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Weidemann DE, Singh A, Grima R, Hauf S. The minimal intrinsic stochasticity of constitutively expressed eukaryotic genes is sub-Poissonian. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.03.06.531283. [PMID: 36945401 PMCID: PMC10028819 DOI: 10.1101/2023.03.06.531283] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/18/2023]
Abstract
Stochastic variation in gene products ("noise") is an inescapable by-product of gene expression. Noise must be minimized to allow for the reliable execution of cellular functions. However, noise cannot be suppressed beyond an intrinsic lower limit. For constitutively expressed genes, this limit is believed to be Poissonian, meaning that the variance in mRNA numbers cannot be lower than their mean. Here, we show that several cell division genes in fission yeast have mRNA variances significantly below this limit, which cannot be explained by the classical gene expression model for low-noise genes. Our analysis reveals that multiple steps in both transcription and mRNA degradation are essential to explain this sub-Poissonian variance. The sub-Poissonian regime differs qualitatively from previously characterized noise regimes, a hallmark being that cytoplasmic noise is reduced when the mRNA export rate increases. Our study re-defines the lower limit of eukaryotic gene expression noise and identifies molecular requirements for ultra-low noise which are expected to support essential cell functions.
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Affiliation(s)
- Douglas E Weidemann
- Department of Biological Sciences, Virginia Tech, Blacksburg, VA 24061, USA
- Fralin Life Sciences Institute, Virginia Tech, Blacksburg, VA 24061, USA
| | - Abhyudai Singh
- Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA
- Department of Biomedical Engineering, University of Delaware, Newark, DE 19716, USA
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, Edinburgh, EH9 3JR, Scotland, UK
| | - Silke Hauf
- Department of Biological Sciences, Virginia Tech, Blacksburg, VA 24061, USA
- Fralin Life Sciences Institute, Virginia Tech, Blacksburg, VA 24061, USA
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2
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de Gunst M, Mandjes M, Sollie B. Statistical inference for a quasi birth–death model of RNA transcription. BMC Bioinformatics 2022; 23:105. [PMID: 35346020 PMCID: PMC8961911 DOI: 10.1186/s12859-022-04638-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2021] [Accepted: 03/11/2022] [Indexed: 11/25/2022] Open
Abstract
Background A birth–death process of which the births follow a hypoexponential distribution with L phases and are controlled by an on/off mechanism, is a population process which we call the on/off-seq-L process. It is a suitable model for the dynamics of a population of RNA molecules in a single living cell. Motivated by this biological application, our aim is to develop a statistical method to estimate the model parameters of the on/off-seq-L process, based on observations of the population size at discrete time points, and to apply this method to real RNA data. Methods It is shown that the on/off-seq-L process can be seen as a quasi birth–death process, and an Erlangization technique can be used to approximate the corresponding likelihood function. An extensive simulation-based numerical study is carried out to investigate the performance of the resulting estimation method. Results and conclusion A statistical method is presented to find maximum likelihood estimates of the model parameters for the on/off-seq-L process. Numerical complications related to the likelihood maximization are identified and analyzed, and solutions are presented. The proposed estimation method is a highly accurate method to find the parameter estimates. Based on real RNA data, the on/off-seq-3 process emerges as the best model to describe RNA transcription.
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van Gijtenbeek LA, Kok J. Illuminating Messengers: An Update and Outlook on RNA Visualization in Bacteria. Front Microbiol 2017; 8:1161. [PMID: 28690601 PMCID: PMC5479882 DOI: 10.3389/fmicb.2017.01161] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2017] [Accepted: 06/07/2017] [Indexed: 01/04/2023] Open
Abstract
To be able to visualize the abundance and spatiotemporal features of RNAs in bacterial cells would permit obtaining a pivotal understanding of many mechanisms underlying bacterial cell biology. The first methods that allowed observing single mRNA molecules in individual cells were introduced by Bertrand et al. (1998) and Femino et al. (1998). Since then, a plethora of techniques to image RNA molecules with the aid of fluorescence microscopy has emerged. Many of these approaches are useful for the large eukaryotic cells but their adaptation to study RNA, specifically mRNA molecules, in bacterial cells progressed relatively slow. Here, an overview will be given of fluorescent techniques that can be used to reveal specific RNA molecules inside fixed and living single bacterial cells. It includes a critical evaluation of their caveats as well as potential solutions.
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Affiliation(s)
- Lieke A van Gijtenbeek
- Department of Molecular Genetics, Faculty of Science and Engineering, University of GroningenGroningen, Netherlands
| | - Jan Kok
- Department of Molecular Genetics, Faculty of Science and Engineering, University of GroningenGroningen, Netherlands
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4
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Balomenos AD, Tsakanikas P, Aspridou Z, Tampakaki AP, Koutsoumanis KP, Manolakos ES. Image analysis driven single-cell analytics for systems microbiology. BMC SYSTEMS BIOLOGY 2017; 11:43. [PMID: 28376782 PMCID: PMC5379763 DOI: 10.1186/s12918-017-0399-z] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/07/2016] [Accepted: 01/25/2017] [Indexed: 11/10/2022]
Abstract
BACKGROUND Time-lapse microscopy is an essential tool for capturing and correlating bacterial morphology and gene expression dynamics at single-cell resolution. However state-of-the-art computational methods are limited in terms of the complexity of cell movies that they can analyze and lack of automation. The proposed Bacterial image analysis driven Single Cell Analytics (BaSCA) computational pipeline addresses these limitations thus enabling high throughput systems microbiology. RESULTS BaSCA can segment and track multiple bacterial colonies and single-cells, as they grow and divide over time (cell segmentation and lineage tree construction) to give rise to dense communities with thousands of interacting cells in the field of view. It combines advanced image processing and machine learning methods to deliver very accurate bacterial cell segmentation and tracking (F-measure over 95%) even when processing images of imperfect quality with several overcrowded colonies in the field of view. In addition, BaSCA extracts on the fly a plethora of single-cell properties, which get organized into a database summarizing the analysis of the cell movie. We present alternative ways to analyze and visually explore the spatiotemporal evolution of single-cell properties in order to understand trends and epigenetic effects across cell generations. The robustness of BaSCA is demonstrated across different imaging modalities and microscopy types. CONCLUSIONS BaSCA can be used to analyze accurately and efficiently cell movies both at a high resolution (single-cell level) and at a large scale (communities with many dense colonies) as needed to shed light on e.g. how bacterial community effects and epigenetic information transfer play a role on important phenomena for human health, such as biofilm formation, persisters' emergence etc. Moreover, it enables studying the role of single-cell stochasticity without losing sight of community effects that may drive it.
