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

Perturbation Analysis for Finite-Time Stability and Stabilization of Probabilistic Boolean Networks

This article analyzes the function perturbation impact on the finite-time stability and stabilization of the probabilistic Boolean networks (PBNs). First, the concept of stability in the distribution of PBNs is divided into two disjoint concepts, that is, finite-time stability with probability one (FTSPO) and asymptotical stability with probability one (ASPO), and a new criterion is proposed for the verification of ASPO. Second, by constructing a parameterized set, it is shown that PBNs subject to function perturbation keep FTSPO if and only if the perturbed point does not belong to the parameterized set, while PBNs become ASPO if and only if the perturbed point belongs to the parameterized set. Third, as an application of perturbed stability analysis, the robust state-feedback stabilization is discussed for probabilistic Boolean control networks (PBCNs) with function perturbation. Finally, the obtained results are applied to a WNT5A network and lac operon in the Escherichia coli, respectively.

Structural Bistability Analysis of Flower-Shaped and Chain-Shaped Boolean Networks

Bistability, i.e., the existence of just two stable equilibria, is known to play an important role in biological systems, e.g., cellular differentiation and apoptosis. In this paper, we consider the bistability but as a structural property of a class of network systems, that is, the bistability under the assumption that the information on the network structure is available but the information on the components is not available. First, we introduce Boolean networks as a model of biological network systems and give the notion of structural bistability. We next focus on the systems with a flower-shaped network structure and present a necessary and sufficient condition based on three characteristics of the network topology. Finally, the result is extended to the Boolean networks with a chain-shaped network structure.

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

In this brief, we consider the problem of finding a probabilistic Boolean network (PBN) based on a network structure and desired steady-state properties. In systems biology and synthetic biology, such problems are important as an inverse problem. Using a matrix-based representation of PBNs, a solution method for this problem is proposed. The problem of finding a BN has been studied so far. In the problem of finding a PBN, we must calculate not only the Boolean functions, but also the probabilities of selecting a Boolean function and the number of candidates of the Boolean functions. Hence, the problem of finding a PBN is more difficult than that of finding a BN. The effectiveness of the proposed method is presented by numerical examples.