This paper introduces a dynamic metabolic modelling framework that is a
synthesis of recent ideas on resource allocation and the powerful optimal
control formulation of Ramkrishna and colleagues. In particular, their work is
extended based on the hypothesis that cellular resources are allocated among
elementary flux modes according to the principle of maximum entropy. This
concept both generalises and unifies prior approaches to dynamic metabolic
modelling by establishing a smooth interpolation between dynamic flux balance
analysis and dynamic metabolic models without regulation. The resulting theory
is successful in describing strategies employed by cell populations dealing
with uncertainty in a fluctuating environment, including heterogenous resource
investment, accumulation of reserves in growth-limiting conditions, and the
observed behaviour of yeast growing in batch and continuous cultures. The
maximum entropy principle is also shown to yield an optimal control law
consistent with partitioning resources between elementary flux mode families,
which has important practical implications for model reduction, selection, and
simulation.
arXiv Quantitative Biology
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