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Yadav V, Ullah Irshad I, Kumar H, Sharma AK. Quantitative Modeling of Protein Synthesis Using Ribosome Profiling Data. Front Mol Biosci 2021; 8:688700. [PMID: 34262940 PMCID: PMC8274658 DOI: 10.3389/fmolb.2021.688700] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 05/25/2021] [Indexed: 12/12/2022] Open
Abstract
Quantitative prediction on protein synthesis requires accurate translation initiation and codon translation rates. Ribosome profiling data, which provide steady-state distribution of relative ribosome occupancies along a transcript, can be used to extract these rate parameters. Various methods have been developed in the past few years to measure translation-initiation and codon translation rates from ribosome profiling data. In the review, we provide a detailed analysis of the key methods employed to extract the translation rate parameters from ribosome profiling data. We further discuss how these approaches were used to decipher the role of various structural and sequence-based features of mRNA molecules in the regulation of gene expression. The utilization of these accurate rate parameters in computational modeling of protein synthesis may provide new insights into the kinetic control of the process of gene expression.
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Affiliation(s)
- Vandana Yadav
- Department of Physics, Indian Institute of Technology Madras, Chennai, India
| | | | - Hemant Kumar
- School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, India
| | - Ajeet K Sharma
- Department of Physics, Indian Institute of Technology Jammu, Jammu, India
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Sharma AK. Translational autoregulation of RF2 protein in E. coli through programmed frameshifting. Phys Rev E 2021; 103:062412. [PMID: 34271674 DOI: 10.1103/physreve.103.062412] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Accepted: 06/04/2021] [Indexed: 11/07/2022]
Abstract
Various feedback mechanisms regulate the expression of different genes to ensure the required protein levels inside a cell. In this paper, we develop a kinetic model for one such mechanism that autoregulates RF2 protein synthesis in E. coli through programmed frameshifting. The model finds that the programmed frameshifting autoregulates RF2 protein synthesis by two independent mechanisms. First, it increases the rate of RF2 synthesis from each mRNA transcript at low RF2 concentration. Second, programmed frameshifting can dramatically increase the lifetime of RF2 transcripts when RF2 protein levels are lower than a threshold. This sharp increase in mRNA lifetime is caused by a first-order phase transition from a low to a high ribosome density on an RF2 transcript. The high ribosome density prevents the transcript's degradation by shielding it from nucleases, which increases its average lifetime and hence RF2 protein levels. Our study identifies this quality control mechanism that regulates the cellular protein levels by breaking the hierarchy of processes involved in gene expression.
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Affiliation(s)
- Ajeet K Sharma
- Department of Physics, Indian Institute of Technology, Jammu 181221, India
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Brown AI, Koslover EF. Design principles for the glycoprotein quality control pathway. PLoS Comput Biol 2021; 17:e1008654. [PMID: 33524026 PMCID: PMC7877790 DOI: 10.1371/journal.pcbi.1008654] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 02/11/2021] [Accepted: 12/21/2020] [Indexed: 01/11/2023] Open
Abstract
Newly-translated glycoproteins in the endoplasmic reticulum (ER) often undergo cycles of chaperone binding and release in order to assist in folding. Quality control is required to distinguish between proteins that have completed native folding, those that have yet to fold, and those that have misfolded. Using quantitative modeling, we explore how the design of the quality-control pathway modulates its efficiency. Our results show that an energy-consuming cyclic quality-control process, similar to the observed physiological system, outperforms alternative designs. The kinetic parameters that optimize the performance of this system drastically change with protein production levels, while remaining relatively insensitive to the protein folding rate. Adjusting only the degradation rate, while fixing other parameters, allows the pathway to adapt across a range of protein production levels, aligning with in vivo measurements that implicate the release of degradation-associated enzymes as a rapid-response system for perturbations in protein homeostasis. The quantitative models developed here elucidate design principles for effective glycoprotein quality control in the ER, improving our mechanistic understanding of a system crucial to maintaining cellular health. We explore the architecture and limitations of the quality-control pathway responsible for efficient folding of secretory proteins. Newly-synthesized proteins are tagged by the attachment of a ‘glycan’ sugar chain which facilitates their binding to a chaperone that assists protein folding. Removal of a specific sugar group on the glycan ends the interaction with the chaperone, and not-yet-folded proteins can be re-tagged for another round of chaperone binding. A degradation pathway acts in parallel with the folding cycle, to remove those proteins that have remained unfolded for a sufficiently long time. We develop and solve a mathematical model of this quality-control system, showing that the cyclical design found in living cells is uniquely able to maximize folded protein throughput while avoiding accumulation of unfolded proteins. Although this physiological model provides the best performance, its parameters must be adjusted to perform optimally under different protein production loads, and any single fixed set of parameters leads to poor performance when production rate is altered. We find that a single adjustable parameter, the protein degradation rate, is sufficient to allow optimal performance across a range of conditions. Interestingly, observations of living cells suggest that the degradation speed is indeed rapidly adjusted.
