Controllability Analysis and Control Design of Biological Systems Modeled by Boolean Networks

Cell signaling networks are often modeled using ordinary differential equations (ODEs), which represent network components with continuous variables. However, parameters such as reaction rate constants are needed for ODEs are not always available or known, and discrete approaches such as Boolean networks (BNs) are used in such cases. BNs have been applied in the past, in particular, as means to determine network steady states. The goal of this work is to explore the use of BNs from a control theory point of view, that to help manipulate biological systems more efficiently. In this thesis, we propose two methods to analyze and design control strategies for BNs. The first method, based on the algebraic state-space representation of BNs, consist of defining control strategies to reach predetermined states, namely, given a desired output, find all possible system state transition trajectories to that output, and design an input sequence leading to it. The second method aims at introducing an alternative and an extension of the first method in the sense that it offers broader possibilities for the representation of time and it is scalable to BNs of bigger size. This method is based on binary decision diagrams (BDDs), a data structure very efficient to represent logical functions and allow us to relate outputs of a network to its inputs no matter how many layers it contains and whether or not it has a cyclic structure

Controllability Analysis and Control Design of Biological Systems Modeled by Boolean Networks

Cell signaling networks are often modeled using ordinary differential equations (ODEs), which represent network components with continuous variables. However, parameters such as reaction rate constants are needed for ODEs are not always available or known, and discrete approaches such as Boolean networks (BNs) are used in such cases. BNs have been applied in the past, in particular, as means to determine network steady states. The goal of this work is to explore the use of BNs from a control theory point of view, that to help manipulate biological systems more efficiently. In this thesis, we propose two methods to analyze and design control strategies for BNs. The first method, based on the algebraic state-space representation of BNs, consist of defining control strategies to reach predetermined states, namely, given a desired output, find all possible system state transition trajectories to that output, and design an input sequence leading to it. The second method aims at introducing an alternative and an extension of the first method in the sense that it offers broader possibilities for the representation of time and it is scalable to BNs of bigger size. This method is based on binary decision diagrams (BDDs), a data structure very efficient to represent logical functions and allow us to relate outputs of a network to its inputs no matter how many layers it contains and whether or not it has a cyclic structure

Output feedback stabilization of Boolean control networks

In the paper output feedback control of Boolean control networks (BCNs) is investigated. First, necessary and sufficient conditions for the existence of a time-invariant output feedback (TIOF) law, stabilizing the BCN to some equilibrium point, are given, and constructive algorithms to test the existence of such a feedback law are proposed. Two sufficient conditions for the existence of a stabilizing time-varying output feedback (TVOF) are then given. Finally, an example concerning the lac Operon in the bacterium Escherichia Coli is presented, to illustrate the effectiveness of the proposed techniques