 of the docked protein-ligand complex.Isomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application

[0034] More specifically, the system 100 can receive data characterizing a protein, e.g., the protein data 102, and data characterizing one or more ligands, e.g., ligand data 104, to generate a predicted joint 3D complex structure 165 that includes the protein and the one or more ligands. The predicted joint 3D structure 165 defines a respective predicted 3D spatial location of each atom in the complex, i.e., of each atom in the protein and of each atom in each of the one or more ligands. The predicted joint 3D structure 165 can define a structure of the complex where one or more of the ligands are bound to respective binding sites on the protein.

[0035] The protein data 102 can include any appropriate data characterizing the protein, e.g., data defining one or more amino acid sequences of the protein, or data defining an MSA for the protein, or data characterizing a respective structure of each of one or more “template” proteins, or a combination thereof. A template protein can refer to a protein that is “similar” to the protein represented by the protein data 102, e.g., such that the value of a similarity measure between the template protein and the protein represented by the protein data 102 satisfies (e.g., exceeds) a threshold (e.g., 0.8, or 0.9, or 0.99, or any other appropriate threshold). Similarity between a first protein and a second protein can be measured using any appropriate similarity measure, e.g., a sequence identity or percent identity similarity measure between the respective amino acid sequence(s) of the first protein and the second protein. The structure of a template protein can be represented in any appropriate manner, e.g., by a contact map, or by data defining a respective 3D spatial position of each atom in the template protein. Optionally, the protein data 102 can exclude any data that directly defines the 3D structure of the protein, e.g., the 3D spatial locations of the atoms or amino acid residues in a 3D conformation of the protein.

[0036] The ligand data 104 can include any appropriate data characterizing each ligand in a set of one or more ligands. For instance, the ligand data 104 can include, for each ligand, a respective textual representation of one or more of a chemical structure of the ligand (e.g., the arrangement of atoms and bonds in the ligand), the atom types in the ligand and their connectivity, the chirality of the bonds in the ligand, or any functional groups (e.g., hydroxyl groups, amino groups, carboxyl groups, and so forth) included in the ligand. The respective textual representation of each ligand can include, e.g., a SMILES string characterizing the ligand. As another example, the ligand data 104 can include, for each ligand, a respective representation of the ligand by way of graph data representing a graph, e.g., where the nodes in the graph represent atoms in the ligand and the edges in the graph represent bonds between atoms in the ligand. Optionally, the ligand data 104 can exclude any data that directly defines the 3D structure of each ligand, e.g., the 3D spatial locations of the atoms in a 3D conformation of the ligand.Isomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application

[0037] The ligand data 104 can include data characterizing any appropriate number of ligands. In some cases, the ligand data 104 characterizes one ligand. In other cases, the ligand data characterizes more than one ligand, e.g., two ligands, or three ligands, or four ligands, or five ligands.

[0038] More specifically, the system 100 can process the molecular system data 105 using a structure prediction subsystem 110 that includes a generative diffusion model 115 and a physics scoring engine 140, each of which will be described in more detail below.

[0039] The generative diffusion model 115 can have any appropriate neural network architecture configured to transform an initial state representing a random arrangement of molecules in the molecular structure specified by the molecular system data 105 through a sequence of denoising transformations to generate the predicted 3D structure 160, e.g., the predicted 3D docked complex 165. Generally, the generative diffusion model 115 can be implemented as a latent diffusion model that includes an encoder block to map the model input that identifies the one or more molecules included in the molecular system data 105 to a lowerdimensional latent space before applying the sequence of transformations (maintaining the same dimensionality) and a decoder block to map from the lower-dimensional latent space back into the space of the structural data 105.

[0040] For example, the generative diffusion model 115 can be implemented as a combination random forest diffusion model, e.g., the RFdiffusion model as described in “De novo design of protein structure and function with RFdiffusion” Nature 2023 Aug; 620(7976): 1089-1100. doi: 10.1038 / s41586-023-06415-8., which leverages a random forest ensemble to better model complexity in the conditional distribution of the learned data distribution. As another example, the generative diffusion model 115 can be implemented as a transformer-based model, e.g., an encoder-only transformer, decoder-only transformer, or encoder-decoder transformer. In this case, the generative diffusion model 115 can be implemented using a stable diffusion model, normalizing flow diffusion model, or iterative refinement neural network, e.g., the AlphaFold3 model as described in “Accurate structure prediction of biomolecular interactions with AlphaFold 3” Nature 2024 Jun; 630(8016):493-500, doi: 10.1038 / s41586-024-07487-w, which leverages the attention mechanism of a transformer with the spatial modeling capabilities of a graph neural network.

[0041] In the particular example depicted, the generative diffusion model 115 is implemented using a denoising neural network 120. In this case, the system 100 can generate an initial noisy structure, e.g., by randomly sampling the spatial positions of each of the atoms in the molecular structure, and can progressively denoise, e.g., transform, the noisy structure at each of a numberIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application of denoising iterations using the denoising neural network 120 to refine the spatial positions of each of the atoms in the molecular structure until the predicted 3D structure 160 is achieved.

[0042] As an example, the denoising neural network 120 can be implemented as a U-Net that includes skip connections that allow the diffusion model 115 to combine both coarse features from the beginning of the sequence of transformations and fine features from the end of the sequence of transformations to improve the generated predicted 3D structure 160.

[0043] In particular, the structure prediction subsystem 110 can process the molecular system data 105 using the generative diffusion model 115 to generate a respective initial 3D spatial position for each atom in the molecular system represented by the data 105, e.g., the docked protein-ligand complex including the protein and one or more ligands. For instance, the structure prediction subsystem 110 can sample a random 3D spatial position of each atom in the molecular system from a probability distribution over 3D space, e.g., a standard Normal distribution over 3D space.

[0044] The structure prediction subsystem 110 can then process and denoise the current iteration structure data 130 at each of a number of denoising iterations. In this case, the initial structure data is the current iteration structure data 130 at a first iteration. In some cases, the number of iterations can be a predetermined number. For example, the subsystem 110 can perform the denoising process using the structure prediction engine 110 over any appropriate number of denoising iterations, e.g., 3 iterations, 10 iterations, or 100 iterations. In other cases, the subsystem 110 can continue iterating to a next denoising iteration until the current iteration structure data 130 satisfies a criterion.

[0045] At each denoising iteration, the structure prediction engine 110 can generate a denoising output 122, e.g., using the denoising neural network 120, and can also generate a physics score 145, e.g., using a physics scoring engine 140 that evaluates one or more biophysical and biochemical constraints. In the particular example depicted, the physics scoring engine 140 includes one or more physics scoring model(s) 142. As an example, the one or more physics scoring model(s) 142 can each generate a respective physics score corresponding with a respective biophysical or biochemical constraint. Both the denoising output 122 and the physics score 145 can be used to determine a next update to the current iteration structure data 130, e.g., as is described in more detail below.

[0046] The denoising output 120 can be any appropriate data that enables estimation of the “final” 3D spatial position of each atom in the molecular system. For instance, the denoising output 122 can define, for each atom in the molecular system, a predicted error in the 3D spatial position of the atom at the current denoising iteration. As another example, the denoising outputIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application122 can directly define, for each atom in the molecular system, a predicted 3D spatial position of the atom.

[0047] As yet another example, the denoising output 122 can define, for each atom in the molecular system, both: (i) a predicted error in the 3D spatial position of the atom, and (ii) a predicted 3D spatial position of the atom at the current denoising iteration. As another example, the denoising output 122 can define, for each atom in the molecular system, a prediction for a value that is a linear combination of (i) an actual 3D spatial position of the atom, and (ii) an error between the 3D spatial position of the atom at the current denoising iteration and the actual 3D spatial position of the atom, e.g., as implemented by the v-parametrization described in: Tim Salimans, Jonathan Ho, “Progressive distillation for fast sampling of diffusion models,” ICLR 2022, arXiv:2202.00512v2.

[0048] Likewise, the physics score 145 can be any appropriate data that is a differentiable function of the atom positions. The physics score 145 facilitates estimation of the “final” 3D spatial position of each atom in the molecular system. In this case, the physics score 145 is indicative of a physical viability of the current iteration structure data 130, e.g., based on one or more biophysically or biochemically determined constraints. More specifically, the physics score 145 can represent whether the current iteration structure data 130 satisfies a desired chirality, a specified minimum allowable distance between atoms, and the expected bond length and angle between atoms of a particular type.

[0049] In particular, the subsystem 110 can process the current iteration structure data 130 using one or more physics scoring model(s) 142 to evaluate the physical viability of current iteration structure data 130. For example, each of the physics scoring model(s) 142 can be any appropriate model, e.g., a rules-based evaluator or a computationally-lightweight machine learning model, configured to generate the appropriate physics-based output, e.g., a chirality score characterizing the handedness of the molecular structure, a minimum distance criterion between atoms in the chemical structure, a bond length criteria, and a bond angle criteria. In the case that all the physics scoring model(s) 142 are implemented as rules-based evaluators, the physics-based guidance is deterministic.

[0050] Example methods for evaluating the current iteration structure data 130 against a bond length and angle constraint and a minimum distance criterion using rules-based evaluators will be described in more detail with respect to FIG. 2. An example method for determining a chirality score characterizing a handedness of the current iteration structure data 130 will be described in more detail with respect to FIG. 3.Isomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application

[0051] In the case that one or more of the physics scoring model(s) 142 are implemented as machine learning models, the physics scoring model(s) can be implemented by a differentiable model that includes one or more of: a neural network, a linear regression model, a logistic regression model, a soft-margin support-vector machine, and so forth. For instance, the physics scoring model(s) 142 can be implemented as a neural network model that includes appropriate number of neural network layers (e.g., 5 layers, 10 layers, or 15 layers) of any appropriate type (e.g., fully-connected layers, attention layers, convolutional layers, etc.) and connected in any appropriate configuration (e.g., as a linear sequence of layers, or as a directed graph of layers). In particular, the physics scoring model(s) 142 can be implemented as a computationally- lightweight machine learning model, e.g., a model that includes less machine learning model parameters than a computationally-heavy machine learning model.

[0052] The structure prediction subsystem 110 can generate an estimate 135 of the 3D spatial position for each atom in the molecular system at the next iteration using the denoising output 122 and the physics score 145. The subsystem 110 can generate a combined adjustment 124 for the current iteration that includes a respective denoising adjustment 126 and a respective physics adjustment 150 to the spatial position of each of the atoms in the current molecular structure data 130. More specifically, the subsystem 110 can steer the generation of physically- viable molecular structures by correcting for biophysical and biochemical constraints that may not be implicitly evaluated by the denoising neural network, e.g., a chirality constraint, a minimum distance constraint, a bond length constraint, a bond angle constraint, etc.

