E. colitranslation strategies differ across nutrient conditions

For cells to grow faster they must increase their protein production rate. Microorganisms have traditionally been thought to accomplish this increase by producing more ribosomes to enhance protein synthesis capacity, leading to the linear relationship between ribosome level and growth rate observed under most growth conditions previously examined. Past studies have suggested that this linear relationship represents an optimal resource allocation strategy for each growth rate, independent of any specific nutrient state. Here we investigate protein production strategies in continuous cultures limited for carbon, nitrogen, and phosphate, which differentially impact substrate supply for protein versus nucleic acid metabolism. Unexpectedly, we find that at slow growth rates,E. coliachieves the same protein production rate using three different strategies under the three different nutrient limitations. Upon phosphate (P) limitation, translation is slow due to a particularly low abundance of ribosomes, which are RNA-rich and thus particularly costly for phosphorous-limited cells. In nitrogen (N) limitation, translation is slowed by limited glutamine and stalling at glutamine codons, resulting is slow elongation. In carbon (C) limitation, translation is slowed by accumulation of inactive ribosomes not bound to mRNA. These extra ribosomes enable rapid growth acceleration upon nutrient upshift. Thus, bacteria tune ribosome usage across different limiting nutrients to enable balanced nutrient-limited growth while also preparing for future nutrient upshifts.

Ribosome flow model with extended objects

We study a deterministic mechanistic model for the flow of ribosomes along the mRNA molecule, called the ribosome flow model with extended objects (RFMEO). This model encapsulates many realistic features of translation including non-homogeneous transition rates along mRNA, the fact that every ribosome covers several codons, and the fact that ribosomes cannot overtake one another. The RFMEO is a mean-field approximation of an important model from statistical mechanics called the totally asymmetric simple exclusion process with extended objects (TASEPEO). We demonstrate that the RFMEO describes biophysical aspects of translation better than previous mean-field approximations, and that its predictions correlate well with those of TASEPEO. However, unlike TASEPEO, the RFMEO is amenable to rigorous analysis using tools from systems and control theory. We show that the ribosome density profile along the mRNA in the RFMEO converges to a unique steady-state density that depends on the length of the mRNA, the transition rates along it, and the number of codons covered by every ribosome, but not on the initial density of ribosomes along the mRNA. In particular, the protein production rate also converges to a unique steady state. Furthermore, if the transition rates along the mRNA are periodic with a common period T then the ribosome density along the mRNA and the protein production rate converge to a unique periodic pattern with period T , that is, the model entrains to periodic excitations in the transition rates. Analysis and simulations of the RFMEO demonstrate several counterintuitive results. For example, increasing the ribosome footprint may sometimes lead to an increase in the production rate. Also, for large values of the footprint the steady-state density along the mRNA may be quite complex (e.g. with quasi-periodic patterns) even for relatively simple (and non-periodic) transition rates along the mRNA. This implies that inferring the transition rates from the ribosome density may be non-trivial. We believe that the RFMEO could be useful for modelling, understanding and re-engineering translation as well as other important biological processes.

Maximizing protein translation rate in the non-homogeneous ribosome flow model: a convex optimization approach

Translation is an important stage in gene expression. During this stage, macro-molecules called ribosomes travel along the mRNA strand linking amino acids together in a specific order to create a functioning protein. An important question, related to many biomedical disciplines, is how to maximize protein production. Indeed, translation is known to be one of the most energy-consuming processes in the cell, and it is natural to assume that evolution shaped this process so that it maximizes the protein production rate. If this is indeed so then one can estimate various parameters of the translation machinery by solving an appropriate mathematical optimization problem. The same problem also arises in the context of synthetic biology, namely, re-engineer heterologous genes in order to maximize their translation rate in a host organism. We consider the problem of maximizing the protein production rate using a computational model for translation–elongation called the ribosome flow model (RFM). This model describes the flow of the ribosomes along an mRNA chain of length n using a set of n first-order nonlinear ordinary differential equations. It also includes n + 1 positive parameters: the ribosomal initiation rate into the mRNA chain, and n elongation rates along the chain sites. We show that the steady-state translation rate in the RFM is a strictly concave function of its parameters. This means that the problem of maximizing the translation rate under a suitable constraint always admits a unique solution, and that this solution can be determined using highly efficient algorithms for solving convex optimization problems even for large values of n . Furthermore, our analysis shows that the optimal translation rate can be computed based only on the optimal initiation rate and the elongation rate of the codons near the beginning of the ORF. We discuss some applications of the theoretical results to synthetic biology, molecular evolution, and functional genomics.

Controlling translation elongation efficiency: tRNA regulation of ribosome flux on the mRNA

Gene expression can be regulated by a wide variety of mechanisms. One example concerns the growing body of evidence that the protein-production rate can be regulated at the level of translation elongation by controlling ribosome flux across the mRNA. Variations in the abundance of tRNA molecules cause different rates of translation of their counterpart codons. This, in turn, produces a variable landscape of translational rate across each and every mRNA, with the dynamic formation and deformation of ribosomal queues being regulated by both tRNA availability and the rates of translation initiation and termination. In the present article, a range of examples of tRNA control of gene expression are reviewed, and the use of mathematical modelling to develop a predictive understanding of the consequences of that regulation is discussed and explained. These findings encourage a view that predicting the protein-synthesis rate of each mRNA requires a holistic understanding of how each stage of translation, including elongation, contributes to the overall protein-production rate.