Abstract
The primary challenge with biological sciences is to control gene regulatory networks (GRNs), thereby creating therapeutic intervention methods that alter network dynamics in the desired manner. The optimal control of GRNs with probabilistic Boolean control networks (PBCNs) as the underlying structure is a solution to this challenge. Owing to the exponential growth in network size with the increase in the number of genes, we need an optimal control approach that scales to large systems without imposing any limitations on network dynamics. Furthermore, we are encouraged to use the graphics processing unit (GPU) to reduce time complexity utilizing the easily available and enhanced computational resources. The optimal control of PBCNs in the Markovian framework is developed in this paper employing an information-theoretic approach which includes Kullback-Leibler (KL) divergence. We convert the nonlinear optimal control problem of PBCN to a linear problem by using the exponential transformation of the cost function, also known as the desirability function. The linear formulation enables us to compute an optimal control using the path integral (PI) method. Furthermore, we offer sampling-based methodologies for approximating PI and therefore optimizing PBCN control. The sampling-based method can be implemented in parallel, which solves the optimal control problem for large PBCNs.
Highlights
T HE popularity of Boolean networks (BNs) has increased gradually since Kauffman introduced them [1]
Inspired by the preceding discussion, we develop a novel information-theoretic strategy to effectively solve the optimal control of probabilistic Boolean control networks (PBCNs) and implement the same using a graphics processing unit (GPU) based parallel processing framework
PRELIMINARIES In the following, we present a brief review of Probabilistic Boolean control networks (PBCNs) in the Markovian framework, Markov decision processes (MDPs), and informationtheoretic control framework
Summary
T HE popularity of Boolean networks (BNs) has increased gradually since Kauffman introduced them [1]. The framework of linearly-solvable MDP (LMDP) [43] achieves a comparable formulation for discrete state space with the restriction of information cost in terms of KL divergence and the transition probabilities denoting continuous inputs. The following are the key contributions of the proposed framework in this paper: 1) To get the advantage of the inherent stochastic behavior of PBCNs, an information-theoretic formulation utilizing the augmented state space is proposed for optimal control of PBCNs. 2) To obtain the solution to information-theoretic control through approximation and overcome limitations of the Monte Carlo sampling method, an entropy-based improved Monte Carlo sampling technique is proposed. Logical AND, OR, n and NOT operations are denoted by ∧, ∨, and ¬, respectively
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