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 broadly applied 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 predicts accumulation of storage compounds in constant environments, as well as overshoot uptake metabolism after periods of nutrient scarcity. TOA shows that organisms with internal temporal degrees of freedom, such as storage, can in most environments outperform organisms with a static intracellular composition. Furthermore, TOA reveals that organisms adapted to better growth conditions than present in the environment ("optimists") typically outperform organisms adapted to poorer growth conditions ("pessimists").