Maximizing Protein Translation Rate in the Nonhomogeneous Ribosome Flow Model: A Convex Optimization Approach

TL;DR

This paper models and optimizes protein translation rates using a convex optimization approach applied to the ribosome flow model, enabling efficient determination of parameters that maximize protein production in biological systems.

Contribution

It proves the concavity of the translation rate in the RFM parameters and develops a convex optimization method for finding the unique optimal translation parameters.

Findings

The steady-state translation rate is a strictly concave function of model parameters.

Optimal translation rate depends mainly on initiation and early elongation rates.

Efficient algorithms can determine the optimal parameters even for large mRNA chains.

Abstract

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 is how to maximize protein production. Indeed, translation is known to consume most of the cell's energy 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 ODEs. 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.