Reverse engineering cellular decisions for hybrid reconfigurable network modeling

Abstract

Cells as microorganisms and within multicellular organisms make robust decisions. Knowing how these complex cells make decisions is essential to explain, predict or mimic their behavior. The discovery of multi-layer multiple feedback loops in the signaling pathways of these modular hybrid systems suggests their decision making is sophisticated. Hybrid systems coordinate and integrate signals of various kinds: discrete on/off signals, continuous sensory signals, and stochastic and continuous fluctuations to regulate chemical concentrations. Such signaling networks can form reconfigurable networks of attractors and repellors giving them an extra level of organization that has resilient decision making built in. Work on generic attractor and repellor networks and on the already identified feedback networks and dynamic reconfigurable regulatory topologies in biological cells suggests that biological systems probably exploit such dynamic capabilities. We present a simple behavior of the swimming unicellular alga Chlamydomonas that involves interdependent discrete and continuous signals in feedback loops. We show how to rigorously verify a hybrid dynamical model of a biological system with respect to a declarative description of a cell's behavior. The hybrid dynamical systems we use are based on a unification of discrete structures and continuous topologies developed in prior work on convergence spaces. They involve variables of discrete and continuous types, in the sense of type theory in mathematical logic. A unification such as afforded by convergence spaces is necessary if one wants to take account of the affect of the structural relationships within each type on the dynamics of the system.