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Affiliation(s)
- Aidan I. Brown
- Department of Physics, University of California, San Diego, San Diego, California, United States of America
| | - Elena F. Koslover
- Department of Physics, University of California, San Diego, San Diego, California, United States of America
- * E-mail:
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Dutta A, Schütz GM, Chowdhury D. Stochastic thermodynamics and modes of operation of a ribosome: A network theoretic perspective. Phys Rev E 2021; 101:032402. [PMID: 32289926 DOI: 10.1103/physreve.101.032402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2019] [Accepted: 02/14/2020] [Indexed: 12/29/2022]
Abstract
The ribosome is one of the largest and most complex macromolecular machines in living cells. It polymerizes a protein in a step-by-step manner as directed by the corresponding nucleotide sequence on the template messenger RNA (mRNA) and this process is referred to as "translation" of the genetic message encoded in the sequence of mRNA transcript. In each successful chemomechanical cycle during the (protein) elongation stage, the ribosome elongates the protein by a single subunit, called amino acid, and steps forward on the template mRNA by three nucleotides called a codon. Therefore, a ribosome is also regarded as a molecular motor for which the mRNA serves as the track, its step size is that of a codon and two molecules of GTP and one molecule of ATP hydrolyzed in that cycle serve as its fuel. What adds further complexity is the existence of competing pathways leading to distinct cycles, branched pathways in each cycle, and futile consumption of fuel that leads neither to elongation of the nascent protein nor forward stepping of the ribosome on its track. We investigate a model formulated in terms of the network of discrete chemomechanical states of a ribosome during the elongation stage of translation. The model is analyzed using a combination of stochastic thermodynamic and kinetic analysis based on a graph-theoretic approach. We derive the exact solution of the corresponding master equations. We represent the steady state in terms of the cycles of the underlying network and discuss the energy transduction processes. We identify the various possible modes of operation of a ribosome in terms of its average velocity and mean rate of GTP hydrolysis. We also compute entropy production as functions of the rates of the interstate transitions and the thermodynamic cost for accuracy of the translation process.
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Affiliation(s)
- Annwesha Dutta
- Department of Physics, Indian Institute of Technology, Kanpur 208016, India
| | - Gunter M Schütz
- Institute of Complex Systems II, Forschungszentrum Jülich, 52425 Jülich, Germany
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Sharma AK, Sormanni P, Ahmed N, Ciryam P, Friedrich UA, Kramer G, O’Brien EP. A chemical kinetic basis for measuring translation initiation and elongation rates from ribosome profiling data. PLoS Comput Biol 2019; 15:e1007070. [PMID: 31120880 PMCID: PMC6559674 DOI: 10.1371/journal.pcbi.1007070] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2018] [Revised: 06/11/2019] [Accepted: 05/06/2019] [Indexed: 01/23/2023] Open
Abstract
Analysis methods based on simulations and optimization have been previously developed to estimate relative translation rates from next-generation sequencing data. Translation involves molecules and chemical reactions, hence bioinformatics methods consistent with the laws of chemistry and physics are more likely to produce accurate results. Here, we derive simple equations based on chemical kinetic principles to measure the translation-initiation rate, transcriptome-wide elongation rate, and individual codon translation rates from ribosome profiling experiments. Our methods reproduce the known rates from ribosome profiles generated from detailed simulations of translation. By applying our methods to data from S. cerevisiae and mouse embryonic stem cells, we find that the extracted rates reproduce expected correlations with various molecular properties, and we also find that mouse embryonic stem cells have a global translation speed of 5.2 AA/s, in agreement with previous reports that used other approaches. Our analysis further reveals that a codon can exhibit up to 26-fold variability in its translation rate depending upon its context within a transcript. This broad distribution means that the average translation rate of a codon is not representative of the rate at which most instances of that codon are translated, and it suggests that translational regulation might be used by cells to a greater degree than previously thought.
