A model of protein translation including codon bias, nonsense errors, and ribosome recycling

A data-driven estimation of the ribosome drop-off rate in S. cerevisiae reveals a correlation with the genes length

Ribosomes are the molecular machinery that catalyse all the fundamental steps involved in the translation of mRNAs into proteins. Given the complexity of this process, the efficiency of protein synthesis depends on a large number of factors among which ribosome drop-off (i.e. the premature detachment of the ribosome from the mRNA template) plays an important role. However, an in vitro quantification of the extent to which ribosome drop-off occurs is not trivial due to difficulties in obtaining the needed experimental evidence. In this work we focus on the study of ribosome drop-off in Saccharomyces cerevisiae by using 'Ribofilio', a novel software tool that relies on a high sensitive strategy to estimate the ribosome drop-off rate from ribosome profiling data. Our results show that ribosome drop-off events occur at a significant rate also when S. cerevisiae is cultured in standard conditions. In this context, we also identified a correlation between the ribosome drop-off rate and the genes length: the longer the gene, the lower the drop-off rate.

Modeling mRNA Translation With Ribosome Abortions

We derive a deterministic mathematical model for the flow of ribosomes along a mRNA called the ribosome flow model with extended objects and abortions (RFMEOA). This model incorporates important cellular features such as every ribosome covers several codons and they may detach from various regions along the track due to more realistic biological situations including phenomena of ribosome-ribosome collisions. We prove that the ribosome density profile along the mRNA in the RFMEOA and in particular, the protein production rate converge to a unique steady-state. Simulations of the RFMEOA demonstrate a surprising result that an increase in the initiation rate may sometimes lead to a decrease in the production rate. We believe that this model could be helpful to provide insight into the effects of premature termination on the protein expression and be useful for understanding and re-engineering the translation process.

Quantifying shifts in natural selection on codon usage between protein regions: a population genetics approach

Background

Codon usage bias (CUB), the non-uniform usage of synonymous codons, occurs across all domains of life. Adaptive CUB is hypothesized to result from various selective pressures, including selection for efficient ribosome elongation, accurate translation, mRNA secondary structure, and/or protein folding. Given the critical link between protein folding and protein function, numerous studies have analyzed the relationship between codon usage and protein structure. The results from these studies have often been contradictory, likely reflecting the differing methods used for measuring codon usage and the failure to appropriately control for confounding factors, such as differences in amino acid usage between protein structures and changes in the frequency of different structures with gene expression.

Results

Here we take an explicit population genetics approach to quantify codon-specific shifts in natural selection related to protein structure in S. cerevisiae and E. coli. Unlike other metrics of codon usage, our approach explicitly separates the effects of natural selection, scaled by gene expression, and mutation bias while naturally accounting for a region’s amino acid usage. Bayesian model comparisons suggest selection on codon usage varies only slightly between helix, sheet, and coil secondary structures and, similarly, between structured and intrinsically-disordered regions. Similarly, in contrast to prevous findings, we find selection on codon usage only varies slightly at the termini of helices in E. coli. Using simulated data, we show this previous work indicating “non-optimal” codons are enriched at the beginning of helices in S. cerevisiae was due to failure to control for various confounding factors (e.g. amino acid biases, gene expression, etc.), and rather than selection to modulate cotranslational folding.

Conclusions

Our results reveal a weak relationship between codon usage and protein structure, indicating that differences in selection on codon usage between structures are slight. In addition to the magnitude of differences in selection between protein structures being slight, the observed shifts appear to be idiosyncratic and largely codon-specific rather than systematic reversals in the nature of selection. Overall, our work demonstrates the statistical power and benefits of studying selective shifts on codon usage or other genomic features from an explicitly evolutionary approach. Limitations of this approach and future potential research avenues are discussed.

Supplementary Information

The online version contains supplementary material available at (10.1186/s12864-022-08635-0).

Modeling transport of extended interacting objects with drop-off phenomenon

We study a deterministic framework for important cellular transport phenomena involving a large number of interacting molecules called the excluded flow of extended interacting objects with drop-off effect (EFEIOD). This model incorporates many realistic features of biological transport process including the length of biological "particles" and the fact that they can detach along the biological 'tracks'. The flow between the consecutive sites is unidirectional and is described by a "soft" simple exclusion principle and by repelling or attracting forces between neighboring particles. We show that the model admits a unique steady-state. Furthermore, if the parameters are periodic with common period T, then the steady-state profile converge to a unique periodic solution of period T. Simulations of the EFEIOD demonstrate several non-trivial effects of the interactions on the system steady-state profile. For example, detachment rates may help in increasing the steady-state flow by alleviating traffic jams that can exist due to several reasons like bottleneck rate or interactive forces between the particles. We also analyze the special case of our model, when there are no forces exerted by neighboring particles, and called it as the ribosome flow model of extended objects with drop-off effect (RFMEOD), and study the sensitivity of its steady-state to variations in the parameters.

Introducing Parameter Clustering to the OED Procedure for Model Calibration of a Synthetic Inducible Promoter in S. cerevisiae

In recent years, synthetic gene circuits for adding new cell features have become one of the most powerful tools in biological and pharmaceutical research and development. However, because of the inherent non-linearity and noisy experimental data, the experiment-based model calibration of these synthetic parts is perceived as a laborious and time-consuming procedure. Although the optimal experimental design (OED) based on the Fisher information matrix (FIM) has been proved to be an effective means to improve the calibration efficiency, the required calculation increases dramatically with the model size (parameter number). To reduce the OED complexity without losing the calibration accuracy, this paper proposes two OED approaches with different parameter clustering methods and validates the accuracy of calibrated models with in-silico experiments. A model of an inducible synthetic promoter in S. cerevisiae is adopted for bench-marking. The comparison with the traditional off-line OED approach suggests that the OED approaches with both of the clustering methods significantly reduce the complexity of OED problems (for at least 49.0%), while slightly improving the calibration accuracy (11.8% and 19.6% lower estimation error in average for FIM-based and sensitivity-based approaches). This study implicates that for calibrating non-linear models of biological pathways, cluster-based OED could be a beneficial approach to improve the efficiency of optimal experimental design.

