Controllability of Conjunctive Boolean Networks with Application to Gene Regulation

TL;DR

This paper studies how to control conjunctive Boolean networks, which model gene regulation, by establishing conditions and control laws for steering the system to desired states or periodic orbits.

Contribution

It provides necessary and sufficient conditions for orbit- and state-controllability of conjunctive Boolean networks, along with explicit control strategies.

Findings

Conditions for orbit-controllability established

Conditions for state-controllability established

Explicit control laws derived

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.