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Affiliation(s)
- Athanasios D Balomenos
- Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Ilissia, Greece
| | - Panagiotis Tsakanikas
- Biomedical Research Foundation of the Academy of Athens, 4 Soranou Ephessiou Street, Athens, Greece
| | - Zafiro Aspridou
- Laboratory of Food Microbiology and Hygiene, Department of Food Science and Technology, School of Agriculture, Forestry and Natural Environment, Aristotle University of Thessaloniki, Thessaloniki, Greece
| | - Anastasia P Tampakaki
- Department of Agricultural Biotechnology, Agricultural University of Athens, Athens, Greece
| | - Konstantinos P Koutsoumanis
- Laboratory of Food Microbiology and Hygiene, Department of Food Science and Technology, School of Agriculture, Forestry and Natural Environment, Aristotle University of Thessaloniki, Thessaloniki, Greece
| | - Elias S Manolakos
- Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Ilissia, Greece. .,Northeastern University, Boston, USA. .,Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, USA.
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5
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Gupta A, Lloyd-Price J, Ribeiro AS. In silico analysis of division times of Escherichia coli populations as a function of the partitioning scheme of non-functional proteins. In Silico Biol 2016; 12:9-21. [PMID: 25318468 PMCID: PMC4923715 DOI: 10.3233/isb-140462] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
Recent evidence suggests that cells employ functionally asymmetric partitioning schemes in division to cope with aging. We explore various schemes in silico, with a stochastic model of Escherichia coli that includes gene expression, non-functional proteins generation, aggregation and polar retention, and molecule partitioning in division. The model is implemented in SGNS2, which allows stochastic, multi-delayed reactions within hierarchical, transient, interlinked compartments. After setting parameter values of non-functional proteins’ generation and effects that reproduce realistic intracellular and population dynamics, we investigate how the spatial organization of non-functional proteins affects mean division times of cell populations in lineages and, thus, mean cell numbers over time. We find that division times decrease for increasingly asymmetric partitioning. Also, increasing the clustering of non-functional proteins decreases division times. Increasing the bias in polar segregation further decreases division times, particularly if the bias favors the older pole and aggregates’ polar retention is robust. Finally, we show that the non-energy consuming retention of inherited non-functional proteins at the older pole via nucleoid occlusion is a source of functional asymmetries and, thus, is advantageous. Our results suggest that the mechanisms of intracellular organization of non-functional proteins, including clustering and polar retention, affect the vitality of E. coli populations.
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Affiliation(s)
| | | | - Andre S. Ribeiro
- Corresponding author: Andre S. Ribeiro, Department of Signal Processing, Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland. Tel.: +358 408490736; Fax: +358 331154989;
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6
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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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7
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Häkkinen A, Ribeiro AS. Characterizing rate limiting steps in transcription from RNA production times in live cells. Bioinformatics 2016; 32:1346-52. [PMID: 26722120 DOI: 10.1093/bioinformatics/btv744] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2015] [Accepted: 12/15/2015] [Indexed: 11/13/2022] Open
Abstract
MOTIVATION Single-molecule measurements of live Escherichia coli transcription dynamics suggest that this process ranges from sub- to super-Poissonian, depending on the conditions and on the promoter. For its accurate quantification, we propose a model that accommodates all these settings, and statistical methods to estimate the model parameters and to select the relevant components. RESULTS The new methodology has improved accuracy and avoids overestimating the transcription rate due to finite measurement time, by exploiting unobserved data and by accounting for the effects of discrete sampling. First, we use Monte Carlo simulations of models based on measurements to show that the methods are reliable and offer substantial improvements over previous methods. Next, we apply the methods on measurements of transcription intervals of different promoters in live E. coli, and show that they produce significantly different results, both in low- and high-noise settings, and that, in the latter case, they even lead to qualitatively different results. Finally, we demonstrate that the methods can be generalized for other similar purposes, such as for estimating gene activation kinetics. In this case, the new methods allow quantifying the inducer uptake dynamics as opposed to just comparing them between cases, which was not previously possible. We expect this new methodology to be a valuable tool for functional analysis of cellular processes using single-molecule or single-event microscopy measurements in live cells. AVAILABILITY AND IMPLEMENTATION Source code is available under Mozilla Public License at http://www.cs.tut.fi/%7Ehakkin22/censored/ CONTACT andre.ribeiro@tut.fi or andre.sanchesribeiro@tut.fi SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Antti Häkkinen
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, P.O. box 553, 33101, Tampere, Finland
| | - Andre S Ribeiro
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, P.O. box 553, 33101, Tampere, Finland
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8
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Zimmer C, Häkkinen A, Ribeiro AS. Estimation of kinetic parameters of transcription from temporal single-RNA measurements. Math Biosci 2015; 271:146-53. [PMID: 26522167 DOI: 10.1016/j.mbs.2015.10.001] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2015] [Revised: 09/07/2015] [Accepted: 10/01/2015] [Indexed: 11/27/2022]
Abstract
Gene expression dynamics in prokaryotes is largely controlled by the multi-step process of transcription initiation whose kinetics is subject to regulation. Since the number and duration of these steps cannot be currently measured in vivo, we propose a novel method for estimating them from time series of RNA numbers in individual cells. We demonstrate the method's applicability on measurements of fluorescence-tagged RNA molecules in Escherichia coli cells, and compare with a previous method. We show that the results of the two methods agree for equal data. We also show that, when incorporating additional data, the new method produces significantly different estimates, which are in closer agreement with qPCR measurements. Unlike the previous method, the new method requires no preprocessing of the RNA numbers, using maximal information from the RNA time series. In addition, it can use data outside of the observed RNA productions. Overall, the new method characterizes the transcription initiation process with enhanced detail.
