A model for competition for ribosomes in the cell

Reversing the relative time courses of the peptide bond reaction with oligopeptides of different lengths and charged amino acid distributions in the ribosome exit tunnel

The kinetics of the protein elongation cycle by the ribosome depends on intertwined factors. One of these factors is the electrostatic interaction of the nascent protein with the ribosome exit tunnel. In this computational biology theoretical study, we focus on the rate of the peptide bond formation and its dependence on the ribosome exit tunnel electrostatic potential profile. We quantitatively predict how oligopeptides of variable lengths can affect the peptide bond formation rate. We applied the Michaelis-Menten model as previously extended to incorporate the mechano-biochemical effects of forces on the rate of reaction at the catalytic site of the ribosome. For a given pair of carboxy-terminal amino acid substrate at the P- and an aminoacyl-tRNA at the A-sites, the relative time courses of the peptide bond formation reaction can be reversed depending on the oligopeptide sequence embedded in the tunnel and their variable lengths from the P-site. The reversal is predicted to occur from a shift in positions of charged amino acids upstream in the oligopeptidyl-tRNA at the P-site. The position shift must be adjusted by clever design of the oligopeptide probes using the electrostatic potential profile along the exit tunnel axial path. These predicted quantitative results bring strong evidence of the importance and relative contribution of the electrostatic interaction of the ribosome exit tunnel with the nascent peptide chain during elongation.

Effects of mRNA conformational switching on translational noise in gene circuits

Intragenic translational heterogeneity describes the variation in translation at the level of transcripts for an individual gene. A factor that contributes to this source of variation is the mRNA structure. Both the composition of the thermodynamic ensemble, i.e., the stationary distribution of mRNA structures, and the switching dynamics between those play a role. The effect of the switching dynamics on intragenic translational heterogeneity remains poorly understood. We present a stochastic translation model that accounts for mRNA structure switching and is derived from a Markov model via approximate stochastic filtering. We assess the approximation on various timescales and provide a method to quantify how mRNA structure dynamics contributes to translational heterogeneity. With our approach, we allow quantitative information on mRNA switching from biophysical experiments or coarse-grain molecular dynamics simulations of mRNA structures to be included in gene regulatory chemical reaction network models without an increase in the number of species. Thereby, our model bridges a gap between mRNA structure kinetics and gene expression models, which we hope will further improve our understanding of gene regulatory networks and facilitate genetic circuit design.

Persistence and stability of generalized ribosome flow models with time-varying transition rates

In this paper some important qualitative dynamical properties of generalized ribosome flow models are studied. Ribosome flow models known from the literature are generalized by allowing an arbitrary directed network structure between compartments, and by assuming general time-varying rate functions corresponding to the transitions. Persistence of the dynamics is shown using the chemical reaction network (CRN) representation of the system where the state variables correspond to ribosome density and the amount of free space in the compartments. The L1 contractivity of solutions is also proved in the case of periodic reaction rates having the same period. Further we prove the stability of different compartmental structures including strongly connected ones with entropy-like logarithmic Lyapunov functions through embedding the model into a weakly reversible CRN with time-varying reaction rates in a reduced state space. Moreover, it is shown that different Lyapunov functions may be assigned to the same model depending on the non-unique factorization of the reaction rates. The results are illustrated through several examples with biological meaning including the classical ribosome flow model on a ring.

eIF3 mRNA selectivity profiling reveals eIF3k as a cancer-relevant regulator of ribosome content

eIF3, whose subunits are frequently overexpressed in cancer, regulates mRNA translation from initiation to termination, but mRNA-selective functions of individual subunits remain poorly defined. Using multiomic profiling upon acute depletion of eIF3 subunits, we observed that while eIF3a, b, e, and f markedly differed in their impact on eIF3 holo-complex formation and translation, they were each required for cancer cell proliferation and tumor growth. Remarkably, eIF3k showed the opposite pattern with depletion promoting global translation, cell proliferation, tumor growth, and stress resistance through repressing the synthesis of ribosomal proteins, especially RPS15A. Whereas ectopic expression of RPS15A mimicked the anabolic effects of eIF3k depletion, disruption of eIF3 binding to the 5'-UTR of RSP15A mRNA negated them. eIF3k and eIF3l are selectively downregulated in response to endoplasmic reticulum and oxidative stress. Supported by mathematical modeling, our data uncover eIF3k-l as a mRNA-specific module which, through controlling RPS15A translation, serves as a rheostat of ribosome content, possibly to secure spare translational capacity that can be mobilized during stress.

A blueprint for a synthetic genetic feedback optimizer

Biomolecular control enables leveraging cells as biomanufacturing factories. Despite recent advancements, we currently lack genetically encoded modules that can be deployed to dynamically fine-tune and optimize cellular performance. Here, we address this shortcoming by presenting the blueprint of a genetic feedback module to optimize a broadly defined performance metric by adjusting the production and decay rate of a (set of) regulator species. We demonstrate that the optimizer can be implemented by combining available synthetic biology parts and components, and that it can be readily integrated with existing pathways and genetically encoded biosensors to ensure its successful deployment in a variety of settings. We further illustrate that the optimizer successfully locates and tracks the optimum in diverse contexts when relying on mass action kinetics-based dynamics and parameter values typical in Escherichia coli.

On the gain of entrainment in the n-dimensional ribosome flow model

The ribosome flow model (RFM) is a phenomenological model for the flow of particles along a one-dimensional chain of n sites. It has been extensively used to study ribosome flow along the mRNA molecule during translation. When the transition rates along the chain are time-varying and jointly T-periodic the RFM entrains, i.e. every trajectory of the RFM converges to a unique T-periodic solution that depends on the transition rates, but not on the initial condition. In general, entrainment to periodic excitations like the 24 h solar day or the 50 Hz frequency of the electric grid is important in numerous natural and artificial systems. An interesting question, called the gain of entrainment (GOE) in the RFM, is whether proper coordination of the periodic translation rates along the mRNA can lead to a larger average protein production rate. Analysing the GOE in the RFM is non-trivial and partial results exist only for the RFM with dimensions n = 1, 2. We use a new approach to derive several results on the GOE in the general n-dimensional RFM. Perhaps surprisingly, we rigorously characterize several cases where there is no GOE, so to maximize the average production rate in these cases, the best choice is to use constant transition rates all along the chain.

