On the Ribosomal Density that Maximizes Protein Translation Rate

Multi-omics reveals largely distinct transcript- and protein-level responses to the environment in an intertidal mussel

Organismal responses to stressful environments are influenced by numerous transcript- and protein-level mechanisms, and the relationships between expression changes at these levels are not always straightforward. Here, we used paired transcriptomic and proteomic datasets from two previous studies from gill of the California mussel, Mytilus californianus, to explore how simultaneous transcript and protein abundance patterns may diverge under different environmental scenarios. Field-acclimatized mussels were sampled from two disparate intertidal sites; individuals from one site were subjected to three further treatments (common garden, low-intertidal or high-intertidal outplant) that vary in temperature and feeding time. Assessing 1519 genes shared between the two datasets revealed that both transcript and protein expression patterns differentiated the treatments at a global level, despite numerous underlying discrepancies. There were far more instances of differential expression between treatments in transcript only (1451) or protein only (226) than of the two levels shifting expression concordantly (68 instances). Upregulated expression of cilium-associated transcripts (likely related to feeding) was associated with relatively benign field treatments. In the most stressful treatment, transcripts, but not proteins, for several molecular chaperones (including heat shock proteins and endoplasmic reticulum chaperones) were more abundant, consistent with a threshold model for induction of translation of constitutively available mRNAs. Overall, these results suggest that the relative importance of transcript- and protein-level regulation (translation and/or turnover) differs among cellular functions and across specific microhabitats or environmental contexts. Furthermore, the degree of concordance between transcript and protein expression can vary across benign versus acutely stressful environmental conditions.

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.

Principles of gene regulation quantitatively connect DNA to RNA and proteins in bacteria

Protein concentrations are set by a complex interplay between gene-specific regulatory processes and systemic factors, including cell volume and shared gene expression machineries. Elucidating this interplay is crucial for discerning and designing gene regulatory systems. We quantitatively characterized gene-specific and systemic factors that affect transcription and translation genome-wide for Escherichia coli across many conditions. The results revealed two design principles that make regulation of gene expression insulated from concentrations of shared machineries: RNA polymerase activity is fine-tuned to match translational output, and translational characteristics are similar across most messenger RNAs (mRNAs). Consequently, in bacteria, protein concentration is set primarily at the promoter level. A simple mathematical formula relates promoter activities and protein concentrations across growth conditions, enabling quantitative inference of gene regulation from omics data.

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.

Synergistic Regulation of Transcription and Translation in Escherichia coli Revealed by Codirectional Increases in mRNA Concentration and Translation Efficiency

Translational regulation was investigated at the genome-scale in Escherichia coli cells. Using the polysome profiling method, the ribosome occupancy (RO) and ribosome density (RD) of different mRNA copies were determined for several hundred mRNAs during the exponential- and stationary-phases, providing the most complete characterization of such regulation in E. coli. Although for most genes, nearly all mRNAs (>90%) were undergoing translation, they were loaded with far fewer than the theoretical maximum number of ribosomes, suggesting translation limitation at the initiation step. Multiple linear regression was used to identify key intrinsic factors involved in the genome-wide regulation of RO and RD (i.e., open reading frame GC%, protein function, and localization). Unexpectedly, mRNA concentration, a factor that depends on cell physiology, was predicted to positively regulate RO and RD during the exponential- and stationary-phases. Using a set of selected genes controlled by an inducible promoter, we confirmed that increasing the mRNA concentration upon transcription induction led to increases in both RO and ribosome load. The fact that this relationship between mRNA concentration and translation parameters was also effective when E. coli cells naturally adapted to carbon source changes demonstrates its physiological relevance. This work demonstrated that translation regulation is positively controlled by transcript availability. This new mechanism contributed to the codirectional regulation of transcription and translation with synergistic effects on gene expression and provided a systemic understanding of E. coli cell function. IMPORTANCE The process of gene expression is divided into translation and transcription. Considerable efforts have been made in bacteria to characterize the mechanisms underlying translational regulation and identify the regulatory factors for particular mRNAs. However, to understand bacterial physiology and adaptation, it is important to elucidate genome-wide translational regulation and examine its coordination with transcriptional regulation. Here, we provided a genome-wide picture of translational regulation in Escherichia coli. For most genes, nearly all mRNA copies were found to undergo translation but were loaded with a low number of ribosomes. We showed that mRNA concentration had a positive effect on translation regulation, linking translational regulation to transcriptional regulation as well as to cell physiology and growth conditions. The codirectional regulation of transcription and translation had synergistic effects on gene expression, contributing to E. coli cell function optimization. This finding could be used in biotechnology to optimize strategies for recombinant protein synthesis.

