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A Novel Approach for Calculating Exact Forms of mRNA Distribution in Single-Cell Measurements. MATHEMATICS 2021. [DOI: 10.3390/math10010027] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Gene transcription is a stochastic process manifested by fluctuations in mRNA copy numbers in individual isogenic cells. Together with mathematical models of stochastic transcription, the massive mRNA distribution data that can be used to quantify fluctuations in mRNA levels can be fitted by Pm(t), which is the probability of producing m mRNA molecules at time t in a single cell. Tremendous efforts have been made to derive analytical forms of Pm(t), which rely on solving infinite arrays of the master equations of models. However, current approaches focus on the steady-state (t→∞) or require several parameters to be zero or infinity. Here, we present an approach for calculating Pm(t) with time, where all parameters are positive and finite. Our approach was successfully implemented for the classical two-state model and the widely used three-state model and may be further developed for different models with constant kinetic rates of transcription. Furthermore, the direct computations of Pm(t) for the two-state model and three-state model showed that the different regulations of gene activation can generate discriminated dynamical bimodal features of mRNA distribution under the same kinetic rates and similar steady-state mRNA distribution.
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Oliveira SMD, Goncalves NSM, Kandavalli VK, Martins L, Neeli-Venkata R, Reyelt J, Fonseca JM, Lloyd-Price J, Kranz H, Ribeiro AS. Chromosome and plasmid-borne P LacO3O1 promoters differ in sensitivity to critically low temperatures. Sci Rep 2019; 9:4486. [PMID: 30872616 PMCID: PMC6418193 DOI: 10.1038/s41598-019-39618-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2018] [Accepted: 01/28/2019] [Indexed: 12/31/2022] Open
Abstract
Temperature shifts trigger genome-wide changes in Escherichia coli's gene expression. We studied if chromosome integration impacts on a gene's sensitivity to these shifts, by comparing the single-RNA production kinetics of a PLacO3O1 promoter, when chromosomally-integrated and when single-copy plasmid-borne. At suboptimal temperatures their induction range, fold change, and response to decreasing temperatures are similar. At critically low temperatures, the chromosome-integrated promoter becomes weaker and noisier. Dissection of its initiation kinetics reveals longer lasting states preceding open complex formation, suggesting enhanced supercoiling buildup. Measurements with Gyrase and Topoisomerase I inhibitors suggest hindrance to escape supercoiling buildup at low temperatures. Consistently, similar phenomena occur in energy-depleted cells by DNP at 30 °C. Transient, critically-low temperatures have no long-term consequences, as raising temperature quickly restores transcription rates. We conclude that the chromosomally-integrated PLacO3O1 has higher sensitivity to low temperatures, due to longer-lasting super-coiled states. A lesser active, chromosome-integrated native lac is shown to be insensitive to Gyrase overexpression, even at critically low temperatures, indicating that the rate of escaping positive supercoiling buildup is temperature and transcription rate dependent. A genome-wide analysis supports this, since cold-shock genes exhibit atypical supercoiling-sensitivities. This phenomenon might partially explain the temperature-sensitivity of some transcriptional programs of E. coli.
