Genetic Algorithm for Constrained Molecular Inverse Design

1 INTRODUCTION . When the search space is complex or partially known , it is difficult to optimize current solutions using gradient descent ( Jin & Ha , 1997 ; Ahmad et al. , 2010 ) . Because genetic algorithms find approximate solutions , they are effective in exploring vast unknown space such as molecular search space . ( Holland , 1992 ; Jin & Ha , 1997 ; Ahmad et al. , 2010 ; Henault et al. , 2020 ) . In drug discovery , optimizing complex pharmacological properties using genetic algorithms have been widely studied and extended ( Leardi , 2001 ) . Deep learning-based molecular design is being actively conducted to improve pharmacological properties and has served as a powerful tool ( Gómez-Bombarelli et al. , 2018 ) . However , inferred drug candidates depending on the architecture did not satisfy the heuristic guidelines set by chemical researchers ( George & Hautier , 2020 ) . Furthermore , this not only produces nonsynthesizable molecules but also causes optimization problems for non-linear structure-activity relationships ( Gómez-Bombarelli et al. , 2018 ; Vanhaelen et al. , 2020 ) . Most molecular design methods first generate molecular structures and then calculate properties of the structures resulting in high computational cost ( Duvenaud et al. , 2015 ; Gilmer et al. , 2017 ; Feinberg et al. , 2018 ; Yang et al. , 2019 ) . Conversely , inverse molecular design specifies target properties in advance and then systematically explores the chemical space to discover molecular structures that have the desired properties ( Sanchez-Lengeling & Aspuru-Guzik , 2018 ) . Recent advances in molecular inverse design of genetic algorithms compete with or even surpass deep learning-based methods ( Yoshikawa et al. , 2018 ; Jensen , 2019 ; Nigam et al. , 2019 ; Polishchuk , 2020 ; Ahn et al. , 2020 ; Nigam et al. , 2021b ; a ) . This indicates that the computational methods of genetic algorithms in a chemical domain are more effective for exploring the vast chemical space ( Ahn et al. , 2020 ) . However , the genetic operators cause difficulty in lead optimization where the molecular structure is constrained ( Hasançebi & Erbatur , 2000 ) . A common molecular design strategy is to narrow the chemical search space , starting with known potential molecules ( Lim et al. , 2020 ) . The scaffold , which is the ” core ” of the molecule is intentionally maintained to preserve basic bioactivity ( Hu et al. , 2016 ) . This is directly involved in the interaction with the target protein ( Zhao & Dietrich , 2015 ; Lim et al. , 2020 ) . In lead identification process , scaffolds with biological activity to the target protein are identified ( Zhao & Dietrich , 2015 ) . In lead optimization process , it is important to optimize the SAR ( Structure-Activity Relationship ) properties while staying in the chemical space associated with the privileged scaffold ( Langevin et al. , 2020 ) . Lead optimization can be described as a multiple optimization problem in scaffold constraints ( Langevin et al. , 2020 ) . Most studies have focused on the application of generative models to the field of medicinal chemistry , and studies related to structure-constrained lead optimization have not been extensively explored . In this regard , we introduce a genetic algorithm featuring constrained molecular inverse design . We use graph and SELFIES descriptors to generate valid molecules through a two-phase GA-based pipeline . In addition , we introduced a two-phase optimization to ensure that molecular generation does not fail to optimize for specific properties while adhering to structural constraints . 2 RELATED WORK . Among the various methods for constrained optimization in a genetic algorithm , the basic one is designing effective penalty functions ( Yeniay , 2005 ) . The functions , which impose a penalty to fitness value , are widely used for constrained optimization ( Yeniay , 2005 ; Fletcher , 2013 ) . The individual fitness value is determined by combining the objective function value with the constraint violation penalty . A dominant relationship exists between the constraint penalty and the objective function value ( Coello , 2000 ) . One of the various methods is focusing on the selection of practicable solutions . To solve the problem of constrained optimization using a genetic algorithm , a two-phase framework which is MultiObjective Evolutionary Algorithm ( MOEA ) was introduced ( Venkatraman & Yen , 2005 ) . In the first phase , MoEA confirms the constraint satisfaction of solutions using a penalty function . The algorithm ranks solutions based on violations of constraints , completely disregarding objective function . When one or more feasible solutions are identified , the second phase continues . In the second phase , individual fitness is reassigned according to the objective function-constraint violation space and bi-objective optimization is performed ( Venkatraman & Yen , 2005 ) . Structure-constrained molecular optimization work was first presented in the JT-VAE ( Jin et al. , 2018a ) study . In this study , they create a tree-structured scaffold for constraining the structure of a molecule and then generate a molecular graph using a message-passing network ( Jin et al. , 2018a ) . GCPN ( You et al. , 2018 ) uses goal-directed reinforcement learning to generate molecules with desired properties and similarities . VJTNN ( Jin et al. , 2018b ) treated molecular optimization as a graph-to-graph translation problem and solved it through MMPA ( Matched Molecular Pair Analysis ) ( Dalke et al. , 2018 ) dataset . DEFactor ( Assouel et al. , 2018 ) generated molecules with optimized penalized LogP while maintaining molecular similarity through differentiable conditional probability-based graph VAE . Glen & Payne proposed a method for generating molecules through domain-specific rule-based crossover and mutation to ensure molecular structure constraints ( Glen & Payne , 1995 ) . To produce offspring molecules with the parent ’ s substructures , the crossover is used as a strategy to cut the end part of the molecule and link it to the end part of another similar molecule . To produce new molecules , twelve operators of mutation were defined : atomic insertion , atomic deletion , etc ( Glen & Payne , 1995 ) . ChemGE ( Yoshikawa et al. , 2018 ) uses the grammatical evolution of SMILES ( Simplified Molecular-Input Line-Entry System ) ( Weininger , 1988 ) to optimize penalized LogP and KITH protein inhibitors . Their study converts SMILES into integer sequences using a chromosomal mapping process ( Yoshikawa et al. , 2018 ) . Subsequently , operators of mutation are used to optimize grammatical evolutionary molecular populations . GA-GB ( Jensen , 2019 ) and MolFinder ( Kwon & Lee , 2021 ) defined expert rules for operators of crossover and mutation to ensure the validity of the structure when generating molecules . GEGL ( Ahn et al. , 2020 ) created optimized SMILES strings for penalized LogP by presenting a reinforcement learning contained expert policy . Various studies have proposed SMILES-based approaches since they are convenient to convert a complex 3D chemical structure to a simple 1D string ( Yoshikawa et al. , 2018 ; Kwon & Lee , 2021 ; Ahn et al. , 2020 ) . However , adding atoms or square brackets to a string indeed changes the structure globally not locally ( Dalke , 2018 ) . It is difficult to generate a completely valid molecule because SMILES are context sensitive ( Dalke , 2018 ; Kwon & Lee , 2021 ) . Recently , the development and application of SELFIES ( Self-Referencing Embedded Strings ) , which is a 100 % valid string representation , has been implemented in the molecular inverse design to cope with this problem ( Krenn et al. , 2020 ) . The GA-D ( Nigam et al. , 2019 ) generated SELFIES strings using a random operator of mutation while maintaining validity . Furthermore , this study maintained the molecular diversity of the population through an adaptive penalty of the deep neural discriminator ( Nigam et al. , 2019 ) . The STONED ( Nigam et al. , 2021b ) study was introduced for performing local chemical space search and molecular interpolation using SELFIES . Furthermore , the mutation site was limited to terminal 10 % to maintain the molecular scaffold ( Nigam et al. , 2021b ) . SELFIES makes it possible to generate new molecules through the random operation without relying on expert rules in operations of mutation ( Nigam et al. , 2021b ) . 