Information theory in biochemical regulatory networks: a theoretical study

In this Thesis we consider the optimization of information transmission as a viable design principle for biochemical networks. We apply this principle to a simple model regulatory circuit, given by an input and a delayed output that switch randomly between two states in continuous time. First we maximize the transmitted information in the network at a given output delay, when the system has no external constraints and it is in steady state or can optimize its initial condition. We find that optimal network topologies correspond to common biological circuits linked to stress response and that circuits functioning out of steady state may exploit absorbing states to be more informative than in steady state. We then take into account that biological regulatory networks need to dissipate energy in order to transmit biochemical signals and that such signaling often happens in challenging environmental conditions. Hence we explore the system's trade-offs between information transmission and energetic efficiency. At fixed delay and dissipated energy, we determine the most informative networks both in the absence and in the presence of feedback. We find that negative feedback loops are optimal at high dissipation, whereas positive feedback loops become more informative close to equilibrium conditions. Moreover, feedback allows the system to transmit almost the maximum available information at a given delay, even in the absence of dissipation. Finally, within a game-theoretic maximin approach, we ask how a biochemical network should be constructed to be most informative in the worst possible initial condition set by the environment. We find that, in the limit of large energy dissipation, the system tunes the ratio of the input and output timescales so that the environmental disturbance is marginalized as much as possible.