Understanding metabolic regulation and cellular resource allocation through optimization
This thesis is a contribution to the field of systems biology, where mathematical and computational models are used to study large biological networks such as the metabolism or the signaling pathways of living organisms. These models are simplified representations of the studied biological systems and come in different granularities and abstraction levels, depending on the size of the networks and on the modeling formalisms. One of the largest networks studied within systems biology is the metabolism, which comprises all the biochemical reactions happening inside a cell. Until recently, such large metabolic networks have been studied mainly in isolation and under stationary conditions, without considering the environment dynamics or the enzymatic resources needed to catalyze all the biochemical reactions. This has been mainly done using constraint-based analysis and optimization. While proven to be very successful in predicting cellular behavior in some cases, this approach is not suited for microorganisms living under changing environments. Two examples are cyanobacteria, whose metabolism is adapted to the daily changes in the sunlight availability, and yeasts living in large bioreactors and thus moving in an environment governed by local heterogeneities. This thesis builds on top of recent developments in dynamic resource allocation formalisms for metabolism, which use tools from dynamic optimization and optimal control. We focus on modeling and understanding resource allocation in large (sometimes genome-scale) metabolic models. After giving an overview of existing tools for the study of metabolic resource allocation, the thesis presents a new mathematical derivation of the widely used steady-state assumption for metabolic networks and shows how this can be used to provide upper bounds on dynamic resource allocation solutions. In preparation for the case studies, we present a guide for generating a dynamic resource allocation model using information from online databases, as well as guidelines and useful problem transformations. All the theory developed so far is then applied in two case studies. One of them investigates the cyanobacterium Synechococcus elongatus PCC 7942. This is the first genome-scale dynamic resource allocation study. It gives insight into the temporal organization of enzyme synthesis processes following light availability and shows that the linear pattern of glycogen accumulation throughout the day period is an optimal behavior that arises as a tradeoff between several conflicting resource allocation objectives. The second case study concerns the yeast Saccharomyces cerevisiae. We aim to understand what mechanisms enable some of the cells to survive environmental transitions. We show that overflow metabolism and diauxie, which are phenomenons widely spread in nature, are optimal behaviors from a resource allocation perspective. Moreover, we investigate how one can use resource allocation models to understand how yeast adapts to oxygen and nutrient availability shifts. We end with a perspectives chapter which provides some preliminary results for using time courses from dynamic resource allocation models to infer the regulatory structures that implement these optimal behaviors.