[0053] The subsystem 110 can determine the denoising adjustment 128 using the denoising output 122, e.g., the denoising output 122 can define, for each atom, a predicted error in the 3D spatial position of the atom at the current denoising iteration. The subsystem 110 can also determine the physics adjustment 150 using the physics score 145. As an example, the subsystem 110 can generate the physics adjustment 150 for each of the atoms in the molecular system as the gradient of the physics score 145 with respect to the spatial position of the atom.

[0054] In this case, the structure prediction subsystem 110 can determine the estimate 135 of the 3D spatial position for each atom in the molecular system as an aggregation of the spatial positions specified by the current molecular structure data 130 and the combined adjustment 124, e.g., the denoising adjustment 126 and the physics adjustment 150, e.g. on a per-atom basis. The denoising neural network 120 can process the estimate 135 to generate the current molecular structure data 130 for the next denoising iteration.

[0055] For example, the estimate 135 of the 3D spatial position for each atom in the molecular system at the next iteration can be determined using a linear combination:Isomorphic Labs Limited F&R Ref.: 53672-0025W01 PCT ApplicationMSi+i(xj) = MSi (xj) + Adi (xj) + Api (xj) where i indexes each denoising iteration, j indexes each atom x, and MS i+i is the estimate 135 of the 3D spatial position for each atom in the molecular system at the next denoising iteration. In particular MS i+i is determined by adding MSi, e.g., the current iteration structure data 130, the denoising adjustment 126 Adi at the current iteration, and the physics adjustment 150 Api at the current iteration.

[0056] Each term in the linear combination can be scaled by a respective constant value that is dependent on the denoising iteration. In some cases, the physics adjustment 150 can be weighted, e.g., using a physics scaling factor 155, e.g., to modify the relative importance of the denoising adjustment 126 and the physics adjustment 150 in the estimate 135. In particular, the system 100 can have selected the value of the physics scaling factor 155 at each of the denoising iterations in accordance with a predefined physics scaling schedule.

[0057] For example, the system 100 can have learned the value of the physics scaling factor 155 for each of the denoising iterations in the physics scaling schedule, e.g., by jointly training the physics scaling factor 155 for the current denoising iteration with the denoising neural network 120. An example for jointly training the physics scaling factor with the denoising neural network will be described in more detail with respect to FIG. 5.

[0058] In some cases, the subsystem 110 can generate a first spatial position xt-xfor an atom in the molecular system, without the physics adjustment 150, and then correct the first spatial positions by combining the first spatial positions with the physics adjustment 150. In one example, the denoising output 122 is the denoising adjustment 126, e.g., the denoising output 122 defines, for each atom, a respective prediction for the 3D spatial position of the atom. In this example, the respective predicted 3D spatial position for each atom defines the first spatial position for the atom: MSi (xj) + Adi (xj).

[0059] As another example, the denoising output 122 can define, for each atom, both: (i) a predicted 3D spatial position of the atom, and (ii) a predicted error in the 3D spatial position of the atom at the current denoising iteration. In this example, the subsystem 110 can generate the first spatial position of each atom as a combination (e.g., an average) of: (i) the predicted 3D spatial position of the atom as specified by the denoising output 122, and (ii) a predicted 3D spatial position of the atom that is derived from the predicted error in the 3D spatial position of the atom at the current denoising iteration, e.g., using:where t indexes the current denoising iteration, at, at, and <Jtare constants specific toIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application denoising iteration t, and ee(xt, t) is the predicted error in the 3D spatial position of the atom, e.g., the denoising adjustment 126. In the notation of equation (1), the denoising iterations decrement, such that denoising iteration t — 1 is the “next” denoising iteration after denoising iteration t. The constants in equation (1) (at, at, and <Jt) can be selected in accordance with a predefined noise schedule (see, e.g. Ho et al., “Denoising Diffusion Probabilistic Models”, arXiv:2006.11239v2, Dec 2020), e.g., along with the values of the physics scaling factor 155.

[0060] As a further example, the denoising output 122 can be expressed using a v- parametrization, and the subsystem 110 can generate a respective first spatial position of the atom for each atom using the techniques described in Tim Salimans, Jonathan Ho, “Progressive distillation for fast sampling of diffusion models,” ICLR 2022, arXiv:2202.00512v2.

[0061] In the case that the subsystem 110 determines the first spatial position MSi (xj) + Adi (xj) using the denoising output 122, the subsystem 110 can combine the first spatial positions for each of the atoms with the physics adjustment 150. In particular, the physics adjustment 150 can separately correct for aspects of physical viability that may not be accounted for in the denoising output 122.

[0062] If the current denoising iteration is the final denoising iteration (i.e., in the sequence of denoising iterations), the structure prediction subsystem 110 can output the estimate 135 of the 3D spatial position of each atom in the molecular system as the predicted 3D structure of the molecular system 160.

[0063] In the case that the current denoising iteration is not the final denoising iteration, the subsystem 110 can generate the next iteration structure data, e.g., the current iteration structure data 130, for the next denoising iteration based on the estimate 135 of the 3D spatial positions of the atoms using an appropriate diffusion sampling technique. A few examples of possible diffusion sampling techniques are described next.

[0064] For example, the subsystem 110 can generate the 3D spatial position of each atom in the current iteration structure data 130 for the current denoising iteration by combining random noise with the estimate 135 of the 3D spatial position of the atom. For instance, for each atom, the subsystem 110 can add respective random noise to the estimate 135 of the 3D spatial position of the atom, e.g., as determined from the previous iteration’s combined adjustment 124. The random noise can be sampled from a probability distribution over 3D space. The probability distribution over 3D space can vary based on the denoising iteration, e.g., such that the variance of the noise combined with the previous iteration 3D spatial positions of the atoms decreases over the sequence of denoising iterations.Isomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application

[0065] As another example, the subsystem 110 can generate the 3D spatial position of each atom in the current iteration structure data 130 for the current denoising iteration using a deterministic diffusion sampling technique, i.e., that does not rely on random noise. An example of a deterministic diffusion sampling technique is the denoising diffusion implicit model (DDIM), e.g., as described in: Jiaming Song, ChenlinMeng, Stefano Ermon, “Denoising diffusion implicit models,” ICLR 2021, arXiv:2010.02502v4.

[0066] Optionally, the generative diffusion model 115 can generate multiple distinct predicted 3D structures of the molecular system 160. In this case, the subsystem 110 can perform the denoising process multiple times to generate multiple samples from the distribution over the space of possible 3D structures of the molecular system. In this case, differences between the predicted 3D structures generated by the generative model 115 can reflect both uncertainty in the predicted structure 160, e.g., as a result of stochasticity in the random sampling performed to generate the initial position of the atoms, or in the denoising process, and also, e.g., in the case of a docked protein-ligand complex, the various structural modes of the protein and the one or more ligands.

[0067] The physics-based denoising system 100 and methods described herein can be used to obtain a ligand (i.e. a ligand molecule or ligand molecule complex) such as a drug or a ligand of an industrial enzyme. In general, the drug or industrial enzyme may be a molecule that inhibits or catalyzes a chemical or biochemical process. The molecule complex may include, for example, a protein, a ribozyme (ribonucleic acid enzyme), or a deoxyribozyme (deoxyribonucleic acid enzyme). For example, a method of obtaining a ligand may include obtaining a target amino acid sequence, in particular the amino acid sequence of a target protein molecule (or target protein molecule complex), e.g. a drug target, and processing an input based on the target amino acid sequence using the generative diffusion model 115 to determine a (tertiary) structure of the target protein molecule, e.g., a predicted structure of a complex comprising the target protein molecule and the candidate ligand. The method may then include evaluating an interaction of one or more candidate ligands with the target protein molecule. The method may further include selecting one or more of the candidate ligands as the ligand dependent on a result of the evaluating of the interaction. Predicting the structure of a complex comprising the target protein molecule and a candidate ligand may preferably account for changes in the structure of molecule caused by binding of the candidate ligand and / or changes in the structure of the candidate ligand. Evaluating the interaction of the one or more candidate ligands with the target protein molecule may, for example, comprise determining a binding energy or an equilibrium constant for the formation of the complex.Isomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application

[0068] In some implementations, evaluating the interaction may include evaluating binding of the candidate ligand with the structure of the target protein molecule. For example, evaluating the interaction may include identifying a ligand that binds with sufficient affinity for a biological effect. In some other implementations, evaluating the interaction may include evaluating an association of the candidate ligand with the target protein molecule which has an effect on a function of the target protein molecule, e.g., an enzyme. The evaluating may include evaluating an affinity between the candidate ligand and the target protein molecule or complex, or evaluating a selectivity of the interaction. The candidate ligand(s) may be selected according to which have the highest affinity. Evaluating the interaction may additionally comprise simulating a dynamical behavior of the ligand and target protein molecule, such as through molecular dynamics (or Monte Carlo) simulations, which may allow kinetic aspects of the interaction to be taken into account.

[0069] The candidate ligand(s) may be derived from a database of candidate ligands, and / or may be derived by modifying ligands in a database of candidate ligands, e.g., by modifying a structure or amino acid sequence of a candidate ligand, and / or may be derived by stepwise or iterative assembly / optimization of a candidate ligand. The candidate ligand(s) may alternately or additionally include one or more candidate ligands generated using a generative model conditioned on (the structure of) the target protein molecule or part of the target protein molecule, e.g., a structure of a binding site or other part of the target protein molecule.

[0070] The evaluation of the interaction of a candidate ligand with the target protein molecule may be performed using a computer-aided approach in which graphical models of the candidate ligand and target protein molecule structure are displayed for user-manipulation, and / or the evaluation may be performed partially or completely automatically, for example using standard molecular (e.g. protein-ligand) docking software. In some implementations the evaluation may include determining an interaction score for the candidate ligand, where the interaction score includes a measure of an interaction between the candidate ligand and the target protein molecule. The interaction score may be dependent upon a strength and / or specificity of the interaction, e.g., a score dependent on binding free energy. A candidate ligand may be selected dependent upon its score.

[0071] In some implementations the target protein molecule includes a receptor or enzyme and the ligand is an agonist or antagonist of the receptor or enzyme. In some implementations the method may be used to identify the structure of a cell surface marker. This may then be used to identify a ligand, e.g., an antibody or aptamer or a label such as a fluorescent label, which binds to the cell surface marker. This may be used to identify and / or treat cancerous cells.Isomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application

[0072] In some implementations the ligand is a drug and the interaction of each of a plurality of target protein molecules with each of the candidate ligands is evaluated. Then one or more of the candidate ligands may be selected either to obtain a ligand that (functionally) interacts with each of the target protein molecules, or to obtain a ligand that (functionally) interacts with only one of the target protein molecules. For example, in some implementations it may be desirable to obtain a drug that is effective against multiple drug targets. Also or instead, it may be desirable to screen a drug for off-target effects. For example, in agriculture it can be useful to determine that a drug designed for use with one plant species does not interact with another, different plant species and / or an animal species.