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Affiliation(s)
- Samuel M D Oliveira
- Laboratory of Biosystem Dynamics and Multi-Scaled Biodata Analysis and Modelling Research Community, Faculty of Medicine and Health Technology, Tampere University, Korkeakoulunkatu 7, 33720, Tampere, Finland
| | - Nadia S M Goncalves
- Laboratory of Biosystem Dynamics and Multi-Scaled Biodata Analysis and Modelling Research Community, Faculty of Medicine and Health Technology, Tampere University, Korkeakoulunkatu 7, 33720, Tampere, Finland
| | - Vinodh K Kandavalli
- Laboratory of Biosystem Dynamics and Multi-Scaled Biodata Analysis and Modelling Research Community, Faculty of Medicine and Health Technology, Tampere University, Korkeakoulunkatu 7, 33720, Tampere, Finland
| | - Leonardo Martins
- Laboratory of Biosystem Dynamics and Multi-Scaled Biodata Analysis and Modelling Research Community, Faculty of Medicine and Health Technology, Tampere University, Korkeakoulunkatu 7, 33720, Tampere, Finland
- CA3 CTS/UNINOVA. Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal
| | - Ramakanth Neeli-Venkata
- Laboratory of Biosystem Dynamics and Multi-Scaled Biodata Analysis and Modelling Research Community, Faculty of Medicine and Health Technology, Tampere University, Korkeakoulunkatu 7, 33720, Tampere, Finland
| | - Jan Reyelt
- Gene Bridges, Im Neuenheimer Feld 584, 69120, Heidelberg, Germany
| | - Jose M Fonseca
- CA3 CTS/UNINOVA. Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal
| | - Jason Lloyd-Price
- Biostatistics Department, Harvard T.H. Chan School of Public Health, Boston, MA, 02115, USA
- Infectious Disease and Microbiome Program, Broad Institute, Cambridge, MA, 02142, USA
| | - Harald Kranz
- Gene Bridges, Im Neuenheimer Feld 584, 69120, Heidelberg, Germany
| | - Andre S Ribeiro
- Laboratory of Biosystem Dynamics and Multi-Scaled Biodata Analysis and Modelling Research Community, Faculty of Medicine and Health Technology, Tampere University, Korkeakoulunkatu 7, 33720, Tampere, Finland.
- CA3 CTS/UNINOVA. Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal.
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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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Viswanathan A, Anufrieva O, Sala A, Yli-Harja O, Kandhavelu M. Phase-dependent dynamics of the lac promoter under nutrient stress. Res Microbiol 2016; 167:451-61. [PMID: 27106257 DOI: 10.1016/j.resmic.2016.04.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2016] [Revised: 04/04/2016] [Accepted: 04/04/2016] [Indexed: 11/26/2022]
Abstract
To survive, a bacterial population must sense nutrient availability and adjust its growth phase accordingly. Few studies have quantitatively analyzed the single-cell behavior of stress and growth phase-related transcriptional changes in Escherichia coli. To investigate the dynamic changes in transcription during different growth phases and starvation, we analyzed the single-cell transcriptional dynamics of the E. coli lac promoter. Cells were grown under different starvation conditions, including glucose, magnesium, phosphate and thiamine limitations, and transcription dynamics was quantified using a single RNA detection method at different phases. Differences in gene expression over conditions and phases indicate that stochasticity in transcription dynamics is directly connected to cell phase and availability of nutrients. Except for glucose, the pattern of transcription dynamics under all starvation conditions appears to be similar. Transcriptional bursts were more prominent in lag and stationary phase cells starved for energy sources. Identical behavior was observed in exponential phase cells starved for phosphate and thiamine. Noise measurements under all nutrient exhaustion conditions indicate that intrinsic noise is higher than extrinsic noise. Our results, obtained in a relA1 mutational background, which led to suboptimal production of ppGpp, suggest that the single-cell transcriptional changes we observed were largely ppGpp-independent. Taken together, we propose that, under different starvation conditions, cells are able to decrease the trend in cell-to-cell variability in transcription as a common means of adaptation.
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Affiliation(s)
- Anisha Viswanathan
- Molecular Signaling Lab, Computational Systems Biology Research Group, Department of Signal Processing, Tampere University of Technology, P.O.Box 553, 33101 Tampere, Finland
| | - Olga Anufrieva
- Molecular Signaling Lab, Computational Systems Biology Research Group, Department of Signal Processing, Tampere University of Technology, P.O.Box 553, 33101 Tampere, Finland
| | - Adrien Sala
- Molecular Signaling Lab, Computational Systems Biology Research Group, Department of Signal Processing, Tampere University of Technology, P.O.Box 553, 33101 Tampere, Finland
| | - Olli Yli-Harja
- Molecular Signaling Lab, Computational Systems Biology Research Group, Department of Signal Processing, Tampere University of Technology, P.O.Box 553, 33101 Tampere, Finland; Institute for Systems Biology, 1441N 34th Street, Seattle, WA, 98103-8904, USA
| | - Meenakshisundaram Kandhavelu
- Molecular Signaling Lab, Computational Systems Biology Research Group, Department of Signal Processing, Tampere University of Technology, P.O.Box 553, 33101 Tampere, Finland.
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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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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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