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Affiliation(s)
- Christoph Zimmer
- BIOMS, University of Heidelberg, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany.
| | - Antti Häkkinen
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, Korkeakoulunkatu 1, 33720 Tampere, Finland
| | - Andre S Ribeiro
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, Korkeakoulunkatu 1, 33720 Tampere, Finland
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9
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Tran H, Oliveira SMD, Goncalves N, Ribeiro AS. Kinetics of the cellular intake of a gene expression inducer at high concentrations. MOLECULAR BIOSYSTEMS 2015. [PMID: 26223179 DOI: 10.1039/c5mb00244c] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
From in vivo single-event measurements of the transient and steady-state transcription activity of a single-copy lac-ara-1 promoter in Escherichia coli, we characterize the intake kinetics of its inducer (IPTG) from the media. We show that the empirical data are well-fit by a model of intake assuming a bilayer membrane, with the passage through the second layer being rate-limiting, coupled to a stochastic, sub-Poissonian, multi-step transcription process. Using this model, we show that for a wide range of extracellular inducer levels (up to 1.25 mM) the intake process is diffusive-like, suggesting unsaturated membrane permeability. Inducer molecules travel from the periplasm to the cytoplasm in, on average, 31.7 minutes, strongly affecting cells' response time. The novel methodology followed here should aid the study of cellular intake mechanisms at the single-event level.
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Affiliation(s)
- Huy Tran
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, FI-33101 Tampere, Finland.
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10
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Wang Y, Zhang Z, Wang H, Bi S. Segmentation of the Clustered Cells with Optimized Boundary Detection in Negative Phase Contrast Images. PLoS One 2015; 10:e0130178. [PMID: 26066315 PMCID: PMC4467081 DOI: 10.1371/journal.pone.0130178] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2014] [Accepted: 05/18/2015] [Indexed: 11/19/2022] Open
Abstract
Cell image segmentation plays a central role in numerous biology studies and clinical applications. As a result, the development of cell image segmentation algorithms with high robustness and accuracy is attracting more and more attention. In this study, an automated cell image segmentation algorithm is developed to get improved cell image segmentation with respect to cell boundary detection and segmentation of the clustered cells for all cells in the field of view in negative phase contrast images. A new method which combines the thresholding method and edge based active contour method was proposed to optimize cell boundary detection. In order to segment clustered cells, the geographic peaks of cell light intensity were utilized to detect numbers and locations of the clustered cells. In this paper, the working principles of the algorithms are described. The influence of parameters in cell boundary detection and the selection of the threshold value on the final segmentation results are investigated. At last, the proposed algorithm is applied to the negative phase contrast images from different experiments. The performance of the proposed method is evaluated. Results show that the proposed method can achieve optimized cell boundary detection and highly accurate segmentation for clustered cells.
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Affiliation(s)
- Yuliang Wang
- Robotics Institute, School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, P.R. China
- * E-mail:
| | - Zaicheng Zhang
- Robotics Institute, School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, P.R. China
| | - Huimin Wang
- Department of Materials Science and Engineering, The Ohio State University, 2041 College Rd., Columbus, Ohio 43210, United States of America
| | - Shusheng Bi
- Robotics Institute, School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, P.R. China
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11
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Gupta A, Lloyd-Price J, Oliveira SMD, Yli-Harja O, Muthukrishnan AB, Ribeiro AS. Robustness of the division symmetry inEscherichia coliand functional consequences of symmetry breaking. Phys Biol 2014; 11:066005. [DOI: 10.1088/1478-3975/11/6/066005] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
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12
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Rieckh G, Tkačik G. Noise and information transmission in promoters with multiple internal States. Biophys J 2014; 106:1194-204. [PMID: 24606943 DOI: 10.1016/j.bpj.2014.01.014] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2013] [Revised: 01/07/2014] [Accepted: 01/07/2014] [Indexed: 01/01/2023] Open
Abstract
Based on the measurements of noise in gene expression performed during the past decade, it has become customary to think of gene regulation in terms of a two-state model, where the promoter of a gene can stochastically switch between an ON and an OFF state. As experiments are becoming increasingly precise and the deviations from the two-state model start to be observable, we ask about the experimental signatures of complex multistate promoters, as well as the functional consequences of this additional complexity. In detail, we i), extend the calculations for noise in gene expression to promoters described by state transition diagrams with multiple states, ii), systematically compute the experimentally accessible noise characteristics for these complex promoters, and iii), use information theory to evaluate the channel capacities of complex promoter architectures and compare them with the baseline provided by the two-state model. We find that adding internal states to the promoter generically decreases channel capacity, except in certain cases, three of which (cooperativity, dual-role regulation, promoter cycling) we analyze in detail.
