Optimal Allocation of Bacterial Protein Resources under Nonlethal Protein Maturation Stress

Under different environmental stresses, bacteria optimize the allocation of cellular resources through a variety of mechanisms. Recently, researchers have used phenomenological models to quantitatively characterize the allocation of bacterial protein resources under metabolic and translational limitations. Some stresses interfere with protein maturation, thereby enhancing the expression of chaperones and proteases. However, the reallocation of protein resources caused by such environmental stresses has not been modeled quantitatively. Here, we developed a dynamic model of coarse-grained protein resource fluxes based on a self-replicator that includes protein maturation and degradation. Through flux balance analysis, it produces a constrained optimization problem that can be solved analytically. Accordingly, we predicted protein allocation fractions as functions of growth rate under different limitations, which are basically in line with empirical data. We cultured Escherichia coli in media containing different concentrations of chloramphenicol, acetic acid, and paraquat and measured the functional relationship between the expression level of β-galactosidase driven by a constitutive promoter and the bacterial growth rate, respectively. Taking into account the possible mode of stress limitation on the fluxes, our model reproduces this experimentally measured relationship. In addition, our model is in good agreement with the experimental relationship between growth rate and proteome fraction of unnecessary protein in E. coli, considering the unoptimized upregulation of chaperones with useless protein overexpression. The results provide a more systematic view of bacterial stress adaptation that may help in designing for bioengineering or medical interventions.