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: This paper proposes a genetic algorithm for constrained molecular optimization. To generate molecules with better properties while staying similar to the starting molecule (lead), this paper proposes a two phase procedure. The first stage (constraint satisfaction) searches for feasible molecules that are similar to the lead compound. The second stage optimizes the objective function (property). The crossover operation is the same as GB-GA (Jensen 2019) and the mutation operation introduces random modifications on SELFIES string representation. The method is evaluated on logP optimization task, with minor improvement over previous work GA-DNN (Table 1).