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Affiliation(s)
- Ajeet K. Sharma
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania, United States of America
| | - Pietro Sormanni
- Centre for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
| | - Nabeel Ahmed
- Bioinformatics and Genomics Graduate Program, The Huck Institutes of the Life Sciences, Pennsylvania State University, University Park, Pennsylvania, United States of America
| | - Prajwal Ciryam
- Centre for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
| | - Ulrike A. Friedrich
- Center for Molecular Biology of the Heidelberg University (ZMBH), DKFZ-ZMBH Alliance, Heidelberg, Germany
- German Cancer Research Center (DKFZ), Heidelberg, Germany
| | - Günter Kramer
- Center for Molecular Biology of the Heidelberg University (ZMBH), DKFZ-ZMBH Alliance, Heidelberg, Germany
- German Cancer Research Center (DKFZ), Heidelberg, Germany
| | - Edward P. O’Brien
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania, United States of America
- Bioinformatics and Genomics Graduate Program, The Huck Institutes of the Life Sciences, Pennsylvania State University, University Park, Pennsylvania, United States of America
- Institute for CyberScience, Pennsylvania State University, University Park, Pennsylvania, United States of America
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6
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Structural conditions on complex networks for the Michaelis-Menten input-output response. Proc Natl Acad Sci U S A 2018; 115:9738-9743. [PMID: 30194237 DOI: 10.1073/pnas.1808053115] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
The Michaelis-Menten (MM) fundamental formula describes how the rate of enzyme catalysis depends on substrate concentration. The familiar hyperbolic relationship was derived by timescale separation for a network of three reactions. The same formula has subsequently been found to describe steady-state input-output responses in many biological contexts, including single-molecule enzyme kinetics, gene regulation, transcription, translation, and force generation. Previous attempts to explain its ubiquity have been limited to networks with regular structure or simplifying parametric assumptions. Here, we exploit the graph-based linear framework for timescale separation to derive general structural conditions under which the MM formula arises. The conditions require a partition of the graph into two parts, akin to a "coarse graining" into the original MM graph, and constraints on where and how the input variable occurs. Other features of the graph, including the numerical values of parameters, can remain arbitrary, thereby explaining the formula's ubiquity. For systems at thermodynamic equilibrium, we derive a necessary and sufficient condition. For systems away from thermodynamic equilibrium, especially those with irreversible reactions, distinct structural conditions arise and a general characterization remains open. Nevertheless, our results accommodate, in much greater generality, all examples known to us in the literature.
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Identifying feasible operating regimes for early T-cell recognition: The speed, energy, accuracy trade-off in kinetic proofreading and adaptive sorting. PLoS One 2018; 13:e0202331. [PMID: 30114236 PMCID: PMC6095552 DOI: 10.1371/journal.pone.0202331] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2018] [Accepted: 08/01/2018] [Indexed: 01/09/2023] Open
Abstract
In the immune system, T cells can quickly discriminate between foreign and self ligands with high accuracy. There is evidence that T-cells achieve this remarkable performance utilizing a network architecture based on a generalization of kinetic proofreading (KPR). KPR-based mechanisms actively consume energy to increase the specificity beyond what is possible in equilibrium. An important theoretical question that arises is to understand the trade-offs and fundamental limits on accuracy, speed, and dissipation (energy consumption) in KPR and its generalization. Here, we revisit this question through numerical simulations where we simultaneously measure the speed, accuracy, and energy consumption of the KPR and adaptive sorting networks for different parameter choices. Our simulations highlight the existence of a "feasible operating regime" in the speed-energy-accuracy plane where T-cells can quickly differentiate between foreign and self ligands at reasonable energy expenditure. We give general arguments for why we expect this feasible operating regime to be a generic property of all KPR-based biochemical networks and discuss implications for our understanding of the T cell receptor circuit.
