Genome-Scale Analysis of Translation Elongation with a Ribosome Flow Model

We describe the first large scale analysis of gene translation that is based on a model that takes into account the physical and dynamical nature of this process. The Ribosomal Flow Model (RFM) predicts fundamental features of the translation process, including translation rates, protein abundance levels, ribosomal densities and the relation between all these variables, better than alternative (‘non-physical’) approaches. In addition, we show that the RFM can be used for accurate inference of various other quantities including genes' initiation rates and translation costs. These quantities could not be inferred by previous predictors. We find that increasing the number of available ribosomes (or equivalently the initiation rate) increases the genomic translation rate and the mean ribosome density only up to a certain point, beyond which both saturate. Strikingly, assuming that the translation system is tuned to work at the pre-saturation point maximizes the predictive power of the model with respect to experimental data. This result suggests that in all organisms that were analyzed (from bacteria to Human), the global initiation rate is optimized to attain the pre-saturation point. The fact that similar results were not observed for heterologous genes indicates that this feature is under selection. Remarkably, the gap between the performance of the RFM and alternative predictors is strikingly large in the case of heterologous genes, testifying to the model's promising biotechnological value in predicting the abundance of heterologous proteins before expressing them in the desired host

Analyzing Linear Communication Networks using the Ribosome Flow Model

The Ribosome Flow Model (RFM) describes the unidirectional movement of interacting particles along a one-dimensional chain of sites. As a site becomes fuller, the effective entry rate into this site decreases. The RFM has been used to model and analyze mRNA translation, a biological process in which ribosomes (the particles) move along the mRNA molecule (the chain), and decode the genetic information into proteins. Here we propose the RFM as an analytical framework for modeling and analyzing linear communication networks. In this context, the moving particles are data-packets, the chain of sites is a one dimensional set of ordered buffers, and the decreasing entry rate to a fuller buffer represents a kind of decentralized backpressure flow control. For an RFM with homogeneous link capacities, we provide closed-form expressions for important network metrics including the throughput and end-to-end delay. We use these results to analyze the hop length and the transmission probability (in a contention access mode) that minimize the end-to-end delay in a multihop linear network, and provide closed-form expressions for the optimal parameter values

On Three Generalizations of Contraction

We introduce three forms of generalized contraction (GC). Roughly speaking, these are motivated by allowing contraction to take place after small transients in time and/or amplitude. Indeed, contraction is usually used to prove asymptotic properties, like convergence to an attractor or entrainment to a periodic excitation, and allowing initial transients does not affect this asymptotic behavior. We provide sufficient conditions for GC, and demonstrate their usefulness using examples of systems that are not contractive, with respect to any norm, yet are GC

Gene length as a regulator for ribosome recruitment and protein synthesis : theoretical insights

The authors would like to acknowledge the funding provided by the European Union Seventh Framework Programme [FP7/2007–2013] (NICHE; grant agreement 289384) (LDF). LDF also acknowledges the funding provided by the São Paulo Research Foundation (FAPESP - grant #2015/26989-4). AM was partially funded by the UK Biotechnology and Biological Research Council (BBSRC), through grant BB/N015711/1. LC would like to acknowledge Maria Carmen Romano, Jean Hausser, Marco Cosentino Lagomarsino, Jean-Charles Walter and Norbert Kern for early discussions on this work, and the CNRS for having granted him a “demi-délégation” (2017–18). We would like to dedicate this work in memory of Maxime Clusel and Vladimir Lorman.Peer reviewedPublisher PDFPublisher PD

Maximizing Protein Translation Rate in the Ribosome Flow Model: the Homogeneous Case

Gene translation is the process in which intracellular macro-molecules, called ribosomes, decode genetic information in the mRNA chain into the corresponding proteins. Gene translation includes several steps. During the elongation step, ribosomes move along the mRNA in a sequential manner and link amino-acids together in the corresponding order to produce the proteins. The homogeneous ribosome flow model(HRFM) is a deterministic computational model for translation-elongation under the assumption of constant elongation rates along the mRNA chain. The HRFM is described by a set of n first-order nonlinear ordinary differential equations, where n represents the number of sites along the mRNA chain. The HRFM also includes two positive parameters: ribosomal initiation rate and the (constant) elongation rate. In this paper, we show that the steady-state translation rate in the HRFM is a concave function of its parameters. This means that the problem of determining the parameter values that maximize the translation rate is relatively simple. Our results may contribute to a better understanding of the mechanisms and evolution of translation-elongation. We demonstrate this by using the theoretical results to estimate the initiation rate in M. musculus embryonic stem cell. The underlying assumption is that evolution optimized the translation mechanism. For the infinite-dimensional HRFM, we derive a closed-form solution to the problem of determining the initiation and transition rates that maximize the protein translation rate. We show that these expressions provide good approximations for the optimal values in the n-dimensional HRFM already for relatively small values of n. These results may have applications for synthetic biology where an important problem is to re-engineer genomic systems in order to maximize the protein production rate