Molecular representation method and electronic device

Abstract

Embodiments of the present disclosure relate to a molecular representation method and an electronic device. The molecular representation method comprises: determining a molecular surface of a molecule, the molecular surface being a continuous Riemannian manifold and comprising a plurality of discrete surface nodes; determining geometric features of the molecule based on the molecular surface; determining chemical features of the molecule by mapping atomic information inside the molecule to the plurality of surface nodes; determining unified features of the molecule by integrating the geometric features and the chemical features; and determining time-evolving multi-scale features of the molecule based on the unified features by using a time-evolving neural network model. In this way, in embodiments of the present disclosure, a Riemannian manifold-based molecular representation method different from existing molecular representation methods is provided by the time-evolving multi-scale features. The time-evolving multi-scale features comprise the geometric features and the chemical features of the molecule, thereby being capable of comprehensively representing overall information of the molecule.

Description

Technical Field

[0001] This disclosure generally relates to the fields of computer science and bioinformatics, and more specifically to molecular representation methods and electronic devices. Background Technology

[0002] In recent years, leveraging artificial intelligence (AI) technologies (such as machine learning and deep learning) to accelerate new drug development has become a crucial direction in the biopharmaceutical field. Compared to traditional wet laboratory methods, such as experts synthesizing new drugs and testing their activity in the lab, AI-based drug development can significantly accelerate the development rate through computer simulation and high-throughput screening. However, AI technology cannot directly operate on drug molecules in the laboratory. Instead, drug molecules need to be characterized using molecular representation methods to achieve computer modeling. Common molecular representation methods include molecular graphs, point clouds, and 3D voxels.

[0003] However, current common molecular representation methods cannot comprehensively represent the overall information of a molecule. Therefore, a more universal molecular representation method is needed. Summary of the Invention

[0004] According to an example embodiment of this disclosure, a molecular representation method is provided to determine the time-dependent multi-scale features of molecular evolution based on the Riemannian manifold on the molecular surface.

[0005] In a first aspect of this disclosure, a molecular representation method is provided, comprising: determining a molecular surface of a molecule, wherein the molecular surface is a continuous Riemannian manifold and the molecular surface includes a plurality of discrete surface nodes; determining geometric features of the molecule based on the molecular surface; determining chemical features of the molecule by mapping atomic information inside the molecule to the plurality of surface nodes; determining a unified feature of the molecule by integrating the geometric features and the chemical features; and determining time-dependent evolutionary multiscale features of the molecule based on the unified features by using a time-dependent evolutionary neural network model.

[0006] In a second aspect of the present disclosure, an electronic device is provided, comprising: at least one processing unit; and at least one memory coupled to the at least one processing unit and storing instructions for execution by the at least one processing unit, the instructions causing the electronic device to perform the method described in the first aspect of the present disclosure when executed by the at least one processing unit.

[0007] In a third aspect of the present disclosure, a computer-readable storage medium is provided having machine-executable instructions stored thereon, which, when executed by a device, cause the device to perform the method described in the first aspect of the present disclosure.

[0008] In a fourth aspect of the present disclosure, a computer program product is provided, including computer-executable instructions, wherein the computer-executable instructions, when executed by a processor, implement the method described in the first aspect of the present disclosure.

[0009] In a fifth aspect of this disclosure, an electronic device is provided, including: a processing circuit configured to perform the method described in the first aspect of this disclosure.

[0010] The summary section is provided to introduce a series of concepts in a simplified form, which will be further described in the detailed description below. The summary section is not intended to identify key or essential features of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0011] The above and other features, advantages, and aspects of the embodiments of this disclosure will become more apparent from the accompanying drawings and the following detailed description. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein:

[0012] Figure 1 Schematic diagrams are shown of various molecular representations of the benzene molecule;

[0013] Figure 2 A schematic flowchart of example processes according to some embodiments of the present disclosure is shown;

[0014] Figure 3 A schematic diagram of the electron density field of a benzene molecule according to some embodiments of the present disclosure is shown;

[0015] Figure 4A and Figure 4B Schematic diagrams of molecular surfaces represented by triangulation according to some embodiments of the present disclosure are shown respectively;

[0016] Figure 5A A schematic diagram is shown of nodes that project chemical information of atoms onto the surface of molecules according to some embodiments of the present disclosure;

[0017] Figure 5B A schematic diagram of the electrostatic potential energy function of a molecular surface according to some embodiments of the present disclosure is shown;

[0018] Figure 6 A schematic diagram showing the distribution of the first six eigenfunctions of a molecule on the molecular surface according to some embodiments of the present disclosure is illustrated.

[0019] Figure 7A schematic diagram illustrating the change of thermal distribution on a molecular surface over time according to some embodiments of the present disclosure is shown;

[0020] Figure 8 A schematic diagram illustrating the determination of time-dependent evolutionary multiscale features according to some embodiments of the present disclosure is shown;

[0021] Figure 9 A schematic diagram illustrating the spatial relationship between a pair of mirror-symmetric chiral molecules and a set of function gradients corresponding to a surface, according to some embodiments of the present disclosure;

[0022] Figure 10 Block diagrams of example apparatuses according to some embodiments of the present disclosure are shown; and

[0023] Figure 11 A block diagram of an example device that can be used to implement embodiments of the present disclosure is shown. Detailed Implementation

[0024] Embodiments of this disclosure will now be described in more detail with reference to the accompanying drawings. While some embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this disclosure. It should be understood that the accompanying drawings and embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure.

[0025] As mentioned earlier, artificial intelligence techniques such as machine learning can accelerate the testing of drug molecule activity. Drug molecules can be characterized using molecular representation methods for quantitative modeling. When the number of known molecules is limited, machine learning models based on molecular representation methods (e.g., representations containing rich analytical information) can predict molecular properties. However, current molecular representation methods cannot comprehensively represent molecular information. Even though machine learning can learn some features not included in the original representation from large datasets, in situations with limited data, such as in many biopharmaceutical problems, a more efficient molecular representation method is needed to more comprehensively represent molecular information.

