Spin Glass Theory of Interacting Metabolic Networks

TL;DR

This paper models interacting cellular metabolisms using spin glass theory, revealing complex phenotypic states and specialization patterns driven by interactions and selective pressures.

Contribution

It introduces a novel statistical mechanics framework for analyzing metabolic networks as disordered spin systems, providing a general solution for arbitrary networks.

Findings

Metabolic interactions create a complex, multi-minima phenotypic space.

Cells can specialize in metabolite production or consumption.

The model predicts diverse stable phenotypic states in cell populations.

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.