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Affiliation(s)
- Georg Rieckh
- Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, Austria.
| | - Gašper Tkačik
- Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, Austria
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13
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Muthukrishnan AB, Martikainen A, Neeli-Venkata R, Ribeiro AS. In vivo transcription kinetics of a synthetic gene uninvolved in stress-response pathways in stressed Escherichia coli cells. PLoS One 2014; 9:e109005. [PMID: 25268540 PMCID: PMC4182640 DOI: 10.1371/journal.pone.0109005] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2014] [Accepted: 08/29/2014] [Indexed: 11/27/2022] Open
Abstract
The fast adaptation of Escherichia coli to stressful environments includes the regulation of gene expression rates, mainly of transcription, by specific and global stress-response mechanisms. To study the effects of mechanisms acting on a global level, we observed with single molecule sensitivity the effects of mild acidic shift and oxidative stress on the in vivo transcription dynamics of a probe gene encoding an RNA target for MS2d-GFP, under the control of a synthetic promoter. After showing that this promoter is uninvolved in fast stress-response pathways, we compared its kinetics of transcript production under stress and in optimal conditions. We find that, following the application of either stress, the mean rates of transcription activation and of subsequent RNA production of the probe gene are reduced, particularly under oxidative stress. Meanwhile, the noise in RNA production decreases under oxidative stress, but not under acidic shift. From distributions of intervals between consecutive RNA productions, we infer that the number and duration of the rate-limiting steps in transcription initiation change, following the application of stress. These changes differ in the two stress conditions and are consistent with the changes in noise in RNA production. Overall, our measurements of the transcription initiation kinetics of the probe gene indicate that, following sub-lethal stresses, there are stress-specific changes in the dynamics of transcription initiation of the probe gene that affect its mean rate and noise of transcript production. Given the non-involvement of the probe gene in stress-response pathways, we suggest that these changes are caused by global response mechanisms of E. coli to stress.
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Affiliation(s)
- Anantha-Barathi Muthukrishnan
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, Tampere, Finland
| | - Antti Martikainen
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, Tampere, Finland
| | - Ramakanth Neeli-Venkata
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, Tampere, Finland
| | - Andre S. Ribeiro
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, Tampere, Finland
- * E-mail:
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14
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Lloyd-Price J, Tran H, Ribeiro AS. Dynamics of small genetic circuits subject to stochastic partitioning in cell division. J Theor Biol 2014; 356:11-9. [DOI: 10.1016/j.jtbi.2014.04.018] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2013] [Revised: 02/20/2014] [Accepted: 04/15/2014] [Indexed: 11/30/2022]
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15
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Pitchiaya S, Heinicke LA, Custer TC, Walter NG. Single molecule fluorescence approaches shed light on intracellular RNAs. Chem Rev 2014; 114:3224-65. [PMID: 24417544 PMCID: PMC3968247 DOI: 10.1021/cr400496q] [Citation(s) in RCA: 64] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Sethuramasundaram Pitchiaya
- Single Molecule Analysis in Real-Time (SMART)
Center, University of Michigan, Ann Arbor, MI 48109-1055, USA
- Single Molecule Analysis Group, Department of
Chemistry, University of Michigan, Ann Arbor, MI 48109-1055, USA
| | - Laurie A. Heinicke
- Single Molecule Analysis Group, Department of
Chemistry, University of Michigan, Ann Arbor, MI 48109-1055, USA
| | - Thomas C. Custer
- Program in Chemical Biology, University of Michigan,
Ann Arbor, MI 48109-1055, USA
| | - Nils G. Walter
- Single Molecule Analysis in Real-Time (SMART)
Center, University of Michigan, Ann Arbor, MI 48109-1055, USA
- Single Molecule Analysis Group, Department of
Chemistry, University of Michigan, Ann Arbor, MI 48109-1055, USA
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SANCHEZ-OSORIO ISMAEL, RAMOS FERNANDO, MAYORGA PEDRO, DANTAN EDGAR. FOUNDATIONS FOR MODELING THE DYNAMICS OF GENE REGULATORY NETWORKS: A MULTILEVEL-PERSPECTIVE REVIEW. J Bioinform Comput Biol 2014; 12:1330003. [DOI: 10.1142/s0219720013300037] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
A promising alternative for unraveling the principles under which the dynamic interactions among genes lead to cellular phenotypes relies on mathematical and computational models at different levels of abstraction, from the molecular level of protein-DNA interactions to the system level of functional relationships among genes. This review article presents, under a bottom–up perspective, a hierarchy of approaches to modeling gene regulatory network dynamics, from microscopic descriptions at the single-molecule level in the spatial context of an individual cell to macroscopic models providing phenomenological descriptions at the population-average level. The reviewed modeling approaches include Molecular Dynamics, Particle-Based Brownian Dynamics, the Master Equation approach, Ordinary Differential Equations, and the Boolean logic abstraction. Each of these frameworks is motivated by a particular biological context and the nature of the insight being pursued. The setting of gene network dynamic models from such frameworks involves assumptions and mathematical artifacts often ignored by the non-specialist. This article aims at providing an entry point for biologists new to the field and computer scientists not acquainted with some recent biophysically-inspired models of gene regulation. The connections promoting intuition between different abstraction levels and the role that approximations play in the modeling process are highlighted throughout the paper.