Translation in the cell under fierce competition for shared resources: a mathematical model

During translation, mRNAs 'compete' for shared resources. Under stress conditions, during viral infection and also in high-throughput heterologous gene expression, these resources may become scarce, e.g. the pool of free ribosomes is starved, and then the competition may have a dramatic effect on the global dynamics of translation in the cell. We model this scenario using a network that includes m ribosome flow models (RFMs) interconnected via a pool of free ribosomes. Each RFM models ribosome flow along an mRNA molecule, and the pool models the shared resource. We assume that the number of mRNAs is large, so many ribosomes are attached to the mRNAs, and the pool is starved. Our analysis shows that adding an mRNA has an intricate effect on the total protein production. The new mRNA produces new proteins, but the other mRNAs produce less proteins, as the pool that feeds these mRNAs now has a smaller abundance of ribosomes. As the number of mRNAs increases, the marginal utility of adding another mRNA diminishes, and the total protein production rate saturates to a limiting value. We demonstrate our approach using an example of insulin protein production in a cell-free system.

Epigenetic factor competition reshapes the EMT landscape

The emergence of and transitions between distinct phenotypes in isogenic cells can be attributed to the intricate interplay of epigenetic marks, external signals, and gene-regulatory elements. These elements include chromatin remodelers, histone modifiers, transcription factors, and regulatory RNAs. Mathematical models known as gene-regulatory networks (GRNs) are an increasingly important tool to unravel the workings of such complex networks. In such models, epigenetic factors are usually proposed to act on the chromatin regions directly involved in the expression of relevant genes. However, it has been well-established that these factors operate globally and compete with each other for targets genome-wide. Therefore, a perturbation of the activity of a regulator can redistribute epigenetic marks across the genome and modulate the levels of competing regulators. In this paper, we propose a conceptual and mathematical modeling framework that incorporates both local and global competition effects between antagonistic epigenetic regulators, in addition to local transcription factors, and show the counterintuitive consequences of such interactions. We apply our approach to recent experimental findings on the epithelial-mesenchymal transition (EMT). We show that it can explain the puzzling experimental data, as well as provide verifiable predictions.

A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities

We study the stochasticity in a dynamical model: ribosome flow model with different site sizes that models the unidirectional movement of particles controlled by transition rates along a lattice having different site sizes. Our work models the parameters as random variables with known distributions and investigates the steady-state flow rate under this notion by using tools from the random matrix theory. Some closed-form theoretical results are derived for the steady-state flow rate under some restrictive assumptions such as random variables being independent and identically distributed. Furthermore, for arbitrary but bounded stochastic transition rates, stochastic site capacities, or both, we establish bounds for the steady-state flow rate. Our analysis can be generalized and applied to study the flow of particles in numerous transport systems in the stochastic environment.

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.

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.

Ribosome exit tunnel electrostatics

The impact of ribosome exit tunnel electrostatics on the protein elongation rate or on forces acting upon the nascent polypeptide chain are currently not fully elucidated. In the past, researchers have measured the electrostatic potential inside the ribosome polypeptide exit tunnel at a limited number of spatial points, at least in rabbit reticulocytes. Here we present a basic electrostatic model of the exit tunnel of the ribosome, providing a quantitative physical description of the tunnel interaction with the nascent proteins at all centro-axial points inside the tunnel. We show that a strong electrostatic screening is due to water molecules (not mobile ions) attracted to the ribosomal nucleic acid phosphate moieties buried in the immediate vicinity of the tunnel wall. We also show how the tunnel wall components and local ribosomal protein protrusions impact on the electrostatic potential profile and impede charged amino acid residues from progressing through the tunnel, affecting the elongation rate in a range of -40% to +85% when compared to the average elongation rate. The time spent by the ribosome to decode the genetic encrypted message is constrained accordingly. We quantitatively derive, at single-residue resolution, the axial forces acting on the nascent peptide from its particular sequence embedded in the tunnel. The model sheds light on how the experimental data point measurements of the potential are linked to the local structural chemistry of the inner wall, shape, and size of the tunnel. The model consistently connects experimental observations coming from different fields in molecular biology, x-ray crystallography, physical chemistry, biomechanics, and synthetic and multiomics biology. Our model should be a valuable tool to gain insight into protein synthesis dynamics, translational control, and the role of the ribosome's mechanochemistry in the cotranslational protein folding.

Analysis of eukaryotic lincRNA sequences indicates signatures of hindered translation linked to selection pressure

Long intergenic noncoding RNAs (lincRNAs) represent a large fraction of transcribed loci in eukaryotic genomes. Although classified as noncoding, most lincRNAs contain open reading frames (ORFs), and it remains unclear why cytoplasmic lincRNAs are not or very inefficiently translated. Here, we analyzed signatures of hindered translation in lincRNA sequences from five eukaryotes, covering a range of natural selection pressures. In fission yeast and Caenorhabditis elegans, that is, species under strong selection, we detected significantly shorter ORFs, a suboptimal sequence context around start codons for translation initiation, and trinucleotides (“codons”) corresponding to less abundant tRNAs than for neutrally evolving control sequences, likely impeding translation elongation. For human, we detected signatures for cell-type-specific hindrance of lincRNA translation, in particular codons in abundant cytoplasmic lincRNAs corresponding to lower expressed tRNAs than control codons, in three out of five human cell lines. We verified that varying tRNA expression levels between cell lines are reflected in the amount of ribosomes bound to cytoplasmic lincRNAs in each cell line. We further propose that codons at ORF starts are particularly important for reducing ribosome-binding to cytoplasmic lincRNA ORFs. Altogether, our analyses indicate that in species under stronger selection lincRNAs evolved sequence features generally hindering translation and support cell-type-specific hindrance of translation efficiency in human lincRNAs. The sequence signatures we have identified may improve predicting peptide-coding and genuine noncoding lincRNAs in a cell type.

