ILP/SMT-Based Method for Design of Boolean Networks Based on Singleton Attractors

Abstract

Attractors in gene regulatory networks represent cell types or states of cells. In system biology and synthetic biology, it is important to generate gene regulatory networks with desired attractors. In this paper, we focus on a singleton attractor, which is also called a fixed point. Using a Boolean network (BN) model, we consider the problem of finding Boolean functions such that the system has desired singleton attractors and has no undesired singleton attractors. To solve this problem, we propose a matrix-based representation of BNs. Using this representation, the problem of finding Boolean functions can be rewritten as an Integer Linear Programming (ILP) problem and a Satisfiability Modulo Theories (SMT) problem. Furthermore, the effectiveness of the proposed method is shown by a numerical example on a WNT5A network, which is related to melanoma. The proposed method provides us a basic method for design of gene regulatory networks.

Attractor-Based Simultaneous Design of the Minimum Set of Control Nodes and Controllers in Boolean Networks

“…If the set  (i.e.,  ) is given, Problem 1 has been already solved in [10]. Problem 1 is more general than the problem studied in [10].…”

“…Problem 1 is more general than the problem studied in [10]. By solving Problem 1, we can obtain both the minimum set of control nodes and the controller.…”

“…In order to solve the simultaneous design problem, a matrix-based representation of BNs [10] is utilized. Using this representation, this problem can be rewritten as an integer linear programming problem.…”

Design of Probabilistic Boolean Networks Based on Network Structure and Steady-State Probabilities

“…Furthermore, in BNs, attractors such as fixed points and limit cycles represent cell types or states of cells, and are important for understanding the biological property [15]. In [12], [18], [26], the problem of finding a BN with the desired fixed points has been studied as an inverse problem. Instead of attractors, we focus on a steady-state probability distribution in PBNs.…”

“…This representation is an extension of that for BNs [18], and can be obtained from truth tables and selection probabilities. A matrix-based representation obtained by the semi-tensor product (STP) method [4], [5], [6], [23] can be also used.…”