[0026] Figure 1 Schematic diagrams are shown of various molecular representations for benzene molecule 100. Figure 1The diagram illustrates molecular formula representation 110, smiley face representation 120, graph representation 130, ball-and-stick representation 140, molecular orbital representation 150, and electron density field representation 160. Any of molecular representations 110 to 160 can be used to model the benzene molecule, but the molecular information contained in different representations differs. For example, molecular formula representation 110 does not contain any 3D structural information. Graph representation 130, a Kekulé structure, effectively represents the connections between atoms but does not explicitly express the spatial distribution of its electron cloud, such as the spatial occupancy of the molecule.

[0027] While various molecular representation methods can be applied to different scenarios, common methods typically do not model the molecule as a whole; instead, they model only local structural and chemical information. However, actual physicochemical processes are multi-scale; for example, electrostatic forces are long-range interactions. Therefore, current local-based molecular representation methods cannot accurately model the physical laws of physics. Furthermore, this limitation prevents corresponding machine learning models from effectively modeling the quantitative structure-activity relationship of molecules, thus affecting the success rate of downstream biopharmaceutical tasks.

[0028] To address at least the aforementioned problems and other potential issues, embodiments of this disclosure provide a molecular representation scheme. Specifically, based on the Riemannian manifold of the molecular surface, the time-dependent evolutionary multi-scale characteristics of the molecule are determined, characterizing the molecule's chemical and geometric information. This encompasses both local and overall molecular features, resulting in more comprehensive information. The molecular representation method described in the embodiments of this disclosure can be used for modeling in artificial intelligence techniques such as machine learning, for example, to more effectively characterize molecular activity and improve the success rate of biopharmaceutical tasks.

[0029] Figure 2 A schematic flowchart of example process 200 according to some embodiments of the present disclosure is shown. At block 210, the molecular surface of a molecule is determined, the molecular surface being a continuous Riemannian manifold and comprising a discrete plurality of surface nodes. At block 220, the geometric features of the molecule are determined based on the molecular surface. At block 230, the chemical features of the molecule are determined by mapping atomic information within the molecule to the plurality of surface nodes. At block 240, a unified feature of the molecule is determined by integrating the geometric and chemical features. At block 250, the time-dependent evolutionary multiscale features of the molecule are determined based on the unified features using a time-dependent evolutionary neural network model.

[0030] For example, the molecules in the embodiments of this disclosure can be biological macromolecules, such as proteins, DNA, etc.; or they can be small molecules, such as small molecules of aspirin. This disclosure is not limited in this respect.

[0031] Exemplary embodiments of this disclosure can determine chemical and geometric features based on the molecular surface of a Riemannian manifold. Exemplary embodiments can determine geometric features based on the eigenfunctions and eigenvalues ​​of the Laplace operator. The following will combine... Figures 3 to 10 Some embodiments of this disclosure are described in more detail.

[0032] In some exemplary embodiments of this disclosure, the molecular surface of a molecule can be determined based on the isosurface of the electron density field of the molecule.

[0033] Biomolecules are generally measured in units of 10⁻⁶. -10 Using the meter (angstrom) as the unit, at this microscopic scale, biomolecules generally follow the physical laws described by quantum mechanics and statistical mechanics, rather than Newtonian mechanics at the macroscopic scale. From the perspective of microscopic electronic structure, molecules consist of positively charged atomic nuclei and negatively charged electron clouds. Intuitively, molecules can be understood as electron density fields. Different biomolecules have different chemical compositions and 3D geometric structures, thus exhibiting different physicochemical properties. For example, specific drug molecules bind to certain protein receptors in the human body to achieve therapeutic effects. That is to say, different molecules have their unique electron density fields, and therefore, different molecules can be represented by describing the shape and chemical properties of this density field. Specifically, the isosurface of the density field can be determined, which is called the molecular surface of the molecule.

[0034] As an example, such as Figure 3 The electron density field 300 of a benzene molecule, as shown in an embodiment of this disclosure, is... Figure 3 In the diagram, curve 310 represents the isosurface.

[0035] For example, the analyzed electron density field can be represented as the electron density function of a molecule. Optionally, the electron density function of a molecule can be determined by quantum chemical simulations. Further, the molecular surface can be determined based on the isosurface of the electron density function of the molecule. For example, the electron density function of a molecule may have multiple isosurfaces, and in some embodiments of this disclosure, the molecular surface can be determined by selecting one of these isosurfaces.

[0036] In some exemplary embodiments of this disclosure, the molecular surface can also be determined using other molecular surface calculation methods. For example, the molecular surface can be determined using MSMS calculation software.

[0037] In some exemplary embodiments of this disclosure, the molecular surface of a molecule can also be determined based on sampling of the solvent-accessible or inaccessible surfaces of the molecule.

[0038] It is understood that in other examples, other methods may be used to determine the molecular surface of the molecule in the embodiments of this disclosure, and this disclosure is not limited thereto.

[0039] In some examples, a molecular surface can be represented as a discrete set of nodes and the connections between them. Exemplarily, surface information can be further determined based on the defined molecular surface. For instance, mesh representation methods such as triangulation can be used to store the surface information. Figure 4A and Figure 4B A schematic diagram of a molecular surface represented by triangulation is shown. As shown, the surface is shown with triangulation nodes (referred to as "nodes"), and these nodes may be connected. That is, the molecular surface includes multiple surface nodes, such as multiple triangulation nodes.