Determinants of efficient modulation of ribosomal traffic jams

mRNA translation is the process which consumes most of the cellular energy. Thus, this process is under strong evolutionary selection for its optimization and rational optimization or reduction of the translation efficiency can impact the cell growth rate. Algorithms for modulating cell growth rate can have various applications in biotechnology, medicine, and agriculture. In this study, we demonstrate that the analysis of these algorithms can also be used for understanding translation.

We specifically describe and analyze various generic algorithms, based on comprehensive computational models and whole cell simulations of translation, for introducing silent mutations that can either reduce or increase ribosomal traffic jams along the mRNA. As a result, more or less resources are available, for the cell, promoting improved or reduced cells growth-rate, respectively. We then explore the cost of these algorithms' performance, in terms of their computational time, the number of mutations they introduce, the modified genomic region, the effect on local translation rates, and the properties of the modified genes.

Among others, we show that mRNA levels of a gene are much stronger predictors for the effect of its engineering on the ribosomal pool than the ribosomal density of the gene. We also demonstrate that the mutations at the ends of the coding regions have a stronger effect on the ribosomal pool. Furthermore, we report two optimization algorithms that exhibit a tread-off between the number of mutations they introduce and their executing time.

The reported results here are fundamental both for understanding the biophysics and evolution of translation, as well as for developing efficient approaches for its engineering.

The role of OncoSnoRNAs and Ribosomal RNA 2'-O-methylation in Cancer

Ribosomes are essential nanomachines responsible for all protein production in cells. Ribosome biogenesis and function are energy costly processes, they are tightly regulated to match cellular needs. In cancer, major pathways that control ribosome biogenesis and function are often deregulated to ensure cell survival and to accommodate the continuous proliferation of tumour cells. Ribosomal RNAs (rRNAs) are abundantly modified with 2'-O-methylation (Nm, ribomethylation) being one of the most common modifications. In eukaryotic ribosomes, ribomethylation is performed by the methyltransferase Fibrillarin guided by box C/D small nucleolar RNAs (snoRNAs). Accumulating evidences indicate that snoRNA expression and ribosome methylation profiles are altered in cancer. Here we review our current knowledge on differential snoRNA expression and rRNA 2ʹ-O methylation in the context of human malignancies, and discuss the consequences and opportunities for cancer diagnostics, prognostics, and therapeutics.

Stochastic Effects in Retrotransposon Dynamics Revealed by Modeling under Competition for Cellular Resources

Transposons are genomic elements that can relocate within a host genome using a ‘cut’- or ‘copy-and-paste’ mechanism. They make up a significant part of many genomes, serve as a driving force for genome evolution, and are linked with Mendelian diseases and cancers. Interactions between two specific retrotransposon types, autonomous (e.g., LINE1/L1) and nonautonomous (e.g., Alu), may lead to fluctuations in the number of these transposons in the genome over multiple cell generations. We developed and examined a simple model of retrotransposon dynamics under conditions where transposon replication machinery competed for cellular resources: namely, free ribosomes and available energy (i.e., ATP molecules). Such competition is likely to occur in stress conditions that a malfunctioning cell may experience as a result of a malignant transformation. The modeling revealed that the number of actively replicating LINE1 and Alu elements in a cell decreases with the increasing competition for resources; however, stochastic effects interfere with this simple trend. We stochastically simulated the transposon dynamics in a cell population and showed that the population splits into pools with drastically different transposon behaviors. The early extinction of active Alu elements resulted in a larger number of LINE1 copies occurring in the first pool, as there was no competition between the two types of transposons in this pool. In the other pool, the competition process remained and the number of L1 copies was kept small. As the level of available resources reached a critical value, both types of dynamics demonstrated an increase in noise levels, and both the period and the amplitude of predator–prey oscillations rose in one of the cell pools. We hypothesized that the presented dynamical effects associated with the impact of the competition for cellular resources inflicted on the dynamics of retrotransposable elements could be used as a characteristic feature to assess a cell state, or to control the transposon activity.

Context-Dependent Stability and Robustness of Genetic Toggle Switches with Leaky Promoters

Multistable switches are ubiquitous building blocks in both systems and synthetic biology. Given their central role, it is thus imperative to understand how their fundamental properties depend not only on the tunable biophysical properties of the switches themselves, but also on their genetic context. To this end, we reveal in this article how these factors shape the essential characteristics of toggle switches implemented using leaky promoters such as their stability and robustness to noise, both at single-cell and population levels. In particular, our results expose the roles that competition for scarce transcriptional and translational resources, promoter leakiness, and cell-to-cell heterogeneity collectively play. For instance, the interplay between protein expression from leaky promoters and the associated cost of relying on shared cellular resources can give rise to tristable dynamics even in the absence of positive feedback. Similarly, we demonstrate that while promoter leakiness always acts against multistability, resource competition can be leveraged to counteract this undesirable phenomenon. Underpinned by a mechanistic model, our results thus enable the context-aware rational design of multistable genetic switches that are directly translatable to experimental considerations, and can be further leveraged during the synthesis of large-scale genetic systems using computer-aided biodesign automation platforms.

Genes with 5' terminal oligopyrimidine tracts preferentially escape global suppression of translation by the SARS-CoV-2 Nsp1 protein

Viruses rely on the host translation machinery to synthesize their own proteins. Consequently, they have evolved varied mechanisms to co-opt host translation for their survival. SARS-CoV-2 relies on a nonstructural protein, Nsp1, for shutting down host translation. However, it is currently unknown how viral proteins and host factors critical for viral replication can escape a global shutdown of host translation. Here, using a novel FACS-based assay called MeTAFlow, we report a dose-dependent reduction in both nascent protein synthesis and mRNA abundance in cells expressing Nsp1. We perform RNA-seq and matched ribosome profiling experiments to identify gene-specific changes both at the mRNA expression and translation levels. We discover that a functionally coherent subset of human genes is preferentially translated in the context of Nsp1 expression. These genes include the translation machinery components, RNA binding proteins, and others important for viral pathogenicity. Importantly, we uncovered a remarkable enrichment of 5' terminal oligo-pyrimidine (TOP) tracts among preferentially translated genes. Using reporter assays, we validated that 5' UTRs from TOP transcripts can drive preferential expression in the presence of Nsp1. Finally, we found that LARP1, a key effector protein in the mTOR pathway, may contribute to preferential translation of TOP transcripts in response to Nsp1 expression. Collectively, our study suggests fine-tuning of host gene expression and translation by Nsp1 despite its global repressive effect on host protein synthesis.

