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Jiao F, Lin G, Yu J. Approximating gene transcription dynamics using steady-state formulas. Phys Rev E 2021; 104:014401. [PMID: 34412315 DOI: 10.1103/physreve.104.014401] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2021] [Accepted: 06/02/2021] [Indexed: 01/01/2023]
Abstract
Understanding how genes in a single cell respond to dynamically changing signals has been a central question in stochastic gene transcription research. Recent studies have generated massive steady-state or snapshot mRNA distribution data of individual cells, and inferred a large spectrum of kinetic transcription parameters under varying conditions. However, there have been few algorithms to convert these static data into the temporal variation of kinetic rates. Real-time imaging has been developed to monitor stochastic transcription processes at the single-cell level, but the immense technicality has prevented its application to most endogenous loci in mammalian cells. In this article, we introduced a stochastic gene transcription model with variable kinetic rates induced by unstable cellular conditions. We approximated the transcription dynamics using easily obtained steady-state formulas in the model. We tested the approximation against experimental data in both prokaryotic and eukaryotic cells and further solidified the conditions that guarantee the robustness of the method. The method can be easily implemented to provide convenient tools for quantifying dynamic kinetics and mechanisms underlying the widespread static transcription data, and may shed a light on circumventing the limitation of current bursting data on transcriptional real-time imaging.
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Affiliation(s)
- Feng Jiao
- Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, People's Republic of China.,College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 51006, People's Republic of China
| | - Genghong Lin
- Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, People's Republic of China.,College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 51006, People's Republic of China
| | - Jianshe Yu
- Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, People's Republic of China
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Efficiency and Robustness of Processes Driven by Nucleoid Exclusion in Escherichia coli. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2020. [PMID: 32894477 DOI: 10.1007/978-3-030-46886-6_4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/24/2024]
Abstract
The internal spatial organization of prokaryotic organisms, including Escherichia coli, is essential for the proper functioning of processes such as cell division. One source of this organization in E. coli is the nucleoid, which causes the exclusion of macromolecules - e.g. protein aggregates and the chemotaxis network - from midcell. Similarly, following DNA replication, the nucleoid(s) assist in placing the Z-ring at midcell. These processes need to be efficient in optimal conditions and robust to suboptimal conditions. After reviewing recent findings on these topics, we make use of past data to study the efficiency of the spatial constraining of Z-rings, chemotaxis networks, and protein aggregates, as a function of the nucleoid(s) morphology. Also, we compare the robustness of these processes to nonoptimal temperatures. We show that Z-rings, Tsr clusters, and protein aggregates have temperature-dependent spatial distributions along the major cell axis that are consistent with the nucleoid(s) morphology and the volume-exclusion phenomenon. Surprisingly, the consequences of the changes in nucleoid size with temperature are most visible in the kurtosis of these spatial distributions, in that it has a statistically significant linear correlation with the mean nucleoid length and, in the case of Z-rings, with the distance between nucleoids prior to cell division. Interestingly, we also find a negative, statistically significant linear correlation between the efficiency of these processes at the optimal condition and their robustness to suboptimal conditions, suggesting a trade-off between these traits.
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Häkkinen A, Oliveira SMD, Neeli-Venkata R, Ribeiro AS. Transcription closed and open complex formation coordinate expression of genes with a shared promoter region. J R Soc Interface 2019; 16:20190507. [PMID: 31822223 DOI: 10.1098/rsif.2019.0507] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Many genes are spaced closely, allowing coordination without explicit control through shared regulatory elements and molecular interactions. We study the dynamics of a stochastic model of a gene-pair in a head-to-head configuration, sharing promoter elements, which accounts for the rate-limiting steps in transcription initiation. We find that only in specific regions of the parameter space of the rate-limiting steps is orderly coexpression exhibited, suggesting that successful cooperation between closely spaced genes requires the coevolution of compatible rate-limiting step configuration. The model predictions are validated using in vivo single-cell, single-RNA measurements of the dynamics of pairs of genes sharing promoter elements. Our results suggest that, in E. coli, the kinetics of the rate-limiting steps in active transcription can play a central role in shaping the dynamics of gene-pairs sharing promoter elements.
