Inference of General Mass Action-Based State Equations for Oscillatory Biochemical Reaction Systems Using <i>k</i>-Step Genetic Programming

Abstract

Systems biology requires the development of algorithms that use omics data to infer interaction networks among biomolecules working within an organism. One major type of evolutionary algorithm, genetic programming (GP), is useful for its high heuristic ability as a search method for obtaining suitable solutions expressed as tree structures. However, because GP determines the values of parameters such as coefficients by random values, it is difficult to apply in the inference of state equations that describe oscillatory biochemical reaction systems with high nonlinearity. Accordingly, in this study, we propose a new GP procedure called “ k -step GP” intended for inferring the state equations of oscillatory biochemical reaction systems. The k -step GP procedure consists of two algorithms: 1) Parameter optimization using the modified Powell method—after genetic operations such as crossover and mutation, the values of parameters such as coefficients are optimized by applying the modified Powell method with secondary convergence. 2) GP using divided learning data—to improve the inference efficiency, imposes perturbations through the addition of learning data at various intervals and adaptations to these changes result in state equations with higher fitness. We are confident that k -step GP is an algorithm that is particularly well suited to inferring state equations for oscillatory biochemical reaction systems and contributes to solving inverse problems in systems biology.