1
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Banerjee B, Das D. Effects of bursty synthesis in organelle biogenesis. Math Biosci 2024; 370:109156. [PMID: 38346665 DOI: 10.1016/j.mbs.2024.109156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2023] [Revised: 01/31/2024] [Accepted: 02/03/2024] [Indexed: 02/16/2024]
Abstract
A fundamental question of cell biology is how cells control the number of organelles. The processes of organelle biogenesis, namely de novo synthesis, fission, fusion, and decay, are inherently stochastic, producing cell-to-cell variability in organelle abundance. In addition, experiments suggest that the synthesis of some organelles can be bursty. We thus ask how bursty synthesis impacts intracellular organelle number distribution. We develop an organelle biogenesis model with bursty de novo synthesis by considering geometrically distributed burst sizes. We analytically solve the model in biologically relevant limits and provide exact expressions for the steady-state organelle number distributions and their means and variances. We also present approximate solutions for the whole model, complementing with exact stochastic simulations. We show that bursts generally increase the noise in organelle numbers, producing distinct signatures in noise profiles depending on different mechanisms of organelle biogenesis. We also find different shapes of organelle number distributions, including bimodal distributions in some parameter regimes. Notably, bursty synthesis broadens the parameter regime of observing bimodality compared to the 'non-bursty' case. Together, our framework utilizes number fluctuations to elucidate the role of bursty synthesis in producing organelle number heterogeneity in cells.
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Affiliation(s)
- Binayak Banerjee
- Department of Biological Sciences, Indian Institute of Science Education and Research Kolkata, Nadia 741 246, West Bengal, India
| | - Dipjyoti Das
- Department of Biological Sciences, Indian Institute of Science Education and Research Kolkata, Nadia 741 246, West Bengal, India.
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2
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Adhikary R, Roy A, Jolly MK, Das D. Effects of microRNA-mediated negative feedback on gene expression noise. Biophys J 2023; 122:4220-4240. [PMID: 37803829 PMCID: PMC10645566 DOI: 10.1016/j.bpj.2023.09.019] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Revised: 07/19/2023] [Accepted: 09/28/2023] [Indexed: 10/08/2023] Open
Abstract
MicroRNAs (miRNAs) are small noncoding RNAs that regulate gene expression post-transcriptionally in eukaryotes by binding with target mRNAs and preventing translation. miRNA-mediated feedback motifs are ubiquitous in various genetic networks that control cellular decision making. A key question is how such a feedback mechanism may affect gene expression noise. To answer this, we have developed a mathematical model to study the effects of a miRNA-dependent negative-feedback loop on mean expression and noise in target mRNAs. Combining analytics and simulations, we show the existence of an expression threshold demarcating repressed and expressed regimes in agreement with earlier studies. The steady-state mRNA distributions are bimodal near the threshold, where copy numbers of mRNAs and miRNAs exhibit enhanced anticorrelated fluctuations. Moreover, variation of negative-feedback strength shifts the threshold locations and modulates the noise profiles. Notably, the miRNA-mRNA binding affinity and feedback strength collectively shape the bimodality. We also compare our model with a direct auto-repression motif, where a gene produces its own repressor. Auto-repression fails to produce bimodal mRNA distributions as found in miRNA-based indirect repression, suggesting the crucial role of miRNAs in creating phenotypic diversity. Together, we demonstrate how miRNA-dependent negative feedback modifies the expression threshold and leads to a broader parameter regime of bimodality compared to the no-feedback case.
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Affiliation(s)
- Raunak Adhikary
- Department of Biological Sciences, Indian Institute of Science Education And Research Kolkata Mohanpur, Nadia, West Bengal, India
| | - Arnab Roy
- Department of Biological Sciences, Indian Institute of Science Education And Research Kolkata Mohanpur, Nadia, West Bengal, India
| | - Mohit Kumar Jolly
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bengaluru, India
| | - Dipjyoti Das
- Department of Biological Sciences, Indian Institute of Science Education And Research Kolkata Mohanpur, Nadia, West Bengal, India.
