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

TL;DR

This paper analyzes the homogeneous ribosome flow model to identify how to optimize protein translation rates, providing theoretical insights and practical formulas for maximizing translation efficiency in biological and synthetic systems.

Contribution

It proves the concavity of the steady-state translation rate in the HRFM and derives closed-form solutions for optimal parameters, advancing understanding of translation mechanisms.

Findings

Steady-state translation rate is a concave function of parameters.

Closed-form solutions for optimal initiation and transition rates.

Approximate solutions are effective even for small system sizes.

Abstract

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.