Molecular Graph Generation Research Articles

Learning Joint 2-D and 3-D Graph Diffusion Models for Complete Molecule Generation.

Designing new molecules is essential for drug discovery and material science. Recently, deep generative models that aim to model molecule distribution have made promising progress in narrowing down the chemical research space and generating high-fidelity molecules. However, current generative models only focus on modeling 2-D bonding graphs or 3-D geometries, which are two complementary descriptors for molecules. The lack of ability to jointly model them limits the improvement of generation quality and further downstream applications. In this article, we propose a joint 2-D and 3-D graph diffusion model (JODO) that generates geometric graphs representing complete molecules with atom types, formal charges, bond information, and 3-D coordinates. To capture the correlation between 2-D molecular graphs and 3-D geometries in the diffusion process, we develop a diffusion graph transformer (DGT) to parameterize the data prediction model that recovers the original data from noisy data. The DGT uses a relational attention mechanism that enhances the interaction between node and edge representations. This mechanism operates concurrently with the propagation and update of scalar attributes and geometric vectors. Our model can also be extended for inverse molecular design targeting single or multiple quantum properties. In our comprehensive evaluation pipeline for unconditional joint generation, the experimental results show that JODO remarkably outperforms the baselines on the QM9 and GEOM-Drugs datasets. Furthermore, our model excels in few-step fast sampling, as well as in inverse molecule design and molecular graph generation. Our code is provided in https://github.com/GRAPH-0/JODO.

AMCG: a graph dual atomic-molecular conditional molecular generator

Drug design is both a time consuming and expensive endeavour. Computational strategies offer viable options to address this task; deep learning approaches in particular are indeed gaining traction for their capability of dealing with chemical structures. A straightforward way to represent such structures is via their molecular graph, which in turn can be naturally processed by graph neural networks. This paper introduces AMCG, a dual atomic-molecular, conditional, latent-space, generative model built around graph processing layers able to support both unconditional and conditional molecular graph generation. Among other features, AMCG is a one-shot model allowing for fast sampling, explicit atomic type histogram assignation and property optimization via gradient ascent. The model was trained on the Quantum Machines 9 (QM9) and ZINC datasets, achieving state-of-the-art performances. Together with classic benchmarks, AMCG was also tested by generating large-scale sampled sets, showing robustness in terms of sustainable throughput of valid, novel and unique molecules.

Goal-directed molecule generation with fine-tuning by policy gradient

Graph-structured drug molecule representations often struggle to generate molecules by particular intentions, which results in generated molecules without pharmacological properties. To address the problem, we propose a de novo molecular generation method that utilizes the policy gradient algorithm of reinforcement learning to fine-tune the molecular graph generation model. The training process of the method is divided into the pre-training stage and the fine-tuning stage. During the pre-training stage, it uses graph neural networks and multilayer perceptrons to train a molecule graph generation model. During the fine-tuning stage, scoring functions are devised for multiple goal-directed generation tasks, and subsequently, the policy loss function is formulated based on the reward shaping mechanism. A value network is designed to calculate the value of taking an action based on the current graph state during agent sampling to guide policy updates. To mitigate the issue of molecular uniqueness decline during the learning process, we dynamically adjust the weights of the two learning processes in the policy loss function, aiming to generate desirable molecules with high probability and reduce the descent of uniqueness. The experiments showed that after fine-tuning, the generative model exhibits a higher probability of generating molecules with desired properties compared to other models. Furthermore, our method effectively mitigates the issue of molecular uniqueness declining during the learning process when compared to alternative fine-tuning methods.

STAGAN: An approach for improve the stability of molecular graph generation based on generative adversarial networks

With the wide application of deep learning in Drug Discovery, deep generative model has shown its advantages in drug molecular generation. Generative adversarial networks can be used to learn the internal structure of molecules, but the training process may be unstable, such as gradient disappearance and model collapse, which may lead to the generation of molecules that do not conform to chemical rules or a single style. In this paper, a novel method called STAGAN was proposed to solve the difficulty of model training, by adding a new gradient penalty term in the discriminator and designing a parallel layer of batch normalization used in generator. As an illustration of method, STAGAN generated higher valid and unique molecules than previous models in training datasets from QM9 and ZINC-250K. This indicates that the proposed method can effectively solve the instability problem in the model training process, and can provide more instructive guidance for the further study of molecular graph generation.

