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

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