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Sharma AK, Ahmed N, O'Brien EP. Determinants of translation speed are randomly distributed across transcripts resulting in a universal scaling of protein synthesis times. Phys Rev E 2018; 97:022409. [PMID: 29548178 DOI: 10.1103/physreve.97.022409] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2017] [Indexed: 06/08/2023]
Abstract
Ribosome profiling experiments have found greater than 100-fold variation in ribosome density along mRNA transcripts, indicating that individual codon elongation rates can vary to a similar degree. This wide range of elongation times, coupled with differences in codon usage between transcripts, suggests that the average codon translation-rate per gene can vary widely. Yet, ribosome run-off experiments have found that the average codon translation rate for different groups of transcripts in mouse stem cells is constant at 5.6 AA/s. How these seemingly contradictory results can be reconciled is the focus of this study. Here, we combine knowledge of the molecular factors shown to influence translation speed with genomic information from Escherichia coli, Saccharomyces cerevisiae and Homo sapiens to simulate the synthesis of cytosolic proteins in these organisms. The model recapitulates a near constant average translation rate, which we demonstrate arises because the molecular determinants of translation speed are distributed nearly randomly amongst most of the transcripts. Consequently, codon translation rates are also randomly distributed and fast-translating segments of a transcript are likely to be offset by equally probable slow-translating segments, resulting in similar average elongation rates for most transcripts. We also show that the codon usage bias does not significantly affect the near random distribution of codon translation rates because only about 10% of the total transcripts in an organism have high codon usage bias while the rest have little to no bias. Analysis of Ribo-Seq data and an in vivo fluorescent assay supports these conclusions.
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Affiliation(s)
- Ajeet K Sharma
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Nabeel Ahmed
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Bioinformatics and Genomics Graduate Program, The Huck Institutes of the Life Sciences, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Edward P O'Brien
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Bioinformatics and Genomics Graduate Program, The Huck Institutes of the Life Sciences, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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Sharma AK, O'Brien EP. Increasing Protein Production Rates Can Decrease the Rate at Which Functional Protein Is Produced and Their Steady-State Levels. J Phys Chem B 2017. [PMID: 28650169 DOI: 10.1021/acs.jpcb.7b01700] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The rate at which soluble, functional protein is produced by the ribosome has recently been found to vary in complex and unexplained ways as various translation-associated rates are altered through synonymous codon substitutions. To understand this phenomenon, here, we combine a well-established ribosome-traffic model with a master-equation model of cotranslational domain folding to explore the scenarios that are possible for the protein production rate, J, and the functional-nascent protein production rate, F, as the rates of various translation processes are altered for five different E. coli proteins. We find that while J monotonically increases as the rates of translation-initiation, -elongation, and -termination increase, F can either increase or decrease. We show that F's nonmonotonic behavior arises within the model from two opposing trends: the tendency for increased translation rates to produce more total protein but less cotranslationally folded protein. We further demonstrate that under certain conditions these nonmonotonic changes in F can result in nonmonotonic variations in post-translational, steady-state levels of functional protein. These results provide a potential explanation for recent experimental observations in which the specific activity of enzymatic proteins decreased with increased synthesis rates. Additionally our model has the potential to be used to rationally design transcripts to maximize the production of functional nascent protein by simultaneously optimizing translation initiation, elongation, and termination rates.
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Affiliation(s)
- Ajeet K Sharma
- Department of Chemistry, Pennsylvania State University , University Park, Pennsylvania 16802, United States
| | - Edward P O'Brien
- Department of Chemistry, Pennsylvania State University , University Park, Pennsylvania 16802, United States
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A Generalized Michaelis–Menten Equation in Protein Synthesis: Effects of Mis-Charged Cognate tRNA and Mis-Reading of Codon. Bull Math Biol 2017; 79:1005-1027. [DOI: 10.1007/s11538-017-0266-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2016] [Accepted: 03/15/2017] [Indexed: 02/07/2023]
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Zur H, Tuller T. Predictive biophysical modeling and understanding of the dynamics of mRNA translation and its evolution. Nucleic Acids Res 2016; 44:9031-9049. [PMID: 27591251 PMCID: PMC5100582 DOI: 10.1093/nar/gkw764] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2016] [Accepted: 08/19/2016] [Indexed: 12/12/2022] Open
Abstract
mRNA translation is the fundamental process of decoding the information encoded in mRNA molecules by the ribosome for the synthesis of proteins. The centrality of this process in various biomedical disciplines such as cell biology, evolution and biotechnology, encouraged the development of dozens of mathematical and computational models of translation in recent years. These models aimed at capturing various biophysical aspects of the process. The objective of this review is to survey these models, focusing on those based and/or validated on real large-scale genomic data. We consider aspects such as the complexity of the models, the biophysical aspects they regard and the predictions they may provide. Furthermore, we survey the central systems biology discoveries reported on their basis. This review demonstrates the fundamental advantages of employing computational biophysical translation models in general, and discusses the relative advantages of the different approaches and the challenges in the field.