[0040] Exemplarily, the surface encapsulates molecules and can represent the shape of the molecules. In embodiments of this disclosure, the stored surface information may include: atomic information within the molecule, and the 3D coordinates of each node on the molecular surface and the connections between nodes. For example, the atomic information within the molecule includes the three-dimensional coordinates of atoms and related chemical information such as atom types. It is understood that the molecular surface is a two-dimensional Riemannian manifold, which is itself continuous and smooth. In subsequent processing of embodiments of this disclosure, this continuous and smooth Riemannian manifold can be discretized, for example, by triangulating the nodes.

[0041] In some exemplary embodiments of this disclosure, for each of a plurality of surface nodes, the chemical environment characteristics of the node are obtained by mapping the atomic information of a plurality of atoms associated with the node to the node; based on the chemical environment characteristics of each of the plurality of surface nodes, a fully connected neural network is used to determine the chemical characteristics. Exemplarily, the plurality of atoms associated with the node may include: a plurality of atoms whose distance from the node is less than a distance threshold. Or, exemplarily, the plurality of atoms associated with the node may include: a fixed number of neighboring atoms (e.g., 8 nearest neighbor atoms) closest to the node. For example, the atoms may be sorted according to their distance from the node, and a fixed number (e.g., 8) of the nearest neighbors may be determined from the sorted atoms.

[0042] Specifically, the chemical potential distribution on a molecular surface can be determined based on the surface information of the molecule. Alternatively, the chemical potential distribution can also be referred to as the chemical function distribution, such as the electrostatic potential distribution.

[0043] For example, for any node on an analytical surface, the distances between that node and all atoms within a specific distance range can be determined. For instance, atoms within a distance threshold range can be termed neighboring atoms. Subsequently, the angle between each neighboring atom and the normal to the tangent plane of the surface containing the node, as well as the corresponding atom type, can be determined, serving as an initial representation of the node's chemical environment. For example, the chemical function distribution of a molecular surface can be extracted using a fully connected neural network. That is, a fully connected neural network can learn the representation of the chemical environment surrounding a surface node.

[0044] In this way, by mapping (also known as projecting) the chemical information of the internal atoms onto the nodes on the surface, the chemical information of the entire molecule can be characterized through the nodes on the molecular surface. Figure 5A A schematic diagram is shown of projecting the chemical information of atoms onto nodes on a molecular surface. As shown, for node 510, atoms within a specific distance range 520 can be identified. The chemical information of the identified atoms can then be projected onto node 510 to determine an initial representation of the chemical environment of node 510, such as the chemical environment characteristics of the node.

[0045] It should be noted that in the embodiments of this disclosure, the chemical information of atoms can be used to update the chemical representation of nodes on the molecular surface. However, the node information does not feed back or change the chemical information of atoms; that is, this projection belongs to a one-way information transmission relationship. This differs from the bidirectional updating of molecular graph neural networks. It is understood that although graph neural networks can achieve long-distance information exchange through graph information transmission, this exchange mechanism is inefficient when the number of nodes is large (e.g., the triangulation representation of a molecule's surface typically has tens of thousands of nodes). Conversely, the embodiments of this disclosure, through the one-way information transmission relationship from atomic information to nodes, can improve the processing efficiency of information exchange.

[0046] For example, a fully connected neural network can be used to determine the chemical characteristics of a molecular surface based on the chemical environment characteristics of each node in a multi-surface network. Alternatively, as an example, the chemical information of atoms can be represented as a multi-dimensional (e.g., 5-dimensional) array, and the surface chemical characteristics can be represented as a multi-dimensional (e.g., 16-dimensional) array.

[0047] Figure 5B A schematic diagram of the electrostatic potential energy function 530 of a molecular surface is shown. For example, this electrostatic potential energy function can be obtained by extraction based on, for example, the first dimension of a chemical feature in a 16-dimensional array. It is understood that, although... Figure 5B The electrostatic potential energy function is used as an example for illustration, but the embodiments disclosed herein are not limited to this. For example, users can customize other chemical information, or learn other chemical representations through neural networks or other means.

[0048] In this way, the distribution of chemical potential on the molecular surface can simultaneously contain both geometric and chemical information. For example, the distribution of chemical potential functions, such as the electrostatic potential function, on the molecular surface belongs to the surface Riemannian manifold space representation of the molecule; that is, chemical information can exist in the surface Riemannian manifold space of the molecule in the form of functions. In other words, in the embodiments of this disclosure, the surface of the molecule is regarded as a continuous and smooth Riemannian manifold space, and chemically related functions are defined in this two-dimensional manifold space.

[0049] In some exemplary embodiments of this disclosure, the geometric features may include one or more of the following: thermal kernel feature function, wave kernel feature function, Gaussian curvature of the molecular surface, or average curvature of the molecular surface.

[0050] For example, the eigenfunctions (or simply Laplace eigenfunctions) and eigenvalues ​​of the Laplace operator on the molecular surface (Riemannian manifold) can be determined, and the thermal core characteristic function and / or wave core characteristic function can be determined based on the eigenfunctions and eigenvalues.

[0051] For example, the eigenfunctions and eigenvalues ​​of the Laplace-Beltramioperator on the Riemannian manifold of each molecule surface can be determined as follows: (1)

[0052] Δφ i =λ i φ i (1)

[0053] In equation (1), Δ represents the Laplace operator, and its meaning is as follows in equation (2):

[0054]

[0055] In equation (1), Let λ represent the i-th eigenfunction. i Let represent the i-th eigenvalue. In equation (2), Let f denote the gradient operator, and let f denote any function distributed on the Riemannian manifold. Eigenfunctions can be determined using known algorithms (e.g., SciPy numerical computation software) or algorithms developed in the future, but this disclosure is not limited in this regard.

