Systems of chemical reactions in biology : dynamics, stochasticity, spatial effects and model reduction

Abstract

Cells are continuously sensing and processing information from their environments and responding to it in sensible ways. The communication networks on which such information is handled often consist of systems of chemical reactions, such as signaling pathways or metabolic networks. This thesis studies the dynamics of systems of chemical reactions in the context of biological cells. The first part of this thesis analyzes the osmo-regulation network in yeast, responsible for the regulation of internal osmolarity. We measure the system's step response in single cells, and find that the steady state is independent of the input, a property termed perfect adaptation that relies on integral feedback control. We then consider the signaling cycle, a pattern of chemical reactions that is often present in signaling pathways, in which a protein can be either active (e.g., phosphorylated) or inactive (e.g., unphosphorylated). We identify new regimes of static and dynamic operation, and find that these cycles can be tuned to transmit or digitize time-varying signals, while filtering input noise. The second part of this thesis considers systems of chemical reactions where stochastic effects are relevant, and simplifies the standard models. We develop an approximate model for the time-evolution of the average concentrations and their variances and covariances in systems with and without spatial gradients. We also describe a framework to identify and derive approximate models for variables that evolve at different time scales in systems without spatial gradients. These tools can help study the impact of stochastic and spatial effects on system behavior.