Conditional Diffusion Based on Discrete Graph Structures for Molecular Graph Generation

Learning the underlying distribution of molecular graphs and generating high-fidelity samples is a fundamental research problem in drug discovery and material science. However, accurately modeling distribution and rapidly generating novel molecular graphs remain crucial and challenging goals. To accomplish these goals, we propose a novel Conditional Diffusion model based on discrete Graph Structures (CDGS) for molecular graph generation. Specifically, we construct a forward graph diffusion process on both graph structures and inherent features through stochastic differential equations (SDE) and derive discrete graph structures as the condition for reverse generative processes. We present a specialized hybrid graph noise prediction model that extracts the global context and the local node-edge dependency from intermediate graph states. We further utilize ordinary differential equation (ODE) solvers for efficient graph sampling, based on the semi-linear structure of the probability flow ODE. We also combine the solvers with gradient guidance from the molecule property predictor for similarity-constrained molecule optimization. Experiments on diverse datasets validate the effectiveness of our framework. Particularly, the proposed method still generates high-quality molecular graphs in a limited number of steps.

Molecular Graph Generation by Decomposition and Reassembling.

Designing molecular structures with desired chemical properties is an essential task in drug discovery and materials design. However, finding molecules with the optimized desired properties is still a challenging task due to combinatorial explosion of the candidate space of molecules. Here we propose a novel decomposition-and-reassembling-based approach, which does not include any optimization in hidden space, and our generation process is highly interpretable. Our method is a two-step procedure: In the first decomposition step, we apply frequent subgraph mining to a molecular database to collect a smaller size of subgraphs as building blocks of molecules. In the second reassembling step, we search desirable building blocks guided via reinforcement learning and combine them to generate new molecules. Our experiments show that our method not only can find better molecules in terms of two standard criteria, the penalized log P and druglikeness, but also can generate drug molecules showing the valid intermediate molecules.

Deep multi-agent fusion Q-Network for graph generation

Deep Generative models for graph generation have made important advances in medicine, and particularly in drug research. Using graph representations of the molecules, these models proved efficient for predicting new molecular drug candidates with chemically valid structures. The main objective of the molecular graph generation task is to provide new molecular structures with the required chemical properties. Using a Reinforcement Learning (RL) agent to conduct the generation process while defining the reward function as the target chemical property, enables to generate new molecular drug candidates. However, sampling molecular candidates from the huge chemical space can be challenging, if only one single RL agent is deployed. Thus, we propose the Deep Fusion Q-Network (DFQN), a multi-agent RL-based Deep Neural Network for graph generation. We disclose that DFQN allows a better exploration of the environment, since multiple RL agents are exploited to generate candidate graph structures. Using a heterogeneous graph representation and an attention based fusion network, DFQN promotes coordination and communication between agents to jointly generate new graph structures with the required target properties. We investigate the optimal number of RL-agents using different degrees of communication in order to generate new graph structures under different property constraints. Moreover, we propose to conduct an adversarial training to incorporate prior knowledge of realistic drug molecules in the newly generated molecular graphs. We propose a new approach to check the chemical validity of the designed molecules in each iteration of the generation process. We evaluate the performance of our model for generating new molecules with different chemical properties and achieve remarkable results compared to state-of-the-art models for molecular graph generation.

An equivariant generative framework for molecular graph-structure Co-design.

Designing molecules with desirable physiochemical properties and functionalities is a long-standing challenge in chemistry, material science, and drug discovery. Recently, machine learning-based generative models have emerged as promising approaches for de novo molecule design. However, further refinement of methodology is highly desired as most existing methods lack unified modeling of 2D topology and 3D geometry information and fail to effectively learn the structure-property relationship for molecule design. Here we present MolCode, a roto-translation equivariant generative framework for molecular graph-structure Co-design. In MolCode, 3D geometric information empowers the molecular 2D graph generation, which in turn helps guide the prediction of molecular 3D structure. Extensive experimental results show that MolCode outperforms previous methods on a series of challenging tasks including de novo molecule design, targeted molecule discovery, and structure-based drug design. Particularly, MolCode not only consistently generates valid (99.95% validity) and diverse (98.75% uniqueness) molecular graphs/structures with desirable properties, but also generates drug-like molecules with high affinity to target proteins (61.8% high affinity ratio), which demonstrates MolCode's potential applications in material design and drug discovery. Our extensive investigation reveals that the 2D topology and 3D geometry contain intrinsically complementary information in molecule design, and provide new insights into machine learning-based molecule representation and generation.

Powerful molecule generation with simple ConvNet.

