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arXiv · 1705.00759

Controllability of Conjunctive Boolean Networks with Application to Gene Regulation

Zuguang Gao·Xudong Chen·Tamer Başar
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Abstract

A Boolean network is a finite state discrete time dynamical system. At each step, each variable takes a value from a binary set. The value update rule for each variable is a local function which depends only on a selected subset of variables. Boolean networks have been used in modeling gene regulatory networks. We focus in this paper on a special class of Boolean networks, namely the conjunctive Boolean networks (CBNs), whose value update rule is comprised of only logic AND operations. It is known that any trajectory of a Boolean network will enter a periodic orbit. Periodic orbits of a CBN have been completely understood. In this paper, we investigate the orbit-controllability and state-controllability of a CBN: We ask the question of how one can steer a CBN to enter any periodic orbit or to reach any final state, from any initial state. We establish necessary and sufficient conditions for a CBN to be orbit-controllable and state-controllable. Furthermore, explicit control laws are presented along the analysis.

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Zuguang Gao, Xudong Chen, Tamer Başar. 2017-05-02. Controllability of Conjunctive Boolean Networks with Application to Gene Regulation. https://arxiv.org/abs/1705.00759

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