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Translation is a key step in the synthesis of proteins. Accordingly, cells have evolved an intricate array of control mechanisms to regulate this process. By constructing a multicomponent mathematical framework we uncover how translation may be controlled via interacting feedback loops. Our results reveal that this interplay gives rise to a remarkable range of protein synthesis dynamics, including oscillations, step change, and bistability. This suggests that cells may have recourse to a much richer set of control mechanisms than was previously understood.

One of the greatest challenges in biophysical models of translation is to identify coding sequence features that affect the rate of translation and therefore the overall protein production in the cell. We propose an analytic method to solve a translation model based on the inhomogeneous totally asymmetric simple exclusion process, which allows us to unveil simple design principles of nucleotide sequences determining protein production rates. Our solution shows an excellent agreement when compared to numerical genome-wide simulations of S. cerevisiae transcript sequences and predicts that the first 10 codons, which is the ribosome footprint length on the mRNA, together with the value of the initiation rate, are the main determinants of protein production rate under physiological conditions. Finally, we interpret the obtained analytic results based on the evolutionary role of the codons' choice for regulating translation rates and ribosome densities.

The well established phenomenon of ribosome drop-off plays crucial roles in translational accuracy and nutrient starvation responses during protein translation. When cells are under stress conditions, such as amino acid starvation or aminoacyl-tRNA depletion due to a high level of recombinant protein expression, ribosome drop-off can substantially affect the efficiency of protein expression. Here we introduce a mathematical model that describes the effects of ribosome drop-off on the ribosome density along the mRNA and on the concomitant protein synthesis rate. Our results show that ribosome premature termination may lead to non-intuitive ribosome density profiles, such as a ribosome density which increases from the 5' to the 3' end. Importantly, the model predicts that the effects of ribosome drop-off on the translation rate are mRNA-specific, and we quantify their resilience to drop-off, showing that the mRNAs which present ribosome queues are much less affected by ribosome drop-off than those which do not. Moreover, among those mRNAs that do not present ribosome queues, resilience to drop-off correlates positively with the elongation rate, so that sequences using fast codons are expected to be less affected by ribosome drop-off. This result is consistent with a genome-wide analysis of S. cerevisiae, which reveals that under favourable growth conditions mRNAs coding for proteins involved in the translation machinery, known to be highly codon biased and using preferentially fast codons, are highly resilient to ribosome drop-off. Moreover, in physiological conditions, the translation rate of mRNAs coding for regulatory, stress-related proteins, is less resilient to ribosome drop-off. This model therefore allows analysis of variations in the translational efficiency of individual mRNAs by accounting for the full range of known ribosome behaviours, as well as explaining mRNA-specific variations in ribosome density emerging from ribosome profiling studies.

tRNA gene copy number is a primary determinant of tRNA abundance and therefore the rate at which each tRNA delivers amino acids to the ribosome during translation. Low-abundance tRNAs decode rare codons slowly, but it is unclear which genes might be subject to tRNA-mediated regulation of expression. Here, those mRNA targets were identified via global simulation of translation. In-silico mRNA translation rates were compared for each mRNA in both wild-type and a [Formula: see text] sup70-65 mutant, which exhibits a pseudohyphal growth phenotype and a 75% slower CAG codon translation rate. Of 4900 CAG-containing mRNAs, 300 showed significantly reduced in silico translation rates in a simulated tRNA mutant. Quantitative immunoassay confirmed that the reduced translation rates of sensitive mRNAs were [Formula: see text] concentration-dependent. Translation simulations showed that reduced [Formula: see text] concentrations triggered ribosome queues, which dissipated at reduced translation initiation rates. To validate this prediction experimentally, constitutive gcn2 kinase mutants were used to reduce in vivo translation initiation rates. This repaired the relative translational rate defect of target mRNAs in the sup70-65 background, and ameliorated sup70-65 pseudohyphal growth phenotypes. We thus validate global simulation of translation as a new tool to identify mRNA targets of tRNA-specific gene regulation., (© The Author(s) 2016. Published by Oxford University Press on behalf of Nucleic Acids Research.)

