A Coarse-Grained Biophysical Model of E. coli and Its Application to Perturbation of the rRNA Operon Copy Number

Abstract

We propose a biophysical model of Escherichia coli that predicts growth rate and an effective cellular composition from an effective, coarse-grained representation of its genome. We assume that E. coli is in a state of balanced exponential steady-state growth, growing in a temporally and spatially constant environment, rich in resources. We apply this model to a series of past measurements, where the growth rate and rRNA-to-protein ratio have been measured for seven E. coli strains with an rRNA operon copy number ranging from one to seven (the wild-type copy number). These experiments show that growth rate markedly decreases for strains with fewer than six copies. Using the model, we were able to reproduce these measurements. We show that the model that best fits these data suggests that the volume fraction of macromolecules inside E. coli is not fixed when the rRNA operon copy number is varied. Moreover, the model predicts that increasing the copy number beyond seven results in a cytoplasm densely packed with ribosomes and proteins. Assuming that under such overcrowded conditions prolonged diffusion times tend to weaken binding affinities, the model predicts that growth rate will not increase substantially beyond the wild-type growth rate, as indicated by other experiments. Our model therefore suggests that changing the rRNA operon copy number of wild-type E. coli cells growing in a constant rich environment does not substantially increase their growth rate. Other observations regarding strains with an altered rRNA operon copy number, such as nucleoid compaction and the rRNA operon feedback response, appear to be qualitatively consistent with this model. In addition, we discuss possible design principles suggested by the model and propose further experiments to test its validity. A bacterium like E. coli can be thought of as a self-replicating factory, where inventory synthesis, degradation, and management is concerted according to a well-defined set of rules encoded in the organism's genome. Since the organism's survival depends on this set of rules, these rules were most likely optimized by evolution. Therefore, by writing down these rules, what could one learn about Escherichia coli? We examined E. coli growing in the simplest imaginable environment, one constant in space and time and rich in resources, and attempted to identify the rules that relate the genome to the cell composition and self-replication time. With more than 4,400 genes, a full-scale model would be prohibitively complicated, and therefore we “coarse-grained” E. coli by lumping together genes and proteins of similar function. We used this model to examine measurements of strains with reduced copy number of ribosomal-RNA genes, and also to show that increasing this copy number overcrowds the cell with ribosomes and proteins. As a result, there appears to be an optimum copy number with respect to the wild-type genome, in agreement with observation. We hope that this model will improve and further challenge our understanding of bacterial physiology, also in more complicated environments.