Relationship between fitness and heterogeneity in exponentially growing microbial populations

Abstract

Microbial metabolic networks perform the basic function of harvesting energy from nutrients to generate the work and free energy required for survival, growth and replication. The robust physiological outcomes they generate across vastly different organisms in spite of major environmental and genetic differences represent an especially remarkable trait. Most notably, it suggests that metabolic activity in bacteria may follow universal principles, the search for which is a long-standing issue. Most theoretical approaches to modeling metabolism assume that cells optimize specific evolutionarily-motivated objective functions (like their growth rate) under general physico-chemical or regulatory constraints. While conceptually and practically useful in many situations, the idea that certain objectives are optimized is hard to validate in data. Moreover, it is not clear how optimality can be reconciled with the degree of single-cell variability observed within microbial populations. To shed light on these issues, we propose here an inverse modeling framework that connects fitness to variability through the Maximum-Entropy guided inference of metabolic flux distributions from data. While no clear optimization emerges, we find that, as the medium gets richer, Escherichia coli populations slowly approach the theoretically optimal performance defined by minimal reduction of phenotypic variability at given mean growth rate. Inferred flux distributions provide multiple biological insights, including on metabolic reactions that are experimentally inaccessible. These results suggest that bacterial metabolism is crucially shaped by a population-level trade-off between fitness and cell-to-cell heterogeneity.

Inferring metabolic fluxes in nutrient-limited continuous cultures: A Maximum Entropy Approach with minimum information

“…The most significant is related with the definition of the biomass equation, which is determined by experimentally measuring the average cellular composition [53]. In principle, this constraint (dashed line in the Figure (2)) should be considered to be affecting only V. But we made the widely adopted simplification [17,31,34,62] of taking it as a hard constraint over V. In the current formulation, M E is only capable to encode average constraints over the reaction bounds (like equations ( 7) and ( 8)), not balance constraints such that the biomass equation. In the particular case of a limiting-nutrient chemostat culture, this might be a fundamental source of bias given the tendency of the culture to maximizes z/ ūg (see results at Figure (8) Panel A).…”

“…Traditionally, this issue has been addressed by introducing further constraints based on available experimental data (e.g. fixing a fraction of the fluxes [31]) or in the case of F BA by defining an objective function (or a stack of them). In the latter case, the objective function tries to represent those unknown non-environmental constraints that are driving the system to a specific state inside the very degenerated feasible solution space.…”

“…A more general methodology that exploits the Maximum Entropy Principle (M E) [30] combined with a constraint-based model, in order to formulate a probabilistic description of the metabolic state of cells in the culture, has been used recently [31][32][33][34]. In particular, it has been shown that M E distributions provide a better fit to measured flux observables than plain F BA models [32].…”

“…Also, M E-derived growth rate distributions have been compared to experiments with good results, using single-cell data at different sub-inhibitory antibiotic concentrations [32]. A more recent formulation exploits the availability of experimental data from the culture, to further limit the available solution space for the metabolism [31]. In practice, the authors of [31] not only fix the growth rate, but all the experimental fluxes.…”

“…A more recent formulation exploits the availability of experimental data from the culture, to further limit the available solution space for the metabolism [31]. In practice, the authors of [31] not only fix the growth rate, but all the experimental fluxes. This approach however, leaves open relevant questions: i) What is the minimum number of fluxes that we need to fix to have a proper description of the system?…”