Time-Optimal Adaptation in Metabolic Network Models

Analysis of metabolic models using constraint-based optimization has emerged as an important computational technique to elucidate and eventually predict cellular metabolism and growth. In this work, we introduce time-optimal adaptation (TOA), a new constraint-based modeling approach that allows us to evaluate the fastest possible adaptation to a pre-defined cellular state while fulfilling a given set of dynamic and static constraints. TOA falls into the mathematical problem class of time-optimal control problems, and, in its general form, can be applied in a broad sense and thereby extends most existing constraint-based modeling frameworks. Specifically, We introduce a general mathematical framework that captures many existing constraint-based methods and define TOA within this framework. We then exemplify TOA using a coarse-grained self-replicator model and demonstrate that TOA allows us to explain several well known experimental phenomena that are difficult to explore using existing constraint-based analysis methods. We show that TOA can explain accumulation of storage compounds in constant environments, as well as overshoot uptake metabolism after a period of nutrient scarcity. TOA reveals that organisms with internal temporal degrees of freedom, such as storage, can in most environments outperform organisms with a static intracellular composition. Furthermore, TOA shows that organisms adapted to better growth conditions than present in the environment ("optimists") typically outperform organisms adapted to poorer growth conditions ("pessimists").