Colloidal physics modeling reveals how per-ribosome productivity increases with growth rate in E. coli

Faster growing cells must synthesize proteins more quickly. Increased ribosome abundance only partly accounts for increases in total protein synthesis rates. The productivity of individual ribosomes must increase too, almost doubling by an unknown mechanism. Prior models point to diffusive transport as a limiting factor but surface a paradox: faster growing cells are more crowded, yet crowding slows diffusion. We suspected physical crowding, transport, and stoichiometry, considered together, might reveal a more nuanced explanation. To investigate, we built a first-principles physics-based model of E. coli cytoplasm in which Brownian motion and diffusion arise directly from physical interactions between individual molecules of finite size, density, and physiological abundance. Using our microscopically-detailed model, we predict that physical transport of individual ternary complexes accounts for ~80% of translation elongation latency. We also find that volumetric crowding increases at faster growth even as cytoplasmic mass density remains relatively constant. Despite slowed diffusion, we predict that improved proximity between ternary complexes and ribosomes wins out, illustrating a simple physics-based mechanism for how individual elongating ribosomes become more productive. We speculate how crowding imposes a physical limit on growth rate and undergirds cellular behavior more broadly. Unfitted colloidal-scale modeling offers systems biology a complementary "physics engine" for exploring how cellular-scale behaviors arise from physical transport and reactions among individual molecules.