Maximizing average throughput in oscillatory biochemical synthesis systems: an optimal control approach

A dynamical system entrains to a periodic input if its state converges globally to an attractor with the same period. In particular, for a constant input, the state converges to a unique equilibrium point for any initial condition. We consider the problem of maximizing a weighted average of the system's output along the periodic attractor. The gain of entrainment is the benefit achieved by using a non-constant periodic input relative to a constant input with the same time average. Such a problem amounts to optimal allocation of resources in a periodic manner. We formulate this problem as a periodic optimal control problem, which can be analysed by means of the Pontryagin maximum principle or solved numerically via powerful software packages. We then apply our framework to a class of nonlinear occupancy models that appear frequently in biological synthesis systems and other applications. We show that, perhaps surprisingly, constant inputs are optimal for various architectures. This suggests that the presence of non-constant periodic signals, which frequently appear in biological occupancy systems, is a signature of an underlying time-varying objective functional being optimized.

Trade-offs among transcription elongation rate, number, and duration of ubiquitous pauses on highly transcribed bacterial genes

In this paper, we study the limitations imposed on the transcription process by the presence of short ubiquitous pauses and crowding. These effects are especially pronounced in highly transcribed genes such as ribosomal genes (rrn) in fast growing bacteria. Our model indicates that the quantity and duration of pauses reported for protein-coding genes is incompatible with the average elongation rate observed in rrn genes. When maximal elongation rate is high, pause-induced traffic jams occur, increasing promoter occlusion, thereby lowering the initiation rate. This lowers average transcription rate and increases average transcription time. Increasing maximal elongation rate in the model is insufficient to match the experimentally observed average elongation rate in rrn genes. This suggests that there may be rrn-specific modifications to RNAP, which then experience fewer pauses, or pauses of shorter duration than those in protein-coding genes. We identify model parameter triples (maximal elongation rate, mean pause duration time, number of pauses) which are compatible with experimentally observed elongation rates. Average transcription time and average transcription rate are the model outputs investigated as proxies for cell fitness. These fitness functions are optimized for different parameter choices, opening up a possibility of differential control of these aspects of the elongation process, with potential evolutionary consequences. As an example, a gene's average transcription time may be crucial to fitness when the surrounding medium is prone to abrupt changes. This paper demonstrates that a functional relationship among the model parameters can be estimated using a standard statistical analysis, and this functional relationship describes the various trade-offs that must be made in order for the gene to control the elongation process and achieve a desired average transcription time. It also demonstrates the robustness of the system when a range of maximal elongation rates can be balanced with transcriptional pause data in order to maintain a desired fitness.

Genes with 5' terminal oligopyrimidine tracts preferentially escape global suppression of translation by the SARS-CoV-2 Nsp1 protein

Viruses rely on the host translation machinery to synthesize their own proteins. Consequently, they have evolved varied mechanisms to co-opt host translation for their survival. SARS-CoV-2 relies on a non-structural protein, Nsp1, for shutting down host translation. However, it is currently unknown how viral proteins and host factors critical for viral replication can escape a global shutdown of host translation. Here, using a novel FACS-based assay called MeTAFlow, we report a dose-dependent reduction in both nascent protein synthesis and mRNA abundance in cells expressing Nsp1. We perform RNA-Seq and matched ribosome profiling experiments to identify gene-specific changes both at the mRNA expression and translation level. We discover a functionally-coherent subset of human genes are preferentially translated in the context of Nsp1 expression. These genes include the translation machinery components, RNA binding proteins, and others important for viral pathogenicity. Importantly, we uncovered a remarkable enrichment of 5' terminal oligo-pyrimidine (TOP) tracts among preferentially translated genes. Using reporter assays, we validated that 5' UTRs from TOP transcripts can drive preferential expression in the presence of NSP1. Finally, we found that LARP1, a key effector protein in the mTOR pathway may contribute to preferential translation of TOP transcripts in response to Nsp1 expression. Collectively, our study suggests fine tuning of host gene expression and translation by Nsp1 despite its global repressive effect on host protein synthesis.

Stability and Robustness of Unbalanced Genetic Toggle Switches in the Presence of Scarce Resources

While the vision of synthetic biology is to create complex genetic systems in a rational fashion, system-level behaviors are often perplexing due to the context-dependent dynamics of modules. One major source of context-dependence emerges due to the limited availability of shared resources, coupling the behavior of disconnected components. Motivated by the ubiquitous role of toggle switches in genetic circuits ranging from controlling cell fate differentiation to optimizing cellular performance, here we reveal how their fundamental dynamic properties are affected by competition for scarce resources. Combining a mechanistic model with nullcline-based stability analysis and potential landscape-based robustness analysis, we uncover not only the detrimental impacts of resource competition, but also how the unbalancedness of the switch further exacerbates them. While in general both of these factors undermine the performance of the switch (by pushing the dynamics toward monostability and increased sensitivity to noise), we also demonstrate that some of the unwanted effects can be alleviated by strategically optimized resource competition. Our results provide explicit guidelines for the context-aware rational design of toggle switches to mitigate our reliance on lengthy and expensive trial-and-error processes, and can be seamlessly integrated into the computer-aided synthesis of complex genetic systems.

Variability in mRNA translation: a random matrix theory approach

The rate of mRNA translation depends on the initiation, elongation, and termination rates of ribosomes along the mRNA. These rates depend on many "local" factors like the abundance of free ribosomes and tRNA molecules in the vicinity of the mRNA molecule. All these factors are stochastic and their experimental measurements are also noisy. An important question is how protein production in the cell is affected by this considerable variability. We develop a new theoretical framework for addressing this question by modeling the rates as identically and independently distributed random variables and using tools from random matrix theory to analyze the steady-state production rate. The analysis reveals a principle of universality: the average protein production rate depends only on the of the set of possible values that the random variable may attain. This explains how total protein production can be stabilized despite the overwhelming stochasticticity underlying cellular processes.

