The New Geometric “State-Action” Space Representation for Q-Learning Algorithm for Protein Structure Folding Problem

Abstract

Introduction. The spatial protein structure folding is an important and actual problem in computational biology. Considering the mathematical model of the task, it can be easily concluded that finding an optimal protein conformation in a three dimensional grid is a NP-hard problem. Therefore some reinforcement learning techniques such as Q-learning approach can be used to solve the problem. The article proposes a new geometric “state-action” space representation which significantly differs from all alternative representations used for this problem. The purpose of the article is to analyze existing approaches of different states and actions spaces representations for Q-learning algorithm for protein structure folding problem, reveal their advantages and disadvantages and propose the new geometric “state-space” representation. Afterwards the goal is to compare existing and the proposed approaches, make conclusions with also describing possible future steps of further research. Result. The work of the proposed algorithm is compared with others on the basis of 10 known chains with a length of 48 first proposed in [16]. For each of the chains the Q-learning algorithm with the proposed “state-space” representation outperformed the same Q-learning algorithm with alternative existing “state-space” representations both in terms of average and minimal energy values of resulted conformations. Moreover, a plenty of existing representations are used for a 2D protein structure predictions. However, during the experiments both existing and proposed representations were slightly changed or developed to solve the problem in 3D, which is more computationally demanding task. Conclusion. The quality of the Q-learning algorithm with the proposed geometric “state-action” space representation has been experimentally confirmed. Consequently, it’s proved that the further research is promising. Moreover, several steps of possible future research such as combining the proposed approach with deep learning techniques has been already suggested. Keywords: Spatial protein structure, combinatorial optimization, relative coding, machine learning, Q-learning, Bellman equation, state space, action space, basis in 3D space.