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Affiliation(s)
- Antti Häkkinen
- BioMediTech Institute and Department of Signal Processing, Tampere University of Technology, PO Box 553 33101, Tampere, Finland
| | - Samuel M D Oliveira
- BioMediTech Institute and Department of Signal Processing, Tampere University of Technology, PO Box 553 33101, Tampere, Finland
| | - Ramakanth Neeli-Venkata
- BioMediTech Institute and Department of Signal Processing, Tampere University of Technology, PO Box 553 33101, Tampere, Finland
| | - Andre S Ribeiro
- BioMediTech Institute and Department of Signal Processing, Tampere University of Technology, PO Box 553 33101, Tampere, Finland
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Estimating RNA numbers in single cells by RNA fluorescent tagging and flow cytometry. J Microbiol Methods 2019; 166:105745. [PMID: 31654657 DOI: 10.1016/j.mimet.2019.105745] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2019] [Revised: 10/11/2019] [Accepted: 10/15/2019] [Indexed: 12/13/2022]
Abstract
Estimating the statistics of single-cell RNA numbers has become a key source of information on gene expression dynamics. One of the most informative methods of in vivo single-RNA detection is MS2d-GFP tagging. So far, it requires microscopy and laborious semi-manual image analysis, which hampers the amount of collectable data. To overcome this limitation, we present a new methodology for quantifying the mean, standard deviation, and skewness of single-cell distributions of RNA numbers, from flow cytometry data on cells expressing RNA tagged with MS2d-GFP. The quantification method, based on scaling flow-cytometry data from microscopy single-cell data on integer-valued RNA numbers, is shown to readily produce precise, big data on in vivo single-cell distributions of RNA numbers and, thus, can assist in studies of transcription dynamics.
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Startceva S, Kandavalli VK, Visa A, Ribeiro AS. Regulation of asymmetries in the kinetics and protein numbers of bacterial gene expression. BIOCHIMICA ET BIOPHYSICA ACTA-GENE REGULATORY MECHANISMS 2019; 1862:119-128. [DOI: 10.1016/j.bbagrm.2018.12.005] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2018] [Revised: 12/04/2018] [Accepted: 12/05/2018] [Indexed: 01/21/2023]
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Neeli-Venkata R, Oliveira SMD, Martins L, Startceva S, Bahrudeen M, Fonseca JM, Minoia M, Ribeiro AS. The precision of the symmetry in Z-ring placement in Escherichia coli is hampered at critical temperatures. Phys Biol 2018; 15:056002. [PMID: 29717708 DOI: 10.1088/1478-3975/aac1cb] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Cell division in Escherichia coli is morphologically symmetric due to, among other things, the ability of these cells to place the Z-ring at midcell. Studies have reported that, at sub-optimal temperatures, this symmetry decreases at the single-cell level, but the causes remain unclear. Using fluorescence microscopy, we observe FtsZ-GFP and DAPI-stained nucleoids to assess the robustness of the symmetry of Z-ring formation and positioning in individual cells under sub-optimal and critical temperatures. We find the Z-ring formation and positioning to be robust at sub-optimal temperatures, as the Z-ring's mean width, density and displacement from midcell maintain similar levels of correlation to one another as at optimal temperatures. However, at critical temperatures, the Z-ring displacement from midcell is greatly increased. We present evidence showing that this is due to enhanced distance between the replicated nucleoids and, thus, reduced Z-ring density, which explains the weaker precision in setting a morphologically symmetric division site. This also occurs in rich media and is cumulative, i.e. combining richer media and critically high temperatures enhances the asymmetries in division, which is evidence that the causes are biophysical. To further support this, we show that the effects are reversible, i.e. shifting cells from optimal to critical, and then to optimal again, reduces and then enhances the symmetry in Z-ring positioning, respectively, as the width and density of the Z-ring return to normal values. Overall, our findings show that the Z-ring positioning in E. coli is a robust biophysical process under sub-optimal temperatures, and that critical temperatures cause significant asymmetries in division.
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Affiliation(s)
- Ramakanth Neeli-Venkata
- Laboratory of Biosystem Dynamics, BioMediTech Institute and Faculty of Biomedical Sciences and Engineering, Tampere University of Technology, 33101, Tampere, Finland
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Goncalves NSM, Startceva S, Palma CSD, Bahrudeen MNM, Oliveira SMD, Ribeiro AS. Temperature-dependence of the single-cell variability in the kinetics of transcription activation in Escherichia coli. Phys Biol 2018; 15:026007. [PMID: 29182518 DOI: 10.1088/1478-3975/aa9ddf] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
From in vivo single-cell, single-RNA measurements of the activation times and subsequent steady-state active transcription kinetics of a single-copy Lac-ara-1 promoter in Escherichia coli, we characterize the intake kinetics of the inducer (IPTG) from the media, following temperature shifts. For this, for temperature shifts of various degrees, we obtain the distributions of transcription activation times as well as the distributions of intervals between consecutive RNA productions following activation in individual cells. We then propose a novel methodology that makes use of deconvolution techniques to extract the mean and the variability of the distribution of intake times. We find that cells, following shifts to low temperatures, have higher intake times, although, counter-intuitively, the cell-to-cell variability of these times is lower. We validate the results using a new methodology for direct estimation of mean intake times from measurements of activation times at various inducer concentrations. The results confirm that E. coli's inducer intake times from the environment are significantly higher following a shift to a sub-optimal temperature. Finally, we provide evidence that this is likely due to the emergence of additional rate-limiting steps in the intake process at low temperatures, explaining the reduced cell-to-cell variability in intake times.