Specificity of RNA Folding and Its Association with Evolutionarily Adaptive mRNA Secondary Structures

The secondary structure is a fundamental feature of both noncoding and messenger RNAs. However, our understanding of the secondary structure of mRNA, especially that of the coding regions, remains elusive, likely due to translation and the lack of RNA-binding proteins that sustain the consensus structure, such as those that bind to noncoding RNA. Indeed, mRNA has recently been found to adopt diverse alternative structures, the overall functional significance of which remains untested. We hereby approached this problem by estimating the folding specificity, i.e., the probability that a fragment of RNA folds back to the same partner once refolded. We showed that the folding specificity of mRNA is lower than that of noncoding RNA and exhibits moderate evolutionary conservation. Notably, we found that specific rather than alternative folding is likely evolutionarily adaptive since specific folding is frequently associated with functionally important genes or sites within a gene. Additional analysis in combination with ribosome density suggests the ability to modulate ribosome movement as one potential functional advantage provided by specific folding. Our findings revealed a novel facet of the RNA structurome with important functional and evolutionary implications and indicated a potential method for distinguishing the mRNA secondary structures maintained by natural selection from molecular noise.

Stochastic thermodynamics and modes of operation of a ribosome: A network theoretic perspective

The ribosome is one of the largest and most complex macromolecular machines in living cells. It polymerizes a protein in a step-by-step manner as directed by the corresponding nucleotide sequence on the template messenger RNA (mRNA) and this process is referred to as "translation" of the genetic message encoded in the sequence of mRNA transcript. In each successful chemomechanical cycle during the (protein) elongation stage, the ribosome elongates the protein by a single subunit, called amino acid, and steps forward on the template mRNA by three nucleotides called a codon. Therefore, a ribosome is also regarded as a molecular motor for which the mRNA serves as the track, its step size is that of a codon and two molecules of GTP and one molecule of ATP hydrolyzed in that cycle serve as its fuel. What adds further complexity is the existence of competing pathways leading to distinct cycles, branched pathways in each cycle, and futile consumption of fuel that leads neither to elongation of the nascent protein nor forward stepping of the ribosome on its track. We investigate a model formulated in terms of the network of discrete chemomechanical states of a ribosome during the elongation stage of translation. The model is analyzed using a combination of stochastic thermodynamic and kinetic analysis based on a graph-theoretic approach. We derive the exact solution of the corresponding master equations. We represent the steady state in terms of the cycles of the underlying network and discuss the energy transduction processes. We identify the various possible modes of operation of a ribosome in terms of its average velocity and mean rate of GTP hydrolysis. We also compute entropy production as functions of the rates of the interstate transitions and the thermodynamic cost for accuracy of the translation process.

Dynamics of ribosomes in mRNA translation under steady- and nonsteady-state conditions

Recent advances in DNA sequencing and fluorescence imaging have made it possible to monitor the dynamics of ribosomes actively engaged in messenger RNA (mRNA) translation. Here, we model these experiments within the inhomogeneous totally asymmetric simple exclusion process (TASEP) using realistic kinetic parameters. In particular, we present analytic expressions to describe the following three cases: (a) translation of a newly transcribed mRNA, (b) translation in the steady state and, specifically, the dynamics of individual (tagged) ribosomes, and (c) runoff translation after inhibition of translation initiation. In cases (b) and (c) we develop an effective medium approximation to describe many-ribosome dynamics in terms of a single tagged ribosome in an effective medium. The predictions are in good agreement with stochastic simulations.

The molecular aetiology of tRNA synthetase depletion: induction of a GCN4 amino acid starvation response despite homeostatic maintenance of charged tRNA levels

During protein synthesis, charged tRNAs deliver amino acids to translating ribosomes, and are then re-charged by tRNA synthetases (aaRS). In humans, mutant aaRS cause a diversity of neurological disorders, but their molecular aetiologies are incompletely characterised. To understand system responses to aaRS depletion, the yeast glutamine aaRS gene (GLN4) was transcriptionally regulated using doxycycline by tet-off control. Depletion of Gln4p inhibited growth, and induced a GCN4 amino acid starvation response, indicative of uncharged tRNA accumulation and Gcn2 kinase activation. Using a global model of translation that included aaRS recharging, Gln4p depletion was simulated, confirming slowed translation. Modelling also revealed that Gln4p depletion causes negative feedback that matches translational demand for Gln-tRNA^Gln to aaRS recharging capacity. This maintains normal charged tRNA^Gln levels despite Gln4p depletion, confirmed experimentally using tRNA Northern blotting. Model analysis resolves the paradox that Gln4p depletion triggers a GCN4 response, despite maintenance of tRNA^Gln charging levels, revealing that normally, the aaRS population can sequester free, uncharged tRNAs during aminoacylation. Gln4p depletion reduces this sequestration capacity, allowing uncharged tRNA^Gln to interact with Gcn2 kinase. The study sheds new light on mutant aaRS disease aetiologies, and explains how aaRS sequestration of uncharged tRNAs can prevent GCN4 activation under non-starvation conditions.

An analytical theory of balanced cellular growth

The biological fitness of microbes is largely determined by the rate with which they replicate their biomass composition. Mathematical models that maximize this balanced growth rate while accounting for mass conservation, reaction kinetics, and limits on dry mass per volume are inevitably non-linear. Here, we develop a general theory for such models, termed Growth Balance Analysis (GBA), which provides explicit expressions for protein concentrations, fluxes, and growth rates. These variables are functions of the concentrations of cellular components, for which we calculate marginal fitness costs and benefits that are related to metabolic control coefficients. At maximal growth rate, the net benefits of all concentrations are equal. Based solely on physicochemical constraints, GBA unveils fundamental quantitative principles of cellular resource allocation and growth; it accurately predicts the relationship between growth rates and ribosome concentrations in E. coli and yeast and between growth rate and dry mass density in E. coli.

Power series method for solving TASEP-based models of mRNA translation

We develop a method for solving mathematical models of messenger RNA (mRNA) translation based on the totally asymmetric simple exclusion process (TASEP). Our main goal is to demonstrate that the method is versatile and applicable to realistic models of translation. To this end we consider the TASEP with codon-dependent elongation rates, premature termination due to ribosome drop-off and translation reinitiation due to circularisation of the mRNA. We apply the method to the model organism Saccharomyces cerevisiae under physiological conditions and find an excellent agreement with the results of stochastic simulations. Our findings suggest that the common view on translation as being rate-limited by initiation is oversimplistic. Instead we find theoretical evidence for ribosome interference and also theoretical support for the ramp hypothesis which argues that codons at the beginning of genes have slower elongation rates in order to reduce ribosome density and jamming.