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Affiliation(s)
- ISMAEL SANCHEZ-OSORIO
- Department of Computer Science, Monterrey Institute of Technology and Higher Education Campus Cuernavaca, Autopista del Sol km 104, Xochitepec, Morelos 62790, Mexico
| | - FERNANDO RAMOS
- Department of Computer Science, Monterrey Institute of Technology and Higher Education Campus Cuernavaca, Autopista del Sol km 104, Xochitepec, Morelos 62790, Mexico
| | - PEDRO MAYORGA
- Department of Computer Science, Monterrey Institute of Technology and Higher Education Campus Cuernavaca, Autopista del Sol km 104, Xochitepec, Morelos 62790, Mexico
| | - EDGAR DANTAN
- Centro de Investigación en Biotecnología, Universidad Autónoma del Estado de Morelos, Avenida Universidad 1001, Cuernavaca, Morelos 62209, Mexico
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Häkkinen A, Tran H, Yli-Harja O, Ingalls B, Ribeiro AS. Effects of multimerization on the temporal variability of protein complex abundance. BMC SYSTEMS BIOLOGY 2013; 7 Suppl 1:S3. [PMID: 24267954 PMCID: PMC3750523 DOI: 10.1186/1752-0509-7-s1-s3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We explore whether the process of multimerization can be used as a means to regulate noise in the abundance of functional protein complexes. Additionally, we analyze how this process affects the mean level of these functional units, response time of a gene, and temporal correlation between the numbers of expressed proteins and of the functional multimers. We show that, although multimerization increases noise by reducing the mean number of functional complexes it can reduce noise in comparison with a monomer, when abundance of the functional proteins are comparable. Alternatively, reduction in noise occurs if both monomeric and multimeric forms of the protein are functional. Moreover, we find that multimerization either increases the response time to external signals or decreases the correlation between number of functional complexes and protein production kinetics. Finally, we show that the results are in agreement with recent genome-wide assessments of cell-to-cell variability in protein numbers and of multimerization in essential and non-essential genes in Escherichia coli, and that the effects of multimerization are tangible at the level of genetic circuits.
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18
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Lloyd-Price J, Ribeiro AS. Bistability in a stochastic RNA-mediated gene network. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032714. [PMID: 24125301 DOI: 10.1103/physreve.88.032714] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2013] [Revised: 07/10/2013] [Indexed: 06/02/2023]
Abstract
Small regulatory RNAs (srRNAs) are important regulators of gene expression in eukaryotes and prokaryotes. A common motif containing srRNA is a bistable two-gene motif where one gene codes for a transcription factor (TF) which represses the transcription of the second gene, whose transcript is a srRNA which targets the first gene's transcript. Here, we investigate the properties of this motif in a stochastic model which takes the low copy numbers of the RNA components into account. First, we examine the conditions for stability of the two "noisy attractors." We find that for realistic low copy numbers, extreme, but within realistic intervals, mutual repression strengths are required to compensate for the variability of the RNA numbers and thus, achieve long-term bistability. Second, the promoter initiation kinetics is found to strongly influence the bistability of the switch. Super-Poissonian RNA production disrupts the ability of the srRNA to silence its target, though sub-Poissonian RNA production does not rule out the need for strong mutual repression. Finally, we show that asymmetry between the two interactions forming the switch allows an external input to induce the transition from "high srRNA" to "'high TF" more easily (i.e., with a shorter input) than in the opposite direction. We hypothesize that this asymmetric switching property allows these circuits to be more sensitive to one external input, without sacrificing the stability of one of the noisy attractors.
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Affiliation(s)
- Jason Lloyd-Price
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, P.O. Box 527, FI-33101 Tampere, Finland
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19
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Cell segmentation by multi-resolution analysis and maximum likelihood estimation (MAMLE). BMC Bioinformatics 2013; 14 Suppl 10:S8. [PMID: 24267594 PMCID: PMC3750476 DOI: 10.1186/1471-2105-14-s10-s8] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Cell imaging is becoming an indispensable tool for cell and molecular biology research. However, most processes studied are stochastic in nature, and require the observation of many cells and events. Ideally, extraction of information from these images ought to rely on automatic methods. Here, we propose a novel segmentation method, MAMLE, for detecting cells within dense clusters. METHODS MAMLE executes cell segmentation in two stages. The first relies on state of the art filtering technique, edge detection in multi-resolution with morphological operator and threshold decomposition for adaptive thresholding. From this result, a correction procedure is applied that exploits maximum likelihood estimate as an objective function. Also, it acquires morphological features from the initial segmentation for constructing the likelihood parameter, after which the final segmentation is obtained. CONCLUSIONS We performed an empirical evaluation that includes sample images from different imaging modalities and diverse cell types. The new method attained very high (above 90%) cell segmentation accuracy in all cases. Finally, its accuracy was compared to several existing methods, and in all tests, MAMLE outperformed them in segmentation accuracy.
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20
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Häkkinen A, Tran H, Yli-Harja O, Ribeiro AS. Effects of rate-limiting steps in transcription initiation on genetic filter motifs. PLoS One 2013; 8:e70439. [PMID: 23940576 PMCID: PMC3734270 DOI: 10.1371/journal.pone.0070439] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2013] [Accepted: 06/18/2013] [Indexed: 11/19/2022] Open
Abstract
The behavior of genetic motifs is determined not only by the gene-gene interactions, but also by the expression patterns of the constituent genes. Live single-molecule measurements have provided evidence that transcription initiation is a sequential process, whose kinetics plays a key role in the dynamics of mRNA and protein numbers. The extent to which it affects the behavior of cellular motifs is unknown. Here, we examine how the kinetics of transcription initiation affects the behavior of motifs performing filtering in amplitude and frequency domain. We find that the performance of each filter is degraded as transcript levels are lowered. This effect can be reduced by having a transcription process with more steps. In addition, we show that the kinetics of the stepwise transcription initiation process affects features such as filter cutoffs. These results constitute an assessment of the range of behaviors of genetic motifs as a function of the kinetics of transcription initiation, and thus will aid in tuning of synthetic motifs to attain specific characteristics without affecting their protein products.