[0056] In some examples, the Laplace eigenfunctions and their corresponding eigenvalues ​​of each molecular surface manifold are unique and depend only on the shape of the molecule itself, unaffected by the molecule's position and orientation in three-dimensional space. Therefore, the eigenfunctions of Riemannian manifolds are also referred to as "shape DNA." For each molecule's surface manifold, all its eigenfunctions and eigenvalues ​​can be determined. Exemplarily, the eigenvalues ​​can be further sorted by magnitude, for example, in ascending order, and then the first k eigenvalues ​​(e.g., k = 100 or other values) can be selected, thus reducing computational complexity.

[0057] Understandably, different biomolecules have different shapes, and therefore different surface manifold eigenfunctions. Figure 6 The diagram illustrates the distribution of the first six eigenfunctions of a molecule on its surface according to some embodiments of the present disclosure. Exemplarily, the first six eigenfunctions are distributed on... Figure 6 The middle is shown as In some examples, the eigenfunctions are in Figure 6 The region exhibits regional fluctuations, and correspondingly, the eigenfunctions can be understood as Fourier basis functions in two-dimensional manifold space (for example, they can be understood as two-dimensional standing waves), which correspond to sine and cosine functions on a one-dimensional straight line.

[0058] In some exemplary embodiments of this disclosure, geometric features can be represented as geometric characteristic functions. The geometric characteristic functions of a molecular surface can be determined based on the eigenfunctions and eigenvalues ​​of the Laplacian operator on the molecular surface manifold. Optionally, the geometric characteristic functions may include heat kernel signature (HKS) and / or wave kernel signature (WKS).

[0059] For example, it can be based on the aforementioned determined eigenfunctions and eigenvalues ​​λ i The HKS and WKS are constructed as follows:

[0060]

[0061]

[0062] In equations (3) and (4), t and ∈ represent time and energy, respectively, which can be set by the user.

[0063] Optionally, the geometric characteristic functions of the molecular surface may also include the Gaussian curvature and / or mean curvature on the molecular surface (Riemannian manifold). It is understood that the Gaussian curvature and mean curvature can be calculated geometrically, which will not be elaborated upon here.

[0064] In some exemplary embodiments of this disclosure, a unified molecule characteristic can be determined by integrating geometric and chemical characteristics. For example, if the geometric characteristics are represented as geometric characteristic functions and the chemical characteristics are represented as chemical potential distributions, then a unified molecule surface characteristic can be determined based on the chemical potential distribution and the geometric characteristic functions of the molecule surface. This unified characteristic (e.g., represented as a surface characteristic function) represents an integration of chemical and geometric information.

[0065] For example, a fully connected neural network can be used to integrate the chemical and geometric features of each node to obtain a surface feature function for each node. For instance, assuming the chemical features are represented as a 16-dimensional array and the geometric features as a 32-dimensional array, a fully connected neural network can non-linearly transform the chemical and geometric features into a 64-dimensional surface feature function. It is understood that the dimension of the surface feature function is not limited to 64 dimensions; it can be user-defined, such as 128 dimensions or other dimensions, and this disclosure does not limit it.

[0066] For example, a fully connected neural network can be trained on a molecular dataset, specifically, the molecular dataset being related to the application scenario of the embodiments of this disclosure (e.g., a downstream prediction task).

[0067] In some exemplary embodiments of this disclosure, time-dependent evolutionary multi-scale features can be determined based on a unified feature model using a time-dependent evolutionary neural network model. For example, the time-dependent evolutionary multi-scale features represent the multi-scale features of the molecular surface.

[0068] For example, the time-dependent evolutionary neural network model includes an evolutionary operator that is at least based on a Laplace operator and / or on a surface potential term.

[0069] For example, time-dependent evolution operators can be applied to surface feature functions to obtain functions that characterize multi-scale features. For instance, a time-dependent evolution operator can be represented as... or in For Hamiltonian operators, such as Δ represents the Laplace operator, and V represents the surface potential term. For example, the surface potential term V can be a function distribution on a user-defined manifold.

[0070] In some embodiments, when the time-dependent evolution operator is represented as For the initial function u0, the function distribution at time t can be determined by the following equation (5):

[0071]

[0072] To simplify the example, we can assume V = 0, so equation (5) can be simplified to equation (6) as follows:

[0073] u t =e -iΔt u0 (6)

[0074] Equation (6) describes the change of an initial function u0 in the manifold space (i.e., the molecular surface) over time. By controlling different evolution times t, the new function distribution u after evolving over different times can be obtained. t It is understandable that the u obtained from equation (6) t It is a complex number, while the input u0 is a real number. In practice, u can be... t Modulo, thus obtaining the result with u t The corresponding real number.

[0075] Because different molecules have different geometric structures, their Riemannian manifold spaces are also unique, and the evolution of the function u0 on different manifolds is determined by that manifold space. Therefore, the evolved function can serve as a new representation of molecular information, and this representation contains both global and local information about the manifold.

[0076] In other embodiments, when the time-dependent evolution operator is represented as And when V = 0, for the initial function v0, the function distribution at time t can be determined by the following equation (7):

[0077] v t =e -Δt v0 (7)

[0078] Equation (7) can be understood as replacing the imaginary time-dependent evolution operator in equation (6) above with the real time-dependent evolution operator (removing i). It can be understood that equation (6) belongs to the quantum mechanical framework, while equation (7) belongs to the classical mechanical framework. In practical applications, both frameworks can be used to realize the Riemannian manifold representation of molecules.

[0079] In embodiments of this disclosure, the initial function u0 or v0 can be the aforementioned unified feature, i.e., the surface feature function of the molecule. In this way, embodiments of this disclosure can obtain time-dependent evolutionary multi-scale features based on time-dependent evolution operators, i.e., u t or v t .

[0080] For example, the time-dependent evolution operator e in equation (7) -Δt This can be called a heat operator, which describes the distribution of the initial heat distribution v0 in the manifold space after time t. t .