Population Genetics Based Phylogenetics Under Stabilizing Selection for an Optimal Amino Acid Sequence: A Nested Modeling Approach

We present a new phylogenetic approach, selection on amino acids and codons (SelAC), whose substitution rates are based on a nested model linking protein expression to population genetics. Unlike simpler codon models that assume a single substitution matrix for all sites, our model more realistically represents the evolution of protein-coding DNA under the assumption of consistent, stabilizing selection using a cost-benefit approach. This cost-benefit approach allows us to generate a set of 20 optimal amino acid-specific matrix families using just a handful of parameters and naturally links the strength of stabilizing selection to protein synthesis levels, which we can estimate. Using a yeast data set of 100 orthologs for 6 taxa, we find SelAC fits the data much better than popular models by 104-105 Akike information criterion units adjusted for small sample bias. Our results also indicated that nested, mechanistic models better predict observed data patterns highlighting the improvement in biological realism in amino acid sequence evolution that our model provides. Additional parameters estimated by SelAC indicate that a large amount of nonphylogenetic, but biologically meaningful, information can be inferred from existing data. For example, SelAC prediction of gene-specific protein synthesis rates correlates well with both empirical (r=0.33-0.48) and other theoretical predictions (r=0.45-0.64) for multiple yeast species. SelAC also provides estimates of the optimal amino acid at each site. Finally, because SelAC is a nested approach based on clearly stated biological assumptions, future modifications, such as including shifts in the optimal amino acid sequence within or across lineages, are possible.

Quantifying codon usage in signal peptides: Gene expression and amino acid usage explain apparent selection for inefficient codons

The Sec secretion pathway is found across all domains of life. A critical feature of Sec secreted proteins is the signal peptide, a short peptide with distinct physicochemical properties located at the N-terminus of the protein. Previous work indicates signal peptides are biased towards translationally inefficient codons, which is hypothesized to be an adaptation driven by selection to improve the efficacy and efficiency of the protein secretion mechanisms. We investigate codon usage in the signal peptides of E. coli using the Codon Adaptation Index (CAI), the tRNA Adaptation Index (tAI), and the ribosomal overhead cost formulation of the stochastic evolutionary model of protein production rates (ROC-SEMPPR). Comparisons between signal peptides and 5'-end of cytoplasmic proteins using CAI and tAI are consistent with a preference for inefficient codons in signal peptides. Simulations reveal these differences are due to amino acid usage and gene expression - we find these differences disappear when accounting for both factors. In contrast, ROC-SEMPPR, a mechanistic population genetics model capable of separating the effects of selection and mutation bias, shows codon usage bias (CUB) of the signal peptides is indistinguishable from the 5'-ends of cytoplasmic proteins. Additionally, we find CUB at the 5'-ends is weaker than later segments of the gene. Results illustrate the value in using models grounded in population genetics to interpret genetic data. We show failure to account for mutation bias and the effects of gene expression on the efficacy of selection against translation inefficiency can lead to a misinterpretation of codon usage patterns.

Computational analysis of the oscillatory behavior at the translation level induced by mRNA levels oscillations due to finite intracellular resources

Recent studies have demonstrated how the competition for the finite pool of available gene expression factors has important effect on fundamental gene expression aspects. In this study, based on a whole-cell model simulation of translation in S. cerevisiae, we evaluate for the first time the expected effect of mRNA levels fluctuations on translation due to the finite pool of ribosomes. We show that fluctuations of a single gene or a group of genes mRNA levels induce periodic behavior in all S. cerevisiae translation factors and aspects: the ribosomal densities and the translation rates of all S. cerevisiae mRNAs oscillate. We numerically measure the oscillation amplitudes demonstrating that fluctuations of endogenous and heterologous genes can cause a significant fluctuation of up to 50% in the steady-state translation rates of the rest of the genes. Furthermore, we demonstrate by synonymous mutations that oscillating the levels of mRNAs that experience high ribosomal occupancy (e.g. ribosomal “traffic jam”) induces the largest impact on the translation of the S. cerevisiae genome.

The results reported here should provide novel insights and principles related to the design of synthetic gene expression circuits and related to the evolutionary constraints shaping gene expression of endogenous genes.

Each cell contains a limited number of macromolecules and factors that participate in the gene expression process. These expression resources are shared between the different molecules that encode the genetic code, resulting in non-trivial couplings and competitions between the different gene expression stages. Such competitions should be considered when analyzing the cellular economy of the cell, the genome evolution, and the design of synthetic expression circuits. Here we study the effect of couplings and competitions for ribosomes by performing a whole-cell simulation of translation of S. cerevisiae, with parameters estimated from experimental data. We demonstrate that by periodically changing the mRNA levels of a single gene (endogenous or heterologous) or a set of genes, the translation of all S. cerevisiae genes are affected in a periodic manner. We numerically estimate the exact impact of the mRNA levels periodicity on the translation process dynamics, as well as on the dynamics of the free ribosomal pool and the way it is affected by parameters such as the codon composition of the oscillating gene, its initiation rate and mRNA levels. Furthermore, we show that the codon compositions of synthetically highly expressed heterologous genes that are expected to oscillate must be carefully considered. For example, synonymous mutations resulting in “traffic jams” of ribosomes along the fluctuated mRNAs may cause significant fluctuations of up to 50% in the steady-state translation rates of all genes.

Deciphering mRNA Sequence Determinants of Protein Production Rate

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.

Influence of multiplicative stochastic variation on translational elongation rates

Experimental data indicate that stochastic effects exerted at the level of translation contribute substantially to the variation in abundance of proteins expressed at moderate to high levels. This study analyzes the theoretical consequences of fluctuations in residue-specific elongation rates during translation. A simple analytical framework shows that rate variation during elongation gives rise to protein production rates that consist of sums of products of random variables. Simulations show that because the contribution to total variation of products of random variables greatly exceeds that of sums of random variables, the overall distribution exhibits approximately log-normal behavior. Empirical fits of the data can be satisfied by either sums of log-normal distributions, or sums of log-normal and log-logistic distributions. Elongation rate stochastic variation offers an accounting for a major component of biological variation. The analysis provided here highlights a probability distribution that is a natural extension of the Poisson and has broad applicability to many types of multiplicative noise processes.

A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics

In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological "particles" move along some kind of "tracks". The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation.

