Stochastic theory of protein synthesis and polysome: Ribosome profile on a single mRNA transcript

TIR predictor and optimizer: Web-tools for accurate prediction of translation initiation rate and precision gene design in Saccharomyces cerevisiae

Translation initiation is the primary determinant of the rate of protein production. The variation in the rate with which this step occurs can cause up to three orders of magnitude differences in cellular protein levels. Several mRNA features, including mRNA stability in proximity to the start codon, coding sequence length, and presence of specific motifs in the mRNA molecule, have been shown to influence the translation initiation rate. These molecular factors acting at different strengths allow precise control of in vivo translation initiation rate and thus the rate of protein synthesis. However, despite the paramount importance of translation initiation rate in protein synthesis, accurate prediction of the absolute values of initiation rate remains a challenge. In fact, as of now, there is no available model for predicting the initiation rate in Saccharomyces cerevisiae. To address this, we train a machine learning model for predicting the in vivo initiation rate in S. cerevisiae transcripts. The model is trained using a diverse set of mRNA transcripts, enabling the comparison of initiation rates across different transcripts. Our model exhibited excellent accuracy in predicting the translation initiation rate and demonstrated its effectiveness with both endogenous and exogenous transcripts. Then, by combining the machine learning model with the Monte-Carlo search algorithm, we have also devised a method to optimize the nucleotide sequence of any gene to achieve a specific target initiation rate. The machine learning model we've developed for predicting translation initiation rates, along with the gene optimization method, are deployed as a web server. Both web servers are accessible for free at the following link: ajeetsharmalab.com/TIRPredictor. Thus, this research advances our fundamental understanding of translation initiation processes, with direct applications in biotechnology.

Decoding stoichiometric protein synthesis in E. coli through translation rate parameters

E. coli is one of the most widely used organisms for understanding the principles of cellular and molecular genetics. However, we are yet to understand the origin of several experimental observations related to the regulation of gene expression in E. coli. One of the prominent examples in this context is the proportional synthesis in multiprotein complexes where all of their obligate subunits are produced in proportion to their stoichiometry. In this work, by combining the next-generation sequencing data with the stochastic simulations of protein synthesis, we explain the origin of proportional protein synthesis in multicomponent complexes. We find that the estimated initiation rates for the translation of all subunits in those complexes are proportional to their stoichiometry. This constraint on protein synthesis kinetics enforces proportional protein synthesis without requiring any feedback mechanism. We also find that the translation initiation rates in E. coli are influenced by the coding sequence length and the enrichment of A and C nucleotides near the start codon. Thus, this study rationalizes the role of conserved and nonrandom features of genes in regulating the translation kinetics and unravels a key principle of the regulation of protein synthesis.

Large-scale mRNA translation and the intricate effects of competition for the finite pool of ribosomes

We present a new theoretical framework for large-scale mRNA translation using a network of models called the ribosome flow model with Langmuir kinetics (RFMLK), interconnected via a pool of free ribosomes. The input to each RFMLK depends on the pool density, and it affects the initiation rate and potentially also the internal ribosome entry rates along each RFMLK. Ribosomes that detach from an RFMLK owing to termination or premature drop-off are fed back into the pool. We prove that the network always converges to a steady state, and study its sensitivity to variations in the parameters. For example, we show that if the drop-off rate at some site in some RFMLK is increased then the pool density increases and consequently the steady-state production rate in all the other RFMLKs increases. Surprisingly, we also show that modifying a parameter of a certain RFMLK can lead to arbitrary effects on the densities along the modified RFMLK, depending on the parameters in the entire network. We conclude that the competition for shared resources generates an indirect and intricate web of mutual effects between the mRNA molecules that must be accounted for in any analysis of translation.

Combinations of slow-translating codon clusters can increase mRNA half-life in Saccharomyces cerevisiae

The presence of a single cluster of nonoptimal codons was found to decrease a transcript's half-life through the interaction of the ribosome-associated quality control machinery with stalled ribosomes in Saccharomyces cerevisiae The impact of multiple nonoptimal codon clusters on a transcript's half-life, however, is unknown. Using a kinetic model, we predict that inserting a second nonoptimal cluster near the 5' end can lead to synergistic effects that increase a messenger RNA's (mRNA's) half-life in S. cerevisiae Specifically, the 5' end cluster suppresses the formation of ribosome queues, reducing the interaction of ribosome-associated quality control factors with stalled ribosomes. We experimentally validate this prediction by introducing two nonoptimal clusters into three different genes and find that their mRNA half-life increases up to fourfold. The model also predicts that in the presence of two clusters, the cluster closest to the 5' end is the primary determinant of mRNA half-life. These results suggest the "translational ramp," in which nonoptimal codons are located near the start codon and increase translational efficiency, may have the additional biological benefit of allowing downstream slow-codon clusters to be present without decreasing mRNA half-life. These results indicate that codon usage bias plays a more nuanced role in controlling cellular protein levels than previously thought.