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Affiliation(s)
- Hadas Zur
- Department of Biomedical Engineering, the Engineering Faculty, Tel Aviv University, Tel-Aviv 69978, Israel
| | - Tamir Tuller
- Department of Biomedical Engineering, the Engineering Faculty, Tel Aviv University, Tel-Aviv 69978, Israel
- The Sagol School of Neuroscience, Tel Aviv University, Tel-Aviv 69978, Israel
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Dwell-Time Distribution, Long Pausing and Arrest of Single-Ribosome Translation through the mRNA Duplex. Int J Mol Sci 2015; 16:23723-44. [PMID: 26473825 PMCID: PMC4632723 DOI: 10.3390/ijms161023723] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2015] [Revised: 09/18/2015] [Accepted: 09/23/2015] [Indexed: 12/31/2022] Open
Abstract
Proteins in the cell are synthesized by a ribosome translating the genetic information encoded on the single-stranded messenger RNA (mRNA). It has been shown that the ribosome can also translate through the duplex region of the mRNA by unwinding the duplex. Here, based on our proposed model of the ribosome translation through the mRNA duplex we study theoretically the distribution of dwell times of the ribosome translation through the mRNA duplex under the effect of a pulling force externally applied to the ends of the mRNA to unzip the duplex. We provide quantitative explanations of the available single molecule experimental data on the distribution of dwell times with both short and long durations, on rescuing of the long paused ribosomes by raising the pulling force to unzip the duplex, on translational arrests induced by the mRNA duplex and Shine-Dalgarno(SD)-like sequence in the mRNA. The functional consequences of the pauses or arrests caused by the mRNA duplex and the SD sequence are discussed and compared with those obtained from other types of pausing, such as those induced by "hungry" codons or interactions of specific sequences in the nascent chain with the ribosomal exit tunnel.
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Ciandrini L, Romano MC, Parmeggiani A. Stepping and crowding of molecular motors: statistical kinetics from an exclusion process perspective. Biophys J 2015; 107:1176-1184. [PMID: 25185553 DOI: 10.1016/j.bpj.2014.07.012] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2013] [Revised: 06/17/2014] [Accepted: 07/01/2014] [Indexed: 10/24/2022] Open
Abstract
Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These macromolecules, nowadays investigated with advanced experimental techniques to unveil their molecular mechanisms and the properties of their kinetic cycles, are implicated in many biological processes, ranging from biopolymerization (e.g., RNA polymerases and ribosomes) to intracellular transport (motor proteins such as kinesins or dyneins). Although the kinetics of individual motors is well studied on both theoretical and experimental grounds, the repercussions of their stepping cycle on the collective dynamics still remains unclear. Advances in this direction will improve our comprehension of transport process in the natural intracellular medium, where processive motor enzymes might operate in crowded conditions. In this work, we therefore extend contemporary statistical kinetic analysis to study collective transport phenomena of motors in terms of lattice gas models belonging to the exclusion process class. Via numerical simulations, we show how to interpret and use the randomness calculated from single particle trajectories in crowded conditions. Importantly, we also show that time fluctuations and non-Poissonian behavior are intrinsically related to spatial correlations and the emergence of large, but finite, clusters of comoving motors. The properties unveiled by our analysis have important biological implications on the collective transport characteristics of processive motor enzymes in crowded conditions.