[0081] As an example, Figure 7 A schematic diagram showing the change in heat distribution on the molecular surface over time is shown. It can be understood that this change can be quantitatively described by a time-dependent evolution process as shown in Equation (7).

[0082] from Figure 7 As can be seen, the range of heat transfer increases with time t. Therefore, by controlling different evolution times t, multi-scale information transfer can be achieved in the Riemannian manifold space on the molecular surface (short time corresponds to small-scale information transfer, and long time corresponds to large-scale information transfer). Thus, time-dependent evolution-based neural networks can be used to learn the geometric and chemical information of molecules at different scales, thereby improving the ability to represent molecules.

[0083] In embodiments of this disclosure, the eigenfunctions and eigenvalues ​​of the Laplace operator are described above in conjunction with equation (1). Therefore, the time-dependent evolution operator can be based on the eigenfunctions and eigenvalues ​​of the Laplace operator on the Riemannian manifold. Based on this, equation (7) can be further expressed as equation (8) below:

[0084]

[0085] Similarly, equation (6) can be further expressed as equation (9) as follows:

[0086]

[0087] In this way, embodiments of the present disclosure enable time-dependent evolution in the eigenspace by using the eigenfunctions and eigenvalues ​​of the Riemannian manifold and its Laplace operator, which is more efficient than operations in the real space.

[0088] As mentioned above, the uniform features can be represented, for example, as 64-dimensional surface feature functions. That is, each node on the molecular surface can be represented by a 64-dimensional array to represent the uniform features of that node. Then, based on Equation (8) or Equation (9), time-dependent masking can be performed on the 64-dimensional functions respectively. It is understood that each function can have its unique evolution time; for example, t can be used as a parameter of the neural network used for time-dependent evolution or can be set by the user. After time-dependent evolution, multi-scale features on the molecular surface can be obtained, including a series of geometric and chemical features at various scales.

[0089] As described above Figures 3 to 7 It describes in more detail, such as Figure 2 The process of determining time-dependent evolutionary multi-scale features in

[200] . As an example, Figure 8 A schematic diagram illustrating the determination of time-dependent evolutionary multi-scale features according to an embodiment of the present disclosure is shown. (Refer to...) Figure 8For biomolecules, such as protein molecules 801, the molecular surface 810 can be extracted, and geometric features 814 can be obtained by determining the eigenfunctions and eigenvalues ​​812 of the Laplacian operator. Using the atomic structure 820 and molecular surface 810 obtained from protein molecule 801, chemical features 824 can be obtained by mapping chemical information to the surface. Furthermore, a unified feature can be obtained based on geometric features 814 and chemical features 824, for example, using a feature integration network. Additionally, time-dependent evolutionary multi-scale features 830 can be obtained based on a time-dependent evolutionary neural network. It is understandable that, although... Figure 8 The present invention takes protein molecule 801 as an example, but it is not limited to this. In fact, the present invention is not limited to the type or size of molecules.

[0090] Alternatively or additionally, the overall features of a molecule can be determined by average pooling or max pooling based on time-dependent evolutionary multi-scale features. This simplifies the representation of features.

[0091] In the embodiments of this disclosure, a Riemannian manifold-based molecular representation method, distinct from existing methods, is provided through time-dependent evolutionary multi-scale features. These time-dependent evolutionary multi-scale features include both geometric and chemical characteristics of the molecule, enhancing the ability to describe molecular features. Furthermore, it is understood that although the interactions between molecules in real systems (e.g., the human body) are dynamic processes, and molecular conformations constantly change, the molecular representation method of this disclosure can effectively represent different molecular conformations.

[0092] It is understood that the molecular representation methods in the embodiments of this disclosure can be applied to downstream biopharmaceutical applications. For example, they can be provided to machine learning models for molecular modeling. Because this disclosure provides more comprehensive features to machine learning models explicitly, it can improve the learning performance of machine learning models, enabling them to better understand the quantitative structure-activity relationship of molecules and enhance the generalization ability of machine learning.

[0093] As an example, the scheme of this disclosure can be used to determine the chirality of mirror-symmetric molecules. Exemplarily, the chirality of mirror-symmetric molecules can be determined based on the directional gradient of time-dependent multi-scale features on a Riemannian manifold.

[0094] It is understood that the representation of time-dependent evolutionary multi-scale features obtained in the embodiments of this disclosure only contains scalar features and does not have directional (i.e., vector) information. However, since the real molecular surface is a two-dimensional Riemannian manifold existing in three-dimensional space, its symmetry needs to be considered in the process of molecular drug development.

[0095] In some embodiments, mirror-symmetric molecules can be characterized by the directional gradients of time-dependent evolutionary multi-scale features on a Riemannian manifold. That is, the directional gradients of time-dependent evolutionary multi-scale features on a Riemannian manifold are used as features of mirror-symmetric molecules.

[0096] Specifically, for any function f, its gradient on the Riemannian manifold can be expressed as equation (10):

[0097]

[0098] In equation (10), v i and v j f(v) represents two different nodes on the molecular surface. i ) and f(v j These represent the function values ​​at these two different nodes, respectively. For gradient operators, It is the gradient of the function f on the manifold.

[0099] Based on equation (10), if A is defined i =v j -v i and D i =f(v j )-f(v i Then, the gradient of the function can be obtained through the following equation (11):

[0100]

[0101] For a pair of mirror-symmetric chiral molecules, their respective function gradient vectors can be obtained through equation (11). For example... Figure 9 A schematic diagram illustrating the spatial relationship between a pair of mirror-symmetric chiral molecules and a set of function gradients corresponding to the surface is shown. Based on this, it can be determined that...