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Affiliation(s)
- Antti Häkkinen
- Department of Signal Processing, Tampere University of Technology, Tampere, Finland
| | - Huy Tran
- Department of Signal Processing, Tampere University of Technology, Tampere, Finland
| | - Olli Yli-Harja
- Department of Signal Processing, Tampere University of Technology, Tampere, Finland
- Institute for Systems Biology, Seattle, Washington, United States of America
| | - Andre S. Ribeiro
- Department of Signal Processing, Tampere University of Technology, Tampere, Finland
- * E-mail:
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21
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Ribeiro AS. Kinetics of gene expression in bacteria — From models to measurements, and back again. CAN J CHEM 2013. [DOI: 10.1139/cjc-2012-0409] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Dennis Salahub has contributed to several scientific areas. Likely, one of the lesser known contributions is the one on the study of the kinetics of gene expression in prokaryotes, which resulted in a delayed stochastic model of transcription and translation dynamics in bacteria. The model has become the basis for modeling stochastic genetic circuits and has provided a framework for interpreting recent measurements of transcripts production dynamics in live cells, one event at a time. Here, we review the contributions by Salahub and colleagues to the modeling strategies of gene expression as a multi-delayed stochastic process. Next, we describe recent findings, which build upon this work and provide experimental validation of the models. Finally, we discuss potential future developments in this field of research.
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Affiliation(s)
- Andre S. Ribeiro
- Laboratory of Biosystem Dynamics, Computational Biology Research Group, Department of Signal Processing, Tampere University of Technology, P.O. box 553, 33101 Tampere, Finland
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22
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Mäkelä J, Kandhavelu M, Oliveira SMD, Chandraseelan JG, Lloyd-Price J, Peltonen J, Yli-Harja O, Ribeiro AS. In vivo single-molecule kinetics of activation and subsequent activity of the arabinose promoter. Nucleic Acids Res 2013; 41:6544-52. [PMID: 23644285 PMCID: PMC3711423 DOI: 10.1093/nar/gkt350] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Using a single-RNA detection technique in live Escherichia coli cells, we measure, for each cell, the waiting time for the production of the first RNA under the control of PBAD promoter after induction by arabinose, and subsequent intervals between transcription events. We find that the kinetics of the arabinose intake system affect mean and diversity in RNA numbers, long after induction. We observed the same effect on Plac/ara-1 promoter, which is inducible by arabinose or by IPTG. Importantly, the distribution of waiting times of Plac/ara-1 is indistinguishable from that of PBAD, if and only if induced by arabinose alone. Finally, RNA production under the control of PBAD is found to be a sub-Poissonian process. We conclude that inducer-dependent waiting times affect mean and cell-to-cell diversity in RNA numbers long after induction, suggesting that intake mechanisms have non-negligible effects on the phenotypic diversity of cell populations in natural, fluctuating environments.
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Affiliation(s)
- Jarno Mäkelä
- Laboratory of Biosystem Dynamics, Computational Systems Biology Research Group, Department of Signal Processing, Tampere University of Technology, FI-33101 Tampere, Finland
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23
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Chandraseelan JG, Oliveira SMD, Häkkinen A, Tran H, Potapov I, Sala A, Kandhavelu M, Ribeiro AS. Effects of temperature on the dynamics of the LacI-TetR-CI repressilator. MOLECULAR BIOSYSTEMS 2013; 9:3117-23. [DOI: 10.1039/c3mb70203k] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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24
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Zhi X, Leng F. Dependence of transcription-coupled DNA supercoiling on promoter strength in Escherichia coli topoisomerase I deficient strains. Gene 2012. [PMID: 23201416 DOI: 10.1016/j.gene.2012.11.011] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Transcription by RNA polymerase can induce the formation of hypernegatively supercoiled DNA in vitro and in vivo. This phenomenon has been nicely explained by a "twin-supercoiled-domain" model of transcription where a positively supercoiled domain is generated ahead of the RNA polymerase and a negatively supercoiled domain behind it. In Escherichia coli topA strains, DNA gyrase selectively converts the positively supercoiled domain into negative supercoils to produce hypernegatively supercoiled DNA. In this article, in order to examine whether promoter strength affects transcription-coupled DNA supercoiling (TCDS), we developed a two-plasmid system in which a linear, non-supercoiled plasmid was used to express lac repressor constitutively while a circular plasmid was used to gage TCDS in E. coli cells. Using this two-plasmid system, we found that TCDS in topA strains is dependent on promoter strength. We also demonstrated that transcription-coupled hypernegative supercoiling of plasmid DNA did not need the expression of a membrane-insertion protein for strong promoters; however, it might require co-transcriptional synthesis of a polypeptide. Furthermore, we found that for weak promoters the expression of a membrane-insertion tet gene was not sufficient for the production of hypernegatively supercoiled DNA. Our results can be explained by the "twin-supercoiled-domain" model of transcription where the friction force applied to E. coli RNA polymerase plays a critical role in the generation of hypernegatively supercoiled DNA.