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Affiliation(s)
- Luca Ciandrini
- Laboratoire de Dynamique des Interactions Membranaires Normales et Pathologiques UMR 5235, Université Montpellier II and Centre National de la Recherche Scientifique, Montpellier, France; Laboratoire Charles Coulomb UMR 5221, Université Montpellier II and Centre National de la Recherche Scientifique, Montpellier, France.
| | - M Carmen Romano
- Institute for Complex Systems and Mathematical Biology, Scottish Universities Physics Alliance, University of Aberdeen, King's College, Aberdeen, United Kingdom; Institute of Medical Sciences, Foresterhill, University of Aberdeen, Aberdeen, United Kingdom
| | - Andrea Parmeggiani
- Laboratoire de Dynamique des Interactions Membranaires Normales et Pathologiques UMR 5235, Université Montpellier II and Centre National de la Recherche Scientifique, Montpellier, France; Laboratoire Charles Coulomb UMR 5221, Université Montpellier II and Centre National de la Recherche Scientifique, Montpellier, France
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Thompson CDK, Sharma AK, Frank J, Gonzalez RL, Chowdhury D. Quantitative Connection between Ensemble Thermodynamics and Single-Molecule Kinetics: A Case Study Using Cryogenic Electron Microscopy and Single-Molecule Fluorescence Resonance Energy Transfer Investigations of the Ribosome. J Phys Chem B 2015; 119:10888-10901. [PMID: 25785884 DOI: 10.1021/jp5128805] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
At equilibrium, thermodynamic and kinetic information can be extracted from biomolecular energy landscapes by many techniques. However, while static, ensemble techniques yield thermodynamic data, often only dynamic, single-molecule techniques can yield the kinetic data that describe transition-state energy barriers. Here we present a generalized framework based upon dwell-time distributions that can be used to connect such static, ensemble techniques with dynamic, single-molecule techniques, and thus characterize energy landscapes to greater resolutions. We demonstrate the utility of this framework by applying it to cryogenic electron microscopy (cryo-EM) and single-molecule fluorescence resonance energy transfer (smFRET) studies of the bacterial ribosomal pre-translocation complex. Among other benefits, application of this framework to these data explains why two transient, intermediate conformations of the pre-translocation complex, which are observed in a cryo-EM study, may not be observed in several smFRET studies.
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15
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Xie P. Biphasic character of ribosomal translocation and non-Michaelis-Menten kinetics of translation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062703. [PMID: 25615125 DOI: 10.1103/physreve.90.062703] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2014] [Indexed: 06/04/2023]
Abstract
We study theoretically the kinetics of mRNA translocation in the wild-type (WT) Escherichia coli ribosome, which is composed of a small 30S and large 50S subunit, and the ribosomes with mutations to some intersubunit bridges such as B1a, B4, B7a, and B8. The theoretical results reproduce well the available in vitro experimental data on the biphasic kinetics of the forward mRNA translocation catalyzed by elongation factor G (EF-G) hydrolyzing GTP, which can be best fit by the sum of two exponentials, and the monophasic kinetics of the spontaneous reverse mRNA translocation in the absence of the elongation factor, which can be best fit by a single-exponential function, in both the WT and mutant ribosomes. We show that both the mutation-induced increase in the maximal rate of the slow phase for the forward mRNA translocation and that in the rate of the spontaneous reverse mRNA translocation result from a reduction in the intrinsic energy barrier to resist the rotational movements between the two subunits, giving the same degree of increase in the two rates. The mutation-induced increase in the maximal rate of the fast phase for the forward mRNA translocation results mainly from the increase in the rate of the ribosomal unlocking, a conformational change in the ribosome that widens the mRNA channel for the mRNA translocation to take place, which could be partly due to the effect of the mutation on the intrasubunit 30S head rotation. Moreover, we study the translation rate of the WT and mutant ribosomes. It is shown that the translation rate versus the concentration of EF-G-GTP does not follow the Michaelis-Menten (MM) kinetics, which is in sharp contrast to the general property of other enzymes that the rate of the enzymatic reaction versus the concentration of a substrate follows the MM kinetics. The physical origin of this non-MM kinetics for the ribosome is revealed.
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Affiliation(s)
- Ping Xie
- Key Laboratory of Soft Matter Physics and Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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Caniparoli L, Lombardo P. Nonequilibrium stochastic model for tRNA binding time statistics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012712. [PMID: 24580262 DOI: 10.1103/physreve.89.012712] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2013] [Indexed: 06/03/2023]
Abstract
Protein translation is one of the most important processes in cell life, but despite being well-understood biochemically, the implications of its intrinsic stochastic nature have not been fully elucidated. In this paper we develop a microscopic and stochastic model which describes a crucial step in protein translation, namely the binding of the tRNA to the ribosome. Our model explicitly takes into consideration tRNA recharging dynamics, spatial inhomogeneity, and stochastic fluctuations in the number of charged tRNAs around the ribosome. By analyzing this nonequilibrium system we are able to derive the statistical distribution of the times needed by the tRNAs to bind to the ribosome, and to show that it deviates from an exponential due to the coupling between the fluctuations of charged and uncharged populations of tRNA.