In Saccharomyces cerevisiae, the SUP70 gene encodes the CAG-decoding tRNA(Gln)(CUG). A mutant allele, sup70-65, induces pseudohyphal growth on rich medium, an inappropriate nitrogen starvation response. This mutant tRNA is also a UAG nonsense suppressor via first base wobble. To investigate the basis of the pseudohyphal phenotype, 10 novel sup70 UAG suppressor alleles were identified, defining positions in the tRNA(Gln)(CUG) anticodon stem that restrict first base wobble. However, none conferred pseudohyphal growth, showing altered CUG anticodon presentation cannot itself induce pseudohyphal growth. Northern blot analysis revealed the sup70-65 tRNA(Gln)(CUG) is unstable, inefficiently charged, and 80% reduced in its effective concentration. A stochastic model simulation of translation predicted compromised expression of CAG-rich ORFs in the tRNA(Gln)(CUG)-depleted sup70-65 mutant. This prediction was validated by demonstrating that luciferase expression in the mutant was 60% reduced by introducing multiple tandem CAG (but not CAA) codons into this ORF. In addition, the sup70-65 pseudohyphal phenotype was partly complemented by overexpressing CAA-decoding tRNA(Gln)(UUG), an inefficient wobble-decoder of CAG. We thus show that introducing codons decoded by a rare tRNA near the 5' end of an ORF can reduce eukaryote translational expression, and that the mutant tRNA(CUG)(Gln) constitutive pseudohyphal differentiation phenotype correlates strongly with reduced CAG decoding efficiency., (© 2012 Blackwell Publishing Ltd.)

To understand the complex relationship governing transcript abundance and the level of the encoded protein, we integrate genome-wide experimental data of ribosomal density on mRNAs with a novel stochastic model describing ribosome traffic dynamics during translation elongation. This analysis reveals that codon arrangement, rather than simply codon bias, has a key role in determining translational efficiency. It also reveals that translation output is governed both by initiation efficiency and elongation dynamics. By integrating genome-wide experimental data sets with simulation of ribosome traffic on all Saccharomyces cerevisiae ORFs, mRNA-specific translation initiation rates are for the first time estimated across the entire transcriptome. Our analysis identifies different classes of mRNAs characterised by their initiation rates, their ribosome traffic dynamics, and by their response to ribosome availability. Strikingly, this classification based on translational dynamics maps onto key gene ontological classifications, revealing evolutionary optimisation of translation responses to be strongly influenced by gene function.

We examine the dynamics of the translation stage of cellular protein production, in which ribosomes move uni-directionally along an mRNA strand, building amino acid chains as they go. We describe the system using a timed event graph-a class of Petri net useful for studying discrete events, which have to satisfy constraints. We use max-plus algebra to describe a deterministic version of the model, where the constraints represent steric effects which prevent more than one ribosome reading a given codon at a given time and delays associated with the availability of the different tRNAs. We calculate the protein production rate and density of ribosomes on the mRNA and find exact agreement between these analytical results and numerical simulations of the deterministic model, even in the case of heterogeneous mRNAs., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

We study the elongation stage of mRNA translation in eukaryotes and find that, in contrast to the assumptions of previous models, both the supply and the demand for tRNA resources are important for determining elongation rates. We find that increasing the initiation rate of translation can lead to the depletion of some species of aa-tRNA, which in turn can lead to slow codons and queueing. Particularly striking "competition" effects are observed in simulations of multiple species of mRNA which are reliant on the same pool of tRNA resources. These simulations are based on a recent model of elongation which we use to study the translation of mRNA sequences from the Saccharomyces cerevisiae genome. This model includes the dynamics of the use and recharging of amino acid tRNA complexes, and we show via Monte Carlo simulation that this has a dramatic effect on the protein production behaviour of the system.

We introduce slow bottleneck sites into a recent extension of the totally asymmetric exclusion process where hopping rates are allowed to vary dynamically with the availability of resources. In the context of messenger RNA (mRNA) translation in biology, this refers to the availability of amino acid-transfer-RNA (aa-tRNA) complexes which act as the source of amino acids for protein production. We study a simple designer mRNA with a single defect codon in the center. As well as the familiar queuing behavior we also observe a regime within the queuing phase where the queue becomes less severe as the aa-tRNAs become depleted.

Messenger RNA translation is often studied by means of statistical-mechanical models based on the asymmetric simple exclusion process (ASEP), which considers hopping particles (the ribosomes) on a lattice (the polynucleotide chain). In this work we extend this class of models and consider the two fundamental steps of the ribosome's biochemical cycle following a coarse-grained perspective. In order to achieve a better understanding of the underlying biological processes and compare the theoretical predictions with experimental results, we provide a description lying between the minimal ASEP-like models and the more detailed models, which are analytically hard to treat. We use a mean-field approach to study the dynamics of particles associated with an internal stepping cycle. In this framework it is possible to characterize analytically different phases of the system (high density, low density or maximal current phase). Crucially, we show that the transitions between these different phases occur at different parameter values than the equivalent transitions in a standard ASEP, indicating the importance of including the two fundamental steps of the ribosome's biochemical cycle into the model.

We study the current of particles on a lattice, where to each site a different hopping probability has been associated and the particles can move only in one direction. We show that the queueing of the particles behind a slow site can lead to a first-order phase transition, and derive analytical expressions for the configuration of slow sites for this to happen. We apply this stochastic model to describe the translation of mRNAs. We show that the first-order phase transition, uncovered in this work, is the process responsible for the classification of the proteins having different biological functions.