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.

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.

In this article, set stabilization in switched Boolean networks is investigated through link augmentations. Link augmentation is introduced as a selective process for adding specific edges between nodes in the wiring digraph of the network. For the implementation of link augmentation, various variables are integrated into the dynamics governing networks, utilizing basic logical operators. A key aspect of this article is the incorporation of additional functions introduced by the link augmentations into the original dynamics of the system using constrained logical operators. Further, several criteria for set stabilization are formulated, and the link augmentation control strategy is innovatively designed, utilizing the Q-learning Algorithm. Finally, a biological example is presented to demonstrate the effectiveness of the proposed methods.

Attractors in gene regulatory networks represent cell types or states of cells. In system biology and synthetic biology, it is important to generate gene regulatory networks with desired attractors. In this paper, we focus on a singleton attractor, which is also called a fixed point. Using a Boolean network (BN) model, we consider the problem of finding Boolean functions such that the system has desired singleton attractors and has no undesired singleton attractors. To solve this problem, we propose a matrix-based representation of BNs. Using this representation, the problem of finding Boolean functions can be rewritten as an Integer Linear Programming (ILP) problem and a Satisfiability Modulo Theories (SMT) problem. Furthermore, the effectiveness of the proposed method is shown by a numerical example on a WNT5A network, which is related to melanoma. The proposed method provides us a basic method for design of gene regulatory networks.

Demand response is one of the key technologies in energy management systems, and is defined as the changes in electricity usage of end-use consumers that occur as a result of changing the electricity price, the incentive, and so on. In this paper, a design method for demand response is proposed based on model predictive control. Model predictive control is a control method using prediction by a mathematical model, which is used for controlling systems with constraints. Because constraints are considered in the design of demand response, it is appropriate to utilize model predictive control. First, the model predictive-based demand response problem is formulated. By solving this problem, demand response is performed based on the actual power consumption. Next, constraints on the peak shift effect are imposed, and an event-triggered mechanism is introduced. Third, the effects of demand response are theoretically analyzed. Finally, the economic value of the proposed approach is evaluated by numerical simulations. The proposed approach provides us a fundamental result for the design of demand response and aggregators such as retailers.