| Biochemical regulatory networks are involved in many essential processes of life, such as maintaining homeostatic conditions, cell-cycle division, and responding to environmental stimuli. Such networks contain a staggering degree of complexity, inhibiting our ability to understand how they function. Two major challenges in quantitative biology are addressed in this thesis. First, the problem of identifying regulatory models from observational data. Second, characterizing how regulatory networks evolve. Making use of a simple regulatory model that is based on piecewise linear differential equations, investigations into these questions are undertaken.;Regulatory networks share many features across different species, raising the question of how they evolved. A simple evolutionary model in which piecewise linear networks are subject to mutation processes with selective pressure for chaotic dynamics is considered. Investigation into the evolutionary process reveals that the robustness (insensitivity of dynamics to mutations of the components of the network) has an important impact on the ability to innovate increasingly chaotic dynamics. An explicit analytical description of how evolutionary processes affect these regulatory networks is used to show that, counterintuitively, robustness can accelerate the rate of innovation rather than inhibiting it.;A novel method for inferring regulatory networks from knowledge of the dynamics is presented. This result is used to derive an atlas of networks with highly robust limit cycle dynamics in dimensions 3,4 and 5. Additionally, a new theoretical approach is used to identify two families of regulatory networks: cyclic, negative feedback and sequential disinhibition, with robust periodic dynamics that exist in all higher dimensions too. Smooth generalizations of the piecewise linear case, called continuous homologues, are also considered. For the family of cyclic, negative feedback networks it is shown that for the continuous homologue, a limit cycle exists and provided it is hyperbolic, it is asymptotically stable. |