[0102]

[0103] As can be seen, for a pair of mirror-symmetric molecules, the vector products of corresponding vectors have opposite directions (one points inwards and the other outwards). Therefore, embodiments of this disclosure can determine the chirality of mirror-symmetric molecules based on directional gradients. It is understood that distinguishing different chirities is crucial for biopharmaceuticals; for example, certain chiral drug molecules are active, but molecules with different chirality and mirror structures may be harmful to health, such as thalidomide. Therefore, embodiments of this disclosure distinguish chirality through directional gradients, facilitating the screening of active molecules in biopharmaceutical processes.

[0104] Additionally or optionally, information about directional gradients can be combined with the aforementioned time-dependent evolutionary multi-scale features to characterize the feature functions of the molecular surface. Furthermore, neural networks can learn molecular-related information of different chiralities, thereby improving the success rate of downstream pharmaceutical tasks.

[0105] As another example, the scheme of this disclosure can be used to determine the binding site of a protein molecule. Exemplarily, at least one of a plurality of surface nodes on the molecular surface can be determined based on time-dependent evolutionary multi-scale features, wherein at least one node indicates a binding site with a virus.

[0106] For example, a first region of the molecular surface (e.g., a portion or all of the molecular surface) can be obtained. For at least two nodes within this first region, analysis can be performed to determine whether each node can bind to a specific virus, thus achieving binary prediction. As an illustration, Figure 8 Figure 841 shows a schematic diagram of the binding site. For example, this molecule could be an antibody protein. Analysis of this binding site can accelerate the development of drugs to combat viruses.

[0107] As another example, the solutions of this disclosure can be used to determine the biological activity of molecules. Exemplarily, a target region on the molecular surface can be obtained; based on time-dependent evolution multi-scale features, the time-dependent evolution multi-scale features of the region corresponding to the target region on the molecular surface can be determined; based on the region's time-dependent evolution multi-scale features, at least one predetermined molecule associated with the target region can be determined from a variety of predetermined molecules.

[0108] For example, a second region on the molecular surface can be obtained as the target region. For a variety of predetermined molecules, the binding characteristics between molecules in this target region and the predetermined molecules can be determined. For instance, the predetermined molecule with the optimal binding characteristics can be located, and the biological activity of that molecule can be determined based on this located predetermined molecule. As an illustration, Figure 8 Figure 842 shows a schematic diagram of the determined biological activity, in which multiple predetermined molecules include: adenosine diphosphate (ADP), heme, nicotinamide adenine dinucleotide (NAD), and adenosine triphosphate (ATP).

[0109] It should be noted that although the above description of applications in biopharmaceuticals uses binding site and activity analysis as examples, the embodiments of this disclosure are not limited thereto. In fact, the Riemannian-based molecular representation method of this disclosure can be used in a variety of applications based on artificial intelligence technology, which will not be listed here.

[0110] It should be understood that in the embodiments of this disclosure, "first," "second," "third," etc., are only used to indicate that multiple objects may be different, but at the same time, it does not exclude that two objects are the same, and should not be interpreted as any limitation on the embodiments of this disclosure.

[0111] It should also be understood that the manner, situation, category, and division of embodiments in the present disclosure are for the convenience of description only and should not constitute a special limitation. Various manners, categories, situations, and features in the embodiments can be combined with each other where logically consistent.

[0112] It should also be understood that the foregoing is merely to help those skilled in the art better understand the embodiments of this disclosure, and is not intended to limit the scope of the embodiments of this disclosure. Those skilled in the art can make various modifications, variations, or combinations based on the foregoing. Such modifications, variations, or combinations are also within the scope of the embodiments of this disclosure.

[0113] It should also be understood that the above description focuses on highlighting the differences between the various embodiments. Similarities or commonalities can be referenced or learned from each other, and for the sake of brevity, they will not be repeated here.

[0114] Figure 10 A schematic block diagram of an example apparatus 1000 according to some embodiments of the present disclosure is shown. Apparatus 1000 may be implemented by software, hardware, or a combination of both. Figure 10 As shown, the device 1000 includes a molecular surface determination module 1010, a geometric feature determination module 1020, a chemical feature determination module 1030, a unified feature determination module 1040, and a multi-scale feature determination module 1050.

[0115] The molecular surface determination module 1010 is configured to determine the molecular surface of a molecule, wherein the molecular surface is a continuous Riemannian manifold and includes multiple discrete surface nodes. The geometric feature determination module 1020 is configured to determine the geometric features of the molecule based on its molecular surface. The chemical feature determination module 1030 is configured to determine the chemical features of the molecule by mapping atomic information within the molecule to multiple surface nodes. The unified feature determination module 1040 is configured to determine the unified features of the molecule by integrating the geometric and chemical features. The multi-scale feature determination module 1050 is configured to determine the time-dependent evolutionary multi-scale features of the molecule based on the unified features using a time-dependent evolutionary neural network model.

[0116] In some embodiments, the molecular surface determination module 1010 can be configured to determine the molecular surface based on the isosurface of the electron density field of the molecule.

[0117] In some embodiments, the geometric features include thermal kernel feature functions and / or wave kernel feature functions, and the geometric feature determination module 1020 includes: an eigenfunction and eigenvalue determination submodule configured to determine the eigenfunctions and eigenvalues ​​of the Laplacian operator of the molecular surface; a thermal kernel feature function determination submodule configured to determine thermal kernel feature functions based on the eigenfunctions and eigenvalues; and / or a wave kernel feature function determination submodule configured to determine wave kernel feature functions based on the eigenfunctions and eigenvalues.

[0118] Optionally, the geometric feature determination module 1020 can be configured to determine the Gaussian curvature and / or average curvature of the molecular surface, and the geometric features include Gaussian curvature and / or average curvature.

[0119] In some embodiments, the chemical feature determination module 1030 is configured to: for each of the plurality of surface nodes, obtain the chemical environment features of the node by mapping the atomic information of the plurality of atoms associated with the node to the node; and determine the chemical features using a fully connected neural network based on the chemical environment features of each of the plurality of surface nodes.

