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Jain A, Gupta AK. Modeling mRNA Translation With Ribosome Abortions. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2023; 20:1600-1605. [PMID: 36044491 DOI: 10.1109/tcbb.2022.3203171] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
We derive a deterministic mathematical model for the flow of ribosomes along a mRNA called the ribosome flow model with extended objects and abortions (RFMEOA). This model incorporates important cellular features such as every ribosome covers several codons and they may detach from various regions along the track due to more realistic biological situations including phenomena of ribosome-ribosome collisions. We prove that the ribosome density profile along the mRNA in the RFMEOA and in particular, the protein production rate converge to a unique steady-state. Simulations of the RFMEOA demonstrate a surprising result that an increase in the initiation rate may sometimes lead to a decrease in the production rate. We believe that this model could be helpful to provide insight into the effects of premature termination on the protein expression and be useful for understanding and re-engineering the translation process.
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Phan T, He C, Loladze I, Prater C, Elser J, Kuang Y. Dynamics and growth rate implications of ribosomes and mRNAs interaction in E. coli. Heliyon 2022; 8:e09820. [PMID: 35800243 PMCID: PMC9254350 DOI: 10.1016/j.heliyon.2022.e09820] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Revised: 09/15/2021] [Accepted: 06/24/2022] [Indexed: 11/30/2022] Open
Abstract
Understanding how cells grow and adapt under various nutrient conditions is pivotal in the study of biological stoichiometry. Recent studies provide empirical evidence that cells use multiple strategies to maintain an optimal protein production rate under different nutrient conditions. Mathematical models can provide a solid theoretical foundation that can explain experimental observations and generate testable hypotheses to further our understanding of the growth process. In this study, we generalize a modeling framework that centers on the translation process and study its asymptotic behaviors to validate algebraic manipulations involving the steady states. Using experimental results on the growth of E. coli under C-, N-, and P-limited environments, we simulate the expected quantitative measurements to show the feasibility of using the model to explain empirical evidence. Our results support the findings that cells employ multiple strategies to maintain a similar protein production rate across different nutrient limitations. Moreover, we find that the previous study underestimates the significance of certain biological rates, such as the binding rate of ribosomes to mRNA and the transition rate between different ribosomal stages. Furthermore, our simulation shows that the strategies used by cells under C- and P-limitations result in a faster overall growth dynamics than under N-limitation. In conclusion, the general modeling framework provides a valuable platform to study cell growth under different nutrient supply conditions, which also allows straightforward extensions to the coupling of transcription, translation, and energetics to deepen our understanding of the growth process.
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Affiliation(s)
- Tin Phan
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
- Division of Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM 87544, USA
| | - Changhan He
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
| | - Irakli Loladze
- Bryan Medical Center, Bryan College of Health Sciences, Lincoln, NE 68506, USA
| | - Clay Prater
- Department of Integrative Biology, Oklahoma State University, Stillwater, OK 74078, USA
| | - Jim Elser
- Flathead Lake Bio Station, University of Montana, Polson, MT 59860, USA
| | - Yang Kuang
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
- Corresponding author.
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Jain A, Gupta AK. Modeling transport of extended interacting objects with drop-off phenomenon. PLoS One 2022; 17:e0267858. [PMID: 35499998 PMCID: PMC9060384 DOI: 10.1371/journal.pone.0267858] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2021] [Accepted: 04/17/2022] [Indexed: 11/19/2022] Open
Abstract
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.
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Affiliation(s)
- Aditi Jain
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, India
| | - Arvind Kumar Gupta
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, India
- * E-mail:
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Bonnin P, Stansfield I, Romano MC, Kern N. Two-species totally asymmetric simple exclusion process model: From a simple description to intermittency and traveling traffic jams. Phys Rev E 2022; 105:034117. [PMID: 35428133 DOI: 10.1103/physreve.105.034117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2021] [Accepted: 11/05/2021] [Indexed: 06/14/2023]
Abstract
We extend the paradigmatic and versatile totally asymmetric simple exclusion process (TASEP) for stochastic 1D transport to allow for two different particle species, each having specific entry and exit rates. We offer a complete mean-field analysis, including a phase diagram, by mapping this model onto an effective one-species TASEP. Stochastic simulations confirm the results, but indicate deviations when the particle species have very different exit rates. We illustrate that this is due to a phenomenon of intermittency, and formulate a refined "intermittent" mean-field theory for this regime. We discuss how nonstationary effects may further enrich the phenomenology.