Translational autoregulation of RF2 protein in E. coli through programmed frameshifting

Various feedback mechanisms regulate the expression of different genes to ensure the required protein levels inside a cell. In this paper, we develop a kinetic model for one such mechanism that autoregulates RF2 protein synthesis in E. coli through programmed frameshifting. The model finds that the programmed frameshifting autoregulates RF2 protein synthesis by two independent mechanisms. First, it increases the rate of RF2 synthesis from each mRNA transcript at low RF2 concentration. Second, programmed frameshifting can dramatically increase the lifetime of RF2 transcripts when RF2 protein levels are lower than a threshold. This sharp increase in mRNA lifetime is caused by a first-order phase transition from a low to a high ribosome density on an RF2 transcript. The high ribosome density prevents the transcript's degradation by shielding it from nucleases, which increases its average lifetime and hence RF2 protein levels. Our study identifies this quality control mechanism that regulates the cellular protein levels by breaking the hierarchy of processes involved in gene expression.

Systematic Quantification of Sequence and Structural Determinants Controlling mRNA stability in Bacterial Operons

mRNA degradation is a central process that affects all gene expression levels, and yet, the determinants that control mRNA decay rates remain poorly characterized. Here, we applied a synthetic biology, learn-by-design approach to elucidate the sequence and structural determinants that control mRNA stability in bacterial operons. We designed, constructed, and characterized 82 operons in Escherichia coli, systematically varying RNase binding site characteristics, translation initiation rates, and transcriptional terminator efficiencies in the 5' untranslated region (UTR), intergenic, and 3' UTR regions, followed by measuring their mRNA levels using reverse transcription quantitative polymerase chain reaction (RT-qPCR) assays during exponential growth. We show that introducing long single-stranded RNA into 5' UTRs reduced mRNA levels by up to 9.4-fold and that lowering translation rates reduced mRNA levels by up to 11.8-fold. We also found that RNase binding sites in intergenic regions had much lower effects on mRNA levels. Surprisingly, changing the transcriptional termination efficiency or introducing long single-stranded RNA into 3' UTRs had no effect on upstream mRNA levels. From these measurements, we developed and validated biophysical models of ribosome protection and RNase activity with excellent quantitative agreement. We also formulated design rules to rationally control a mRNA's stability, facilitating the automated design of engineered genetic systems with desired functionalities.

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.

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.

A chemical kinetic basis for measuring translation initiation and elongation rates from ribosome profiling data

Analysis methods based on simulations and optimization have been previously developed to estimate relative translation rates from next-generation sequencing data. Translation involves molecules and chemical reactions, hence bioinformatics methods consistent with the laws of chemistry and physics are more likely to produce accurate results. Here, we derive simple equations based on chemical kinetic principles to measure the translation-initiation rate, transcriptome-wide elongation rate, and individual codon translation rates from ribosome profiling experiments. Our methods reproduce the known rates from ribosome profiles generated from detailed simulations of translation. By applying our methods to data from S. cerevisiae and mouse embryonic stem cells, we find that the extracted rates reproduce expected correlations with various molecular properties, and we also find that mouse embryonic stem cells have a global translation speed of 5.2 AA/s, in agreement with previous reports that used other approaches. Our analysis further reveals that a codon can exhibit up to 26-fold variability in its translation rate depending upon its context within a transcript. This broad distribution means that the average translation rate of a codon is not representative of the rate at which most instances of that codon are translated, and it suggests that translational regulation might be used by cells to a greater degree than previously thought.

Theoretical analysis of the distribution of isolated particles in totally asymmetric exclusion processes: Application to mRNA translation rate estimation

The Totally Asymmetric Exclusion Process (TASEP) is a classical stochastic model for describing the transport of interacting particles, such as ribosomes moving along the messenger ribonucleic acid (mRNA) during translation. Although this model has been widely studied in the past, the extent of collision between particles and the average distance between a particle to its nearest neighbor have not been quantified explicitly. We provide here a theoretical analysis of such quantities via the distribution of isolated particles. In the classical form of the model in which each particle occupies only a single site, we obtain an exact analytic solution using the matrix ansatz. We then employ a refined mean-field approach to extend the analysis to a generalized TASEP with particles of an arbitrary size. Our theoretical study has direct applications in mRNA translation and the interpretation of experimental ribosome profiling data. In particular, our analysis of data from Saccharomyces cerevisiae suggests a potential bias against the detection of nearby ribosomes with a gap distance of less than approximately three codons, which leads to some ambiguity in estimating the initiation rate and protein production flux for a substantial fraction of genes. Despite such ambiguity, however, we demonstrate theoretically that the interference rate associated with collisions can be robustly estimated and show that approximately 1% of the translating ribosomes get obstructed.