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Affiliation(s)
- Nadia S M Goncalves
- Laboratory of Biosystem Dynamics, BioMediTech Institute and Faculty of Biomedical Sciences and Engineering, Tampere University of Technology, Tampere 33101, Finland
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Rate-limiting steps in transcription dictate sensitivity to variability in cellular components. Sci Rep 2017; 7:10588. [PMID: 28878283 PMCID: PMC5587725 DOI: 10.1038/s41598-017-11257-2] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2017] [Accepted: 08/21/2017] [Indexed: 12/28/2022] Open
Abstract
Cell-to-cell variability in cellular components generates cell-to-cell diversity in RNA and protein production dynamics. As these components are inherited, this should also cause lineage-to-lineage variability in these dynamics. We conjectured that these effects on transcription are promoter initiation kinetics dependent. To test this, first we used stochastic models to predict that variability in the numbers of molecules involved in upstream processes, such as the intake of inducers from the environment, acts only as a transient source of variability in RNA production numbers, while variability in the numbers of a molecular species controlling transcription of an active promoter acts as a constant source. Next, from single-cell, single-RNA level time-lapse microscopy of independent lineages of Escherichia coli cells, we demonstrate the existence of lineage-to-lineage variability in gene activation times and mean RNA production rates, and that these variabilities differ between promoters and inducers used. Finally, we provide evidence that this can be explained by differences in the kinetics of the rate-limiting steps in transcription between promoters and induction schemes. We conclude that cell-to-cell and consequent lineage-to-lineage variability in RNA and protein numbers are both promoter sequence-dependent and subject to regulation.
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Lloyd-Price J, Startceva S, Kandavalli V, Chandraseelan JG, Goncalves N, Oliveira SMD, Häkkinen A, Ribeiro AS. Dissecting the stochastic transcription initiation process in live Escherichia coli. DNA Res 2016; 23:203-14. [PMID: 27026687 PMCID: PMC4909308 DOI: 10.1093/dnares/dsw009] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2015] [Accepted: 02/11/2016] [Indexed: 02/01/2023] Open
Abstract
We investigate the hypothesis that, in Escherichia coli, while the concentration of RNA polymerases differs in different growth conditions, the fraction of RNA polymerases free for transcription remains approximately constant within a certain range of these conditions. After establishing this, we apply a standard model-fitting procedure to fully characterize the in vivo kinetics of the rate-limiting steps in transcription initiation of the Plac/ara-1 promoter from distributions of intervals between transcription events in cells with different RNA polymerase concentrations. We find that, under full induction, the closed complex lasts ∼788 s while subsequent steps last ∼193 s, on average. We then establish that the closed complex formation usually occurs multiple times prior to each successful initiation event. Furthermore, the promoter intermittently switches to an inactive state that, on average, lasts ∼87 s. This is shown to arise from the intermittent repression of the promoter by LacI. The methods employed here should be of use to resolve the rate-limiting steps governing the in vivo dynamics of initiation of prokaryotic promoters, similar to established steady-state assays to resolve the in vitro dynamics.
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Affiliation(s)
- Jason Lloyd-Price
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, PO Box 553, Office TC336, 33101 Tampere, Finland
| | - Sofia Startceva
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, PO Box 553, Office TC336, 33101 Tampere, Finland
| | - Vinodh Kandavalli
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, PO Box 553, Office TC336, 33101 Tampere, Finland
| | - Jerome G Chandraseelan
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, PO Box 553, Office TC336, 33101 Tampere, Finland
| | - Nadia Goncalves
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, PO Box 553, Office TC336, 33101 Tampere, Finland
| | - Samuel M D Oliveira
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, PO Box 553, Office TC336, 33101 Tampere, Finland
| | - Antti Häkkinen
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, PO Box 553, Office TC336, 33101 Tampere, Finland
| | - Andre S Ribeiro
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, PO Box 553, Office TC336, 33101 Tampere, Finland
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Lampasona AA, Czaplinski K. RNA voyeurism: A coming of age story. Methods 2016; 98:10-17. [DOI: 10.1016/j.ymeth.2015.11.024] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2015] [Revised: 11/24/2015] [Accepted: 11/26/2015] [Indexed: 10/22/2022] Open
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