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Affiliation(s)
- Pierre Bonnin
- Institute for Complex Systems and Mathematical Biology, Department of Physics, Aberdeen AB24 3UE, United Kingdom
- Institute of Medical Sciences, School of Medicine, Medical Sciences and Nutrition, University of Aberdeen, Aberdeen AB25 2ZD, United Kingdom
| | - Ian Stansfield
- Institute of Medical Sciences, School of Medicine, Medical Sciences and Nutrition, University of Aberdeen, Aberdeen AB25 2ZD, United Kingdom
| | - M Carmen Romano
- Institute for Complex Systems and Mathematical Biology, Department of Physics, Aberdeen AB24 3UE, United Kingdom
- Institute of Medical Sciences, School of Medicine, Medical Sciences and Nutrition, University of Aberdeen, Aberdeen AB25 2ZD, United Kingdom
| | - Norbert Kern
- Laboratoire Charles Coulomb (L2C), University of Montpellier, CNRS, F-34095 Montpellier Cedex 5, France
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Gedeon T, Davis L, Weber K, Thorenson J. Trade-offs among transcription elongation rate, number, and duration of ubiquitous pauses on highly transcribed bacterial genes. J Bioinform Comput Biol 2021; 19:2150020. [PMID: 34353243 DOI: 10.1142/s0219720021500207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
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.
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Affiliation(s)
- Tomáš Gedeon
- Department of Mathematical Sciences, Montana State University, P.O. Box 172400, Bozeman, MT 59717-2400, USA
| | - Lisa Davis
- Department of Mathematical Sciences, Montana State University, P.O. Box 172400, Bozeman, MT 59717-2400, USA
| | - Katelyn Weber
- Department of Statistics, London School of Economics and Political Science, London, UK
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Variability in mRNA translation: a random matrix theory approach. Sci Rep 2021; 11:5300. [PMID: 33674667 PMCID: PMC7970873 DOI: 10.1038/s41598-021-84738-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Accepted: 02/19/2021] [Indexed: 01/31/2023] Open
Abstract
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.
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do Couto Bordignon P, Pechmann S. Inferring translational heterogeneity from Saccharomyces cerevisiae ribosome profiling. FEBS J 2021; 288:4541-4559. [PMID: 33539640 DOI: 10.1111/febs.15748] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Revised: 01/27/2021] [Accepted: 02/02/2021] [Indexed: 11/30/2022]
Abstract
Translation of mRNAs into proteins by the ribosome is the most important step of protein biosynthesis. Accordingly, translation is tightly controlled and heavily regulated to maintain cellular homeostasis. Ribosome profiling (Ribo-seq) has revolutionized the study of translation by revealing many of its underlying mechanisms. However, equally many aspects of translation remain mysterious, in part also due to persisting challenges in the interpretation of data obtained from Ribo-seq experiments. Here, we show that some of the variability observed in Ribo-seq data has biological origins and reflects programmed heterogeneity of translation. Through a comparative analysis of Ribo-seq data from Saccharomyces cerevisiae, we systematically identify short 3-codon sequences that are differentially translated (DT) across mRNAs, that is, identical sequences that are translated sometimes fast and sometimes slowly beyond what can be attributed to variability between experiments. Remarkably, the thus identified DT sequences link to mechanisms known to regulate translation elongation and are enriched in genes important for protein and organelle biosynthesis. Our results thus highlight examples of translational heterogeneity that are encoded in the genomic sequences and tuned to optimizing cellular homeostasis. More generally, our work highlights the power of Ribo-seq to understand the complexities of translation regulation.
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Nanikashvili I, Zarai Y, Ovseevich A, Tuller T, Margaliot M. Networks of ribosome flow models for modeling and analyzing intracellular traffic. Sci Rep 2019; 9:1703. [PMID: 30737417 PMCID: PMC6368613 DOI: 10.1038/s41598-018-37864-1] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2018] [Accepted: 12/17/2018] [Indexed: 11/20/2022] Open
Abstract
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.
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Affiliation(s)
- Itzik Nanikashvili
- School of Electrical Engineering, Tel-Aviv University, Tel-Aviv, 69978, Israel
| | - Yoram Zarai
- Department of Biomedical Engineering, Tel-Aviv University, Tel-Aviv, 69978, Israel
| | - Alexander Ovseevich
- Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences and the Russian Quantum Center, Moscow, Russia
| | - Tamir Tuller
- Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv, 69978, Israel. .,Department of Biomedical Engineering, Tel-Aviv University, Tel-Aviv, 69978, Israel.
| | - Michael Margaliot
- School of Electrical Engineering, Tel-Aviv University, Tel-Aviv, 69978, Israel.,Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv, 69978, Israel
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