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

Abstract

SummaryFaster growing cells must make proteins more quickly. This occurs in part through increasing total ribosome abundance. However, the productivity of individual ribosomes also increases, almost doubling via an unknown mechanism. To investigate, we model both physical transport and chemical reactions among ensembles of individual molecules involved in translation elongation in Escherichia coli. We predict that the Damköhler number, the ratio of transport latency to reaction latency, for translation elongation is ~4; physical transport of individual ternary complexes accounts for ~80% of elongation latency. We also model how molecules pack closer together as growth quickens. Although denser cytoplasm both decreases transport distances and hinders motion, we predict that decreasing distance wins out, offering a simple mechanism for how individual elongating ribosomes become more productive as growth quickens. We also quantify how crowding imposes a physical limit on the performance of self-mixing molecular systems and likely undergirds cellular behavior more broadly.

Ultra-weak protein-protein interactions can modulate proteome-wide searching and binding

“…Cytoplasmic transport times – i.e., how long it takes for a protein to diffuse and encounter its nearest neighbor or desired binding partner – are also comparable to the duration of ultra-weak clusters. For example, an EF-Tu::GFP::tRNA ternary complex (with a radius of 5.9 nm (Maheshwari et al, 2022) and in vivo diffusivity of 2.2 μ m 2 /s (Mustafi and Weisshaar, 2018)) will take ∼2 μ s to diffuse the 5.5 nm to its nearest ribosome, or ∼76 ns to diffuse the 1.0 nm to its nearest macromolecular neighbor at a cytoplasm volume fraction of 30% (Maheshwari et al, 2022). This ultra-weak, transient clustering regime also operates below the characteristic timescales of whole-cell and macroscopic phase separation processes (Asthagiri and Lauffenburger, 2003; Molliex et al, 2015; Ramm et al, 2022; Tang et al, 2021; Zia et al, 2014) ( Figure 5 , right), which are readily measured in vivo .…”

“…These results both underscore the centrality of protein synthesis machinery in prokaryotic cytoplasm and support the assertion that ribosome surface charge is a primary regulator of protein dynamics in vivo (Schavemaker et al, 2017). Given the growth-limiting nature of protein synthesis in prokaryotes (Belliveau et al, 2021; Maheshwari et al, 2022), any PPI that increases the speed of translation is likely to have a fitness benefit. As such, we speculate that improved colloidal-scale transport of translation-associated proteins and complexes driven by UW-PPIs could broadly support efficient protein synthesis and overall cellular growth.…”

“…Further, our model provides a basis for investigating how protein behavior varies generally with colloidal-scale molecular and cellular properties. For example, confinement (Aponte-Rivera and Zia, 2022; Aponte-Rivera et al, 2018; Gonzalez et al, 2021) (e.g., by a cell membrane) and size polydispersity (Asakura and Oosawa, 1954; Gonzalez et al, 2021; Maheshwari et al, 2022) can induce structural correlations between molecules, which we might expect to augment co-localization driven by UW-PPIs.…”

“…We chose a total protein volume fraction ϕ = 30%, where and n is the number density of proteins. This volume fraction represents in vivo crowding in prokaryotic cytoplasm at moderate growth rate (Maheshwari et al, 2022) Because of the small characteristic size of proteins, the Reynolds number, Re = ρUa p / η , is vanishingly small and thus fluid motion obeys the Stokes’ equations. Here, U is the characteristic protein velocity.…”