title: Maximizing protein translation rate in the non-homogeneous ribosome flow model: a convex optimization approach.
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, 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.
authors.affiliation: School of EE-Systems, Tel Aviv University, Tel Aviv 69978, Israel.
authors.forename: Gilad
authors.initials: G
authors.lastname: Poker
authors.affiliation: School of EE-Systems, Tel Aviv University, Tel Aviv 69978, Israel.
authors.forename: Yoram
authors.initials: Y
authors.lastname: Zarai
authors.affiliation: School of EE-Systems, Tel Aviv University, Tel Aviv 69978, Israel The Sagol School of Neuroscience, Tel Aviv University, Tel Aviv 69978, Israel.
authors.forename: Michael
authors.initials: M
authors.lastname: Margaliot
authors.affiliation: The Sagol School of Neuroscience, Tel Aviv University, Tel Aviv 69978, Israel Department of Biomedical Engineering, Tel Aviv University, Tel Aviv 69978, Israel tamirtul@post.tau.ac.il.
authors.forename: Tamir
authors.initials: T
authors.lastname: Tuller
mesh_terms: D000465:Algorithms; D003062:Codon / Q000378:metabolism*; D003198:Computer Simulation; D008954:Models, Biological; D016366:Open Reading Frames / Q000502:physiology; D010441:Peptide Chain Elongation, Translational / Q000502:physiology*; D012270:Ribosomes / Q000378:metabolism*
chemical_list: D003062:Codon
keywords: concavity; gene translation; maximizing the protein production rate; synthetic biology; transcript evolution