Feedback Total-Activity Conservation of Boolean Control Networks

The law of conservation is crucial to guarantee the robustness of gene expression and signal transduction processes in biological systems. This brief analyzes the feedback total-activity conservation of Boolean control networks (BCNs) based on the semi-tensor product of matrices. First, by constructing the conservative characteristic matrix, a matrix-based criterion is presented to verify the total-activity conservation of BCNs. Secondly, by establishing the control index set, all possible state feedback controllers are designed to achieve the total-activity conservation for BCNs. Finally, an example of lac operon in the Escherichia coli is given to illustrate the proposed results.