3 PROPOSED METHOD . In this section , we introduce a novel genetic algorithm for constrained optimization in molecular inverse design . Our algorithm generates molecules suitable for the target properties while constraining the structural similarity of a target molecule . We use two strategies to satisfy the constraint conditions . First , our algorithm constructs a population that always satisfies the structural similarity condition in the first phase . Second , the algorithm selects the appropriate molecular descriptors according to the genetic operators to ensure the validity of the molecule . The detailed whole process is shown in figure 1 . The algorithm starts by constructing a population depending on whether the target molecule or similar molecules exist in the dataset . In the case of the target molecule or its similar molecule existing in the dataset , the population consists of molecules above the similarity calculated by the similarity between the molecules in the dataset and the target molecule . On the contrary , a target molecular SMILES is randomly arranged to construct a population according to the population size . Next , our algorithm confirms constraint satisfaction from the population and proceeds with bioptimization for property and constraint conditions . The detailed process is explained in the subsections below . 3.1 TWO-PHASE MOLECULAR OPTIMIZATION . In the work of constrained molecular optimization , the optimization often failed when a large number of molecules were subject to penalty included in the population . Therefore , we focused on ensuring that the population always contains only feasible solutions . Inspired by MOEA ( Venkatraman & Yen , 2005 ) , we divided the process into constraint satisfaction and bi-optimization , each of which is further explained in the following . Constraint Satisfaction for Population In this phase , the algorithm searches for feasible solutions considering only the structural similarity . The objective function is not considered in this process . The algorithm measures the Tanimoto coefficient of how similar it is to the reference molecule ( Nigam et al. , 2019 ) . The similarity between the target molecule m and the product molecule m′ is expressed as sim ( m , m′ ) . SimilarityPenalty ( m ) is given to each molecule according to as follows : SimilarityPenalty ( m ) = { 0 , sim ( m , m′ ) ≥ δ −106 , sim ( m , m′ ) < δ ( 1 ) SimilarityPenalty ( m ) is set to 0 if sim ( m , m′ ) ≥ δ ( Nigam et al. , 2019 ) . Otherwise , a death penalty of −106 is given . Next , the algorithm assigns fitness value to each individual by equation 2 and selects only feasible solutions . A fitness function is expressed as follows : F ( m ) = SimilarityPenalty ( m ) ( 2 ) Bi-Optimization for Property and Constraint Condition In this phase , the algorithm switches to bi-optimization for the fitness function value and the constraint condition when one or more feasible solutions are found . Our work simultaneously is to maximize the penalized LogP value while retaining the molecular structure . The penalized LogP ( J ( m ) ) of each molecule is expressed as follows : J ( m ) = LopP ( m ) − SAScore ( m ) −RingPenalty ( m ) ( 3 ) The higher score for J ( m ) has a more suitable structural profile as a drug ( Yoshikawa et al. , 2018 ) . LogP ( m ) is the octanol-water partition coefficient for the molecule m. SAScore ( m ) is the Synthetic Accessibility score , which is a quantitative score for whether a molecular structure can be synthesized ( Ertl & Schuffenhauer , 2009 ) . The higher the score , the more difficult it is to synthesize molecules . By giving a penalty according to the score , it is possible to prevent the generation of molecules that can not be synthesized.RingPenalty ( m ) is used to give a penalty to prevent the creation of molecules with unrealistically many carbon rings . This function is a penalty for molecules with seven or more rings of carbon ( Yoshikawa et al. , 2018 ) . The algorithm reassigns the fitness value to each individual according to equation 4 and sorted by rank . A fitness function can be represented as follows : F ( m ) = J ( m ) − SimilarityPenalty ( m ) ( 4 ) We wanted not only to preserve the superior individuals but also to replace the inferior individuals through reproduction . A portion of the generated molecules are replaced while the rest of the are kept through the selection module . The probability of replacing a molecule is determined using a smooth logistic function based on a ranking of fitness ( Nigam et al. , 2019 ) .

Summary: The authors proposed a genetic algorithm for molecule generation. The reward is a combination of several objectives like Eqn.(3). The genetic operations include crossover and mutation. The authors conduct experiments to optimize the LogP of molecules.