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.

Codon usage bias affects α-amylase mRNA level by altering RNA stability and cytosine methylation patterns in Escherichia coli

Codon usage bias exists in almost every organism and is reported to regulate protein translation efficiency and folding. Besides translation, the preliminary role of codon usage bias on gene transcription has also been revealed in some eukaryotes such as Neurospora crassa. In this study, we took as an example the α-amylase-coding gene (amyA) and examined the role of codon usage bias in regulating gene expression in the typical prokaryote Escherichia coli. We confirmed the higher translation efficiency on codon-optimized amyA RNAs and found that the RNA level itself was also affected by codon optimization. The decreased RNA level was caused at least in part by altered mRNA stability at the post-transcriptional level. Codon optimization also altered the number of cytosine methylation sites. Examination on dcm knockouts suggested that cytosine methylation may be a minor mechanism adopted by codon bias to regulate gene RNA levels. More studies are required to verify the global effect of codon usage and to reveal its detailed mechanism on transcription.

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/).

Quantitative principles of cis-translational control by general mRNA sequence features in eukaryotes

Background

General translational cis-elements are present in the mRNAs of all genes and affect the recruitment, assembly, and progress of preinitiation complexes and the ribosome under many physiological states. These elements include mRNA folding, upstream open reading frames, specific nucleotides flanking the initiating AUG codon, protein coding sequence length, and codon usage. The quantitative contributions of these sequence features and how and why they coordinate to control translation rates are not well understood.

Results

Here, we show that these sequence features specify 42–81% of the variance in translation rates in Saccharomyces cerevisiae, Schizosaccharomyces pombe, Arabidopsis thaliana, Mus musculus, and Homo sapiens. We establish that control by RNA secondary structure is chiefly mediated by highly folded 25–60 nucleotide segments within mRNA 5′ regions, that changes in tri-nucleotide frequencies between highly and poorly translated 5′ regions are correlated between all species, and that control by distinct biochemical processes is extensively correlated as is regulation by a single process acting in different parts of the same mRNA.

Conclusions

Our work shows that general features control a much larger fraction of the variance in translation rates than previously realized. We provide a more detailed and accurate understanding of the aspects of RNA structure that directs translation in diverse eukaryotes. In addition, we note that the strongly correlated regulation between and within cis-control features will cause more even densities of translational complexes along each mRNA and therefore more efficient use of the translation machinery by the cell.

Electronic supplementary material

The online version of this article (10.1186/s13059-019-1761-9) contains supplementary material, which is available to authorized users.

Protein synthesis rates and ribosome occupancies reveal determinants of translation elongation rates

Although protein synthesis dynamics has been studied both with theoretical models and by profiling ribosome footprints, the determinants of ribosome flux along open reading frames (ORFs) are not fully understood. Combining measurements of protein synthesis rate with ribosome footprinting data, we here inferred translation initiation and elongation rates for over a 1,000 ORFs in exponentially growing wild-type yeast cells. We found that the amino acid composition of synthesized proteins is as important a determinant of translation elongation rate as parameters related to codon and transfer RNA (tRNA) adaptation. We did not find evidence of ribosome collisions curbing the protein output of yeast transcripts, either in high translation conditions associated with exponential growth, or in strains in which deletion of individual ribosomal protein (RP) genes leads to globally increased or decreased translation. Slow translation elongation is characteristic of RP-encoding transcripts, which have markedly lower protein output compared with other transcripts with equally high ribosome densities.

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.

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.

