Title: Controllability of Conjunctive Boolean Networks with Application to Gene Regulation,
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.