Polynomial-time algorithm for controllability test of a class of boolean biological networks

Boolean Modeling of Biological Network Applied to Protein-Protein Interaction Network of Autism Patients

Cellular molecules interact with one another in a structured manner, defining a regulatory network topology that describes cellular mechanisms. Genetic mutations alter these networks' pathways, generating complex disorders such as autism spectrum disorder (ASD). Boolean models have assisted in understanding biological system dynamics since Kauffman's 1969 discovery, and various analytical tools for regulatory networks have been developed. This study examined the protein-protein interaction network created in our previous publication of four ASD patients using the SPIDDOR R package, a Boolean model-based method. The aim is to examine how patients' genetic variations in INTS6L, USP9X, RSK4, FGF5, FLNA, SUMF1, and IDS affect mTOR and Wnt cell signaling convergence. The Boolean network analysis revealed abnormal activation levels of essential proteins such as β-catenin, MTORC1, RPS6, eIF4E, Cadherin, and SMAD. These proteins affect gene expression, translation, cell adhesion, shape, and migration. Patients 1 and 2 showed consistent patterns of increased β-catenin activity and decreased MTORC1, RPS6, and eIF4E activity. However, patient 2 had an independent decrease in Cadherin and SMAD activity due to the FLNA mutation. Patients 3 and 4 have an abnormal activation of the mTOR pathway, which includes the MTORC1, RPS6, and eIF4E genes. The shared mTOR pathway behavior in these patients is explained by a shared mutation in two closely related proteins (SUMF1 and IDS). Diverse activities in β-catenin, MTORC1, RPS6, eIF4E, Cadherin, and SMAD contributed to the reported phenotype in these individuals. Furthermore, it unveiled the potential therapeutic options that could be suggested to these individuals.

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.

Controllability and observability of Boolean networks arising from biology

Boolean networks are currently receiving considerable attention as a computational scheme for system level analysis and modeling of biological systems. Studying control-related problems in Boolean networks may reveal new insights into the intrinsic control in complex biological systems and enable us to develop strategies for manipulating biological systems using exogenous inputs. This paper considers controllability and observability of Boolean biological networks. We propose a new approach, which draws from the rich theory of symbolic computation, to solve the problems. Consequently, simple necessary and sufficient conditions for reachability, controllability, and observability are obtained, and algorithmic tests for controllability and observability which are based on the Gröbner basis method are presented. As practical applications, we apply the proposed approach to several different biological systems, namely, the mammalian cell-cycle network, the T-cell activation network, the large granular lymphocyte survival signaling network, and the Drosophila segment polarity network, gaining novel insights into the control and/or monitoring of the specific biological systems.

Verification and optimal control of context-sensitive probabilistic Boolean networks using model checking and polynomial optimization

One of the significant topics in systems biology is to develop control theory of gene regulatory networks (GRNs). In typical control of GRNs, expression of some genes is inhibited (activated) by manipulating external stimuli and expression of other genes. It is expected to apply control theory of GRNs to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of GRNs, and gene expression is expressed by a binary value (ON or OFF). In particular, a context-sensitive probabilistic Boolean network (CS-PBN), which is one of the extended models of BNs, is used. For CS-PBNs, the verification problem and the optimal control problem are considered. For the verification problem, a solution method using the probabilistic model checker PRISM is proposed. For the optimal control problem, a solution method using polynomial optimization is proposed. Finally, a numerical example on the WNT5A network, which is related to melanoma, is presented. The proposed methods provide us useful tools in control theory of GRNs.

Optimal control of gene regulatory networks with effectiveness of multiple drugs: a Boolean network approach

Developing control theory of gene regulatory networks is one of the significant topics in the field of systems biology, and it is expected to apply the obtained results to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of gene regulatory networks, and gene expression is expressed by a binary value (0 or 1). In the control problem, we assume that the concentration level of a part of genes is arbitrarily determined as the control input. However, there are cases that no gene satisfying this assumption exists, and it is important to consider structural control via external stimuli. Furthermore, these controls are realized by multiple drugs, and it is also important to consider multiple effects such as duration of effect and side effects. In this paper, we propose a BN model with two types of the control inputs and an optimal control method with duration of drug effectiveness. First, a BN model and duration of drug effectiveness are discussed. Next, the optimal control problem is formulated and is reduced to an integer linear programming problem. Finally, numerical simulations are shown.