Stochastic models for single-cell data: Current challenges and the way forward

Although the quantity and quality of single-cell data have progressed rapidly, making quantitative predictions with single-cell stochastic models remains challenging. The stochastic nature of cellular processes leads to at least three challenges in building models with single-cell data: (a) because variability in single-cell data can be attributed to multiple different sources, it is difficult to rule out conflicting mechanistic models that explain the same data equally well; (b) the distinction between interesting biological variability and experimental variability is sometimes ambiguous; (c) the nonstandard distributions of single-cell data can lead to violations of the assumption of symmetric errors in least-squares fitting. In this review, we first discuss recent studies that overcome some of the challenges or set up a promising direction and then introduce some powerful statistical approaches utilized in these studies. We conclude that applying and developing statistical approaches could lead to further progress in building stochastic models for single-cell data.

Algorithms for ribosome traffic engineering and their potential in improving host cells' titer and growth rate

mRNA translation is a fundamental cellular process consuming most of the intracellular energy; thus, it is under extensive evolutionary selection for optimization, and its efficiency can affect the host's growth rate. We describe a generic approach for improving the growth rate (fitness) of any organism by introducing synonymous mutations based on comprehensive computational models. The algorithms introduce silent mutations that may improve the allocation of ribosomes in the cells via the decreasing of their traffic jams during translation respectively. As a result, resources availability in the cell changes leading to improved growth-rate. We demonstrate experimentally the implementation of the method on Saccharomyces cerevisiae: we show that by introducing a few mutations in two computationally selected genes the mutant's titer increased. Our approach can be employed for improving the growth rate of any organism providing the existence of data for inferring models, and with the relevant genomic engineering tools; thus, it is expected to be extremely useful in biotechnology, medicine, and agriculture.

Computational discovery and modeling of novel gene expression rules encoded in the mRNA

The transcript is populated with numerous overlapping codes that regulate all steps of gene expression. Deciphering these codes is very challenging due to the large number of variables involved, the non-modular nature of the codes, biases and limitations in current experimental approaches, our limited knowledge in gene expression regulation across the tree of life, and other factors. In recent years, it has been shown that computational modeling and algorithms can significantly accelerate the discovery of novel gene expression codes. Here, we briefly summarize the latest developments and different approaches in the field.

Whole cell biophysical modeling of codon-tRNA competition reveals novel insights related to translation dynamics

The importance of mRNA translation models has been demonstrated across many fields of science and biotechnology. However, a whole cell model with codon resolution and biophysical dynamics is still lacking. We describe a whole cell model of translation for E. coli. The model simulates all major translation components in the cell: ribosomes, mRNAs and tRNAs. It also includes, for the first time, fundamental aspects of translation, such as competition for ribosomes and tRNAs at a codon resolution while considering tRNAs wobble interactions and tRNA recycling. The model uses parameters that are tightly inferred from large scale measurements of translation. Furthermore, we demonstrate a robust modelling approach which relies on state-of-the-art practices of translation modelling and also provides a framework for easy generalizations. This novel approach allows simulation of thousands of mRNAs that undergo translation in the same cell with common resources such as ribosomes and tRNAs in feasible time. Based on this model, we demonstrate, for the first time, the direct importance of competition for resources on translation and its accurate modelling. An effective supply-demand ratio (ESDR) measure, which is related to translation factors such as tRNAs, has been devised and utilized to show superior predictive power in complex scenarios of heterologous gene expression. The devised model is not only more accurate than the existing models, but, more importantly, provides a framework for analyzing complex whole cell translation problems and variables that haven't been explored before, making it important in various biomedical fields.

mRNA translation is a fundamental process in all living organisms and the importance of its modeling has been demonstrated across many fields of science and biotechnology. Specifically, modeling a whole cell context with a high resolution has been a great challenge in the field, making many important problems un-addressable. In this study we devised a novel model, which allows, for the first time, simultaneous simulation of thousands of mRNAs, along with various bio-physical aspects that affect translation (such as codon-resolution dynamics and shared resources pool of both ribosomes and tRNAs). We demonstrated (using experimental data) that this model is more accurate than existing ones, and, more importantly, provides a framework for addressing complex translation problems (such as heterologous expression) at whole cell scale and in reasonable time. We demonstrated the model using E. coli data, but the model can be easily tailored to other organisms as well. Our model addresses an urgent unmet need for biophysically accurate whole cell translation model with resources coupling and has potential applications in many fields, including medicine and biotechnology.

Modelling and measuring intracellular competition for finite resources during gene expression

Dissecting the competition between genes for shared expressional resources is of fundamental importance for understanding the interplay between cellular components. Owing to the relationship between gene expression and cellular fitness, genomes are shaped by evolution to improve resource allocation. Whereas experimental approaches to investigate intracellular competition require technical resources and human expertise, computational models and in silico simulations allow vast numbers of experiments to be carried out and controlled easily, and with significantly reduced costs. Thus, modelling competition has a pivotal role in understanding the effects of competition on the biophysics of the cell. In this article, we review various computational models proposed to describe the different types of competition during gene expression. We also present relevant synthetic biology experiments and their biotechnological implications, and discuss the open questions in the field.

Widespread non-modular overlapping codes in the coding regions

Messenger RNAs (mRNAs) consist of a coding region (open reading frame (ORF)) and two untranslated regions (UTRs), 5'UTR and 3'UTR. Ribosomes travel along the coding region, translating nucleotide triplets (called codons) to a chain of amino acids. The coding region was long believed to mainly encode the amino acid content of proteins, whereas regulatory signals reside in the UTRs and in other genomic regions. However, in recent years we have learned that the ORF is expansively populated with various regulatory signals, or codes, which are related to all gene expression steps and additional intracellular aspects. In this paper, we review the current knowledge related to overlapping codes inside the coding regions, such as the influence of synonymous codon usage on translation speed (and, in turn, the effect of translation speed on protein folding), ribosomal frameshifting, mRNA stability, methylation, splicing, transcription and more. All these codes come together and overlap in the ORF sequence, ensuring production of the right protein at the right time.

