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MARS: Markov Molecular Sampling for Multi-objective Drug Discovery
Yutong Xie, Chence Shi, Hao Zhou, Yuwei Yang, Weinan Zhang, Yong Yu, Lei Li
TL;DR
Drug discovery needs novel and diverse molecules that satisfy several chemical properties, but searching the enormous molecular space and jointly optimizing objectives remain challenging. MARS iteratively edits molecular fragments using annealed MCMC with an adaptive GNN proposal trained from self-generated samples, achieving state-of-the-art performance across multi-objective tasks, including a 77% improvement in the hardest four-objective setting.
Problem
Drug discovery requires finding novel and diverse molecules that jointly satisfy multiple properties in an enormous chemical space.
Method
MARS iteratively edits molecular-graph fragments and uses annealed MCMC with an adaptive GNN proposal trained on self-generated sample paths.
Results
MARS achieves state-of-the-art performance on five of six tasks and improves the comprehensive evaluation by 77% in the four-objective setting.
Takeaways & Limitations
MARS can discover novel and diverse bioactive molecules that are both drug-like and highly synthesizable.
Takeaways & Limitations
MARS uses an annealed adaptive MCMC process whose convergence depends on diminishing proposal adaptation, achieved through an optimizer with a learning rate that eventually shrinks to zero.
Abstract
from arXiv · showhide
Searching for novel molecules with desired chemical properties is crucial in drug discovery. Existing work focuses on developing neural models to generate either molecular sequences or chemical graphs. However, it remains a big challenge to find novel and diverse compounds satisfying several properties. In this paper, we propose MARS, a method for multi-objective drug molecule discovery. MARS is based on the idea of generating the chemical candidates by iteratively editing fragments of molecular graphs. To search for high-quality candidates, it employs Markov chain Monte Carlo sampling (MCMC) on molecules with an annealing scheme and an adaptive proposal. To further improve sample efficiency, MARS uses a graph neural network (GNN) to represent and select candidate edits, where the GNN is trained on-the-fly with samples from MCMC. Experiments show that MARS achieves state-of-the-art performance in various multi-objective settings where molecular bio-activity, drug-likeness, and synthesizability are considered. Remarkably, in the most challenging setting where all four objectives are simultaneously optimized, our approach outperforms previous methods significantly in comprehensive evaluations. The code is available at https://github.com/yutxie/mars.
1 INTRODUCTION
Multi-objective drug discovery must search an enormous chemical space for molecules that jointly satisfy properties such as activity, drug-likeness, novelty, diversity, and synthesizability. MARS addresses this challenge through adaptive Markov sampling and achieves strong multi-objective results.
- Motivation: The realistic space of synthesizable drug-like chemicals is approximately 10^33, making exhaustive enumeration impractical.Disease-specific targeting further complicates the search for suitable candidates.
- Problem: Prior deep generative methods largely optimize single properties, whereas practical drug discovery requires jointly considering multiple properties.Examples include biological activity, drug-likeness, and synthesizability.
- Method: MARS starts from a seed molecule and iteratively edits molecular-graph fragments while optimizing a total objective composed of multiple property scores.Its sampling framework is designed to satisfy high multi-property scores while producing novel and diverse molecules without external annotated data.
- Method: MARS uses annealed Markov chain Monte Carlo to explore molecules with novel fragments and an adaptive GNN proposal trained on self-generated sample paths.The proposal network is learned on the fly, avoiding reliance on expert annotations or wet-lab data.
- Results: MARS achieves state-of-the-art performance on five of six tasks, with evaluation based on success rate, novelty, and diversity.The method is compared with four baselines spanning established molecular-generation categories.
- Results: In the four-objective setting combining two bio-activities, drug-likeness, and synthesizability, MARS outperforms existing methods by 77% in the comprehensive evaluation.This is identified as the most challenging evaluation setting.
2 RELATED WORK
Prior molecular-generation approaches include latent-space, reinforcement-learning, translation, evolutionary, and sampling methods, but each has limitations for flexible multi-objective discovery. MARS provides a sampling-based alternative aimed at jointly finding bioactive, drug-like, and synthesizable molecules.
- Existing approaches: Molecular property-optimization methods are grouped into Bayesian, reinforcement-learning, encoder-decoder, and evolutionary or genetic approaches.These categories represent distinct strategies for exploring or generating molecules.
- Existing approaches: Reinforcement-learning models directly optimize objectives in chemical space but are usually difficult to train because of high variance.This limitation is stated for the reinforcement-learning category.
- Existing approaches: Translation models map input molecules to high-quality outputs but require many high-quality labeled examples, limiting use when data are scarce.The data requirement is presented as a practical constraint.
- Existing approaches: Evolutionary and genetic algorithms flexibly explore large chemical spaces, with augmented genetic algorithms improving diversity through adversarial fitness evaluation.The cited augmented genetic algorithm outperformed other generative models for logP optimization.
- Multi-objective methods: Rationale-based multi-objective generation assembles extracted rationales, but combining many rationales can produce large molecules that hinder synthesizability and drug-likeness.The difficulty increases as the number of objectives grows.
- Sampling methods: Gibbs sampling generates molecules resembling the observed data distribution but is not directly tailored to property optimization, unlike MARS's general MCMC formulation.MARS turns generation into a sampling procedure for property-directed discovery.
3 PROPOSED MARS APPROACH
MARS formulates multi-objective molecular design as Markov sampling over molecular graphs, using fragment edits, annealing, and an adaptive GNN-based proposal to search desired chemical distributions.