[0120] Optionally, the multiple atoms associated with a node include multiple atoms within a range where the distance between them and the node is less than a distance threshold.

[0121] For example, the time-dependent evolutionary neural network model includes an evolutionary operator, which is determined based on at least one of the following: eigenfunctions of a Laplace operator on a Riemannian manifold, or a surface potential term. Optionally, the surface potential term is a user-defined function distribution on the Riemannian manifold.

[0122] In some examples, the molecules are mirror-symmetric molecules, and the device 1000 may also include a chirality determination module configured to determine the chirality of the mirror-symmetric molecules based on the directional gradient of time-dependent multi-scale features on the Riemannian manifold.

[0123] In some examples, the molecule includes a protein molecule, and the device 1000 may also include a site determination module configured to determine at least one of a plurality of surface nodes on the molecular surface based on time-dependent evolutionary multiscale features, wherein the at least one node indicates a site for binding with a virus.

[0124] In some examples, the device 1000 may also include an activity determination module configured to: acquire a target region on the molecular surface; determine the time-dependent evolution multi-scale features of the region corresponding to the target region on the molecular surface based on the time-dependent evolution multi-scale features; and determine at least one predetermined molecule associated with the target region from a variety of predetermined molecules based on the time-dependent evolution multi-scale features of the region.

[0125] In some examples, the device 1000 may also include an overall feature determination module configured to determine the overall features of the molecule by average pooling based on time-dependent evolutionary multi-scale features.

[0126] Figure 10 The device 1000 can be used to achieve the above-mentioned combination. Figures 2 to 9 For the sake of brevity, the process described will not be repeated here.

[0127] The division of modules or units in the embodiments of this disclosure is illustrative and only represents one logical functional division. In actual implementation, there may be other division methods. Furthermore, the functional units in the disclosed embodiments may be integrated into one unit, exist as separate physical entities, or two or more units may be integrated into one unit. The integrated unit described above can be implemented in hardware or as a software functional unit.

[0128] Figure 11 A block diagram of an example device 1100 that can be used to implement embodiments of the present disclosure is shown. It should be understood that... Figure 11 The device 1100 shown is merely exemplary and should not be construed as limiting the functionality and scope of the implementation described herein. For example, device 1100 can be used to perform the functions described above. Figures 2 to 9 The process described herein. For example, device 1100 can be implemented as a classical computer and / or a quantum computer.

[0129] like Figure 11 As shown, device 1100 is in the form of a general-purpose computing device. Components of computing device 1100 may include, but are not limited to, one or more processors or processing units 1110, memory 1120, storage device 1130, one or more communication units 1140, one or more input devices 1150, and one or more output devices 1160. Processing unit 1110 may be a physical or virtual processor and is capable of performing various processes according to programs stored in memory 1120. In a multiprocessor system, multiple processing units execute computer-executable instructions in parallel to improve the parallel processing capability of computing device 1100.

[0130] Computing device 1100 typically includes multiple computer storage media. Such media can be any available media accessible to computing device 1100, including but not limited to volatile and non-volatile media, removable and non-removable media. Memory 1120 can be volatile memory (e.g., registers, cache, random access memory (RAM)), non-volatile memory (e.g., read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory), or some combination thereof). Storage device 1130 can be removable or non-removable media and may include machine-readable media, such as flash drives, disks, or any other media capable of storing information and / or data (e.g., training data for training) and accessible within computing device 1100.

[0131] The computing device 1100 may further include additional removable / non-removable, volatile / non-volatile storage media. Although not explicitly stated... Figure 11 As shown, disk drives for reading from or writing to removable, non-volatile disks (e.g., "floppy disks") and optical disk drives for reading from or writing to removable, non-volatile optical disks can be provided. In these cases, each drive can be connected to a bus (not shown) via one or more data media interfaces. Memory 1120 may include computer program product 1125 having one or more program modules configured to perform various methods or actions of various implementations of this disclosure.

[0132] The communication unit 1140 enables communication with other computing devices via a communication medium. Additionally, the components of the computing device 1100 can function as a single computing cluster or multiple computing machines capable of communicating via communication connections. Therefore, the computing device 1100 can operate in a networked environment using logical connections to one or more other servers, network personal computers (PCs), or another network node.

[0133] Input device 1150 can be one or more input devices, such as a mouse, keyboard, trackball, etc. Output device 1160 can be one or more output devices, such as a monitor, speaker, printer, etc. Computing device 1100 can also communicate as needed with one or more external devices (not shown) via communication unit 1140. These external devices include storage devices, display devices, etc., and can communicate with one or more devices that enable user interaction with computing device 1100, or with any device (e.g., network card, modem, etc.) that enables computing device 1100 to communicate with one or more other computing devices. Such communication can be performed via an input / output (I / O) interface (not shown).

[0134] According to an exemplary implementation of this disclosure, a computer-readable storage medium is provided that stores computer-executable instructions thereon, wherein the computer-executable instructions are executed by a processor to implement the methods described above. According to an exemplary implementation of this disclosure, a computer program product is also provided, which is tangibly stored on a non-transitory computer-readable medium and includes computer-executable instructions, which are executed by a processor to implement the methods described above. According to an exemplary implementation of this disclosure, a computer program product is provided that stores a computer program thereon, which, when executed by a processor, implements the methods described above.

[0135] Various aspects of this disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatuses, devices, and computer program products implemented according to this disclosure. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0136] These computer-readable program instructions can be provided to a processing unit of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processing unit of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner. Thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0137] Computer-readable program instructions can be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions that execute on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0138] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction, which contains one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0139] Various implementations of this disclosure have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed implementations. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described implementations. The terminology used herein is chosen to best explain the principles, practical applications, or improvements to technology in the market, or to enable others skilled in the art to understand the various implementations disclosed herein.