Automated molecule generation is a crucial step in in-silico drug discovery. Graph-based generation algorithms have seen significant progress over recent years. However, they are often complex to implement, hard to train and can under-perform when generating long-sequence molecules. The development of a simple and powerful alternative can help improve practicality of automated drug discovery method. We proposed a ConvNet-based sequential graph generation algorithm. The molecular graph generation problem is reformulated as a sequence of simple classification tasks. At each step, a convolutional neural network operates on a sub-graph that is generated at previous step, and predicts/classifies an atom/bond adding action to populate the input sub-graph. The proposed model is pretrained by learning to sequentially reconstruct existing molecules. The pretrained model is abbreviated as SEEM (structural encoder for engineering molecules). It is then fine-tuned with reinforcement learning to generate molecules with improved properties. The fine-tuned model is named SEED (structural encoder for engineering drug-like-molecules). The proposed models have demonstrated competitive performance comparing to 16 state-of-the-art baselines on three benchmark datasets. Code is available at https://github.com/yuh8/SEEM and https://github.com/yuh8/SEED. QM9 dataset is availble at http://quantum-machine.org/datasets/, ZINC250k dataset is availble at https://raw.githubusercontent.com/aspuru-guzik-group/chemical_vae/master/models/zinc_properties/250k_rndm_zinc_drugs_clean_3.csv, and ChEMBL dataset is availble at https://www.ebi.ac.uk/chembl/. Supplementary data are available at Bioinformatics online.

Exploring Graph Traversal Algorithms in Graph-Based Molecular Generation.

Here, we explore the impact of different graph traversal algorithms on molecular graph generation. We do this by training a graph-based deep molecular generative model to build structures using a node order determined via either a breadth- or depth-first search algorithm. What we observe is that using a breadth-first traversal leads to better coverage of training data features compared to a depth-first traversal. We have quantified these differences using a variety of metrics on a data set of natural products. These metrics include percent validity, molecular coverage, and molecular shape. We also observe that by using either a breadth- or depth-first traversal it is possible to overtrain the generative models, at which point the results with either graph traversal algorithm are identical.

Compressed graph representation for scalable molecular graph generation

Recently, deep learning has been successfully applied to molecular graph generation. Nevertheless, mitigating the computational complexity, which increases with the number of nodes in a graph, has been a major challenge. This has hindered the application of deep learning-based molecular graph generation to large molecules with many heavy atoms. In this study, we present a molecular graph compression method to alleviate the complexity while maintaining the capability of generating chemically valid and diverse molecular graphs. We designate six small substructural patterns that are prevalent between two atoms in real-world molecules. These relevant substructures in a molecular graph are then converted to edges by regarding them as additional edge features along with the bond types. This reduces the number of nodes significantly without any information loss. Consequently, a generative model can be constructed in a more efficient and scalable manner with large molecules on a compressed graph representation. We demonstrate the effectiveness of the proposed method for molecules with up to 88 heavy atoms using the GuacaMol benchmark.

Constraints for generating graphs with imposed and forbidden patterns: an application to molecular graphs

Although graphs are widely used to encode and solve various computational problems, little research exists on constrained graph construction. The current research was carried out to shed light on the problem of generating graphs, where the construction process is guided by various structural restrictions, like vertex degrees, proximity among vertices, and imposed and forbidden patterns. The main contribution of this paper is an encoding of the constrained graph generation problem in terms of a constraint satisfaction problem (CSP). This approach is motivated by the flurry of efficient solution algorithms available within the constraint programming (CP) framework. The obtained encoding has given rise to the CP-MolGen program, a new open source program dedicated to the generation of molecular graphs with imposed and forbidden fragments. Experimental results on several real-world molecular graph generation instances have shown the effectiveness and efficiency of the proposed program, especially the benefits of forbidding cyclic patterns as induced subgraphs.

Efficient learning of non-autoregressive graph variational autoencoders for molecular graph generation

With the advancements in deep learning, deep generative models combined with graph neural networks have been successfully employed for data-driven molecular graph generation. Early methods based on the non-autoregressive approach have been effective in generating molecular graphs quickly and efficiently but have suffered from low performance. In this paper, we present an improved learning method involving a graph variational autoencoder for efficient molecular graph generation in a non-autoregressive manner. We introduce three additional learning objectives and incorporate them into the training of the model: approximate graph matching, reinforcement learning, and auxiliary property prediction. We demonstrate the effectiveness of the proposed method by evaluating it for molecular graph generation tasks using QM9 and ZINC datasets. The model generates molecular graphs with high chemical validity and diversity compared with existing non-autoregressive methods. It can also conditionally generate molecular graphs satisfying various target conditions.

