Analysis of performance and robustness of biological switches: local tools for non-local dynamical phenomena.

Biological switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. A bistable switch presents two stable steady-states, each of them corresponding to a distinct decision. These two decisions are assumed to result from the interactions between biochemical effectors at the molecular level. Because these molecular interactions are particularly complex, involving many effectors, mathematical models of biological switches are often high dimensional and nonlinear. Therefore, an analysis of these systems is challenging. In this dissertation, we try to identify principles and tools to study the performance and robustness of biological switches. Our first contribution is to highlight the dynamical nature of these switches. A biological switch encodes a decision-making process rather than a static binary code. It captures dynamical phenomena that are important for the decision-making process, such as decision latencies and reversibility. Our second contribution is methodological. While most of the classical analysis tools are based on a linearization of the system around a stable steady-state, a switch is a non local phenomenon involving a transition between two stable steady-sates. Rather than studying the system around stable equilibria, we identify the local rulers of the decision-making process in both the state and parameter spaces and propose a local analysis in the vicinity of these particular points. Our third contribution is to emphasize the added value of an abstract (that is, mathematical) framework for the analysis of biological switches. By studying different models, we point out that the same principles can be used to encode dynamical phenomena in very different cellular processes. Physiological processes as different as apoptosis, the cellular choice of death, and action potential, the cellular choice to emit an electrical spike, share common features when regarded as decision-making processes