Ribosome reinitiation can explain length-dependent translation of messenger RNA

Models of mRNA translation usually presume that transcripts are linear; upon reaching the end of a transcript each terminating ribosome returns to the cytoplasmic pool before initiating anew on a different transcript. A consequence of linear models is that faster translation of a given mRNA is unlikely to generate more of the encoded protein, particularly at low ribosome availability. Recent evidence indicates that eukaryotic mRNAs are circularized, potentially allowing terminating ribosomes to preferentially reinitiate on the same transcript. Here we model the effect of ribosome reinitiation on translation and show that, at high levels of reinitiation, protein synthesis rates are dominated by the time required to translate a given transcript. Our model provides a simple mechanistic explanation for many previously enigmatic features of eukaryotic translation, including the negative correlation of both ribosome densities and protein abundance on transcript length, the importance of codon usage in determining protein synthesis rates, and the negative correlation between transcript length and both codon adaptation and 5' mRNA folding energies. In contrast to linear models where translation is largely limited by initiation rates, our model reveals that all three stages of translation-initiation, elongation, and termination/reinitiation-determine protein synthesis rates even at low ribosome availability.

Novel mRNA-specific effects of ribosome drop-off on translation rate and polysome profile

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.

A priori, de novo mathematical exploration of gene expression mechanism via regression viewpoint with briefly cataloged modeling antiquity

Various algorithms have been devised to mathematically model the dynamic mechanism of the gene expression data. Gillespie’s stochastic simulation (GSSA) has been exceptionally primal for chemical reaction synthesis with future ameliorations. Several other mathematical techniques such as differential equations, thermodynamic models and Boolean models have been implemented to optimally and effectively represent the gene functioning. We present a novel mathematical framework of gene expression, undertaking the mathematical modeling of the transcription and translation phases, which is a detour from conventional modeling approaches. These subprocesses are inherent to every gene expression, which is implicitly an experimental outcome. As we foresee, there can be modeled a generality about some basal translation or transcription values that correspond to a particular assay.

Predictive biophysical modeling and understanding of the dynamics of mRNA translation and its evolution

mRNA translation is the fundamental process of decoding the information encoded in mRNA molecules by the ribosome for the synthesis of proteins. The centrality of this process in various biomedical disciplines such as cell biology, evolution and biotechnology, encouraged the development of dozens of mathematical and computational models of translation in recent years. These models aimed at capturing various biophysical aspects of the process. The objective of this review is to survey these models, focusing on those based and/or validated on real large-scale genomic data. We consider aspects such as the complexity of the models, the biophysical aspects they regard and the predictions they may provide. Furthermore, we survey the central systems biology discoveries reported on their basis. This review demonstrates the fundamental advantages of employing computational biophysical translation models in general, and discusses the relative advantages of the different approaches and the challenges in the field.

Retroactivity effects dependency on the transcription factors binding mechanisms

Downstream connection effects on transcription are caused by retroactivity. When biomolecular dynamical systems interconnect retroactivity is a property that becomes important. The biological functional meaning of these effects is increasingly becoming an area of interest. Downstream targets, which are operator binding sites in transcriptional networks, may induce behaviors such as ultrasensitive responses or even represent an undesired issue in regulation. To the best of our knowledge, the role of the binding mechanisms of transcription factors in relation to minimizing - or enhancing - retroactivity effects has not been previously addressed. Our aim is to evaluate retroactivity effects considering how the binding mechanism impacts the number of free functional transcription factor (FFTF) molecules using a simple model via deterministic and stochastic simulations. We study four transcription factor binding mechanisms (BM): simple monomer binding (SMB), dimer binding (DB), cooperative sequential binding (CSB) and cooperative sequential binding with dimerization (CSB_D). We consider weak and strong binding regimes for each mechanism, where we contrast the cases when the FFTF is bound or unbound to the downstream loads. Upon interconnection, the number of FFTF molecules changed less for the SMB mechanism while for DB they changed the most. Our results show that for the chosen mechanisms (in terms of the corresponding described dynamics), retroactivity effects depend on transcription binding mechanisms. This contributes to the understanding of how the transcription factor regulatory function-such as decision making-and its dynamic needs for the response, may determine the nature of the selected binding mechanism.

Hybrid agent-based model for quantitative in-silico cell-free protein synthesis

An advanced vision of the mRNA translation is presented through a hybrid modeling approach. The dynamics of the polysome formation was investigated by computer simulation that combined agent-based model and fine-grained Markov chain representation of the chemical kinetics. This approach allowed for the investigation of the polysome dynamics under non-steady-state and non-continuum conditions. The model is validated by the quantitative comparison of the simulation results and Luciferase protein production in cell-free system, as well as by testing of the hypothesis regarding the two possible mechanisms of the Edeine antibiotic. Calculation of the Hurst exponent demonstrated a relationship between the microscopic properties of amino acid elongation and the fractal dimension of the translation duration time series. The temporal properties of the amino acid elongation have indicated an anti-persistent behavior under low mRNA occupancy and evinced the appearance of long range interactions within the mRNA-ribosome system for high ribosome density. The dynamic and temporal characteristics of the polysomal system presented here can have a direct impact on the studies of the co-translation protein folding and provide a validated platform for cell-free system studies.

Probabilistic Boolean Network Modelling and Analysis Framework for mRNA Translation

mRNA translation is a complex process involving the progression of ribosomes on the mRNA, resulting in the synthesis of proteins, and is subject to multiple layers of regulation. This process has been modelled using different formalisms, both stochastic and deterministic. Recently, we introduced a Probabilistic Boolean modelling framework for mRNA translation, which possesses the advantage of tools for numerically exact computation of steady state probability distribution, without requiring simulation. Here, we extend this model to incorporate both random sequential and parallel update rules, and demonstrate its effectiveness in various settings, including its flexibility in accommodating additional static and dynamic biological complexities and its role in parameter sensitivity analysis. In these applications, the results from the model analysis match those of TASEP model simulations. Importantly, the proposed modelling framework maintains the stochastic aspects of mRNA translation and provides a way to exactly calculate probability distributions, providing additional tools of analysis in this context. Finally, the proposed modelling methodology provides an alternative approach to the understanding of the mRNA translation process, by bridging the gap between existing approaches, providing new analysis tools, and contributing to a more robust platform for modelling and understanding translation.

Quantitative assessment of ribosome drop-off in E. coli

Premature ribosome drop-off is one of the major errors in translation of mRNA by ribosomes. However, repeated analyses of Ribo-seq data failed to quantify its strength inE. coli Relying on a novel highly sensitive data analysis method we show that a significant rate of ribosome drop-off is measurable and can be quantified also when cells are cultured under non-stressing conditions. Moreover, we find that the drop-off rate is highly variable, depending on multiple factors. In particular, under environmental stress such as amino acid starvation or ethanol intoxication, the drop-off rate markedly increases.