[0073] In some implementations the ligand is a drug and the predicted structure of a target protein that is a protein complex, e.g. a dimer or multimer, is determined. Evaluating the interaction of the one or more candidate ligands with the target protein may then comprise identifying a candidate ligand that interacts with the protein complex, and that might therefore be expected to affect the formation or stability of the complex. This could afterwards be confirmed by experimental screening. Thus, such a process may be used to identify a drug which is able to disrupt a protein complex or inhibit formation of the complex. Some diseases, e.g. neuro degenerative diseases such as dementia, are caused by protein aggregation. The method may thus be used to identify a ligand that is a drug to treat such a disease.

[0074] In some implementations the candidate ligand(s) may include small molecule complex ligands, e.g., organic compounds with a molecular weight of <900 daltons. In some other implementations the candidate ligand(s) may include polypeptide ligands, i.e., defined by an amino acid sequence.

[0075] In another aspect there is provided a method of using the generative diffusion model 115 to obtain a ligand, which may be a biological molecule, such as a polypeptide, polynucleotide, or polynucleoside ligand (e.g., the molecule or its amino acid or nucleotide sequence). For example, the method may include obtaining data defining one or more candidate ligands, e.g. an amino acid sequence of one or more candidate polypeptide or polynucleotide ligands. The method may include selecting a target molecule to which the ligand is to bind. The method may further include, for each of the candidate ligands, using the generative diffusion model to determine (tertiary) structure of a complex comprising the candidate ligand and the target protein molecule. The method may further include obtaining a target protein structure of a target molecule, in silico and / or by physical investigation. The method may comprise evaluating an interaction between each of the one or more candidate ligands and the target protein molecule, e.g. by evaluating an interaction between the predicted structure of theIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application candidate ligand and the structure of the target molecule, or using the predicted structure of the complex comprising the candidate ligand and the target protein molecule. The method may further include selecting one or more of the candidate ligands as the ligand dependent on a result of the evaluation.

[0076] As before, evaluating the interaction may include evaluating binding of the candidate ligand with the structure of the target protein molecule, e.g., identifying a ligand that binds with sufficient affinity for a biological effect, and / or evaluating an association of the candidate ligand with the structure of the target protein molecule which has an effect on a function of the target protein molecule, e.g., an enzyme, and / or evaluating an affinity between the candidate ligand and the structure of the target protein molecule, or evaluating a selectivity of the interaction. In some implementations the ligand may be an aptamer. Again, the candidate ligand(s) may be selected according to which have the highest affinity.

[0077] As before, the selected ligand (e.g. selected polypeptide or polynucleotide ligand) may comprise a receptor or enzyme and the ligand may be an agonist or antagonist of the receptor or enzyme. In some implementations the ligand may comprises an antibody or aptamer and the target protein molecule comprises an antibody or aptamer target, for example a virus, in particular a virus coat protein, or a protein expressed on a cancer cell. In these implementations the antibody or aptamer binds to the antibody or aptamer target to provide a therapeutic effect. For example, the antibody or aptamer may bind to the target and act as an agonist for a particular receptor; alternatively, the antibody or aptamer may prevent binding of another ligand to the target, and hence prevent activation of a relevant biological pathway.

[0078] Implementations of the method may further include synthesizing the ligand, i.e., making, the small molecule, polynucleotide or polypeptide ligand. The ligand may be synthesized by any conventional chemical techniques and / or may already be available, e.g., may be from a compound library or may have been synthesized using combinatorial chemistry.

[0079] The method may further include testing the ligand for biological activity in vitro and / or in vivo. For example, the ligand may be tested for ADME (absorption, distribution, metabolism, excretion) and / or toxicological properties, to screen out unsuitable ligands. The testing may include, e.g., bringing the candidate small molecule, polypeptide or polynucleotide ligand into contact with the target protein molecule and measuring a change in expression or activity of the target molecule.

[0080] In some implementations, a candidate (e.g. polypeptide or polynucleotide) ligand may include: an isolated antibody or aptamer, a fragment of an isolated antibody or aptamer, a single variable domain antibody, a bi- or multi-specific antibody, a multivalent antibody, a dualIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application variable domain antibody, an immuno-conjugate, a fibronectin molecule, an adnectin, an DARPin, an avimer, an affibody, an anticalin, an affilin, a protein epitope mimetic or combinations thereof. A candidate (polypeptide) ligand may include an antibody with a mutated or chemically modified amino acid Fc region, e.g., which prevents or decreases ADCC (antibody-dependent cellular cytotoxicity) activity and / or increases half-life when compared with a wild type Fc region. Candidate (polypeptide or polynucleotide) ligands may include antibodies with different CDRs (Complementarity-Determining Regions).

[0081] As another example, the target protein molecule may be an enzyme comprising a CRISPR associated protein and the ligand may comprise a guide RNA molecule. The method may be performed to identify a combination of guide RNA molecule and CRISPR associated protein, in particular one that operates efficiently to edit genes. Such a method can involve determining a predicted structure of the enzyme, e.g. as described above, in particular to check that the enzyme shape and the guide RNA shape fit and work together effectively. The guide RNA may have a part with a defined 3D structure, e.g. it may be a single guide RNA (sgRNA), incorporating a guide sequence and a tracrRNA sequence.

[0082] More generally, the techniques can be used to determine when any ribonucleoprotein (RNP) complex (between a protein and RNA) is formed, e.g. RNAi (RNA interference), where a protein e.g. from the Argonaute family, binds to a (small) RNA molecule (such as microRNA or siRNA) to form an RNA-Induced Silencing Complex (RISC) (using the RNA molecule as a guide to prevent translation of complementary mRNA into a protein.

[0083] In another example the molecule complex can include DNA and the ligand can be a transcription factor. The system can be used to determine how the presence of a methyl group on cytosine alters the local 3D structure of the DNA double helix (DNA methylation), and how this change affects the binding of a specific protein such as a transcription factor to that DNA sequence, e.g. through steric hindrance. This can be done, e.g., by comparing the binding energy and / or conformation of the protein to bound to both methylated and unmethylated DNA.

[0084] The generative diffusion model 115 described herein can also be used to obtain a diagnostic antibody or aptamer marker of a disease. There is also provided a method that comprises selecting a target protein molecule that is to be recognized by the antibody or aptamer marker, and for each of one or more candidate antibodies or aptamers e.g. as described above, uses the generative diffusion model 115 to determine a predicted structure of a complex comprising the target protein molecule and the candidate antibody or aptamer. The method may also involve, evaluating an interaction between each of the one or more candidate antibodies or aptamers and the target protein molecule, and selecting one of the one or more ofIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application the candidate antibodies or aptamers as the diagnostic antibody or aptamer marker dependent on a result of the evaluating, e.g. selecting one or more candidate antibodies or aptamers that have the highest affinity to the target protein. The method may include making the diagnostic antibody or aptamer marker. The diagnostic antibody or aptamer marker may be used to diagnose a disease by detecting whether it binds to the target protein molecule in a sample obtained from a patient, e.g. a sample of bodily fluid. As described above, a corresponding technique can be used to obtain a therapeutic antibody or aptamer (e.g., polypeptide or polynucleotide ligand).

[0085] In some other aspects a computer-implemented method as described above or herein may be used to identify active / binding / blocking sites on a target protein from its amino acid sequence.

[0086] The folding systems and methods described herein can also be used to determine the structure of a molecule or molecule complex. For example, an experimental technique may be applied to a physical sample comprising a molecule complex (i.e. the physical sample of the molecule complex is “interrogated” using the experimental technique) to measure experiment signals dependent on a structure of the molecule complex. In some implementations, the experimental technique may be a scattering technique or a spectroscopic technique. The experimental technique may, for example, comprise one or more of: x-ray crystallography, nuclear magnetic resonance (NMR), and electron microscopy (e.g. cryogenic electron microscopy, cryo-EM). A generative diffusion model may be used to determine a predicted structure of the molecule complex. The experiment signals may then be compared with corresponding simulated signals generated using the predicted structure of the molecule complex. For example, the predicted structure of the molecule complex can be used to generate predicted x-ray diffraction patterns (e.g. from an electron density distribution determined using the predicted structure) that can be compared with experimentally measured x-ray diffraction patterns. For example, the experiment signals may comprise NMR signals, electron microscope images, or x-ray diffraction patterns; or signals derived therefrom.

[0087] The predicted structure of the molecule complex may be determined by adjusting the predicted structure of the molecule complex dependent upon a result of the comparison. The method may be performed iteratively, wherein for each of one or more iterations, after the predicted structure has been adjusted, the predicted signals may be generated for the adjusted structure, and the comparing and adjusting performed again to refine the predicted structure. Alternatively (or additionally), a plurality of different possible structures of the molecule complex can be predicted and the expected experiment signals from each compared with theIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application actual experiment signals to determine a match, e.g. a best or most likely match, that can be taken as the determined structure of the molecule complex.

[0088] In general, an aptamer as described above may comprise DNA or RNA. An enzyme as described above may comprise a protein or a DNA enzyme, e.g. a deoxyribozyme or “DNAzyme”, or an RNA enzyme, e.g. a ribozyme. As well as the applications described above such enzymes can also be used for biosensors of many types, e.g. DNAzymes and aptamers can be useful for detecting metal ions, and in general aptamer targets can include small molecule complexes, proteins, and cells. Aptamers have many uses including, e.g. as probes in assays, as biosensors (e.g. they can detectably change shape when binding to a target), to modulate the activity of biomolecule complexes, and to provide a controlled release mechanism. The techniques described herein can be used to design, and then make, such aptamers, sometimes referred to as chemical antibodies.

[0089] FIG. 2 illustrates different physical constraints that the system can use to evaluate an output structure for physical viability at a denoising iteration. For example, the system 100 of FIG. 1 can use the physics scoring engine 140 to evaluate the bond length and angle constraint 210 and the minimum distance criterion 230.

[0090] More specifically, the system can evaluate the current iteration structure data for the molecular system at each of the denoising iterations to determine whether the current iteration structure data satisfies the bond length and angle constraint 210 and the minimum distance criterion 230. In particular, the system can determine a physics score that encourages feasible configurations and penalizes infeasible configurations of the molecular system.

[0091] Since molecular systems tend toward configurations with the lowest energies, the relative spatial arrangement of particular pairs or combinations of local atoms in a molecular system is generally predictable based on known bond lengths and angles. In particular, a bond length, e.g., the distance between a pair of bonded atoms can be expected to fall within a tolerance radius (a tolerance in either direction) of an expected bond length, and a bond angle, e.g., an angle between a pair of bonds that share a common atom can be expected to fall within a tolerance radius of an expected bond angle. For example, the bond length can be determined from experimental data or through quantum mechanical models, and the bond angle can be determined as a function of the hybridization of the common atom and the bond orders of the pair of bonds.

