An analytical theory of balanced cellular growth

Abstract

The biological fitness of microbes is largely determined by the rate with which they replicate their biomass composition. Mathematical models that maximize this balanced growth rate while accounting for mass conservation, reaction kinetics, and limits on dry mass per volume are inevitably non-linear. Here, we develop a general theory for such models, termed Growth Balance Analysis (GBA), which provides explicit expressions for protein concentrations, fluxes, and growth rates. These variables are functions of the concentrations of cellular components, for which we calculate marginal fitness costs and benefits that are related to metabolic control coefficients. At maximal growth rate, the net benefits of all concentrations are equal. Based solely on physicochemical constraints, GBA unveils fundamental quantitative principles of cellular resource allocation and growth; it accurately predicts the relationship between growth rates and ribosome concentrations in E. coli and yeast and between growth rate and dry mass density in E. coli.

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

“…A small number of modeling approaches incorporate these two nonlinearities [7,[32][33][34][35][36][37]. The demand for cell synthesis components is calculated by the models instead of imposed on the models, and the growth rate can only be found after solving a nonlinear problem -or by solving a large number of linear problems in which the growth rate is treated as a parameter, as we will see.…”

“…In some modeling methods this density is modeled as an upper bound [32,33,37]. In SI7 we explain the advantages and disadvantages of doing this.…”

“…In SI7 we explain the advantages and disadvantages of doing this. 6 Dependent on the biochemical interpretation of the ρ-parameters, some models include contributions of the metabolite concentrations ρ i x i [7,37].…”

“…Therefore, global optimization software has to be used and it is difficult to ascertain that the found solution is the actual optimum. For these reasons, enzyme kinetics can so far only be included in core models [32] and theoretical work [7,8,37]. The question is if there are constraints, rules and patterns in the changes in (optimal) metabolite levels that would allow us to approximate optimal solutions without global optimisation of the full kinetic model.…”

“…One could also solve the problem for fixed metabolite concentrations[7,37], and then scan over all possible sets of concentrations, but this becomes computationally infeasible in large quantitative models.…”