Community control in cellular protein production: consequences for amino acid starvation

Deprivation of essential nutrients can have stark consequences for many processes in a cell. We consider amino acid starvation, which can result in bottlenecks in mRNA translation when ribosomes stall due to lack of resources, i.e. tRNAs charged with the missing amino acid. Recent experiments also show less obvious effects such as increased charging of other (non-starved) tRNA species and selective charging of isoaccepting tRNAs. We present a mechanism which accounts for these observations and shows that production of some proteins can actually increase under starvation. One might assume that such responses could only be a result of sophisticated control pathways, but here we show that these effects can occur naturally due to changes in the supply and demand for different resources, and that control can be accomplished through selective use of rare codons. We develop a model for translation which includes the dynamics of the charging and use of aminoacylated tRNAs, explicitly taking into account the effect of specific codon sequences. This constitutes a new control mechanism in gene regulation which emerges at the community level, i.e. via resources used by all ribosomes.

A codon model of nucleotide substitution with selection on synonymous codon usage

The quality of phylogenetic inference made from protein-coding genes depends, in part, on the realism with which the codon substitution process is modeled. Here we propose a new mechanistic model that combines the standard M0 substitution model of Yang (1997) with a simplified model from Gilchrist (2007) that includes selection on synonymous substitutions as a function of codon-specific nonsense error rates. We tested the newly proposed model by applying it to 104 protein-coding genes in brewer's yeast, and compared the fit of the new model to the standard M0 model and to the mutation-selection model of Yang and Nielsen (2008) using the AIC. Our new model provided significantly better fit in approximately 85% of the cases considered for the basic M0 model and in approximately 25% of the cases for the M0 model with estimated codon frequencies, but only in a few cases when the mutation-selection model was considered. However, our model includes a parameter that can be interpreted as a measure of the rate of protein production, and the estimates of this parameter were highly correlated with an independent measure of protein production for the yeast genes considered here. Finally, we found that in some cases the new model led to the preference of a different phylogeny for a subset of the genes considered, indicating that substitution model choice may have an impact on the estimated phylogeny.

RiboAbacus: a model trained on polyribosome images predicts ribosome density and translational efficiency from mammalian transcriptomes

Fluctuations in mRNA levels only partially contribute to determine variations in mRNA availability for translation, producing the well-known poor correlation between transcriptome and proteome data. Recent advances in microscopy now enable researchers to obtain high resolution images of ribosomes on transcripts, providing precious snapshots of translation in vivo. Here we propose RiboAbacus, a mathematical model that for the first time incorporates imaging data in a predictive model of transcript-specific ribosome densities and translational efficiencies. RiboAbacus uses a mechanistic model of ribosome dynamics, enabling the quantification of the relative importance of different features (such as codon usage and the 5′ ramp effect) in determining the accuracy of predictions. The model has been optimized in the human Hek-293 cell line to fit thousands of images of human polysomes obtained by atomic force microscopy, from which we could get a reference distribution of the number of ribosomes per mRNA with unmatched resolution. After validation, we applied RiboAbacus to three case studies of known transcriptome-proteome datasets for estimating the translational efficiencies, resulting in an increased correlation with corresponding proteomes. RiboAbacus is an intuitive tool that allows an immediate estimation of crucial translation properties for entire transcriptomes, based on easily obtainable transcript expression levels.

Estimating Gene Expression and Codon-Specific Translational Efficiencies, Mutation Biases, and Selection Coefficients from Genomic Data Alone

Extracting biologically meaningful information from the continuing flood of genomic data is a major challenge in the life sciences. Codon usage bias (CUB) is a general feature of most genomes and is thought to reflect the effects of both natural selection for efficient translation and mutation bias. Here we present a mechanistically interpretable, Bayesian model (ribosome overhead costs Stochastic Evolutionary Model of Protein Production Rate [ROC SEMPPR]) to extract meaningful information from patterns of CUB within a genome. ROC SEMPPR is grounded in population genetics and allows us to separate the contributions of mutational biases and natural selection against translational inefficiency on a gene-by-gene and codon-by-codon basis. Until now, the primary disadvantage of similar approaches was the need for genome scale measurements of gene expression. Here, we demonstrate that it is possible to both extract accurate estimates of codon-specific mutation biases and translational efficiencies while simultaneously generating accurate estimates of gene expression, rather than requiring such information. We demonstrate the utility of ROC SEMPPR using the Saccharomyces cerevisiae S288c genome. When we compare our model fits with previous approaches we observe an exceptionally high agreement between estimates of both codon-specific parameters and gene expression levels ([Formula: see text] in all cases). We also observe strong agreement between our parameter estimates and those derived from alternative data sets. For example, our estimates of mutation bias and those from mutational accumulation experiments are highly correlated ([Formula: see text]). Our estimates of codon-specific translational inefficiencies and tRNA copy number-based estimates of ribosome pausing time ([Formula: see text]), and mRNA and ribosome profiling footprint-based estimates of gene expression ([Formula: see text]) are also highly correlated, thus supporting the hypothesis that selection against translational inefficiency is an important force driving the evolution of CUB. Surprisingly, we find that for particular amino acids, codon usage in highly expressed genes can still be largely driven by mutation bias and that failing to take mutation bias into account can lead to the misidentification of an amino acid's "optimal" codon. In conclusion, our method demonstrates that an enormous amount of biologically important information is encoded within genome scale patterns of codon usage, accessing this information does not require gene expression measurements, but instead carefully formulated biologically interpretable models.

Ribosome recycling induces optimal translation rate at low ribosomal availability

During eukaryotic cellular protein synthesis, ribosomal translation is made more efficient through interaction between the two ends of the messenger RNA (mRNA). Ribosomes reaching the 3′ end of the mRNA can thus recycle and begin translation again on the same mRNA, the so-called ‘closed-loop’ model. Using a driven diffusion lattice model of translation, we study the effects of ribosome recycling on the dynamics of ribosome flow and density on the mRNA. We show that ribosome recycling induces a substantial increase in ribosome current. Furthermore, for sufficiently large values of the recycling rate, the lattice does not transition directly from low to high ribosome density, as seen in lattice models without recycling. Instead, a maximal current phase becomes accessible for much lower values of the initiation rate, and multiple phase transitions occur over a wide region of the phase plane. Crucially, we show that in the presence of ribosome recycling, mRNAs can exhibit a peak in protein production at low values of the initiation rate, beyond which translation rate decreases. This has important implications for translation of certain mRNAs, suggesting that there is an optimal concentration of ribosomes at which protein synthesis is maximal, and beyond which translational efficiency is impaired.