Gene length as a regulator for ribosome recruitment and protein synthesis: theoretical insights

Protein synthesis rates are determined, at the translational level, by properties of the transcript’s sequence. The efficiency of an mRNA can be tuned by varying the ribosome binding sites controlling the recruitment of the ribosomes, or the codon usage establishing the speed of protein elongation. In this work we propose transcript length as a further key determinant of translation efficiency. Based on a physical model that considers the kinetics of ribosomes advancing on the mRNA and diffusing in its surrounding, as well as mRNA circularisation and ribosome drop-off, we explain how the transcript length may play a central role in establishing ribosome recruitment and the overall translation rate of an mRNA. According to our results, the proximity of the 3′ end to the ribosomal recruitment site of the mRNA could induce a feedback in the translation process that would favour the recycling of ribosomes. We also demonstrate how this process may be involved in shaping the experimental ribosome density-gene length dependence. Finally, we argue that cells could exploit this mechanism to adjust and balance the usage of its ribosomal resources.

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.

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.

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.

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 genome-scale integration and analysis of Lactococcus lactis translation data

Protein synthesis is a template polymerization process composed by three main steps: initiation, elongation, and termination. During translation, ribosomes are engaged into polysomes whose size is used for the quantitative characterization of translatome. However, simultaneous transcription and translation in the bacterial cytosol complicates the analysis of translatome data. We established a procedure for robust estimation of the ribosomal density in hundreds of genes from Lactococcus lactis polysome size measurements. We used a mechanistic model of translation to integrate the information about the ribosomal density and for the first time we estimated the protein synthesis rate for each gene and identified the rate limiting steps. Contrary to conventional considerations, we find significant number of genes to be elongation limited. This number increases during stress conditions compared to optimal growth and proteins synthesized at maximum rate are predominantly elongation limited. Consistent with bacterial physiology, we found proteins with similar rate and control characteristics belonging to the same functional categories. Under stress conditions, we found that synthesis rate of regulatory proteins is becoming comparable to proteins favored under optimal growth. These findings suggest that the coupling of metabolic states and protein synthesis is more important than previously thought.

TEMPLATE-DIRECTED BIOPOLYMERIZATION: TAPE-COPYING TURING MACHINES

DNA, RNA and proteins are among the most important macromolecules in a living cell. These molecules are polymerized by molecular machines. These natural nano-machines polymerize such macromolecules, adding one monomer at a time, using another linear polymer as the corresponding template. The machine utilizes input chemical energy to move along the template which also serves as a track for the movements of the machine. In the Alan Turing year 2012, it is worth pointing out that these machines are "tape-copying Turing machines". We review the operational mechanisms of the polymerizer machines and their collective behavior from the perspective of statistical physics, emphasizing their common features in spite of the crucial differences in their biological functions. We also draw the attention of the physics community to another class of modular machines that carry out a different type of template-directed polymerization. We hope this review will inspire new kinetic models for these modular machines.

Ribosome traffic on mRNAs maps to gene ontology: genome-wide quantification of translation initiation rates and polysome size regulation

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.

Gene expression regulation is central to all living systems. Here we introduce a new framework and methodology to study the last stage of protein production in cells, where the genetic information encoded in the mRNAs is translated from the language of nucleotides into functional proteins. The process, on each mRNA, is carried out concurrently by several ribosomes; like cars on a small countryside road, they cannot overtake each other, and can form queues. By integrating experimental data with genome-wide simulations of our model, we analyse ribosome traffic across the entire Saccharomyces cerevisiae genome, and for the first time estimate mRNA-specific translation initiation rates for each transcript. Crucially, we identify different classes of mRNAs characterised by different ribosome traffic dynamics. Remarkably, this classification based on translational dynamics, and the evaluation of mRNA-specific initiation rates, map onto key gene ontological classifications, revealing evolutionary optimisation of translation responses to be strongly influenced by gene function.

Computational studies of molecular machines: the ribosome

The past decade has produced an avalanche of experimental data on the structure and dynamics of the ribosome. Groundbreaking studies in structural biology and kinetics have placed important constraints on ribosome structural dynamics. However, a gulf remains between static structures and time dependent data. In particular, X-ray crystallography and cryo-EM studies produce static models of the ribosome in various states, but lack dynamic information. Single molecule studies produce information on the rates of transitions between these states but do not have high-resolution spatial information. Computational studies have aided in bridging this gap by providing atomic resolution simulations of structural fluctuations and transitions between configurations.