[0092] In particular, the bond length and angle constraint 210 specifies that different chemical configurations, e.g., spatial arrangement of particular connected atoms, respect certain known bond lengths and angles. In this case, the bond length refers to the distance between a first atomIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application and a second atom, e.g., the bond length 216 between atom 212 and atom 214, and the bond angle refers to the angle made by three atoms, e.g., the bond angle 225 made between atoms 212, 214, and 218.

[0093] In the particular example depicted, configuration A 220 represents a known configuration of the atoms in the molecule and configuration B 230 represents an unknown out-of-the-ordinary configuration of the atoms in the molecule, e.g., a configuration that does not respect known bond lengths and angles. In particular, the atoms 232 and 238 have been perturbed from their positions in known configuration A 220. Notably, the repositioning of atoms 232 and 238 has changed the bond angle 235 and the bond length 236. In this case, the system can evaluate the configuration A 220 as a feasible configuration, and configuration B 230 as an infeasible configuration, e.g., based on at least one of the bond lengths and angles exceeding a respective tolerance threshold of the expected bond length or angle.

[0094] As an example, the expected bond angle for a pair of bonds can be determined as a function of a hybridization of the common atom in the bond, e.g., the allowed overlap of the atomic orbitals of the bond based on electronegative effects. In particular, the bond length generally scales inversely with the fraction of s-orbital involvement in a hybridized orbital. As another example, the expected bond angle for a pair of bonds can be determined as a function of the bond orders of the pair of bonds, e.g., in general, higher bond orders, e.g., a triple or double bond, generally correlate with shorter bonds than single bonds.

[0095] For example, the system can encourage feasible configurations and can penalize infeasible configurations with respect to both the bond length and angle constraint 210 by computing a bond length score using a sum of squared deviations from the expected bond length for each pair of atoms, a bond angle score using a sum of squared deviations from the expected bond angles for each pair of bonds, or both. In some cases, the system can compute the bond length score, bond angle score, or both using a weighted sum of squared deviations of the bond lengths, the bond angles, or both, respectively.

[0096] Additionally, the system can ensure that the spatial arrangement of atoms in the current iteration structure data respects a minimum distance criterion 240, e.g., that specifies that two atoms cannot occupy the same spatial position. In particular, the system can evaluate whether the distances between atoms exceeds a threshold distance 245. As an example, the threshold distance 245 can be the minimum distance to prevent atoms from occupying the same spatial position, e.g., 1 Angstrom. In this case, the system can evaluate configuration C 244, e.g., with the atom in the allowed position outside of the threshold distance, as feasible, and can evaluate the configuration D, e.g., with the atom in the unallowed position 242, as infeasible.Isomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application

[0097] For example, the system can encourage feasible configurations and can penalize infeasible configurations with respect to the minimum distance criterion 240 by computing a penalty of the discrepancy between the distances between atoms and the threshold distance 245 using a differentiable function, e.g., SoftPlus, for any atoms that do not satisfy the minimum distance criterion.

[0098] As described with respect to FIG. 1, the system can generate the physics adjustment for each of the atoms in the molecular system as the gradient of the physics score, e.g., the bond length and angle score and the minimum distance score, with respect to the spatial position of the atoms in the current iteration structure data. In both the case of the bond length and angle constraint 210 and the minimum distance criterion 240, the system can penalize the infeasible configurations using the physics adjustment to steer the denoising neural network to generate feasible configurations.

[0099] FIG. 3 illustrates a method for determining a chirality score using the using the determinant of three bond direction vectors in the current iteration structure data in the predicted molecular structure at a denoising iteration. For example, the physics-scoring engine of FIG. 1 can process the current iteration structure data and use the depicted method to determine a chirality score characterizing a handedness of the current iteration structure data.

[0100] In this context, the chirality score can characterize whether a configuration of atoms around a chiral center, e.g., an atom that bonds with other atoms in an asymmetric arrangement, is closer to an R form, e.g., a right-handed form, or an S form, e.g., a left-handed form. The R form and the S form are referred to as enantiomers since they are mirror-images of each other. Generally, in biophysics and biochemistry, a chiral center is a carbon atom, which in some configurations, can bond with four other atoms in an asymmetric tetrahedral arrangement.

[0101] In the particular example depicted, an R form, e.g., the molecule A 310 of the right- handed form 320, and an S form, e.g., molecule B 330 of the left-handed form 340, of a carbon atom forming four single bonds is depicted. More specifically, the chirality of the enantiomers, e.g., molecules 310 and 330, can be determined based on the arrangement of atoms around the chiral centers 315 and 335.

[0102] The system can process the current structure data for an iteration using a continuous and differentiable chirality measurement function to characterize whether a configuration of atoms around each chiral center is closer to an R form, e.g., the molecule 310, or an S form, e.g., the molecule 330. While described here with respect to determining the chirality of two distinct R and S form variations for a single chiral center, e.g., the molecules 310 and 330, the system can use the same process to determine whether a particular current iteration moleculeIsomorphic Labs LimitedF&R Ref.: 53672-0025WO1 PCT Application is closer to an R form or an S form, e.g., where a particular current iteration molecule falls along an R and S form chirality continuum.

[0103] For example, the system can determine a chirality score by aggregating a discrepancy between a measure of chirality for each chirality center in the current iteration structure data and a conformer structure representing the desired chirality, e.g., either the R or S form as specified by the physical constraint. As an example, the conformer structure can be generated by simulating the molecular interactions between a first, second, and third atomic group and the chiral center using a force-field simulation configured to ensure the desired chirality. In particular, the force-field simulation can include electrostatic forces, van der Waals forces, and quantum mechanical corrections. More specifically, the simulation can be configured with the desired absolute configuration for the molecule, e.g., R or S form as specified by the physical constraint, before running the simulation, e.g., to ensure that the correct chirality is preserved in the conformer structure.

[0104] In general, the predicted structure can be related to the conformer structure by rotation about one or more of the bonds. The system can then determine a discrepancy (according to any suitable metric, e.g. mean squared error) between the predicted structure and the conformer structure.

[0105] For example, a differentiable chirality measurement function can be implemented using a continuous and differentiable chirality measurement function, e.g., as: chiral center aP3where each Mpredicted a ifor each chiral center a in the current iteration structure is a matrix of three bond direction vectors vab, vac, vadeach specifying the difference between the spatial position of a respective bond terminus and the spatial position of the chiral center a. The system can then compute the mean-squared error MSEa, / between the predicted determinant (of the matrix) \Mpredicted a i\ and the conformer determinant \Mconformer a i\, and can aggregate the mean-squared error over all chiral centers as the chirality score.

[0106] More specifically, the system can process the current structure data to determine a first bond direction vector, a second bond direction vector, and a third bond direction vector for each chiral center. For example, the system can determine the first, second, and third bond direction vectors based on a difference between a spatial position of the chiral center and a spatial position of a first, second, and third atomic group, respectively, bonded to the chiral center. In this case, the system can identity the first bond direction vectors 312 and 332, theIsomorphic Labs LimitedF&R Ref.: 53672-0025WO1 PCT Application second bond direction vectors 214 and 334, and the third bond direction vectors 316 and 336, for the molecule A 310 and the molecule B 330, respectively.

[0107] In some cases, the system can determine the first bond direction vector, the second bond direction vector, and the third bond direction vector based on guidelines for identifying the absolute chiral configuration of a molecule. For example, the system can identify the bond direction vectors according to the Cahn-Ingold-Prelog (CIP) rules, e.g., by ranking the atomic groups around a chiral center according to atomic number and orienting the molecule such that the lowest atomic number group is pointing into the plane, e.g., the atoms pointing into the page (as designated by dotted lines) in FIG. 3 are the lowest ranked atomic groups in the molecules 310 and 330.

[0108] In some cases, the system can determine different matrices for each subset i of three bonds whose origin is the chiral center. The system can then compute the determinant for each of the subset of three bonds in the predicted structure \Mpredicted a 11 as well as a corresponding target determinant in a reference conformer structure for the particular subset i of three bonds around the chiral center a \Mconformer a i\, e.g., generated using the molecular dynamics (or Monte Carlo) simulation configured to ensure the desired chirality, and can compute the mean-squared error between the determinants for each subset i around chiral center a.

[0109] In this case, the system can determine the chirality score for the predicted molecule by aggregating the discrepancy, e.g., the mean-squared error or other metric, across the subsets i of three bonds around each chiral center a. In a particular example, the system can average the mean-squared error for each subset around a respective chiral center a as the discrepancy for each chiral center and can aggregate the discrepancy between the determinant and the target determinant for each chiral center as the chirality score.

[0110] In other cases, the system can determine a single matrix for each chiral center using a particular subset of three bonds whose origin is the chiral center, e.g., where i is redundant since there is a single configuration of three atomic groups. In this case, the system can determine the determinant for each chiral center using the matrix, the target determinant for the particular three bonds in the conformer for the corresponding chiral center, and can determine the chirality score by aggregating the discrepancy between the determinant and the target determinant for each chiral center.[OHl] As described with respect to FIG. 1, the system can generate the physics adjustment for each of the atoms in the molecular system as the gradient of the chirality score with respect toIsomorphic Labs LimitedF&R Ref.: 53672-0025WO1 PCT Application the spatial position of the atoms in the current iteration structure data. In particular, the system compute the gradient of the discrepancy, e.g., the mean-squared error for each chiral center, with respect to the predicted structure’s atom positions as the physics adjustment.

[0112] In this case, the system can guide the denoising neural network to generate current iteration structure data with either an R or an S form. In particular, the system can encourage the chirality of the current structure data to have an appropriate form for a given context. For example, in a pharmacology application in which the system is used to determine a candidate drug for a target molecule, either the R or S form of an enantiomer may be deemed more efficacious, less toxic, or both.

[0113] FIG. 4 is a flow diagram of an example process for using a physics adjustment to update a chemical structure for a molecular system generated by a diffusion model at each of a number of denoising iterations. For convenience, the process 400 will be described as being performed by a system of one or more computers located in one or more locations. For example, a physicsbased denoising system, e.g., the physics-based denoising system 100 of FIG. 1, appropriately programmed in accordance with this specification, can perform the process 400.

[0114] The system can obtain data identifying one or more molecules in a molecular system (step 410), e.g. the previously described molecular system data. This can be any data that identifies or characterizes the one or more molecules. As an example, the data can include a Simplified Molecular Input Line Entry System (SMILES) string, e.g., which provides a representation of the chemical structure of the molecule in a one-dimensional string, a molecular fingerprint of the molecule or a structural data file, e.g., a protein databank file, structure data file, chemical markup file, etc. In particular, the molecular system can be a docked protein-ligand system and the system can receive data defining the candidate protein and candidate ligand.

