Effects of codon sequence on the dynamics of genetic networks

Potapov, Ilya; Mäkelä, Jarno; Yli‐Harja, Olli; Ribeiro, André S.

doi:10.1016/j.jtbi.2012.08.029

Cited by 8 publications

(8 citation statements)

References 45 publications

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“…We model translation as a continuous-time Markov process as introduced in [ 36 ] to capture the stochastic nature of the ribosomal movement. In contrast to earlier stochastic theories of translation [ 39 , 40 ], our model of translation elongation as depicted in Fig 1 is based on the detailed chemical kinetics as determined for a certain in-vitro assay [ 7 , 41 – 46 ]. For each sense codon c , the ribosome can cycle through twelve ribosomal states, numbered from 0 to 11 as shown in Fig 4(A) .…”

Section: Resultsmentioning

confidence: 99%

“…In fact, for eukaryotic translation experimental findings suggest that most ribosomes do not interfere under physiological conditions [ 47 ]. However, interactions of ribosomes can be easily taken into account if the Markov process is studied by stochastic simulations as for example described in [ 36 , 40 , 48 ]. In [ 36 ], we used such simulations to study the time-dependent incorporation of radioactively labeled amino acids into proteins.…”

Section: Resultsmentioning

confidence: 99%

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Protein Synthesis in E. coli: Dependence of Codon-Specific Elongation on tRNA Concentration and Codon Usage

Rudorf

Lipowsky

2015

PLoS ONE

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To synthesize a protein, a ribosome moves along a messenger RNA (mRNA), reads it codon by codon, and takes up the corresponding ternary complexes which consist of aminoacylated transfer RNAs (aa-tRNAs), elongation factor Tu (EF-Tu), and GTP. During this process of translation elongation, the ribosome proceeds with a codon-specific rate. Here, we present a general theoretical framework to calculate codon-specific elongation rates and error frequencies based on tRNA concentrations and codon usages. Our theory takes three important aspects of in-vivo translation elongation into account. First, non-cognate, near-cognate and cognate ternary complexes compete for the binding sites on the ribosomes. Second, the corresponding binding rates are determined by the concentrations of free ternary complexes, which must be distinguished from the total tRNA concentrations as measured in vivo. Third, for each tRNA species, the difference between total tRNA and ternary complex concentration depends on the codon usages of the corresponding cognate and near-cognate codons. Furthermore, we apply our theory to two alternative pathways for tRNA release from the ribosomal E site and show how the mechanism of tRNA release influences the concentrations of free ternary complexes and thus the codon-specific elongation rates. Using a recently introduced method to determine kinetic rates of in-vivo translation from in-vitro data, we compute elongation rates for all codons in Escherichia coli. We show that for some tRNA species only a few tRNA molecules are part of ternary complexes and, thus, available for the translating ribosomes. In addition, we find that codon-specific elongation rates strongly depend on the overall codon usage in the cell, which could be altered experimentally by overexpression of individual genes.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Protein Synthesis in E. coli: Dependence of Codon-Specific Elongation on tRNA Concentration and Codon Usage

Rudorf

Lipowsky

2015

PLoS ONE

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“…An interesting question for further research is whether the translation rate in other models of translation, including various versions of TASEP [41,62,60,56,10,48], is also a concave function of its parameters.…”

Section: Discussionmentioning

confidence: 99%

Maximizing protein translation rate in the non-homogeneous ribosome flow model: a convex optimization approach

Poker

Zarai

Margaliot

et al. 2014

J. R. Soc. Interface.

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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 energyconsuming 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 þ 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.

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“…This question seems to be technically more demanding, as the Hessian matrix of the ndimensional RFM has dimensions (n + 1) × (n + 1), whereas that of the HRFM is 2×2. A more general question is related to the concavity of other models of translation including various versions of the TASEP model [34], [50], [48], [44], [8], [38].…”

Section: Discussionmentioning

confidence: 99%

“…where | * means that this equation holds for the optimal parameter values. Substituting r from (38) and simplifying yields…”

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confidence: 99%

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

Zarai

Margaliot

Tuller

2014

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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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.

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Effects of codon sequence on the dynamics of genetic networks

Cited by 8 publications

References 45 publications

Protein Synthesis in E. coli: Dependence of Codon-Specific Elongation on tRNA Concentration and Codon Usage

Protein Synthesis in E. coli: Dependence of Codon-Specific Elongation on tRNA Concentration and Codon Usage

Maximizing protein translation rate in the non-homogeneous ribosome flow model: a convex optimization approach

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

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