- 3.1 SAMPLING FROM THE MOLECULAR SPACE: MARS defines an unnormalized molecular distribution by combining scoring functions for multiple desired properties, such as bioactivity, drug-likeness, and synthesizability.The score-combination operator may use summation or multiplication, but increasing objectives makes the joint distribution more complex and sampling non-trivial.
- 3.1 SAMPLING FROM THE MOLECULAR SPACE: MARS defines a Markov chain whose states are explicit molecules and uses a proposal distribution plus acceptance-rejection transitions to sample candidates.Each step proposes a molecule x′ from q(x′ | x) and accepts or rejects it according to an acceptance rate.
- 3.1 SAMPLING FROM THE MOLECULAR SPACE: MARS uses annealed MCMC with α = 1/T, where temperature T follows a cooling schedule to search for molecules that globally maximize the target distribution.The same framework can also instantiate Metropolis-Hastings with α = 1.
- 3.2 ADAPTIVE MOLECULAR GRAPH EDITING PROPOSAL: MARS proposes molecules through fragment adding and deleting actions over molecular graphs, using a finite fragment vocabulary with single attachment positions.Fragments are connected components separated by single bonds, and molecular graph editing examples are illustrated in Figure 2.
- 3.2 ADAPTIVE MOLECULAR GRAPH EDITING PROPOSAL: An MPNN parameterizes probabilities for selecting edit types, atoms, fragments, and bonds, thereby defining the adaptive proposal distribution qθ(x′ | x).For adding, the proposal combines atom and fragment probabilities; for deleting, it uses a bond probability.
- 3.2 ADAPTIVE MOLECULAR GRAPH EDITING PROPOSAL: MARS trains its editing model on-the-fly from sampling paths, collecting candidates that improve objectives and maximizing their production probability by MLE.This self-training strategy avoids relying on training instances that already satisfy all property constraints.
4 EXPERIMENTS
MARS is evaluated across multi-objective molecular-generation settings using bioactivity, drug-likeness, synthesizability, novelty, and diversity criteria. It outperforms baselines on most tasks, with particularly strong results in the four-objective setting and broad molecular-space coverage.
- Experiment Setup: The benchmark combines inhibition objectives for GSK3β and JNK3 with QED and SA in progressively challenging objective settings.QED measures drug-likeness, while rescaled SA measures synthesizability; the four-objective setting jointly optimizes all four properties.
- Experiment Setup: PM multiplies success rate, novelty, and diversity to measure molecules that are simultaneously bioactive, novel, and diverse.Success requires meeting thresholds for all given objectives, while novelty and diversity use fingerprint-based similarity measures.
- Main Results and Analysis: MARS outperforms all baselines on five of six tasks in PM, including a 77% improvement over the best baseline on GSK3β+JNK3+QED+SA.The results are based on ten independent MARS runs.
- Main Results and Analysis: GA+D has high novelty and PM but loses diversity under multiple objectives, whereas MARS covers broader novel regions in the molecular space.The t-SNE visualization shows GA+D concentrated in two large clusters, while MARS is more evenly distributed.
- Main Results and Analysis: MARS generates molecules with high GSK3β, JNK3, QED, and SA scores in the four-objective setting.The paper presents sampled molecules jointly inhibiting both targets while remaining drug-like and highly synthesizable.
- Effects of Proposal and Acceptance Strategy: The adaptive proposal converges 4.6x faster than random proposals, while annealed acceptance outperforms always-accept and hill-climbing strategies.Annealing is reported to help samples jump out of local optima, especially as the number of objectives increases.
5 CONCLUSION AND FUTURE WORK
MARS is a simple, flexible framework for multi-objective drug discovery that uses a trainable molecular-editing proposal. Experiments show it outperforms prior approaches on five of six tasks and finds molecules that are novel, diverse, bioactive, drug-like, and synthesizable.
- MARS uses an MPNN-parameterized trainable proposal to modify chemical graph fragments.
- MARS outperforms prior approaches on five of six molecule generation tasks.
- MARS finds novel and diverse bioactive molecules that are both drug-like and highly synthesizable.
A PROPERTY SCORES OF SAMPLED MOLECULES
The four-objective experiment evaluates property scores and sampling behavior for 5,000 molecules, using success thresholds and tracking success rate, novelty, diversity, and their product.
- 5,000 sampled molecules are evaluated through distributions of GSK3β inhibition, JNK3 inhibition, QED, and SA scores.
- Figure 5 marks success thresholds with red lines across the four property-score distributions.
- Figure 6 reports average sampling curves over 10 runs for success rate, novelty, diversity, and their product.
B SINGLE OBJECTIVE GENERATION
MARS is evaluated on single-objective QED and penalized logP optimization, where it achieves the best reported performance on both tasks. The results also question whether top QED and penalized logP scores reliably distinguish practical methods.
- MARS achieves the best performance on both QED and penalized logP optimization tasks.
- MARS significantly outperforms previous methods on the penalized logP generation task.
- A top QED score of 0.948 is reached by several generative methods, making the metric difficult to distinguish between methods.
- Top penalized logP scores favor larger molecules that generative models hardly produce, although such molecules are unrealistic for practical drug discovery.
C EXAMPLES OF SAMPLED MOLECULES
The paper presents sampled molecules from the four-objective setting, organized by overall property performance and by individual GSK3β, JNK3, QED, and SA scores.
- Examples are sampled from the GSK3β+JNK3+QED+SA setting, with each molecule labeled by four corresponding property scores.
- The examples include 40 molecules with the highest average property scores.
- Separate examples show the 40 molecules with highest GSK3β, JNK3, QED, and SA scores.