AUTHOR=Köbis Markus A. , Bockmayr Alexander , Steuer Ralf 

TITLE=Time-Optimal Adaptation in Metabolic Network Models

JOURNAL=Frontiers in Molecular Biosciences

VOLUME=Volume 9 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/molecular-biosciences/articles/10.3389/fmolb.2022.866676

DOI=10.3389/fmolb.2022.866676

ISSN=2296-889X

ABSTRACT=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'').