[0115] The system can then perform steps 420-460 at each of a number of denoising iterations to denoise 3D structure data generated by a generative diffusion model. The generative diffusion model can have any appropriate neural network architecture configured to transform an initial state representing a random arrangement of molecules in the molecular structure through a sequence of denoising transformations.

[0116] The system can obtain current structure data for the denoising iteration from the generative model (step 420), e.g., using a diffusion sampler. In particular, the current structure data can define a respective spatial position for each of a number of atoms in the molecular system.Isomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application

[0117] The system can process a network input based on (i) the one or more molecules and (ii) the current structure data for the molecular system using a denoising neural network to generate a denoising output (step 430). In particular, the denoising neural network can be configured to generate a denoising output that defines a respective denoising adjustment to the spatial position for each of the number of atoms. For example, the denoising neural network can be implemented as a U-Net.

[0118] The system can process the current structure data using a physics scoring model to generate a physics score (step 440). The physics score can characterize a degree to which the current structure data satisfies one or more physical constraints on the 3D structure of the molecular system. In particular, the system can generate a respective physics score for each of a number of physical constraints and can aggregate the scores, e.g., sum the physics scores, into the overall physics score for the current structure data.

[0119] For example, the one or more physical constraints can include a constraint that each atom in the molecular system be separated from each other atom in the molecular system by at least a minimum threshold distance. In this case, the system can generate the physics score based at least in part on whether a spatial distance between the pair of atoms is at least the minimum threshold distance, e.g., 1 Angstrom to prevent impossible configurations with overlapping atoms. In general a step function, such as a threshold, can be represented as a smooth, differentiable function in many ways; as one example it can be represented as a sigmoid function.

[0120] As another example, the one or more physical constraints can include a chirality constraint. In particular, the system can process the current structure data using a chirality measurement function to generate a chirality score that characterizes the chirality, e.g., the handedness, of the current structure data around a chiral center, e.g., a constraint that a configuration of atoms around the chiral center is either an R form or an S form. In some cases, the chirality score can characterize whether a configuration of atoms is closer to the R form or the S form, e.g., the chirality score can be a continuous differentiable function of the current structure data.

[0121] In particular, processing the current structure data using the chirality measurement function can involve constructing a respective matrix for each chiral center including a first, second, and third bond direction vector corresponding with (e.g. defining a direction to) a respective first, second, and third molecular group attached to the chiral center. The system can then process the respective matrices to generate the chirality score for the current structure data. In particular, the system can determine a respective determinant for each chiral center usingIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application the corresponding respective matrix, and can determine the chirality score by aggregating a discrepancy between the respective determinants of each chiral center at the current iteration and respective target determinants of a corresponding conformer that was generated for each chiral center.

[0122] For example, for each chiral center, the system can construct a respective matrix for a chiral center by determining the first, second, and third bond direction vectors as the columns or rows of the matrix. In particular, the system can determine a first bond direction vector based on a difference between (i) a spatial position of the chiral center and (ii) a spatial position of an atom in a second atomic group attached to the chiral center, a second bond direction vector based on a difference between (i) the spatial position of the chiral center and (ii) the spatial position of an atom in a second atomic group attached to the chiral center, and a third bond direction vector based on a difference between (i) the spatial position of the chiral center and (ii) the spatial position of an atom in a third atomic group attached to the chiral center.

[0123] In some cases, the system can identify the first atomic group, the second atomic group, and the third atomic group in accordance with an ordering of atomic groups attached to the chiral center based on the Cahn-Ingold-Prelog (CIP) priority rules, e.g., that the first atomic group be identified as the atomic group with the highest atomic number or as the atomic group with isotopes with greater atomic weight, etc.

[0124] In some cases, the system can determine multiple matrices for each chiral center. In particular, the system can identify a set of all subsets of three atomic groups attached to the chiral center, and for each subset of three atomic groups, can (i) determine respective first, second, and third bond direction vectors, (ii) determine the determinant and target determinant, and (iii) determine the respective discrepancies between the determinant and the target determinant. The system can then aggregate the respective discrepancies for the set of all subsets of three atomic groups attached to the chiral center as the discrepancy for the chiral center.

[0125] The system can determine a respective target determinant for each chiral center using a target matrix that includes target first, second, and third bond direction vectors that were generated using a molecular dynamics (or Monte Carlo) simulation that is configured to generate the conformer corresponding with the first, second, and third molecular group attached to the chiral center in either the R form or the S form, e.g., as specified by the physical constraint. In the case that the system determines multiple matrices for each chiral center, the system can generate multiple conformers corresponding with each subset of three atomic groups attached to the chiral center.Isomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application

[0126] The system can then determine the chirality score as a discrepancy between the respective determinant for each chiral center and the respective target determinant for each chiral center, e.g., by summing the discrepancy over the respective chiral centers. In the case that the system determines multiple determinants for each subset of three atomic groups attached to the chiral center, the system can aggregate the discrepancy for each subset as the discrepancy for the chiral center, e.g., by computing a mean of the discrepancy between the determinant and target determinant for each subset of three atomic groups, and can further aggregate, e.g., by summing, the discrepancy over the respective chiral centers in the current iteration structure data as the chirality score.

[0127] As yet another example, the one or more physical constraints can include a constraint that each pair of bonded atoms in the molecular system have a bond length that is within a tolerance threshold of an expected bond length for the pair of bonded atoms. In this case, the system can generate the physics score based at least in part on whether the bond length between the pair of bonded atoms is within a tolerance radius of an expected bond length for each pair of bonded atoms in the molecular system. In particular, the expected bond length for a pair of bonded atoms can be determined as a function of (i) elemental types of bonded atoms, and (ii) an order of the bond.

[0128] As a further example, the one or more physical constraints can include a constraint that each pair of bonds sharing a common atom have a bond angle that is within a tolerance threshold of an expected bond angle for the pair of bonds. In this case, the system can generate the physics score based at least in part on whether the bond angle of the pair of bonds is within a tolerance radius of an expected bond angle between each pair of bonds that share a common atom. In particular, the expected bond angle for a pair of bonds can be determined as a function of (i) a hybridization of the common atom, and (ii) bond orders of the pair of bonds.

[0129] The system can then generate a respective physics adjustment based on the physics score (step 450), e.g., a respective physics adjustment to the spatial position of each of the number of atoms in the current structure data. For example, the system can generate the physics adjustment to the spatial position for each atom as a gradient of the physics score with respect to the spatial position of the atom.

[0130] The system can then update current structure data using (i) denoising adjustments and (ii) the physics adjustments for each of the number of atoms in the current structure (step 460). For example, the system can update the spatial position of the atom using a linear combination of (i) the denoising adjustment to the spatial position of the atom and (ii) the physics adjustment to the spatial position of the atom. As an example, in the case that the physics adjustmentIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application includes an adjustment from a chirality score, the system can update the current structure data to encourage the chirality of the current structure data around the chiral center to have either an R or an S form, e.g., based on a desirable form for a given context. In some cases, the system can scale the physics adjustment using a physics scaling factor associated with the denoising iteration.

[0131] After denoising the current structure data over each of a number of denoising iterations using the steps 420-460, The system can then generate and output a model output defining a predicted three-dimensional (3D) structure of the molecular system (step 470). In some cases, the system can synthesize the predicted molecule and can further evaluate the biological activity, e.g., using an in vitro or in vivo experiment. In other cases, the system can compare the predicted 3D structure of the molecular system to experimentally sampled data of a physical sample of the molecular system, e.g., data sampled using an experimental technique, e.g., one or more of x-ray crystallography, nuclear magnetic resonance, and electron microscopy.

[0132] For example, the system can use steps 410-470 to generate a predicted structure of a complex including a target protein molecule and a candidate ligand for one or more candidate ligands, e.g., a polypeptide ligand or polynucleotide ligand. As an example, the target protein molecule can be a receptor or enzyme and the ligand can be an agonist or antagonist of the receptor or enzyme. As another example, the ligand can be an antibody or aptamer and the target protein molecule can be an antibody or aptamer target, e.g., a virus or cancer cell protein that the antibody or aptamer can bind to provide a therapeutic effect.

[0133] In particular, the system can evaluate an interaction of the candidate ligand with the target protein molecule dependent on the predicted structure and can select one or more of the candidate ligands as a drug or ligand of an industrial enzyme based on the evaluation. In particular, the system can determine an interaction score for the candidate ligand as a measure of an interaction between the candidate ligand and the target molecule. As another example, the system can generate the predicted structure of the complex for both (i) one or more target protein molecules and (ii) one or more candidate ligands. In this case, the system can select one or more of the candidate ligands that interacts with each of the target protein molecules or interacts with only one of the target protein molecules.

[0134] Furthermore, the system can be used to obtain a diagnostic antibody or aptamer marker of a disease. In particular, the system can select a target protein molecule, and perform the steps 410-470 for each of one or more candidate antibodies or aptamers to determine a predicted structure of a complex including the candidate antibody or aptamer and the target protein molecule. The system can evaluate the interaction between the candidate antibody or aptamerIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application and the target protein molecule for each of the complexes, and can select one or more of the candidate antibodies or aptamers as the diagnostic antibody or aptamer marker based on the evaluation.

[0135] FIG. 5 is a flow diagram of an example process for jointly training a denoising neural network and the scaling factors applied to the physics adjustment at a denoising iteration. For convenience, the process 500 will be described as being performed by a system of one or more computers located in one or more locations. For example, a physics-based denoising system, e.g., the physics-based denoising system 100 of FIG. 1, appropriately programmed in accordance with this specification, can perform the process 500.

[0136] In some cases, the updating step 460 of FIG. 4 can involve scaling the physics adjustment using a physics scaling factor associated with the denoising iteration. In this case, the physics scaling factors for each denoising iteration can have been jointly trained along with the denoising neural network, e.g., by a machine learning training technique on a set of training examples. As an example, each training example in the set of training examples can correspond to a respective training molecular system and include data defining an actual 3D structure of the training molecular system.

[0137] More specifically, during inference, the generative diffusion model can be configured to perform a sequence of denoising time iterations, e.g., as described with reference to the process 400 of FIG. 4. During training, the system can randomly sample a single denoising time iteration from the sequence of denoising iterations, e.g., in accordance with a uniform distribution over the sequence of denoising iterations.

[0138] In particular, the system can sample a denoising time iteration (step 510) and generate a noisy 3D structure by combining noise with the actual 3D structure (step 520). In particular, the system can generate a respective noisy spatial position for each atom in the actual 3D structure by combining random noise with the actual 3D structure. For instance, the system can sample and apply noise from a random distribution to the actual 3D structure, e.g., for each atom in the structure, the system can generate the noisy spatial position for the atom by adding random noise to the target spatial position of the atom.