Genome-Wide Posttranscriptional Dysregulation by MicroRNAs in Human Asthma as Revealed by Frac-seq

MicroRNAs are small noncoding RNAs that inhibit gene expression posttranscriptionally, implicated in virtually all biological processes. Although the effect of individual microRNAs is generally studied, the genome-wide role of multiple microRNAs is less investigated. We assessed paired genome-wide expression of microRNAs with total (cytoplasmic) and translational (polyribosome-bound) mRNA levels employing subcellular fractionation and RNA sequencing (Frac-seq) in human primary bronchoepithelium from healthy controls and severe asthmatics. Severe asthma is a chronic inflammatory disease of the airways characterized by poor response to therapy. We found genes (i.e., isoforms of a gene) and mRNA isoforms differentially expressed in asthma, with novel inflammatory and structural pathophysiological mechanisms related to bronchoepithelium disclosed solely by polyribosome-bound mRNAs (e.g., IL1A and LTB genes or ITGA6 and ITGA2 alternatively spliced isoforms). Gene expression (i.e., isoforms of a gene) and mRNA expression analysis revealed different molecular candidates and biological pathways, with differentially expressed polyribosome-bound and total mRNAs also showing little overlap. We reveal a hub of six dysregulated microRNAs accounting for ∼90% of all microRNA targeting, displaying preference for polyribosome-bound mRNAs. Transfection of this hub in bronchial epithelial cells from healthy donors mimicked asthma characteristics. Our work demonstrates extensive posttranscriptional gene dysregulation in human asthma, in which microRNAs play a central role, illustrating the feasibility and importance of assessing posttranscriptional gene expression when investigating human disease.

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.

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.

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.

Codon optimality, bias and usage in translation and mRNA decay

The advent of ribosome profiling and other tools to probe mRNA translation has revealed that codon bias - the uneven use of synonymous codons in the transcriptome - serves as a secondary genetic code: a code that guides the efficiency of protein production, the fidelity of translation and the metabolism of mRNAs. Recent advancements in our understanding of mRNA decay have revealed a tight coupling between ribosome dynamics and the stability of mRNA transcripts; this coupling integrates codon bias into the concept of codon optimality, or the effects that specific codons and tRNA concentrations have on the efficiency and fidelity of the translation machinery. In this Review, we first discuss the evidence for codon-dependent effects on translation, beginning with the basic mechanisms through which translation perturbation can affect translation efficiency, protein folding and transcript stability. We then discuss how codon effects are leveraged by the cell to tailor the proteome to maintain homeostasis, execute specific gene expression programmes of growth or differentiation and optimize the efficiency of protein production.

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.

A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics

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

A deterministic model for one-dimensional excluded flow with local interactions

Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental model for the unidirectional flow of particles along a one-dimensional lattice of sites with nearest-neighbor interactions between the particles. The flow between consecutive sites is governed by a “soft” simple exclusion principle and by attracting or repelling forces between neighboring particles. Using tools from contraction theory, we prove that the model admits a unique steady-state and that every trajectory converges to this steady-state. Analysis and simulations of the effect of the attracting and repelling forces on this steady-state highlight the crucial role that these forces may play in increasing the steady-state flow, and reveal that this increase stems from the alleviation of traffic jams along the lattice. Our theoretical analysis clarifies microscopic aspects of complex multi-particle dynamic processes.

Modulation of protein synthesis and degradation maintains proteostasis during yeast growth at different temperatures

To understand how cells regulate each step in the flow of gene expression is one of the most fundamental goals in molecular biology. In this work, we have investigated several protein turnover-related steps in the context of gene expression regulation in response to changes in external temperature in model yeast Saccharomyces cerevisiae. We have found that the regulation of protein homeostasis is stricter than mRNA homeostasis. Although global translation and protein degradation rates are found to increase with temperature, the increase of the catalytic activity of ribosomes is higher than the global translation rate suggesting that yeast cells adapt the amount of translational machinery to the constraints imposed by kinetics in order to minimize energy costs. Even though the transcriptional machinery is subjected to the same constraints, we observed interesting differences between transcription and translation, which may be related to the different energy costs of the two processes as well as the differential functions of mRNAs and proteins.