Evolution of a genome-encoded bias in amino acid biosynthetic pathways is a potential indicator of amino acid dynamics in the environment

Overcoming the stress of starvation is one of an organism’s most challenging phenotypic responses. Those organisms that frequently survive the challenge, by virtue of their fitness, will have evolved genomes that are shaped by their specific environments. Understanding this genotype–environment–phenotype relationship at a deep level will require quantitative predictive models of the complex molecular systems that link these aspects of an organism’s existence. Here, we treat one of the most fundamental molecular systems, protein synthesis, and the amino acid biosynthetic pathways involved in the stringent response to starvation. These systems face an inherent logical dilemma: Building an amino acid biosynthetic pathway to synthesize its product—the cognate amino acid of the pathway—may require that very amino acid when it is no longer available. To study this potential “catch-22,” we have created a generic model of amino acid biosynthesis in response to sudden starvation. Our mathematical analysis and computational results indicate that there are two distinctly different outcomes: Partial recovery to a new steady state, or full system failure. Moreover, the cell’s fate is dictated by the cognate bias, the number of cognate amino acids in the corresponding biosynthetic pathway relative to the average number of that amino acid in the proteome. We test these implications by analyzing the proteomes of over 1,800 sequenced microbes, which reveals statistically significant evidence of low cognate bias, a genetic trait that would avoid the biosynthetic quandary. Furthermore, these results suggest that the pattern of cognate bias, which is readily derived by genome sequencing, may provide evolutionary clues to an organism’s natural environment.

Quantifying the effect of ribosomal density on mRNA stability

Gene expression is a fundamental cellular process by which proteins are eventually synthesized based on the information coded in the genes. This process includes four major steps: transcription of the DNA segment corresponding to a gene to mRNA molecules, the degradation of the mRNA molecules, the translation of mRNA molecules to proteins by the ribosome and the degradation of the proteins. We present an innovative quantitative study of the interaction between the gene translation stage and the mRNA degradation stage using large scale genomic data of S. cerevisiae, which include measurements of mRNA levels, mRNA half-lives, ribosomal densities and protein abundances, for thousands of genes. The reported results support the conjecture that transcripts with higher ribosomal density, which is related to the translation stage, tend to have elevated half-lives, and we suggest a novel quantitative estimation of the strength of this relation. Specifically, we show that on average, an increase of 78% in ribosomal density yields an increase of 25% in mRNA half-life, and that this relation between ribosomal density and mRNA half-life is not function specific. In addition, our analyses demonstrate that ribosomal density along the entire ORF, and not in specific locations, has a significant effect on the transcript half-life. Finally, we show that the reported relation cannot be explained by different expression levels among genes. A plausible explanation for the reported results is that ribosomes tend to protect the mRNA molecules from the exosome complexes degrading them; however, additional non-mutually exclusive possible explanations for the reported relation and experiments for their verifications are discussed in the paper.

Entrainment to periodic initiation and transition rates in a computational model for gene translation

Periodic oscillations play an important role in many biomedical systems. Proper functioning of biological systems that respond to periodic signals requires the ability to synchronize with the periodic excitation. For example, the sleep/wake cycle is a manifestation of an internal timing system that synchronizes to the solar day. In the terminology of systems theory, the biological system must entrain or phase-lock to the periodic excitation. Entrainment is also important in synthetic biology. For example, connecting several artificial biological systems that entrain to a common clock may lead to a well-functioning modular system. The cell-cycle is a periodic program that regulates DNA synthesis and cell division. Recent biological studies suggest that cell-cycle related genes entrain to this periodic program at the gene translation level, leading to periodically-varying protein levels of these genes. The ribosome flow model (RFM) is a deterministic model obtained via a mean-field approximation of a stochastic model from statistical physics that has been used to model numerous processes including ribosome flow along the mRNA. Here we analyze the RFM under the assumption that the initiation and/or transition rates vary periodically with a common period . We show that the ribosome distribution profile in the RFM entrains to this periodic excitation. In particular, the protein synthesis pattern converges to a unique periodic solution with period . To the best of our knowledge, this is the first proof of entrainment in a mathematical model for translation that encapsulates aspects such as initiation and termination rates, ribosomal movement and interactions, and non-homogeneous elongation speeds along the mRNA. Our results support the conjecture that periodic oscillations in tRNA levels and other factors related to the translation process can induce periodic oscillations in protein levels, and may suggest a new approach for re-engineering genetic systems to obtain a desired, periodic, protein synthesis rate.

mRNA translation and protein synthesis: an analysis of different modelling methodologies and a new PBN based approach

Background

mRNA translation involves simultaneous movement of multiple ribosomes on the mRNA and is also subject to regulatory mechanisms at different stages. Translation can be described by various codon-based models, including ODE, TASEP, and Petri net models. Although such models have been extensively used, the overlap and differences between these models and the implications of the assumptions of each model has not been systematically elucidated. The selection of the most appropriate modelling framework, and the most appropriate way to develop coarse-grained/fine-grained models in different contexts is not clear.

Results

We systematically analyze and compare how different modelling methodologies can be used to describe translation. We define various statistically equivalent codon-based simulation algorithms and analyze the importance of the update rule in determining the steady state, an aspect often neglected. Then a novel probabilistic Boolean network (PBN) model is proposed for modelling translation, which enjoys an exact numerical solution. This solution matches those of numerical simulation from other methods and acts as a complementary tool to analytical approximations and simulations. The advantages and limitations of various codon-based models are compared, and illustrated by examples with real biological complexities such as slow codons, premature termination and feedback regulation. Our studies reveal that while different models gives broadly similiar trends in many cases, important differences also arise and can be clearly seen, in the dependence of the translation rate on different parameters. Furthermore, the update rule affects the steady state solution.

Conclusions

The codon-based models are based on different levels of abstraction. Our analysis suggests that a multiple model approach to understanding translation allows one to ascertain which aspects of the conclusions are robust with respect to the choice of modelling methodology, and when (and why) important differences may arise. This approach also allows for an optimal use of analysis tools, which is especially important when additional complexities or regulatory mechanisms are included. This approach can provide a robust platform for dissecting translation, and results in an improved predictive framework for applications in systems and synthetic biology.

A stochastic model of translation with -1 programmed ribosomal frameshifting

Many viruses produce multiple proteins from a single mRNA sequence by encoding overlapping genes. One mechanism to decode both genes, which reside in alternate reading frames, is -1 programmed ribosomal frameshifting. Although recognized for over 25 years, the molecular and physical mechanism of -1 frameshifting remains poorly understood. We have developed a mathematical model that treats mRNA translation and associated -1 frameshifting as a stochastic process in which the transition probabilities are based on the energetics of local molecular interactions. The model predicts both the location and efficiency of -1 frameshift events in HIV-1. Moreover, we compute -1 frameshift efficiencies upon mutations in the viral mRNA sequence and variations in relative tRNA abundances, predictions that are directly testable in experiment.