[0139] For example, the random distribution can be a Gaussian distribution, an exponential distribution, or a Poisson distribution. As another example, the random distribution can be a binomial distribution, a gamma distribution, or a beta distribution. In some cases, the system can scale the random noise combined with the target spatial positions of the atoms by a constant that depends on the sampled denoising iteration, e.g., where the values of the constants corresponding to the denoising iterations are defined by a noise schedule.Isomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application

[0140] The system can then generate a predicted adjustment to the noisy 3D structure (step 530). In particular, the system can generate the predicted adjustment using (i) the denoising neural network, (ii) the physics scoring model, and (iii) the physics scaling factor associated with the denoising time iteration. For example, the system can process the noisy 3D structure to generate the denoising adjustment and the physics adjustment, and combine the denoising adjustment and the physics adjustment as the predicted adjustment. More specifically, the system can process the noisy 3D structure using the denoising neural network to generate the denoising adjustment and can process the noisy 3D structure using the physics scoring model to generate the physics adjustment. In this case, the system can apply the physics scaling factor associated with the denoising time iteration to the physics adjustment, e.g., before combining the physics adjustment with the denoising adjustment.

[0141] The system can determine a target adjustment to the noisy 3D structure based on a difference between the (i) noisy 3D structure and (ii) the actual 3D structure (step 540). For example, the system can subtract a data vector representing the noisy 3D structure from the actual 3D structure to generate a difference vector as the target adjustment to the noisy 3D structure.

[0142] The system can then adjust a set of the neural network parameters of the denoising neural network and the physics scaling factor associated with the denoising time iteration using the target adjustment (step 550). In particular, the system can determine gradients of an objective function that includes a first term that measures an error between the predicted adjustment and the target adjustment to the noisy 3D structure and can adjust the set of parameters of the denoising neural network and the physics scaling factor associated with the denoising time iteration using the gradients.

[0143] The objective function can also include a second term that depends on the denoising output, e.g., the current structure data for the denoising iteration defining the position for each atom in the molecular system. In particular, the system can also determine gradients of an objective function that depends on the denoising output, and use the gradients to update the parameter values of the denoising neural network and the physics scaling factor. As an example, the term can measure an error between: (i) the denoising output of the denoising neural network, and (ii) the actual 3D structure as the target output of the denoising neural network.

[0144] For example, the system can use the gradients, e.g., from the first and second terms of the objective function, to update the parameter values of the set of parameters of the denoisingIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application neural network and the physics scaling factor using the update rule of any appropriate gradient descent optimization algorithm, e.g., RMSprop or Adam.

[0145] Some example databases of suitable training data include data from one or more of the Protein Data Bank (PDB) (Berman et al. “The Protein Data Bank”, Nucleic Acids Research, 28:235-242, 2000); PDBbind (Wanget al. “The PDBbind database: methodologies and updates”, Journal of Medicinal Chemistry, 48(12), 4111-4119, 2005); the Structural Antibody Database (SAbDab) (Dunbar et al. “’’SAbDab: the structural antibody database”, Nucleic Acids Research, 42(D1), D1140-D1146, 2014); PISA (Proteins, Interfaces, Structures and Assemblies) (Krissinel et al., “Inference of macromolecular assemblies from crystalline state”, Journal of Molecular Biology, 372(3), 774-797, 2007); and Catalytic Site Atlas (CSA) (Furnham et al. “The Catalytic Site Atlas 2.0: cataloging catalytic sites and residues in enzymes”, Nucleic Acids Research, 42(D1), D485-D489, 2014).

[0146] In some cases, after training, the sequence of denoising iterations can be partitioned into (i) a first sequence of denoising iterations over which the physics scaling factors are monotonically increasing and (ii) a second sequence of denoising iterations over which the physics scaling factors are monotonically decreasing. In particular, the system can determine to apply smaller physics scaling factors at the beginning and end of the diffusion process and to apply larger physics scaling factors towards the middle of the diffusion process, e.g., since the start of the diffusion process is random and the end of the diffusion process is more focused on finetuning, thereby rendering the physics-based guidance less effective during these stages.

[0147] This specification uses the term “configured” in connection with systems and computer program components. For a system of one or more computers to be configured to perform particular operations or actions means that the system has installed on it software, firmware, hardware, or a combination of them that in operation cause the system to perform the operations or actions. For one or more computer programs to be configured to perform particular operations or actions means that the one or more programs include instructions that, when executed by data processing apparatus, cause the apparatus to perform the operations or actions.

[0148] Embodiments of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly-embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible non-transitory storage medium for execution by, or to control theIsomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application operation of, data processing apparatus. The computer storage medium can be a machine- readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them. Alternatively or in addition, the program instructions can be encoded on an artificially-generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus.

[0149] The term “data processing apparatus” refers to data processing hardware and encompasses all kinds of apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can also be, or further include, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit). The apparatus can optionally include, in addition to hardware, code that creates an execution environment for computer programs, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0150] A computer program, which may also be referred to or described as a program, software, a software application, an app, a module, a software module, a script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages; and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data, e.g., one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, e.g., files that store one or more modules, sub-programs, or portions of code. A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a data communication network.

[0151] In this specification the term “engine” is used broadly to refer to a software-based system, subsystem, or process that is programmed to perform one or more specific functions. Generally, an engine will be implemented as one or more software modules or components, installed on one or more computers in one or more locations. In some cases, one or more computers will be dedicated to a particular engine; in other cases, multiple engines can be installed and running on the same computer or computers.Isomorphic Labs LimitedF&R Ref.: 53672-0025W01 PCT Application

[0152] The processes and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by special purpose logic circuitry, e.g., an FPGA or an ASIC, or by a combination of special purpose logic circuitry and one or more programmed computers.

[0153] Computers suitable for the execution of a computer program can be based on general or special purpose microprocessors or both, or any other kind of central processing unit. Generally, a central processing unit will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and data. The central processing unit and the memory can be supplemented by, or incorporated in, special purpose logic circuitry. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto-optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device, e.g., a universal serial bus (USB) flash drive, to name just a few.

[0154] Computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks.

[0155] To provide for interaction with a user, embodiments of the subject matter described in this specification can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. In addition, a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user; for example, by sending web pages to a web browser on a user’s device in response to requests received from the web browser. Also, a computer can interact with a userIsomorphic Labs LimitedF&R Ref.: 53672-0025WO1 PCT Application by sending text messages or other forms of message to a personal device, e.g., a smartphone that is running a messaging application, and receiving responsive messages from the user in return.

[0156] Data processing apparatus for implementing machine learning models can also include, for example, special-purpose hardware accelerator units for processing common and computeintensive parts of machine learning training or production, i.e., inference, workloads.

[0157] Machine learning models can be implemented and deployed using a machine learning framework, e.g., a TensorFlow framework, or a Jax framework.

[0158] Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back-end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front-end component, e.g., a client computer having a graphical user interface, a web browser, or an app through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network (LAN) and a wide area network (WAN), e.g., the Internet.

[0159] The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. In some embodiments, a server transmits data, e.g., an HTML page, to a user device, e.g., for purposes of displaying data to and receiving user input from a user interacting with the device, which acts as a client. Data generated at the user device, e.g., a result of the user interaction, can be received at the server from the device.

[0160] In addition to the embodiments described above, the following embodiments are also innovative:

[0161] Embodiment l is a method performed by one or more computers, the method comprising: obtaining data identifying one or more molecules included in a molecular system; processing a model input that identifies the one or more molecules included in the molecular system using a generative diffusion model to generate a model output that defines a predicted three-dimensional (3D) structure of the molecular system;Isomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT Application wherein the generative diffusion model generates the predicted 3D structure of the molecular system by denoising 3D structure data for the molecular system over a sequence of denoising iterations, comprising, at each of a plurality of denoising iterations: obtaining current structure data for the denoising iteration that defines a respective spatial position for each of a plurality of atoms in the molecular system; processing a network input that is based on: (i) the one or more molecules included in the molecular system, and (ii) the current structure data for the molecular system, using a denoising neural network to generate a denoising output that defines a respective denoising adjustment to the spatial position for each of the plurality of atoms; processing the current structure data for the molecular system using a physics scoring model to generate a physics score that characterizes a degree to which the current structure data satisfies one or more physical constraints on the 3D structure of the molecular system; and generating a respective physics adjustment to the spatial position for each of the plurality of atoms based on the physics score; and updating the current structure data using: (i) the denoising adjustments, and(ii) the physics adjustments, to the spatial positions of the plurality of atoms; and outputting data defining the predicted 3D structure of the molecular system.

[0162] Embodiment 2 is the method of embodiment 1, wherein processing the current structure data for the molecular system using the physics scoring model to generate the physics score comprises: processing the current structure data using a chirality measurement function to generate a chirality score that characterizes a chirality of the current structure data around a chiral center; wherein the one or more physical constraints include a constraint that a configuration of atoms around the chiral center is either an R form or an S form.

[0163] Embodiment 3 is the method of embodiment 2, wherein the chirality score characterizes whether a configuration of atoms around the chiral center is closer to an R form or an S form.

[0164] Embodiment 4 is the method of any one of embodiments 2-3, wherein the chirality score is a continuous, differentiable function of the current structure data.

[0165] Embodiment 5 is the method of embodiments 2-4, wherein processing the current structure data using the chirality measurement function to generate the chirality score comprises:Isomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT Application constructing a respective matrix for each chiral center comprising a first, second, and third bond direction vector corresponding with a respective first, second, and third molecular group attached to the chiral center; and processing the respective matrices to generate the chirality score for the current structure data.

[0166] Embodiment 6 is the method of embodiment 5, wherein constructing the respective matrix for each chiral center comprises: determining a first bond direction vector based on a difference between: (i) a spatial position of the chiral center, and (ii) a spatial position of an atom in a first atomic group attached to the chiral center; determining a second bond direction vector based on a difference between: (i) a spatial position of the chiral center, and (ii) a spatial position of an atom in a second atomic group attached to the chiral center; and determining a third bond direction vector based on a difference between: (i) a spatial position of the chiral center, and (ii) a spatial position of an atom in a third atomic group attached to the chiral center.

[0167] Embodiment 7 is the method of any one of embodiments 5-6, wherein processing the respective matrices to generate the chirality score for the current structure data comprises: determining a respective determinant for each chiral center using the corresponding respective matrix; determining a respective target determinant for each chiral center using a target matrix comprising target first, second, and third bond direction vectors, wherein the target first, second, and third bond direction vectors were generated for a conformer comprising the first, second, and third atomic groups attached to the chiral center in either the R form or an S form specified by the physical constraint using a molecular dynamics simulation; and determining the chirality score by aggregating a discrepancy between the respective determinants and the respective target determinants for each chiral center.

