Abstract
The metabolic network of a cell can be decomposed into discrete elementary modes that contribute, each with a certain probability, to the overall flux through the metabolism. These modes are cell function supporting, fundamental pathways that represent permissible ‘quantum’ states of the metabolism. For the case that cellular regulatory mechanisms for pathway fluxes evolved in an unbiased way, we demonstrate theoretically that the usage probabilities of individual elementary modes are distributed according to Boltzmann’s distribution law such that the rate of entropy production is maximized. Such distribution can be observed experimentally in highly evolved metabolic networks. Therefore, cell function has a natural tendency to operate at a maximum rate of entropy generation using preferentially efficient pathways with small reaction entropies. Ultimately, evolution of metabolic networks appears to be driven by forces that can be quantified by the distance of the current metabolic state from the state of maximum entropy generation that represents the unbiased, most probable selection of fundamental pathway choices.
Highlights
Elementary modes represent unique, minimal sets of reactions enabling the operation of specific pathways that are embedded in a metabolic network [1,2,3,4,5,6]
The overall operation of the metabolism has to be viewed as a weighted average of all possible elementary modes that individually contribute to the metabolic flux in the cell [14]
We have previously made the experimental observation that the individual contributions of elementary modes to the overall metabolism appear to be correlated with the standard reaction entropy of individual elementary modes as defined by their overall reaction stoichiometry
Summary
Elementary modes represent unique, minimal sets of reactions enabling the operation of specific pathways that are embedded in a metabolic network [1,2,3,4,5,6]. It is shown that the usage probability of individual elementary modes is distributed according to the Boltzmann distribution law such that the rate of entropy production is maximized. The pathways expressed in individual elementary modes have different overall stoichiometries, relating the external metabolites, than the overall growth equation.
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