Statistical mechanics for metabolic networks during steady state growth

Abstract

Which properties of metabolic networks can be derived solely from stoichiometry? Predictive results have been obtained by flux balance analysis (FBA), by postulating that cells set metabolic fluxes to maximize growth rate. Here we consider a generalization of FBA to single-cell level using maximum entropy modeling, which we extend and test experimentally. Specifically, we define for Escherichia coli metabolism a flux distribution that yields the experimental growth rate: the model, containing FBA as a limit, provides a better match to measured fluxes and it makes a wide range of predictions: on flux variability, regulation, and correlations; on the relative importance of stoichiometry vs. optimization; on scaling relations for growth rate distributions. We validate the latter here with single-cell data at different sub-inhibitory antibiotic concentrations. The model quantifies growth optimization as emerging from the interplay of competitive dynamics in the population and regulation of metabolism at the level of single cells.

The common message of constraint-based optimization approaches: overflow metabolism is caused by two growth-limiting constraints

“…The sub-optimality of a population of microorganisms might be due to the high regulatory costs that would be required to steer each individual cell to the optimum. De Martino et al [43] calculated a possible probability distribution for the metabolic states of single cells by maximizing the entropy of this distribution while the average growth rate was fixed to the measured value. This approach leads to a model of single-cell behavior in which the least additional assumptions were made: 'the probability distribution is as general as possible'.…”

Maximum entropy modeling of metabolic networks by constraining growth-rate moments predicts coexistence of phenotypes

“…the threshold for the acetate switch. The sample consists of 35 technical replicates collected from control experiments retrieved in the database [19] (same dataset analyzed in [11]). …”

“…Recent applications of Monte Carlo Markov chain algorithms to integral calculus [9] give rise to the possibility of mapping growth rate distributions into an underlying distribution for the metabolic phenotypes, in the most simple way upon recurring to maximum entropy distributions at fixed average arXiv:1707.00320v1 [q-bio.MN] 2 Jul 2017 growth rate in the space of metabolic steady states [10]. These in turns provide quantitative predictions for experimental estimates of metabolic fluxes as well as for their scaling, correlations and fluctuations [11]. Still this variability does not amount to a substantial phenotypic heterogeneity, since a linear constraint on the average growth leads to simple unimodal distributions.…”

The common message of constraint-based optimization approaches: overflow metabolism is caused by two growth-limiting constraints

“…The sub-optimality of a population of microorganisms might be due to the high regulatory costs that would be required to steer each individual cell to the optimum. De Martino et al [43] calculated a possible probability distribution for the metabolic states of single cells by maximizing the entropy of this distribution while the average growth rate was fixed to the measured value. This approach leads to a model of singlecell behaviour in which the least additional assumptions were made: 'the probability distribution is as general as possible'.…”