[0168] Embodiment 8 is the method of any one of embodiments 5-7, further comprising, for each chiral center: identifying a set of all subsets of three atomic groups attached to the chiral center; for each subset of three atomic groups: determining respective first, second, and third bond direction vectors defined by the subset; determining the determinant and the target determinant for the subset;Isomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT Application determining respective discrepancies between the determinant and the target determinant for the subset; aggregating the respective discrepancies for the set of all subsets of three atomic groups attached to the chiral center as the discrepancy for the chiral center.

[0169] Embodiment 9 is the method of any one of embodiments 5-8, wherein determining the first, second, and third bond direction vectors comprises identifying the first atomic group and the second atomic group in accordance with an ordering of atomic groups attached to the chiral center based on Cahn-Ingold-Prelog (CIP) priority rules.

[0170] Embodiment 10 is the method of any one of embodiments 2-9, wherein updating the current structure data using the physics adjustments encourages the chirality of the current structure data around the chiral center to have either an R form or an S form.

[0171] Embodiment 11 is the method of any one of embodiments 1-10, wherein processing the current structure data for the molecular system using the physics scoring model to generate the physics score comprises: generating the physics score based at least in part on whether, for each of a plurality of pairs of atoms in the molecular system, a spatial distance between the pair of atoms is at least a minimum threshold distance; wherein the one or more physical constraints include a constraint that each atom in the molecular system be separated from each other atom in the molecular system by at least the minimum threshold distance.

[0172] Embodiment 12 is the method of embodiment 11, wherein the minimum threshold distance is 1 Angstrom.

[0173] Embodiment 13 is the method of any one of embodiments 1-12, wherein processing the current structure data for the molecular system using the physics scoring model to generate the physics score comprises: generating the physics score based at least in part on whether, for each of a plurality of pairs of bonded atoms in the molecular system, a length of a bond between the pair of bonded atoms is within a tolerance radius of an expected bond length for the pair of bonded atoms; wherein the one or more physical constraints include a constraint that each pair of bonded atoms in the molecular system have a bond length that is within a tolerance threshold of an expected bond length for the pair of bonded atoms.Isomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT Application

[0174] Embodiment 14 is the method of embodiment 13, wherein for each pair of bonded atoms, the expected bond length for the pair of bonded atoms is determined as a function of:(i) elemental types of the bonded atoms, and (ii) an order of the bond.

[0175] Embodiment 15 is the method of any one of embodiments 1-14, wherein processing the current structure data for the molecular system using the physics scoring model to generate the physics score comprises: generating the physics score based at least in part on whether, for each of a plurality of pairs of bonds that share a common atom, a bond angle of the pair of bonds is within a tolerance radius of an expected bond angle between the pair of bonds; wherein the one or more physical constraints include a constraint that each pair of bonds sharing a common atom have a bond angle that is within a tolerance threshold of an expected bond angle for the pair of bonds.

[0176] Embodiment 16 is the method of embodiment 15, wherein for each pair of bonds that share a common atom, the expected bond angle for the pair of bonds is determined as a function of: (i) a hybridization of the common atom, and (ii) bond orders of the pair of bonds.

[0177] Embodiment 17 is the method of any one of embodiments 1-16, wherein generating the respective physics adjustment to the spatial position for each of the plurality of atoms based on the physics score comprises, for each of the plurality of atoms: generating the physics adjustment to the spatial position for the atom as a gradient of the physics score with respect to the spatial position of the atom.

[0178] Embodiment 18 is the method of any one of embodiments 1-17, wherein updating the current structure data using: (i) the denoising adjustments, and (ii) the physics adjustments, to the spatial positions of the plurality of atoms comprises, for each of the plurality of atoms: updating the spatial position of the atom using a linear combination of: (i) the denoising adjustment to the spatial position of the atom, and (ii) the physics adjustment to the spatial position of the atom.

[0179] Embodiment 19 is the method of any one of embodiments 1-18, wherein each of the plurality of denoising iterations is associated with a respective physics scaling factor, wherein the physics scaling factors vary across the plurality of denoising iterations; and wherein updating the current structure data using: (i) the denoising adjustments, and(ii) the physics adjustments, to the spatial positions of the plurality of atoms comprises, for each of the plurality of atoms:Isomorphic Labs Limited F&R Ref.: 53672-0025W01 PCT Application scaling the physics adjustment using a physics scaling factor associated with the denoising iteration.

[0180] Embodiment 20 is the method of embodiment 19, wherein the physics scaling factors associated with the denoising iterations are jointly trained along with the denoising neural network, by a machine learning training technique and on a set of training examples, to optimize an objective function.

[0181] Embodiment 21 is the method of embodiment 20, wherein each training example in the set of training examples corresponds to a respective training molecular system and includes data defining an actual 3D structure of the training molecular system; and wherein jointly training the physics scaling factors associated with the denoising iterations and the denoising neural network on the training example comprise: sampling a denoising iteration; generating a noisy 3D structure for the training molecular system by combining noise with the actual 3D structure of the training molecular system; generating a predicted adjustment to the noisy 3D structure using: (i) the denoising neural network, (ii) the physics scoring model, and (iii) the physics scaling factor associated with the denoising iteration; determining a target adjustment to the noisy 3D structure based on a difference between: (i) the noisy 3D structure, and (ii) the actual 3D structure; determining gradients of an objective function that measures an error between the predicted adjustment and the target adjustment to the noisy 3D structure; and adjusting a set of neural network parameters of the denoising neural network and the physics scaling factor associated with the denoising iteration using the gradients.

[0182] Embodiment 22 is the method of any one of embodiments 19-21, wherein the sequence of denoising iterations are partitioned into: (i) a first sequence of denoising iterations over which the physics scaling factors are monotonically increasing, and (ii) a second sequence of denoising iterations over which the physics scaling factors are monotonically decreasing.

[0183] Embodiment 23 is a system comprising: one or more computers and one or more storage devices storing instructions that are operable, when executed by the one or more computers, to cause the one or more computers to perform the method of any one of embodiments 1 to 22.Isomorphic Labs Limited F&R Ref.: 53672-0025W01 PCT Application

[0184] Embodiment 24 is a computer storage medium encoded with a computer program, the program comprising instructions that are operable, when executed by data processing apparatus, to cause the data processing apparatus to perform the method of any one of embodiments 1 to 22.

[0185] Embodiment 25 is a method of obtaining a ligand, wherein the ligand is a drug or a ligand of an industrial enzyme, the method comprising: for each of one or more candidate ligands:(a) performing the method of any one of claims 1-22 to determine a predicted structure of a complex comprising a target protein molecule and the candidate ligand; and(b) evaluating an interaction of the candidate ligand with the target protein molecule dependent on the predicted structure; and selecting one or more of the candidate ligands as the ligand dependent on a result of the evaluating.

[0186] Embodiment 26 is the method of embodiment 25, wherein the target protein molecule comprises a receptor or enzyme, and wherein the ligand is an agonist or antagonist of the receptor or enzyme.

[0187] Embodiment 27 is the method of any one of embodiments 25 or 26 wherein the ligand is a drug, and the method comprises: performing steps (a) and (b) for each of a plurality of target protein molecules; and selecting one or more of the candidate ligands as the ligand to either i) obtain a ligand that interacts with each of the target protein molecules, or ii) obtain a ligand that interacts with only one of the target protein molecules.

[0188] Embodiment 28 is the method of embodiment 25, wherein the ligand comprises an antibody or aptamer and the target protein molecule comprises an antibody or aptamer target, in particular a virus or cancer cell protein, and wherein the antibody or aptamer binds to the antibody or aptamer target to provide a therapeutic effect.

[0189] Embodiment 29 is the method of any one of embodiments 25-28, wherein the ligand is a polypeptide ligand, a polynucleotide ligand, or a polynucleotide ligand.

[0190] Embodiment 30 is a method of obtaining a diagnostic antibody or aptamer marker of a disease, the method comprising: selecting a target protein molecule; for each of one or more candidate antibodies or aptamers: performing the method of any one of embodiments 1-22 to determine a predicted structure of a complex comprising the candidate antibody or aptamer and the targetIsomorphic Labs Limited F&R Ref.: 53672-0025W01 PCT Application protein molecule; and evaluating an interaction between the candidate antibody or aptamer and the target protein molecule; and selecting one of the one or more of the candidate antibodies or aptamers as the diagnostic antibody or aptamer marker dependent on a result of the evaluating.

[0191] Embodiment 31 is a method as claimed in any one of embodiments 25-30, wherein the evaluating the interaction of one of the candidate ligands comprises determining an interaction score for the candidate ligand, wherein the interaction score comprises a measure of an interaction between the candidate ligand and the target molecule.

[0192] Embodiment 32 is a method as claimed in any one of embodiments 25-31 further comprising synthesizing the ligand or diagnostic antibody or aptamer marker.

[0193] Embodiment 33 is a method as claimed in embodiment 32, further comprising testing biological activity of the ligand or diagnostic antibody or aptamer marker in vitro and in vivo.

[0194] Embodiment 34 is a method of determining the structure of a molecule complex comprising a protein and one or more ligands, comprising: applying an experimental technique to a physical sample comprising the molecule complex to measure experiment signals dependent on a structure of the molecule complex; performing the method of any one of claims 1-22 to determine a predicted structure of the molecule complex; using the experiment signals and the predicted structure of the molecule complex to determine the structure of the molecule complex.

[0195] Embodiment 35 is a method as claimed in embodiment 34, wherein the experimental technique comprises one or more of: x-ray crystallography, nuclear magnetic resonance, and electron microscopy.

[0196] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any invention or on the scope of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular inventions. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially be claimed as such, one or more features from a claimed combination can in someIsomorphic Labs Limited F&R Ref.: 53672-0025W01 PCT Application cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

[0197] Similarly, while operations are depicted in the drawings and recited in the claims in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system modules and components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0198] Particular embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve desirable results. As one example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some cases, multitasking and parallel processing may be advantageous.

Claims

Isomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT ApplicationCLAIMS1. A method performed by one or more computers, the method comprising: obtaining data identifying one or more molecules included in a molecular system; processing a model input that identifies the one or more molecules included in the molecular system using a generative diffusion model to generate a model output that defines a predicted three-dimensional (3D) structure of the molecular system; wherein the generative diffusion model generates the predicted 3D structure of the molecular system by denoising 3D structure data for the molecular system over a sequence of denoising iterations, comprising, at each of a plurality of denoising iterations: obtaining current structure data for the denoising iteration that defines a respective spatial position for each of a plurality of atoms in the molecular system; processing a network input that is based on: (i) the one or more molecules included in the molecular system, and (ii) the current structure data for the molecular system, using a denoising neural network to generate a denoising output that defines a respective denoising adjustment to the spatial position for each of the plurality of atoms; processing the current structure data for the molecular system using a physics scoring model to generate a physics score that characterizes a degree to which the current structure data satisfies one or more physical constraints on the 3D structure of the molecular system; and generating a respective physics adjustment to the spatial position for each of the plurality of atoms based on the physics score; and updating the current structure data using: (i) the denoising adjustments, and (ii) the physics adjustments, to the spatial positions of the plurality of atoms; and outputting data defining the predicted 3D structure of the molecular system.

