Growth costs of suboptimal protein allocation in nonlinear models of growing cells

Microbial growth depends on how cells allocate their limited proteome among competing functions. Although many proteins are expressed near levels that maximize growth, deviations from these optima are common and can impose substantial fitness costs. Modeling the growth costs of suboptimal protein allocation remains challenging because protein expression influences growth through multiple interacting mechanisms, including biosynthetic demands, enzyme kinetics, and limits on cellular density. Here we analyze these effects using growth balance analysis (GBA), a nonlinear framework that predicts steady-state growth and biomass composition of coarse-grained microbial models from basic cellular constraints. The optimal biomass compositions predicted for these models include not only protein concentrations but also the reactant concentrations required to saturate enzymes through nonlinear rate laws, thereby capturing more complex resource trade-offs than in conventional linear resource allocation models. Using these GBA models, we compute optimal biomass compositions with individual proteins fixed at suboptimal levels. The resulting relationships between suboptimal protein allocation and growth rate are consistent with qualitative experimental patterns in bacteria, with growth effects depending on protein function (including idle proteins), environmental conditions, toxic byproducts, and alternative reactions. These results indicate a practical and tractable approach for modeling growth costs arising from suboptimal protein allocation, and suggest a basis for predictive modeling in metabolic engineering and synthetic biology.