Spin Glass Theory of Interacting Metabolic Networks

Abstract

We cast the metabolism of interacting cells within a statistical mechanics framework considering both, the actual phenotypic capacities of each cell and its interaction with its neighbors. Reaction fluxes will be the components of high-dimensional spin vectors, whose values will be constrained by the stochiometry and the energy requirements of the metabolism. Within this picture, finding the phenotypic states of the population turns out to be equivalent to searching for the equilibrium states of a disordered spin model. We provide a general solution of this problem for arbitrary metabolic networks and interactions. We apply this solution to a simplified model of metabolism and to a complex metabolic network, the central core of the \emph{E. coli}, and demonstrate that the combination of selective pressure and interactions define a complex phenotypic space. Cells may specialize in producing or consuming metabolites complementing each other at the population level and this is described by an equilibrium phase space with multiple minima, like in a spin-glass model.

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Cited by in corpus (4)

• Path-integral solution of MacArthur's resource-competition model for large ecosystems with random species-resources couplings
• Universal scaling relation and criticality in metabolism and growth of Escherichia coli
• Evolutionary emergent metabolic interactions in cell cultures: A Statistical Mechanics point of view
• Cooperative metabolic resource allocation in spatially-structured systems