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Affiliation(s)
- Luca Caniparoli
- International School for Advanced Studies (SISSA), via Bonomea 265, I-34136, Trieste, Italy
| | - Pierangelo Lombardo
- International School for Advanced Studies (SISSA), via Bonomea 265, I-34136, Trieste, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Trieste, Italy
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Challis KJ, Jack MW. Thermal fluctuation statistics in a molecular motor described by a multidimensional master equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062136. [PMID: 24483415 DOI: 10.1103/physreve.88.062136] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2013] [Indexed: 06/03/2023]
Abstract
We present a theoretical investigation of thermal fluctuation statistics in a molecular motor. Energy transfer in the motor is described using a multidimensional discrete master equation with nearest-neighbor hopping. In this theory, energy transfer leads to statistical correlations between thermal fluctuations in different degrees of freedom. For long times, the energy transfer is a multivariate diffusion process with constant drift and diffusion. The fluctuations and drift align in the strong-coupling limit enabling a one-dimensional description along the coupled coordinate. We derive formal expressions for the probability distribution and simulate single trajectories of the system in the near- and far-from-equilibrium limits both for strong and weak coupling. Our results show that the hopping statistics provide an opportunity to distinguish different operating regimes.
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Affiliation(s)
- K J Challis
- Scion, 49 Sala Street, Private Bag 3020, Rotorua 3046, New Zealand
| | - M W Jack
- Scion, 49 Sala Street, Private Bag 3020, Rotorua 3046, New Zealand
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Chowdhury D. Michaelis-Menten at 100 and allosterism at 50: driving molecular motors in a hailstorm with noisy ATPase engines and allosteric transmission. FEBS J 2013; 281:601-11. [DOI: 10.1111/febs.12596] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2013] [Revised: 10/25/2013] [Accepted: 10/28/2013] [Indexed: 11/29/2022]
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Sharma AK, Chowdhury D. First-passage problems in DNA replication: effects of template tension on stepping and exonuclease activities of a DNA polymerase motor. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:374105. [PMID: 23945294 DOI: 10.1088/0953-8984/25/37/374105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
A DNA polymerase (DNAP) replicates a template DNA strand. It also exploits the template as the track for its own motor-like mechanical movement. In the polymerase mode it elongates the nascent DNA by one nucleotide in each step. However, whenever it commits an error by misincorporating an incorrect nucleotide, it can switch to an exonuclease mode. In the latter mode it excises the wrong nucleotide before switching back to its polymerase mode. We develop a stochastic kinetic model of DNA replication that mimics an in vitro experiment where single-stranded DNA, subjected to a mechanical tension F, is converted to double-stranded DNA by a single DNAP. The F-dependence of the average rate of replication, which depends on the rates of both polymerase and exonuclease activities of the DNAP, is in good qualitative agreement with the corresponding experimental results. We introduce nine novel distinct conditional dwell times of a DNAP. Using the method of first-passage times, we also derive the exact analytical expressions for the probability distributions of these conditional dwell times. The predicted F-dependences of these distributions are, in principle, accessible to single-molecule experiments.
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Affiliation(s)
- Ajeet K Sharma
- Department of Physics, Indian Institute of Technology, Kanpur, 208016, India
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SHARMA AJEETK, CHOWDHURY DEBASHISH. TEMPLATE-DIRECTED BIOPOLYMERIZATION: TAPE-COPYING TURING MACHINES. ACTA ACUST UNITED AC 2013. [DOI: 10.1142/s1793048012300083] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
DNA, RNA and proteins are among the most important macromolecules in a living cell. These molecules are polymerized by molecular machines. These natural nano-machines polymerize such macromolecules, adding one monomer at a time, using another linear polymer as the corresponding template. The machine utilizes input chemical energy to move along the template which also serves as a track for the movements of the machine. In the Alan Turing year 2012, it is worth pointing out that these machines are "tape-copying Turing machines". We review the operational mechanisms of the polymerizer machines and their collective behavior from the perspective of statistical physics, emphasizing their common features in spite of the crucial differences in their biological functions. We also draw the attention of the physics community to another class of modular machines that carry out a different type of template-directed polymerization. We hope this review will inspire new kinetic models for these modular machines.