Rate-limiting steps in yeast protein translation

Deep sequencing now provides detailed snapshots of ribosome occupancy on mRNAs. We leverage these data to parameterize a computational model of translation, keeping track of every ribosome, tRNA, and mRNA molecule in a yeast cell. We determine the parameter regimes in which fast initiation or high codon bias in a transgene increases protein yield and infer the initiation rates of endogenous Saccharomyces cerevisiae genes, which vary by several orders of magnitude and correlate with 5′ mRNA folding energies. Our model recapitulates the previously reported 5′-to-3′ ramp of decreasing ribosome densities, although our analysis shows that this ramp is caused by rapid initiation of short genes rather than slow codons at the start of transcripts. We conclude that protein production in healthy yeast cells is typically limited by the availability of free ribosomes, whereas protein production under periods of stress can sometimes be rescued by reducing initiation or elongation rates.

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Computational model of translation tracks all ribosomes, tRNAs, and mRNAs in a cell

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Translation is generally limited by initiation, not elongation

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Model allows inference of initiation rates for all yeast genes

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Ramp of 5′ ribosomes is caused by rapid initiation of short genes

Kinetic signatures of microRNA modes of action

MicroRNAs (miRNAs) are key regulators of all important biological processes, including development, differentiation, and cancer. Although remarkable progress has been made in deciphering the mechanisms used by miRNAs to regulate translation, many contradictory findings have been published that stimulate active debate in this field. Here we contribute to this discussion in three ways. First, based on a comprehensive analysis of the existing literature, we hypothesize a model in which all proposed mechanisms of microRNA action coexist, and where the apparent mechanism that is detected in a given experiment is determined by the relative values of the intrinsic characteristics of the target mRNAs and associated biological processes. Among several coexisting miRNA mechanisms, the one that will effectively be measurable is that which acts on or changes the sensitive parameters of the translation process. Second, we have created a mathematical model that combines nine known mechanisms of miRNA action and estimated the model parameters from the literature. Third, based on the mathematical modeling, we have developed a computational tool for discriminating among different possible individual mechanisms of miRNA action based on translation kinetics data that can be experimentally measured (kinetic signatures). To confirm the discriminatory power of these kinetic signatures and to test our hypothesis, we have performed several computational experiments with the model in which we simulated the coexistence of several miRNA action mechanisms in the context of variable parameter values of the translation.

A max-plus model of ribosome dynamics during mRNA translation

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.

Mathematical and Computational Modelling of Ribosomal Movement and Protein Synthesis: an overview

Translation or protein synthesis consists of a complex system of chemical reactions, which ultimately result in decoding of the mRNA and the production of a protein. The complexity of this reaction system makes it difficult to quantitatively connect its input parameters (such as translation factor or ribosome concentrations, codon composition of the mRNA, or energy availability) to output parameters (such as protein synthesis rates or ribosome densities on mRNAs). Mathematical and computational models of translation have now been used for nearly five decades to investigate translation, and to shed light on the relationship between the different reactions in the system. This review gives an overview over the principal approaches used in the modelling efforts, and summarises some of the major findings that were made.

A systems view of the protein expression process

Many biological processes are regulated by changing the concentration and activity of proteins. The presence of a protein at a given subcellular location at a given time with a certain conformation is the result of an apparently sequential process. The rate of protein formation is influenced by chromatin state, and the rates of transcription, translation, and degradation. There is an exquisite control system where each stage of the process is controlled both by seemingly unregulated proteins as well as through feedbacks mediated by RNA and protein products. Here we review the biological facts and mathematical models for each stage of the protein production process. We conclude that advances in experimental techniques leading to a detailed description of the process have not been matched by mathematical models that represent the details of the process and facilitate analysis. Such an exercise is the first step towards development of a framework for a systems biology analysis of the protein production process.

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The dynamics of supply and demand in mRNA translation

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.

In this paper we show that the rate at which proteins are produced can be controlled at the elongation stage of mRNA translation. Regulation of translation initiation has been a focus of much study, but the subsequent effect of changes in the initiation rate on the overall translation rate, and the role of slow and fast codon usage in mRNA sequences is still not fully understood. We consider a model of elongation in which the dynamics of tRNA use and recharging are considered for real mRNA sequences. We find that the balance between the demand for, and supply of tRNAs is crucial in determining translation rates. Particularly interesting “competition” effects are observed when the simultaneous translation of multiple mRNA is considered. We show indeed that, via the choice of slow or fast codons, it is in principle possible to control how variation of the supply and demand for tRNA resources changes the rate of protein production from different mRNAs.

Interspecific and intragenic differences in codon usage bias among vertebrate myosin heavy-chain genes

Synonymous codon usage bias is a broadly observed phenomenon in bacteria, plants, and invertebrates and may result from selection. However, the role of selective pressures in shaping codon bias is still controversial in vertebrates, particularly for mammals. The myosin heavy-chain (MyHC) gene family comprises multiple isoforms of the major force-producing contractile protein in cardiac and skeletal muscles. Slow and fast genes are tandemly arrayed on separate chromosomes, and have distinct patterns of functionality and expression in muscle. We analyze both full-length MyHC genes (~5400 bp) and a larger collection of partial sequences at the 3' end (~500 bp). The MyHC isoforms are an interesting system in which to study codon usage bias because of their length, expression, and critical importance to organismal mobility. Codon bias and GC content differs among MyHC genes with regards to functional type, isoform, and position within the gene. Codon bias even varies by isoform within a species. We find evidence in favor of both chromosomal influences on nucleotide composition and selection against nonsense errors (SANE) acting on codon usage in MyHC genes. Intragenic variation in codon bias and elongation rate is significant, with a strong trend for increasing codon bias and elongation rate towards the 3' end of the gene, although the trend is dependent upon the degeneracy class of the codons. Therefore, patterns of codon usage in MyHC genes are consistent with models supporting SANE as a major force shaping codon usage.

Analysing GCN4 translational control in yeast by stochastic chemical kinetics modelling and simulation

Background

The yeast Saccharomyces cerevisiae responds to amino acid starvation by inducing the transcription factor Gcn4. This is mainly mediated via a translational control mechanism dependent upon the translation initiation eIF2·GTP·Met-tRNA_i^Met ternary complex, and the four short upstream open reading frames (uORFs) in its 5' mRNA leader. These uORFs act to attenuate GCN4 mRNA translation under normal conditions. During amino acid starvation, levels of ternary complex are reduced. This overcomes the GCN4 translation attenuation effect via a scanning/reinitiation control mechanism dependent upon uORF spacing.