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MESH Headings
- Base Sequence
- Blotting, Western
- DNA Topoisomerases, Type I/genetics
- DNA Topoisomerases, Type I/metabolism
- DNA, Bacterial/chemistry
- DNA, Bacterial/genetics
- DNA, Superhelical/chemistry
- DNA, Superhelical/genetics
- Escherichia coli/genetics
- Escherichia coli/metabolism
- Escherichia coli Proteins/genetics
- Escherichia coli Proteins/metabolism
- Models, Genetic
- Molecular Sequence Data
- Mutation
- Nucleic Acid Conformation
- Plasmids/genetics
- Promoter Regions, Genetic/genetics
- Reverse Transcriptase Polymerase Chain Reaction
- Sequence Homology, Nucleic Acid
- Transcription, Genetic
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Affiliation(s)
- Xiaoduo Zhi
- Department of Chemistry & Biochemistry, Florida International University, 11200 SW 8th Street, Miami, FL 33199, USA
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25
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Ribeiro AS, Häkkinen A, Lloyd-Price J. Effects of gene length on the dynamics of gene expression. Comput Biol Chem 2012; 41:1-9. [PMID: 23142668 DOI: 10.1016/j.compbiolchem.2012.10.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2012] [Revised: 10/11/2012] [Accepted: 10/11/2012] [Indexed: 01/06/2023]
Abstract
In Escherichia coli, the nucleotide length of a gene is bound to affect its expression dynamics. From simulations of a stochastic model of gene expression at the nucleotide and codon levels we show that, within realistic parameter values, the nucleotide length affects RNA and protein mean levels, as well as the expected transient time for RNA and protein numbers to change, following a signal. Fluctuations in RNA and protein numbers are found to be minimized for a small range of lengths, which matches the means of the distributions of lengths found in E. coli of both essential and non-essential genes. The variance of the length distribution for essential genes is found to be smaller than for non-essential genes, implying that these distributions are far from random. Finally, gene lengths are shown to affect the kinetics of a genetic switch, namely, the correlation between temporal proteins numbers, the stability of the two noisy attractors of the switch, and how biased is the choice of noisy attractor. The stability increases with gene length due to increased 'memory' about the previous states of the switch. We argue that, by affecting the dynamics of gene expression and of genetic circuits, gene lengths are subject to selection.
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Affiliation(s)
- Andre S Ribeiro
- Laboratory of Biosystem Dynamics, Computational Systems Biology Research Group, Department of Signal Processing, Tampere University of Technology, PO Box 553, 33101 Tampere, Finland.
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26
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Kandhavelu M, Lloyd-Price J, Gupta A, Muthukrishnan AB, Yli-Harja O, Ribeiro AS. Regulation of mean and noise of the in vivo kinetics of transcription under the control of the lac/ara-1 promoter. FEBS Lett 2012; 586:3870-5. [PMID: 23017207 DOI: 10.1016/j.febslet.2012.09.014] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2012] [Revised: 09/03/2012] [Accepted: 09/06/2012] [Indexed: 11/19/2022]
Abstract
The kinetics of transcription initiation in Escherichia coli depend on the duration of two rate-limiting steps, the closed and the open complex formation. In a lac promoter variant, P(lac/ara-1), the kinetics of these steps is controlled by IPTG and arabinose. From in vivo single-RNA measurements, we find that induction affects the mean and normalized variance of the intervals between consecutive RNA productions. Transcript production is sub-Poissonian in all conditions tested. The kinetics of each step is independently controlled by a different inducer. We conclude that the regulatory mechanism of P(lac/ara-1) allows the stochasticity of gene expression to be environment-dependent.
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Affiliation(s)
- Meenakshisundaram Kandhavelu
- Laboratory of Biosystem Dynamics, Department of Signal Processing, Tampere University of Technology, 33101 Tampere, Finland
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27
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Potapov I, Mäkelä J, Yli-Harja O, Ribeiro AS. Effects of codon sequence on the dynamics of genetic networks. J Theor Biol 2012; 315:17-25. [PMID: 22960571 DOI: 10.1016/j.jtbi.2012.08.029] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2012] [Revised: 08/17/2012] [Accepted: 08/22/2012] [Indexed: 11/27/2022]
Abstract
In prokaryotes, the rate at which codons are translated varies from one codon to the next. Using a stochastic model of transcription and translation at the nucleotide and codon levels, we investigate the effects of the codon sequence on the dynamics of protein numbers. For sequences generated according to the codon frequencies in Escherichia coli, we find that mean protein numbers at near equilibrium differ with the codon sequence, due to the mean codon translation efficiencies, in particular of the codons at the ribosome binding site region. We find close agreement between these predictions and measurements of protein expression levels as a function of the codon sequence. Next, we investigate the effects of short codon sequences at the start/end of the RNA sequence with linearly increasing/decreasing translation efficiencies, known as slow ramps. The ramps affect the mean, but not the fluctuations, in proteins numbers by affecting the rate of translation initiation. Finally, we show that slow ramps affect the dynamics of small genetic circuits, namely, switches and clocks. In switches, ramps affect the frequency of switching and bias the robustness of the noisy attractors. In repressilators, ramps alter the robustness of periodicity. We conclude that codon sequences affect the dynamics of gene expression and genetic circuits and, thus, are likely to be under selection regarding both mean codon frequency as well as spatial arrangement along the sequence.
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Affiliation(s)
- Ilya Potapov
- Computational Systems Biology Research Group, Department of Signal Processing, Tampere University of Technology, P.O. Box 527, FIN-33101, Finland.