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Affiliation(s)
- AJEET K. SHARMA
- Department of Physics, Indian Institute of Technology, Kanpur 208016, India
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Xie P. Dynamics of tRNA occupancy and dissociation during translation by the ribosome. J Theor Biol 2013; 316:49-60. [DOI: 10.1016/j.jtbi.2012.09.023] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2012] [Revised: 09/17/2012] [Accepted: 09/18/2012] [Indexed: 12/23/2022]
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Sanbonmatsu KY. Computational studies of molecular machines: the ribosome. Curr Opin Struct Biol 2012; 22:168-74. [PMID: 22336622 DOI: 10.1016/j.sbi.2012.01.008] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2011] [Revised: 01/19/2012] [Accepted: 01/19/2012] [Indexed: 01/22/2023]
Abstract
The past decade has produced an avalanche of experimental data on the structure and dynamics of the ribosome. Groundbreaking studies in structural biology and kinetics have placed important constraints on ribosome structural dynamics. However, a gulf remains between static structures and time dependent data. In particular, X-ray crystallography and cryo-EM studies produce static models of the ribosome in various states, but lack dynamic information. Single molecule studies produce information on the rates of transitions between these states but do not have high-resolution spatial information. Computational studies have aided in bridging this gap by providing atomic resolution simulations of structural fluctuations and transitions between configurations.
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Sharma AK, Chowdhury D. Stochastic theory of protein synthesis and polysome: Ribosome profile on a single mRNA transcript. J Theor Biol 2011; 289:36-46. [DOI: 10.1016/j.jtbi.2011.08.023] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2011] [Revised: 08/18/2011] [Accepted: 08/19/2011] [Indexed: 12/31/2022]
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Reuveni S, Meilijson I, Kupiec M, Ruppin E, Tuller T. Genome-scale analysis of translation elongation with a ribosome flow model. PLoS Comput Biol 2011; 7:e1002127. [PMID: 21909250 PMCID: PMC3164701 DOI: 10.1371/journal.pcbi.1002127] [Citation(s) in RCA: 120] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2011] [Accepted: 06/06/2011] [Indexed: 11/18/2022] Open
Abstract
We describe the first large scale analysis of gene translation that is based on a model that takes into account the physical and dynamical nature of this process. The Ribosomal Flow Model (RFM) predicts fundamental features of the translation process, including translation rates, protein abundance levels, ribosomal densities and the relation between all these variables, better than alternative ('non-physical') approaches. In addition, we show that the RFM can be used for accurate inference of various other quantities including genes' initiation rates and translation costs. These quantities could not be inferred by previous predictors. We find that increasing the number of available ribosomes (or equivalently the initiation rate) increases the genomic translation rate and the mean ribosome density only up to a certain point, beyond which both saturate. Strikingly, assuming that the translation system is tuned to work at the pre-saturation point maximizes the predictive power of the model with respect to experimental data. This result suggests that in all organisms that were analyzed (from bacteria to Human), the global initiation rate is optimized to attain the pre-saturation point. The fact that similar results were not observed for heterologous genes indicates that this feature is under selection. Remarkably, the gap between the performance of the RFM and alternative predictors is strikingly large in the case of heterologous genes, testifying to the model's promising biotechnological value in predicting the abundance of heterologous proteins before expressing them in the desired host.
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Affiliation(s)
- Shlomi Reuveni
- Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Israel
- School of Chemistry, Tel Aviv University, Ramat Aviv, Israel
| | - Isaac Meilijson
- Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Israel
| | - Martin Kupiec
- Molecular Microbiology and Biotechnology, Tel Aviv University, Ramat Aviv, Israel
| | - Eytan Ruppin
- School of Computer Sciences, Tel Aviv University, Ramat Aviv, Israel
- School of Medicine, Tel Aviv University, Ramat Aviv, Israel
| | - Tamir Tuller
- Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot, Israel
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel
- * E-mail:
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