Results

Using published experimental data, we have developed and validated a probabilistic formulation of GCN4 translation using the Chemical Master Equation (Model 1). Model 1 explains GCN4 translation's nonlinear dependency upon uORF placements, and predicts that an as yet unidentified factor, which was proposed to regulate GCN4 translation under some conditions, only has pronounced effects upon GCN4 translation when intercistronic distances are unnaturally short. A simpler Model 2 that does not include this unidentified factor could well represent the regulation of a natural GCN4 mRNA. Using parameter values optimised for this algebraic Model 2, we performed stochastic simulations by Gillespie algorithm to investigate the distribution of ribosomes in different sections of GCN4 mRNA under distinct conditions. Our simulations demonstrated that ribosomal loading in the 5'-untranslated region is mainly determined by the ratio between the rates of 5'-initiation and ribosome scanning, but was not significantly affected by rate of ternary complex binding. Importantly, the translation rate for codons starved of cognate tRNAs is predicted to be the most significant contributor to the changes in ribosomal loading in the coding region under repressing and derepressing conditions.

Conclusions

Our integrated probabilistic Models 1 and 2 explained GCN4 translation and helped to elucidate the role of a yet unidentified factor. The ensuing stochastic simulations evaluated different factors that may impact on the translation of GCN4 mRNA, and integrated translation status with ribosomal density.

Explaining complex codon usage patterns with selection for translational efficiency, mutation bias, and genetic drift

The genetic code is redundant with most amino acids using multiple codons. In many organisms, codon usage is biased toward particular codons. Understanding the adaptive and nonadaptive forces driving the evolution of codon usage bias (CUB) has been an area of intense focus and debate in the fields of molecular and evolutionary biology. However, their relative importance in shaping genomic patterns of CUB remains unsolved. Using a nested model of protein translation and population genetics, we show that observed gene level variation of CUB in Saccharomyces cerevisiae can be explained almost entirely by selection for efficient ribosomal usage, genetic drift, and biased mutation. The correlation between observed codon counts within individual genes and our model predictions is 0.96. Although a variety of factors shape patterns of CUB at the level of individual sites within genes, our results suggest that selection for efficient ribosome usage is a central force in shaping codon usage at the genomic scale. In addition, our model allows direct estimation of codon-specific mutation rates and elongation times and can be readily applied to any organism with high-throughput expression datasets. More generally, we have developed a natural framework for integrating models of molecular processes to population genetics models to quantitatively estimate parameters underlying fundamental biological processes, such a protein translation.

Analysis and prediction of translation rate based on sequence and functional features of the mRNA

Protein concentrations depend not only on the mRNA level, but also on the translation rate and the degradation rate. Prediction of mRNA's translation rate would provide valuable information for in-depth understanding of the translation mechanism and dynamic proteome. In this study, we developed a new computational model to predict the translation rate, featured by (1) integrating various sequence-derived and functional features, (2) applying the maximum relevance & minimum redundancy method and incremental feature selection to select features to optimize the prediction model, and (3) being able to predict the translation rate of RNA into high or low translation rate category. The prediction accuracies under rich and starvation condition were 68.8% and 70.0%, respectively, evaluated by jackknife cross-validation. It was found that the following features were correlated with translation rate: codon usage frequency, some gene ontology enrichment scores, number of RNA binding proteins known to bind its mRNA product, coding sequence length, protein abundance and 5′UTR free energy. These findings might provide useful information for understanding the mechanisms of translation and dynamic proteome. Our translation rate prediction model might become a high throughput tool for annotating the translation rate of mRNAs in large-scale.

Effect of correlated tRNA abundances on translation errors and evolution of codon usage bias

Despite the fact that tRNA abundances are thought to play a major role in determining translation error rates, their distribution across the genetic code and the resulting implications have received little attention. In general, studies of codon usage bias (CUB) assume that codons with higher tRNA abundance have lower missense error rates. Using a model of protein translation based on tRNA competition and intra-ribosomal kinetics, we show that this assumption can be violated when tRNA abundances are positively correlated across the genetic code. Examining the distribution of tRNA abundances across 73 bacterial genomes from 20 different genera, we find a consistent positive correlation between tRNA abundances across the genetic code. This work challenges one of the fundamental assumptions made in over 30 years of research on CUB that codons with higher tRNA abundances have lower missense error rates and that missense errors are the primary selective force responsible for CUB.

Codon usage bias (CUB) is a ubiquitous and important phenomenon. CUB is thought to be driven primarily due to selection against missense errors. For over 30 years, the standard model of translation errors has implicitly assumed that the relationship between translation errors and tRNA abundances are inversely related. This is based on an implicit and unstated assumption that the distribution of tRNA abundances across the genetic code are uncorrelated. Examining these abundance distributions across 73 bacterial genomes from 20 different genera, we find a consistent positive correlation between tRNA abundances across the genetic code. We further show that codons with higher tRNA abundances are not always “optimal” with respect to reducing the missense error rate and hence cannot explain the observed patterns of CUB.

Role of the particle's stepping cycle in an asymmetric exclusion process: a model of mRNA translation

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.

The origins of time-delay in template biopolymerization processes

Time-delays are common in many physical and biological systems and they give rise to complex dynamic phenomena. The elementary processes involved in template biopolymerization, such as mRNA and protein synthesis, introduce significant time delays. However, there is not currently a systematic mapping between the individual mechanistic parameters and the time delays in these networks. We present here the development of mathematical, time-delay models for protein translation, based on PDE models, which in turn are derived through systematic approximations of first-principles mechanistic models. Theoretical analysis suggests that the key features that determine the time-delays and the agreement between the time-delay and the mechanistic models are ribosome density and distribution, i.e., the number of ribosomes on the mRNA chain relative to their maximum and their distribution along the mRNA chain. Based on analytical considerations and on computational studies, we show that the steady-state and dynamic responses of the time-delay models are in excellent agreement with the detailed mechanistic models, under physiological conditions that correspond to uniform ribosome distribution and for ribosome density up to 70%. The methodology presented here can be used for the development of reduced time-delay models of mRNA synthesis and large genetic networks. The good agreement between the time-delay and the mechanistic models will allow us to use the reduced model and advanced computational methods from nonlinear dynamics in order to perform studies that are not practical using the large-scale mechanistic models.