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28
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Emmert-Streib F, Häkkinen A, Ribeiro AS. Detecting sequence dependent transcriptional pauses from RNA and protein number time series. BMC Bioinformatics 2012; 13:152. [PMID: 22741547 PMCID: PMC3534578 DOI: 10.1186/1471-2105-13-152] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2012] [Accepted: 06/20/2012] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Evidence suggests that in prokaryotes sequence-dependent transcriptional pauses affect the dynamics of transcription and translation, as well as of small genetic circuits. So far, a few pause-prone sequences have been identified from in vitro measurements of transcription elongation kinetics. RESULTS Using a stochastic model of gene expression at the nucleotide and codon levels with realistic parameter values, we investigate three different but related questions and present statistical methods for their analysis. First, we show that information from in vivo RNA and protein temporal numbers is sufficient to discriminate between models with and without a pause site in their coding sequence. Second, we demonstrate that it is possible to separate a large variety of models from each other with pauses of various durations and locations in the template by means of a hierarchical clustering and a random forest classifier. Third, we introduce an approximate likelihood function that allows to estimate the location of a pause site. CONCLUSIONS This method can aid in detecting unknown pause-prone sequences from temporal measurements of RNA and protein numbers at a genome-wide scale and thus elucidate possible roles that these sequences play in the dynamics of genetic networks and phenotype.
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Affiliation(s)
- Frank Emmert-Streib
- Computational Biology and Machine Learning Lab, Center for CancerResearch and Cell Biology, School of Medicine, Dentistry and Biomedical Sciences, Queen’s University Belfast, Belfast, UK
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29
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Muthukrishnan AB, Kandhavelu M, Lloyd-Price J, Kudasov F, Chowdhury S, Yli-Harja O, Ribeiro AS. Dynamics of transcription driven by the tetA promoter, one event at a time, in live Escherichia coli cells. Nucleic Acids Res 2012; 40:8472-83. [PMID: 22730294 PMCID: PMC3458540 DOI: 10.1093/nar/gks583] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
In Escherichia coli, tetracycline prevents translation. When subject to tetracycline, E. coli express TetA to pump it out by a mechanism that is sensitive, while fairly independent of cellular metabolism. We constructed a target gene, PtetA-mRFP1-96BS, with a 96 MS2-GFP binding site array in a single-copy BAC vector, whose expression is controlled by the tetA promoter. We measured the in vivo kinetics of production of individual RNA molecules of the target gene as a function of inducer concentration and temperature. From the distributions of intervals between transcription events, we find that RNA production by PtetA is a sub-Poissonian process. Next, we infer the number and duration of the prominent sequential steps in transcription initiation by maximum likelihood estimation. Under full induction and at optimal temperature, we observe three major steps. We find that the kinetics of RNA production under the control of PtetA, including number and duration of the steps, varies with induction strength and temperature. The results are supported by a set of logical pairwise Kolmogorov-Smirnov tests. We conclude that the expression of TetA is controlled by a sequential mechanism that is robust, whereas sensitive to external signals.
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Affiliation(s)
- Anantha-Barathi Muthukrishnan
- Laboratory of Biosystem Dynamics, Computational Systems Biology Research Group, Department of Signal Processing, Tampere University of Technology, FI-33101 Tampere, Finland
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30
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Martins L, Mäkelä J, Häkkinen A, Kandhavelu M, Yli-Harja O, Fonseca JM, Ribeiro AS. Dynamics of transcription of closely spaced promoters in Escherichia coli, one event at a time. J Theor Biol 2012; 301:83-94. [PMID: 22370562 DOI: 10.1016/j.jtbi.2012.02.015] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2011] [Revised: 02/08/2012] [Accepted: 02/13/2012] [Indexed: 01/18/2023]
Abstract
Many pairs of genes in Escherichia coli are driven by closely spaced promoters. We study the dynamics of expression of such pairs of genes driven by a model at the molecule and nucleotide level with delayed stochastic dynamics as a function of the binding affinity of the RNA polymerase to the promoter region, of the geometry of the promoter, of the distance between transcription start sites (TSSs) and of the repression mechanism. We find that the rate limiting steps of transcription at the TSS, the closed and open complex formations, strongly affect the kinetics of RNA production for all promoter configurations. Beyond a certain rate of transcription initiation events, we find that the interference between polymerases correlates the dynamics of production of the two RNA molecules from the two TSS and affects the distribution of intervals between consecutive productions of RNA molecules. The degree of correlation depends on the geometry, the distance between TSSs and repressors. Small changes in the distance between TSSs can cause abrupt changes in behavior patterns, suggesting that the sequence between adjacent promoters may be subject to strong selective pressure. The results provide better understanding on the sequence level mechanisms of transcription regulation in bacteria and may aid in the genetic engineering of artificial circuits based on closely spaced promoters.
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Affiliation(s)
- Leonardo Martins
- Faculdade de Ciências e Tecnologia Universidade Nova de Lisboa, Monte da Caparica, 2829-516 Caparica, Portugal
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31
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Häkkinen A, Ribeiro AS. Evolving kinetics of gene expression in stochastic environments. Comput Biol Chem 2012; 37:11-6. [PMID: 22410387 DOI: 10.1016/j.compbiolchem.2012.02.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2011] [Revised: 01/18/2012] [Accepted: 02/14/2012] [Indexed: 10/28/2022]
Abstract
Recent studies have shown that the in vivo dynamics of RNA numbers in bacteria is regulated, to a great extent, by the kinetics of rate limiting steps in transcription. Strong evidence suggests that the kinetics of these steps is sequence dependent. We investigate the selective advantages of rate limiting steps of differing kinetics. For that, we model the kinetics of expression of a gene responsible for promoting cell division at the expense of resources in the environment in individual cells of a population. We model mutations that affect the kinetics of the rate limiting steps and selective pressure in various environmental conditions. Depletion of resources leads to cell death. We find that small changes in the evolutionary constraints can favor widely different noise levels in RNA and protein numbers. Increasing the cost in nutrients for division favors noisier expression. The results provide a better understanding of why different genes differ in the kinetics of production of RNA and proteins.
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Affiliation(s)
- Antti Häkkinen
- Laboratory of Biosystem Dynamics, Computational Systems Biology Research Group, Department of Signal Processing, Tampere University of Technology, Finland.
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