Claims

1. A method of representing a molecule, comprising: determining a molecular surface of the molecule, the molecular surface being a continuous Riemannian manifold and the molecular surface comprising a discrete plurality of surface nodes; determining geometric features of the molecule based on the molecular surface; determining chemical features of the molecule by mapping atomic information of atoms inside the molecule to the plurality of surface nodes; determining unified features of the molecule by integrating the geometric features and the chemical features; and determining time-evolution multiscale features of the molecule based on the unified features by using a time-evolution neural network model, wherein the geometric features comprise heat kernel feature functions and / or wave kernel feature functions, and wherein determining geometric features comprises: determining eigenfunctions and eigenvalues of a Laplace operator of the molecular surface; determining the heat kernel feature functions based on the eigenfunctions and the eigenvalues; and / or determining the wave kernel feature functions based on the eigenfunctions and the eigenvalues; and wherein determining chemical features comprises: for each node of the plurality of surface nodes, obtaining a chemical environment feature of the node by mapping atomic information of a plurality of atoms associated with the node to the node; and determining the chemical features using a fully connected neural network based on the chemical environment feature of each node of the plurality of surface nodes.

2. The method of claim 1, wherein determining a molecular surface comprises: determining the molecular surface based on an isosurface of an electron density field of the molecule; or determining the molecular surface based on a sampling of a solvent-accessible surface or a solvent-inaccessible surface of the molecule.

3. The method of claim 1, wherein determining geometric features comprises: determining Gaussian curvatures and / or mean curvatures of the molecular surface, and the geometric features comprise the Gaussian curvatures and / or the mean curvatures.

4. The method of claim 1, wherein the plurality of atoms associated with the node comprises: a plurality of atoms within a range having a distance lower than a distance threshold from the node; or a fixed number of nearest neighbor atoms of the node.

5. The method of claim 1, wherein the time-evolution neural network model comprises an evolution operator, the evolution operator being determined based on at least one of: an eigenfunction of a Laplace operator on the Riemannian manifold, or a surface potential term.

6. The method of claim 5, wherein the surface potential term is a user-specified function distribution on the Riemannian manifold.

7. The method of any one of claims 1-6, the molecule being a mirror-symmetric molecule, the method further comprising: determining a chirality of the mirror-symmetric molecule based on a directional gradient of the time-evolution multiscale features on the Riemannian manifold.

8. The method of any one of claims 1-6, the molecule comprising a protein molecule, the method further comprising: determining at least one node of the plurality of surface nodes of the molecular surface based on the time-evolution multiscale features, the at least one node indicating a binding site to a virus.

9. The method of any one of claims 1-6, further comprising: ​ ​ acquire a target region of the molecular surface; determine a region time-evolution multiscale feature corresponding to the target region of the molecular surface based on the time-evolution multiscale feature; determine at least one predetermined molecule having a correlation with the target region from a plurality of predetermined molecules based on the region time-evolution multiscale feature.

10. The method of any one of claims 1-6, further comprising: determining an overall feature of the molecule by average pooling or max pooling based on the time-evolution multiscale feature.

11. An electronic device, comprising: at least one processing unit; at least one memory coupled to the at least one processing unit and storing instructions for execution by the at least one processing unit, which when executed by the at least one processing unit, cause the electronic device to perform acts comprising: determining a molecular surface of a molecule, the molecular surface being a continuous Riemannian manifold and the molecular surface comprising a discrete plurality of surface nodes; determining a geometric feature of the molecule based on the molecular surface; determining a chemical feature of the molecule by mapping atomic information inside the molecule to the plurality of surface nodes; determining a unified feature of the molecule by integrating the geometric feature and the chemical feature; and determining a time-evolution multiscale feature of the molecule based on the unified feature by using a time-evolution neural network model, wherein the geometric feature comprises a thermal kernel feature function and / or a wave kernel feature function, and wherein determining a geometric feature comprises: determining eigenfunctions and eigenvalues of a Laplacian operator of the molecular surface; determining the thermal kernel feature function based on the eigenfunctions and the eigenvalues; and / or determining the wave kernel feature function based on the eigenfunctions and the eigenvalues; and wherein determining a chemical feature comprises: for each node of the plurality of surface nodes, obtaining a chemical environment feature of the node by mapping atomic information of a plurality of atoms associated with the node to the node; determining the chemical feature using a fully connected neural network based on the chemical environment feature of each node of the plurality of surface nodes.

12. A processing apparatus, comprising: a molecular surface determination module configured to determine a molecular surface of a molecule, the molecular surface being a continuous Riemannian manifold and the molecular surface comprising a discrete plurality of surface nodes; a geometric feature determination module configured to determine a geometric feature of the molecule based on the molecular surface; a chemical feature determination module configured to determine a chemical feature of the molecule by mapping atomic information inside the molecule to the plurality of surface nodes; a unified feature determination module configured to determine a unified feature of the molecule by integrating the geometric feature and the chemical feature; and a multiscale feature determination module configured to determine a time-evolution multiscale feature of the molecule based on the unified feature by using a time-evolution neural network model, wherein the geometric feature determination module is configured to: determine eigenfunctions and eigenvalues of a Laplacian operator of the molecular surface; ​ determine a thermal kernel feature function based on the eigenfunction and the eigenvalue; and / or determine a wave kernel feature function based on the eigenfunction and the eigenvalue; and wherein the chemical feature determining module is configured to: for each node in the plurality of surface nodes, obtain a chemical environment feature of the node by mapping atomic information of atoms associated with the node to the node; determine the chemical feature based on the chemical environment feature of each node in the plurality of surface nodes using a fully connected neural network. 13.A computer readable storage medium having stored thereon a computer program, the program being executed by a processor to implement the method according to any one of claims 1 to 10.

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