Influence of Network Chain Structure on Mechanics of Glassy Polymer Networks

We study the higher‐order cycle structures and topological structure‐property relations of thermosets using coarse‐grained molecular simulations, graph optimization, and graph generation concepts. The topological properties of networks are controlled using a modified Watts‐Strogatz graph‐generation model, which allows the corresponding physical properties to be studied with simulations. The degree of disorder in the polymer network is systematically varied to assess the differences in uniaxial stress response, and in the nature of bond scission of fully cured glassy networks. We show that the architecture of the network strongly affects the onset of bond breaking and ultimate stress, but leaves the modulus and yield point unchanged.

ChemInform Abstract: Generation of Molecular Graphs for QSAR Studies: An Approach Based on Supergraphs.

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

Generation of Molecular Graphs for QSAR Studies: An Approach Based on Supergraphs

A new algorithm for generation of substituted derivatives of a given structure and its software implementation are described. The program has deterministic and stochastic generation modes and efficiently supports various types of structural constraints. The problem of exhaustive and irredundant generation is discussed, and a new algorithm of the complete rejection of isomorphic molecular graphs is proposed. The main application of the generator is QSAR studies; however, applications in combinatorial chemistry are also possible.

Application of the electronegativity indices of organic molecules to tasks of chemical informatics

An efficient structure filtration method for the operation with chemical databases containing information on the structures and properties of organic molecules was proposed. The technique involves the use of electronegativity indices for generation of identification keys and for isomorphism tests of the molecular graphs corresponding to the structural formulas. The test set for the method proposed included a total of 95,000,000 molecules containing up to sixty carbon atoms. Tests revealed a high discriminating capability of the electronegativity indices and high efficiency of the method for solving both general problems (recognition of chemical structures, chemical database management systems) and specific tasks (generation of molecular graphs, etc.) in chemical informatics.

From Wiener Index to Molecules

In this paper we present an algorithm for the generation of molecular graphs with a given value of the Wiener index. The high number of graphs for a given value of the Wiener index is reduced thanks to the application of a set of heuristics taking into account the structural characteristics of the molecules. The selection of parameters as the interval of values for the Wiener index, the diversity and occurrence of atoms and bonds, the size and number of cycles, and the presence of structural patterns guide the processing of the heuristics generating molecular graphs with a considerable saving in computational cost. The modularity in the design of the algorithm allows it to be used as a pattern for the development of other algorithms based on different topological invariants, which allow for its use in areas of interest, say as involving combinatorial databases and screening in chemical databases.

Generation of molecular graphs based on flexible utilization of the available structural information

Classical theory of chemical structure has remained the basis for a comprehensive understanding of organic chemistry. Graph theory provides an extremely useful mathematical language for the description of both chemical structure and its properties. In many practical computer applications such as structure elucidation, synthesis planning and molecular design the generation of sets of candidate-structures (molecular graphs) is required. It is essential, that the generation process is constrained by the input structural information derived from any spectral, physical, chemical, etc., data. On the other hand, in most of the cases this information is incomplete, overlapping and ambiguous, which calls for approaches reflecting these features. Several problems, such as the isomorphism problem, and the combinatorial explosion complicate additionally the generation process. They should find their solutions under these constraints. Hence, the application of any general method for graph generation does not produce satisfactory results. All this calls for the development of specific graphgeneration schemes flexibly constrained by the input structural information. Some procedures treating special classes colored graphs (describing the real chemical structure), and employing sets of subgraphs (molecular fragments), etc., are introduced within the generation scheme. Furthermore, the generation method must reflect the fuzzy character of the information usually available to the chemist and to provide a straightforward pathway to the correct solution in the process of automated reasoning. In the present paper a wide variety of problems emerging from the generation of molecular graphs in the case of computer-aided structure elucidation are addressed and their possible solutions discussed.

MOLMAKER: de novo generation of 3D databases for use in drug design.

A program, MOLMAKER, is described which, in conjunction with a 2D-3D conversion program and 3D database software, can generate de novo 3D databases to aid in drug design. MOLMAKER is based upon graph-theoretical techniques for vertex degree set generation and constructive enumeration of molecular graphs. The generated molecular graphs are then functionalised in a probabilistic manner but in accordance with various constraints specified by the user. The resulting connection tables can be converted into 3D structures by commercial software and loaded into a 3D database for pharmacophore searching. The utility of MOLMAKER is illustrated by two examples of interest from the recent scientific literature: the design of novel protein kinase C agonists and of a bridging ligand for cyclophilin-calcineurin.