Competing endogenous RNA crosstalk at system level

microRNAs (miRNAs) regulate gene expression at post-transcriptional level by repressing target RNA molecules. Competition to bind miRNAs tends in turn to correlate their targets, establishing effective RNA-RNA interactions that can influence expression levels, buffer fluctuations and promote signal propagation. Such a potential has been characterized mathematically for small motifs both at steady state and away from stationarity. Experimental evidence, on the other hand, suggests that competing endogenous RNA (ceRNA) crosstalk is rather weak. Extended miRNA-RNA networks could however favour the integration of many crosstalk interactions, leading to significant large-scale effects in spite of the weakness of individual links. To clarify the extent to which crosstalk is sustained by the miRNA interactome, we have studied its emergent systemic features in silico in large-scale miRNA-RNA network reconstructions. We show that, although generically weak, system-level crosstalk patterns (i) are enhanced by transcriptional heterogeneities, (ii) can achieve high-intensity even for RNAs that are not co-regulated, (iii) are robust to variability in transcription rates, and (iv) are significantly non-local, i.e. correlate weakly with miRNA-RNA interaction parameters. Furthermore, RNA levels are generically more stable when crosstalk is strongest. As some of these features appear to be encoded in the network's topology, crosstalk may functionally be favoured by natural selection. These results suggest that, besides their repressive role, miRNAs mediate a weak but resilient and context-independent network of cross-regulatory interactions that interconnect the transcriptome, stabilize expression levels and support system-level responses.

Pinetree: a step-wise gene expression simulator with codon-specific translation rates

MOTIVATION

Stochastic gene expression simulations often assume steady-state transcript levels, or they model transcription in more detail than translation. Moreover, they lack accessible programing interfaces, which limit their utility.

RESULTS

We present Pinetree, a step-wise gene expression simulator with codon-specific translation rates. Pinetree models both transcription and translation in a stochastic framework with individual polymerase and ribosome-level detail. Written in C++ with a Python front-end, any user familiar with Python can specify a genome and simulate gene expression. Pinetree was designed to be efficient and scale to simulate large plasmids or viral genomes.

AVAILABILITY AND IMPLEMENTATION

Pinetree is available on GitHub (https://github.com/benjaminjack/pinetree) and the Python Package Index (https://pypi.org/project/pinetree/).

Realizing 'integral control' in living cells: how to overcome leaky integration due to dilution?

A major problem in the design of synthetic genetic circuits is robustness to perturbations and uncertainty. Because of this, there have been significant efforts in recent years in finding approaches to implement integral control in genetic circuits. Integral controllers have the unique ability to make the output of a process adapt perfectly to disturbances. However, implementing an integral controller is challenging in living cells. This is because a key aspect of any integral controller is a 'memory' element that stores the accumulation (integral) of the error between the output and its desired set-point. The ability to realize such a memory element in living cells is fundamentally challenged by the fact that all biomolecules dilute as cells grow, resulting in a 'leaky' memory that gradually fades away. As a consequence, the adaptation property is lost. Here, we propose a general principle for designing integral controllers such that the performance is practically unaffected by dilution. In particular, we mathematically prove that if the reactions implementing the integral controller are all much faster than dilution, then the adaptation error due to integration leakiness becomes negligible. We exemplify this design principle with two synthetic genetic circuits aimed at reaching adaptation of gene expression to fluctuations in cellular resources. Our results provide concrete guidance on the biomolecular processes that are most appropriate for implementing integral controllers in living cells.

Networks of ribosome flow models for modeling and analyzing intracellular traffic

The ribosome flow model with input and output (RFMIO) is a deterministic dynamical system that has been used to study the flow of ribosomes during mRNA translation. The input of the RFMIO controls its initiation rate and the output represents the ribosome exit rate (and thus the protein production rate) at the 3′ end of the mRNA molecule. The RFMIO and its variants encapsulate important properties that are relevant to modeling ribosome flow such as the possible evolution of “traffic jams” and non-homogeneous elongation rates along the mRNA molecule, and can also be used for studying additional intracellular processes such as transcription, transport, and more. Here we consider networks of interconnected RFMIOs as a fundamental tool for modeling, analyzing and re-engineering the complex mechanisms of protein production. In these networks, the output of each RFMIO may be divided, using connection weights, between several inputs of other RFMIOs. We show that under quite general feedback connections the network has two important properties: (1) it admits a unique steady-state and every trajectory converges to this steady-state; and (2) the problem of how to determine the connection weights so that the network steady-state output is maximized is a convex optimization problem. These mathematical properties make these networks highly suitable as models of various phenomena: property (1) means that the behavior is predictable and ordered, and property (2) means that determining the optimal weights is numerically tractable even for large-scale networks. For the specific case of a feed-forward network of RFMIOs we prove an additional useful property, namely, that there exists a spectral representation for the network steady-state, and thus it can be determined without any numerical simulations of the dynamics. We describe the implications of these results to several fundamental biological phenomena and biotechnological objectives.

Kinetic Modelling of Competition and Depletion of Shared miRNAs by Competing Endogenous RNAs

Non-coding RNAs play a key role in the post-transcriptional regulation of mRNA translation and turnover in eukaryotes. miRNAs, in particular, interact with their target RNAs through protein-mediated, sequence-specific binding, giving rise to extended and highly heterogeneous miRNA-RNA interaction networks. Within such networks, competition to bind miRNAs can generate an effective positive coupling between their targets. Competing endogenous RNAs (ceRNAs) can in turn regulate each other through miRNA-mediated crosstalk. Albeit potentially weak, ceRNA interactions can occur both dynamically, affecting, e.g., the regulatory clock, and at stationarity, in which case ceRNA networks as a whole can be implicated in the composition of the cell's proteome. Many features of ceRNA interactions, including the conditions under which they become significant, can be unraveled by mathematical and in silico models. We review the understanding of the ceRNA effect obtained within such frameworks, focusing on the methods employed to quantify it, its role in the processing of gene expression noise, and how network topology can determine its reach.

