A switched systems approach for the analysis and control of mode transitions in biological networks

This work presents a methodology for the analysis and control of mode transitions in biological networks. The proposed approach is predicated upon the notion of orchestrating switching between the domains of attraction of the steady-states of the constituent modes. Initially, the overall network is modeled as a switched nonlinear system that consists of multiple modes, each governed by a set of continuous-time differential equations. The transitions between the continuous modes are triggered by discrete events (changes in model parameters that correspond to alterations in physiological conditions). Then, following the characterization of the steady-state behavior of each mode, Lyapunov techniques are used to characterize the domains of attraction of the steady-states. Finally, by analyzing how the domains of attraction of the various modes overlap with one other, a switching rule is derived to determine when, and if, a given mode transition at a given time results in the desired steady-state behavior. The proposed approach has implications both for understanding the outcome of naturally-occurring mode transitions and for the ability to manipulate network behavior by enforcing mode transitions. The proposed approach is demonstrated using a model of a biological network that arises in the bacteriophage λ-switch system.