Statistical mechanics for metabolic networks during steady-state growth

Abstract

Which properties of metabolic networks can be derived solely from stoichiometric information about the network's constituent reactions? Predictive results have been obtained by Flux Balance Analysis (FBA), by postulating that cells set metabolic fluxes within the allowed stoichiometry so as to maximize their growth. Here, we generalize this framework to single cell level using maximum entropy models from statistical physics. We define and compute, for the core metabolism of Escherichia coli, a joint distribution over all fluxes that yields the experimentally observed growth rate. This solution, containing FBA as a limiting case, provides a better match to the measured fluxes in the wild type and several mutants. We find that E. coli metabolism is close to, but not at, the optimality assumed by FBA. Moreover, our model makes a wide range of predictions: (i) on flux variability, its regulation, and flux correlations across individual cells; (ii) on the relative importance of stoichiometric constraints vs. growth rate optimization; (iii) on quantitative scaling relations for singe-cell growth rate distributions. We validate these scaling predictions using data from individual bacterial cells grown in a microfluidic device at different sub-inhibitory antibiotic concentrations. Under mild dynamical assumptions, fluctuation-response relations further predict the autocorrelation timescale in growth data and growth rate adaptation times following an environmental perturbation.

12 pages, 4 figures

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• Spin Glass Theory of Interacting Metabolic Networks
• A Van-Der-Waals picture for metabolic networks from MaxEnt modeling: inherent bistability and elusive coexistence
• Truncated Log-concave Sampling with Reflective Hamiltonian Monte Carlo
• Metabolic coordination and phase transitions in spatially distributed multi-cellular systems
• Optimal metabolic strategies for microbial growth in stationary random environments
• Universal scaling relation and criticality in metabolism and growth of Escherichia coli
• Constraint-based inverse modeling of metabolic networks: a proof of concept
• Matrix approach to generalized ensemble theory for nonequilibrium discrete systems
• Cooperative metabolic resource allocation in spatially-structured systems
• Evolutionary emergent metabolic interactions in cell cultures: A Statistical Mechanics point of view
• Information costs in the control of protein synthesis