Genome-Scale Analysis of Perturbations in Translation Elongation Based on a Computational Model

Perturbations play an important role both in engineered systems and cellular processes. Thus, understanding their effect on protein synthesis should contribute to all biomedical disciplines. Here we describe the first genome-scale analysis of perturbations in translation-related factors in S. cerevisiae. To this end, we used simulations based on a computational model that takes into consideration the fundamental stochastic and bio-physical nature of translation. We found that the initiation rate has a key role in determining the sensitivity to perturbations. For low initiation rates, the first codons of the coding region dominate the sensitivity, which is highly correlated with the ratio between initiation rate and mean elongation rate (r = −0.95), with the open reading frame (ORF) length (r = 0.6) and with protein abundance (r = 0.45). For high initiation rates (that may rise, for example, due to cellular growth), the sensitivity of a gene is dominated by all internal codons and is correlated with the decoding rate. We found that various central intracellular functions are associated with the sensitivity: for example, both genes that are sensitive and genes that are robust to perturbations are over-represented in the group of genes related to translation regulation; this may suggest that robustness to perturbations is a trait that undergoes evolutionary selection in relation to the function of the encoded protein. We believe that the reported results, due to their quantitative value and genome-wide perspective, should contribute to disciplines such as synthetic biology, functional genomics, comparative genomics and molecular evolution.

riboWaltz: Optimization of ribosome P-site positioning in ribosome profiling data

Ribosome profiling is a powerful technique used to study translation at the genome-wide level, generating unique information concerning ribosome positions along RNAs. Optimal localization of ribosomes requires the proper identification of the ribosome P-site in each ribosome protected fragment, a crucial step to determine the trinucleotide periodicity of translating ribosomes, and draw correct conclusions concerning where ribosomes are located. To determine the P-site within ribosome footprints at nucleotide resolution, the precise estimation of its offset with respect to the protected fragment is necessary. Here we present riboWaltz, an R package for calculation of optimal P-site offsets, diagnostic analysis and visual inspection of ribosome profiling data. Compared to existing tools, riboWaltz shows improved accuracies for P-site estimation and neat ribosome positioning in multiple case studies. riboWaltz was implemented in R and is available as an R package at https://github.com/LabTranslationalArchitectomics/RiboWaltz.

Controllability Analysis and Control Synthesis for the Ribosome Flow Model

The ribosomal density along different parts of the coding regions of the mRNA molecule affects various fundamental intracellular phenomena including: protein production rates, global ribosome allocation and organismal fitness, ribosomal drop off, co-translational protein folding, mRNA degradation, and more. Thus, regulating translation in order to obtain a desired ribosomal profile along the mRNA molecule is an important biological problem. We study this problem by using a dynamical model for mRNA translation, called the ribosome flow model (RFM). In the RFM, the mRNA molecule is modeled as an ordered chain of $n$ sites. The RFM includes $n$ state-variables describing the ribosomal density profile along the mRNA molecule, and the transition rates from each site to the next are controlled by $n+1$ positive constants. To study the problem of controlling the density profile, we consider some or all of the transition rates as time-varying controls. We consider the following problem: given an initial and a desired ribosomal density profile in the RFM, determine the time-varying values of the transition rates that steer the system to the desired density profile, if they exist. More specifically, we consider two control problems. In the first, all transition rates can be regulated separately, and the goal is to steer the ribosomal density profile and the protein production rate from a given initial value to a desired value. In the second problem, one or more transition rates are jointly regulated by a single scalar control, and the goal is to steer the production rate to a desired value within a certain set of feasible values. In the first case, we show that the system is controllable, i.e., the control is powerful enough to steer the system to any desired value in finite time, and provide simple closed-form expressions for constant positive control functions (or transition rates) that asymptotically steer the system to the desired value. In the second case, we show that the system is controllable, and provide a simple algorithm for determining the constant positive control value that asymptotically steers the system to the desired value. We discuss some of the biological implications of these results.

The ribosome, (slow) beating heart of cancer (stem) cell

The ribosome has long been considered as a consistent molecular factory, with a rather passive role in the translation process. Recent findings have shifted this obsolete view, revealing a remarkably complex and multifaceted machinery whose role is to orchestrate spatiotemporal control of gene expression. Ribosome specialization discovery has raised the interesting possibility of the existence of its malignant counterpart, an 'oncogenic' ribosome, which may promote tumor progression. Here we weigh the arguments supporting the existence of an 'oncogenic' ribosome and evaluate its role in cancer evolution. In particular, we provide an analysis and perspective on how the ribosome may play a critical role in the acquisition and maintenance of cancer stem cell phenotype.

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.

Genome scale analysis of Escherichia coli with a comprehensive prokaryotic sequence-based biophysical model of translation initiation and elongation

Translation initiation in prokaryotes is affected by the mRNA folding and interaction of the ribosome binding site with the ribosomal RNA. The elongation rate is affected, among other factors, by the local biophysical properties of the coding regions, the decoding rates of different codons, and the interactions among ribosomes. Currently, there is no comprehensive biophysical model of translation that enables the prediction of mRNA translation dynamics based only on the transcript sequence and while considering all of these fundamental aspects of translation. In this study, we provide, for the first time, a computational simulative biophysical model of both translation initiation and elongation with all aspects mentioned above. We demonstrate our model performance and advantages focusing on Escherichia coli genes. We further show that the model enables prediction of translation rate, protein levels, and ribosome densities. In addition, our model enables quantifying the effect of silent mutations on translation rate in different parts of the transcript, the relative effect of mutations on translation initiation and elongation, and the effect of mutations on ribosome traffic jams. Thus, unlike previous models, the proposed one provides comprehensive information, facilitating future research in disciplines such as molecular evolution, synthetic biology, and functional genomics. A toolkit to estimate translation dynamics of transcripts is available at: https://www.cs.tau.ac.il/∼tamirtul/transim.

Entrainment in the master equation

The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24 h solar day in biological systems or periodic traffic lights in a model of vehicular traffic. Using tools from systems and control theory, we prove that under mild technical conditions every solution of the master equation converges to a periodic solution with the same period as the rates. In other words, the master equation entrains (or phase locks) to periodic excitations. We describe two applications of our theoretical results to important models from statistical mechanics and epidemiology.