2. The method of claim 1, wherein processing the current structure data for the molecular system using the physics scoring model to generate the physics score comprises: processing the current structure data using a chirality measurement function to generate a chirality score that characterizes a chirality of the current structure data around a chiral center; wherein the one or more physical constraints include a constraint that a configuration of atoms around the chiral center is either an R form or an S form.43Isomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT Application3. The method of claim 2, wherein the chirality score characterizes whether a configuration of atoms around the chiral center is closer to an R form or an S form.

4. The method of any one of claims 2-3, wherein the chirality score is a continuous, differentiable function of the current structure data.

5. The method of any one of claims 2-4, wherein processing the current structure data using the chirality measurement function to generate the chirality score comprises: constructing a respective matrix for each chiral center comprising a first, second, and third bond direction vector corresponding with a respective first, second, and third molecular group attached to the chiral center; and processing the respective matrices to generate the chirality score for the current structure data.

6. The method of claim 5, wherein constructing the respective matrix for each chiral center comprises: determining a first bond direction vector based on a difference between: (i) a spatial position of the chiral center, and (ii) a spatial position of an atom in a first atomic group attached to the chiral center; determining a second bond direction vector based on a difference between: (i) a spatial position of the chiral center, and (ii) a spatial position of an atom in a second atomic group attached to the chiral center; and determining a third bond direction vector based on a difference between: (i) a spatial position of the chiral center, and (ii) a spatial position of an atom in a third atomic group attached to the chiral center.

7. The method of any one of claims 5-6, wherein processing the respective matrices to generate the chirality score for the current structure data comprises: determining a respective determinant for each chiral center using the corresponding respective matrix; determining a respective target determinant for each chiral center using a target matrix comprising target first, second, and third bond direction vectors, wherein the target first, second, and third bond direction vectors were generated for a conformer comprising the first,44Isomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT Application second, and third atomic groups attached to the chiral center in either the R form or an S form specified by the physical constraint using a molecular dynamics simulation; and determining the chirality score by aggregating a discrepancy between the respective determinants and the respective target determinants for each chiral center.

8. The method of any one of claims 5-7, further comprising, for each chiral center: identifying a set of all subsets of three atomic groups attached to the chiral center; for each subset of three atomic groups: determining respective first, second, and third bond direction vectors defined by the subset; determining the determinant and the target determinant for the subset; determining respective discrepancies between the determinant and the target determinant for the subset; aggregating the respective discrepancies for the set of all subsets of three atomic groups attached to the chiral center as the discrepancy for the chiral center.

9. The method of any of claims 5-8, wherein determining the first, second, and third bond direction vectors comprises identifying the first atomic group and the second atomic group in accordance with an ordering of atomic groups attached to the chiral center based on Cahn-Ingold-Prelog (CIP) priority rules.

10. The method of any one of claims 2-9, wherein updating the current structure data using the physics adjustments encourages the chirality of the current structure data around the chiral center to have either an R form or an S form.

11. The method of any preceding claim, wherein processing the current structure data for the molecular system using the physics scoring model to generate the physics score comprises: generating the physics score based at least in part on whether, for each of a plurality of pairs of atoms in the molecular system, a spatial distance between the pair of atoms is at least a minimum threshold distance; wherein the one or more physical constraints include a constraint that each atom in the molecular system be separated from each other atom in the molecular system by at least the45Isomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT Application minimum threshold distance.

12. The method of claim 11, wherein the minimum threshold distance is 1 Angstrom.

13. The method of any preceding claim, wherein processing the current structure data for the molecular system using the physics scoring model to generate the physics score comprises: generating the physics score based at least in part on whether, for each of a plurality of pairs of bonded atoms in the molecular system, a length of a bond between the pair of bonded atoms is within a tolerance radius of an expected bond length for the pair of bonded atoms; wherein the one or more physical constraints include a constraint that each pair of bonded atoms in the molecular system have a bond length that is within a tolerance threshold of an expected bond length for the pair of bonded atoms.

14. The method of claim 13, wherein for each pair of bonded atoms, the expected bond length for the pair of bonded atoms is determined as a function of: (i) elemental types of the bonded atoms, and (ii) an order of the bond.

15. The method of any preceding claim, wherein processing the current structure data for the molecular system using the physics scoring model to generate the physics score comprises: generating the physics score based at least in part on whether, for each of a plurality of pairs of bonds that share a common atom, a bond angle of the pair of bonds is within a tolerance radius of an expected bond angle between the pair of bonds; wherein the one or more physical constraints include a constraint that each pair of bonds sharing a common atom have a bond angle that is within a tolerance threshold of an expected bond angle for the pair of bonds.

16. The method of claim 15, wherein for each pair of bonds that share a common atom, the expected bond angle for the pair of bonds is determined as a function of: (i) a hybridization of the common atom, and (ii) bond orders of the pair of bonds.Isomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT Application17. The method of any preceding claim, wherein generating the respective physics adjustment to the spatial position for each of the plurality of atoms based on the physics score comprises, for each of the plurality of atoms: generating the physics adjustment to the spatial position for the atom as a gradient of the physics score with respect to the spatial position of the atom.

18. The method of any preceding claim, wherein updating the current structure data using: (i) the denoising adjustments, and (ii) the physics adjustments, to the spatial positions of the plurality of atoms comprises, for each of the plurality of atoms: updating the spatial position of the atom using a linear combination of: (i) the denoising adjustment to the spatial position of the atom, and (ii) the physics adjustment to the spatial position of the atom.

19. The method of any preceding claim, wherein each of the plurality of denoising iterations is associated with a respective physics scaling factor, wherein the physics scaling factors vary across the plurality of denoising iterations; and wherein updating the current structure data using: (i) the denoising adjustments, and (ii) the physics adjustments, to the spatial positions of the plurality of atoms comprises, for each of the plurality of atoms: scaling the physics adjustment using a physics scaling factor associated with the denoising iteration.

20. The method of claim 19, wherein the physics scaling factors associated with the denoising iterations are jointly trained along with the denoising neural network, by a machine learning training technique and on a set of training examples, to optimize an objective function.

21. The method of claim 20, wherein each training example in the set of training examples corresponds to a respective training molecular system and includes data defining an actual 3D structure of the training molecular system; and wherein jointly training the physics scaling factors associated with the denoising iterations and the denoising neural network on the training example comprise: sampling a denoising iteration; generating a noisy 3D structure for the training molecular system byIsomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT Application combining noise with the actual 3D structure of the training molecular system; generating a predicted adjustment to the noisy 3D structure using: (i) the denoising neural network, (ii) the physics scoring model, and (iii) the physics scaling factor associated with the denoising iteration; determining a target adjustment to the noisy 3D structure based on a difference between: (i) the noisy 3D structure, and (ii) the actual 3D structure; determining gradients of an objective function that measures an error between the predicted adjustment and the target adjustment to the noisy 3D structure; and adjusting a set of neural network parameters of the denoising neural network and the physics scaling factor associated with the denoising iteration using the gradients.

22. The method of any one of claims 19-21, wherein the sequence of denoising iterations are partitioned into: (i) a first sequence of denoising iterations over which the physics scaling factors are monotonically increasing, and (ii) a second sequence of denoising iterations over which the physics scaling factors are monotonically decreasing.

23. A system comprising: one or more computers; and one or more storage devices communicatively coupled to the one or more computers, wherein the one or more storage devices store instructions that, when executed by the one or more computers, cause the one or more computers to perform operations of the respective method of any one of claims 1-22.

24. One or more non-transitory computer storage media storing instructions that when executed by one or more computers cause the one or more computers to perform operations of the respective method of any one of claims 1-22.

25. A method of obtaining a ligand, wherein the ligand is a drug or a ligand of an industrial enzyme, the method comprising: for each of one or more candidate ligands:(a) performing the method of any one of claims 1-22 to determine a predicted structure of a complex comprising a target protein molecule and the candidate ligand; and(b) evaluating an interaction of the candidate ligand with the target protein molecule dependent on the predicted structure; and48Isomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT Application selecting one or more of the candidate ligands as the ligand dependent on a result of the evaluating.

26. A method as claimed in claim 25, wherein the target protein molecule comprises a receptor or enzyme, and wherein the ligand is an agonist or antagonist of the receptor or enzyme.

27. A method as claimed in claim 25 or 26 wherein the ligand is a drug, and the method comprises: performing steps (a) and (b) for each of a plurality of target protein molecules; and selecting one or more of the candidate ligands as the ligand to either i) obtain a ligand that interacts with each of the target protein molecules, or ii) obtain a ligand that interacts with only one of the target protein molecules.

28. The method of claim 25, wherein the ligand comprises an antibody or aptamer and the target protein molecule comprises an antibody or aptamer target, in particular a virus or cancer cell protein, and wherein the antibody or aptamer binds to the antibody or aptamer target to provide a therapeutic effect.

29. The method of any one of claims 25-28, wherein the ligand is a polypeptide ligand, a polynucleotide ligand, or a polynucleotide ligand.

30. A method of obtaining a diagnostic antibody or aptamer marker of a disease, the method comprising: selecting a target protein molecule; for each of one or more candidate antibodies or aptamers: performing the method of any one of claims 1-22 to determine a predicted structure of a complex comprising the candidate antibody or aptamer and the target protein molecule; and evaluating an interaction between the candidate antibody or aptamer and the target protein molecule; and selecting one of the one or more of the candidate antibodies or aptamers as the diagnostic antibody or aptamer marker dependent on a result of the evaluating.49Isomorphic Labs Limited F&R Ref.: 53672-0025WO1 PCT Application31. A method as claimed in any one of claims 25-30 wherein the evaluating the interaction of one of the candidate ligands comprises determining an interaction score for the candidate ligand, wherein the interaction score comprises a measure of an interaction between the candidate ligand and the target molecule.

32. A method as claimed in any one of claims 25-31 further comprising synthesizing the ligand or diagnostic antibody or aptamer marker.

33. A method as claimed in claim 32 further comprising testing biological activity of the ligand or diagnostic antibody or aptamer marker in vitro and in vivo.

34. A method of determining the structure of a molecule complex comprising a protein and one or more ligands, comprising: applying an experimental technique to a physical sample comprising the molecule complex to measure experiment signals dependent on a structure of the molecule complex; performing the method of any one of claims 1-22 to determine a predicted structure of the molecule complex; using the experiment signals and the predicted structure of the molecule complex to determine the structure of the molecule complex.

35. A method as claimed in claim 34, wherein the experimental technique comprises one or more of: x-ray crystallography, nuclear magnetic resonance, and electron microscopy.50

Images