Metabolism regulated by network Lyapunov function

Regulation is associated with organizational structures in both social and natural world. In biology, regulated gene expression plays pivotal role in evolution, homoeostasis and diseases. Guided by metabolic study, we look for rules governing regulation at network level. We demonstrate a generic construction of dynamics for regulators, under the assumption that regulation provides stability. The driving force for the regulation process is determined by the dynamical structure of the stochastic network to be regulated in a simple and straight forward manner. The results of such regulation for metabolism are consistent with experiments. In this construction, regulators mutually interact with each other with interaction strength given analytically by the network to be regulated. Through such dependence, the regulatory network and the regulated network merge to be a larger dynamical system. Such regulatory mechanism gives rise to robustness and diversity, emergent properties observed in metabolism.