Ribosomopathies: There's strength in numbers

Ribosomopathies are a group of human disorders most commonly caused by ribosomal protein haploinsufficiency or defects in ribosome biogenesis. These conditions manifest themselves as physiological defects in specific cell and tissue types. We review current molecular models to explain ribosomopathies and attempt to reconcile the tissue specificity of these disorders with the ubiquitous requirement for ribosomes in all cells. Ribosomopathies as a group are diverse in their origins and clinical manifestations; we use the well-described Diamond-Blackfan anemia (DBA) as a specific example to highlight some common features. We discuss ribosome homeostasis as an overarching principle that governs the sensitivity of specific cells and tissue types to ribosomal protein mutations. Mathematical models and experimental insights rationalize how even subtle shifts in the availability of ribosomes, such as those created by ribosome haploinsufficiency, can drive messenger RNA-specific effects on protein expression. We discuss recently identified roles played by ribosome rescue and recycling factors in regulating ribosome homeostasis.

Realizing 'integral control' in living cells: how to overcome leaky integration due to dilution?

A major problem in the design of synthetic genetic circuits is robustness to perturbations and uncertainty. Because of this, there have been significant efforts in recent years in finding approaches to implement integral control in genetic circuits. Integral controllers have the unique ability to make the output of a process adapt perfectly to disturbances. However, implementing an integral controller is challenging in living cells. This is because a key aspect of any integral controller is a 'memory' element that stores the accumulation (integral) of the error between the output and its desired set-point. The ability to realize such a memory element in living cells is fundamentally challenged by the fact that all biomolecules dilute as cells grow, resulting in a 'leaky' memory that gradually fades away. As a consequence, the adaptation property is lost. Here, we propose a general principle for designing integral controllers such that the performance is practically unaffected by dilution. In particular, we mathematically prove that if the reactions implementing the integral controller are all much faster than dilution, then the adaptation error due to integration leakiness becomes negligible. We exemplify this design principle with two synthetic genetic circuits aimed at reaching adaptation of gene expression to fluctuations in cellular resources. Our results provide concrete guidance on the biomolecular processes that are most appropriate for implementing integral controllers in living cells.

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.

A code for transcription elongation speed

The two major steps of gene expression are transcription and translation. While hundreds of studies regarding the effect of sequence features on the translation elongation process have been published, very few connect sequence features to the transcription elongation rate. We suggest, for the first time, that short transcript sub-sequences have a typical effect on RNA polymerase (RNAP) speed: we show that nucleotide 5-mers tend to have typical RNAP speed (or transcription rate), which is consistent along different parts of genes and among different groups of genes with high correlation. We also demonstrate that relative RNAP speed correlates with mRNA levels of endogenous and heterologous genes. Furthermore, we show that the estimated transcription and translation elongation rates correlate in endogenous genes. Finally, we demonstrate that our results are consistent for different high resolution experimental measurements of RNAP densities. These results suggest for the first time that transcription elongation is partly encoded in the transcript, affected by the codon-usage, and optimized by evolution with a significant effect on gene expression and organismal fitness.

Ribosome flow model with extended objects

We study a deterministic mechanistic model for the flow of ribosomes along the mRNA molecule, called the ribosome flow model with extended objects (RFMEO). This model encapsulates many realistic features of translation including non-homogeneous transition rates along mRNA, the fact that every ribosome covers several codons, and the fact that ribosomes cannot overtake one another. The RFMEO is a mean-field approximation of an important model from statistical mechanics called the totally asymmetric simple exclusion process with extended objects (TASEPEO). We demonstrate that the RFMEO describes biophysical aspects of translation better than previous mean-field approximations, and that its predictions correlate well with those of TASEPEO. However, unlike TASEPEO, the RFMEO is amenable to rigorous analysis using tools from systems and control theory. We show that the ribosome density profile along the mRNA in the RFMEO converges to a unique steady-state density that depends on the length of the mRNA, the transition rates along it, and the number of codons covered by every ribosome, but not on the initial density of ribosomes along the mRNA. In particular, the protein production rate also converges to a unique steady state. Furthermore, if the transition rates along the mRNA are periodic with a common period T then the ribosome density along the mRNA and the protein production rate converge to a unique periodic pattern with period T, that is, the model entrains to periodic excitations in the transition rates. Analysis and simulations of the RFMEO demonstrate several counterintuitive results. For example, increasing the ribosome footprint may sometimes lead to an increase in the production rate. Also, for large values of the footprint the steady-state density along the mRNA may be quite complex (e.g. with quasi-periodic patterns) even for relatively simple (and non-periodic) transition rates along the mRNA. This implies that inferring the transition rates from the ribosome density may be non-trivial. We believe that the RFMEO could be useful for modelling, understanding and re-engineering translation as well as other important biological processes.

Reduced Protein Expression in a Virus Attenuated by Codon Deoptimization

A general means of viral attenuation involves the extensive recoding of synonymous codons in the viral genome. The mechanistic underpinnings of this approach remain unclear, however. Using quantitative proteomics and RNA sequencing, we explore the molecular basis of attenuation in a strain of bacteriophage T7 whose major capsid gene was engineered to carry 182 suboptimal codons. We do not detect transcriptional effects from recoding. Proteomic observations reveal that translation is halved for the recoded major capsid gene, and a more modest reduction applies to several coexpressed downstream genes. We observe no changes in protein abundances of other coexpressed genes that are encoded upstream. Viral burst size, like capsid protein abundance, is also decreased by half. Together, these observations suggest that, in this virus, reduced translation of an essential polycistronic transcript and diminished virion assembly form the molecular basis of attenuation.

Optimal Translation Along a Circular mRNA

The ribosome flow model on a ring (RFMR) is a deterministic model for ribosome flow along a circularized mRNA. We derive a new spectral representation for the optimal steady-state production rate and the corresponding optimal steady-state ribosomal density in the RFMR. This representation has several important advantages. First, it provides a simple and numerically stable algorithm for determining the optimal values even in very long rings. Second, it enables efficient computation of the sensitivity of the optimal production rate to small changes in the transition rates along the mRNA. Third, it implies that the optimal steady-state production rate is a strictly concave function of the transition rates. Maximizing the optimal steady-state production rate with respect to the rates under an affine constraint on the rates thus becomes a convex optimization problem that admits a unique solution. This solution can be determined numerically using highly efficient algorithms. This optimization problem is important, for example, when re-engineering heterologous genes in a host organism. We describe the implications of our results to this and other aspects of translation.