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3
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Wang X, Li Y, Jia C. Poisson representation: a bridge between discrete and continuous models of stochastic gene regulatory networks. J R Soc Interface 2023; 20:20230467. [PMID: 38016635 PMCID: PMC10684348 DOI: 10.1098/rsif.2023.0467] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 11/08/2023] [Indexed: 11/30/2023] Open
Abstract
Stochastic gene expression dynamics can be modelled either discretely or continuously. Previous studies have shown that the mRNA or protein number distributions of some simple discrete and continuous gene expression models are related by Gardiner's Poisson representation. Here, we systematically investigate the Poisson representation in complex stochastic gene regulatory networks. We show that when the gene of interest is unregulated, the discrete and continuous descriptions of stochastic gene expression are always related by the Poisson representation, no matter how complex the model is. This generalizes the results obtained in Dattani & Barahona (Dattani & Barahona 2017 J. R. Soc. Interface 14, 20160833 (doi:10.1098/rsif.2016.0833)). In addition, using a simple counter-example, we find that the Poisson representation in general fails to link the two descriptions when the gene is regulated. However, for a general stochastic gene regulatory network, we demonstrate that the discrete and continuous models are approximately related by the Poisson representation in the limit of large protein numbers. These theoretical results are further applied to analytically solve many complex gene expression models whose exact distributions are previously unknown.
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Affiliation(s)
- Xinyu Wang
- Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100193, People’s Republic of China
| | - Youming Li
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
| | - Chen Jia
- Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100193, People’s Republic of China
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4
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Wang Y, He S. Inference on autoregulation in gene expression with variance-to-mean ratio. J Math Biol 2023; 86:87. [PMID: 37131095 PMCID: PMC10154285 DOI: 10.1007/s00285-023-01924-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Revised: 04/14/2023] [Accepted: 04/18/2023] [Indexed: 05/04/2023]
Abstract
Some genes can promote or repress their own expressions, which is called autoregulation. Although gene regulation is a central topic in biology, autoregulation is much less studied. In general, it is extremely difficult to determine the existence of autoregulation with direct biochemical approaches. Nevertheless, some papers have observed that certain types of autoregulations are linked to noise levels in gene expression. We generalize these results by two propositions on discrete-state continuous-time Markov chains. These two propositions form a simple but robust method to infer the existence of autoregulation from gene expression data. This method only needs to compare the mean and variance of the gene expression level. Compared to other methods for inferring autoregulation, our method only requires non-interventional one-time data, and does not need to estimate parameters. Besides, our method has few restrictions on the model. We apply this method to four groups of experimental data and find some genes that might have autoregulation. Some inferred autoregulations have been verified by experiments or other theoretical works.
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Affiliation(s)
- Yue Wang
- Department of Computational Medicine, University of California, Los Angeles, CA, 90095, USA.
- Institut des Hautes Études Scientifiques (IHÉS), Bures-sur-Yvette, 91440, Essonne, France.
| | - Siqi He
- Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, 11794, USA
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5
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Wang Y, He S. Using Fano factors to determine certain types of gene autoregulation. ARXIV 2023:arXiv:2301.06692v2. [PMID: 36713249 PMCID: PMC9882590] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
The expression of one gene might be regulated by its corresponding protein, which is called autoregulation. Although gene regulation is a central topic in biology, autoregulation is much less studied. In general, it is extremely difficult to determine the existence of autoregulation with direct biochemical approaches. Nevertheless, some papers have observed that certain types of autoregulations are linked to noise levels in gene expression. We generalize these results by two propositions on discrete-state continuous-time Markov chains. These two propositions form a simple but robust method to infer the existence of autoregulation in certain scenarios from gene expression data. This method only depends on the Fano factor, namely the ratio of variance and mean of the gene expression level. Compared to other methods for inferring autoregulation, our method only requires non-interventional one-time data, and does not need to estimate parameters. Besides, our method has few restrictions on the model. We apply this method to four groups of experimental data and find some genes that might have autoregulation. Some inferred autoregulations have been verified by experiments or other theoretical works.
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Affiliation(s)
- Yue Wang
- Department of Computational Medicine, University of California, Los Angeles, California, United States of America
- Institut des Hautes Études Scientifiques, Bures-sur-Yvette, Essonne, France
| | - Siqi He
- Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, New York, United States of America
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6
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Chen L, Zhu C, Jiao F. A generalized moment-based method for estimating parameters of stochastic gene transcription. Math Biosci 2022; 345:108780. [DOI: 10.1016/j.mbs.2022.108780] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2021] [Revised: 12/27/2021] [Accepted: 01/13/2022] [Indexed: 12/22/2022]
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7
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Skinner DJ, Dunkel J. Estimating Entropy Production from Waiting Time Distributions. PHYSICAL REVIEW LETTERS 2021; 127:198101. [PMID: 34797138 DOI: 10.1103/physrevlett.127.198101] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2021] [Accepted: 08/17/2021] [Indexed: 06/13/2023]
Abstract
Living systems operate far from thermal equilibrium by converting the chemical potential of ATP into mechanical work to achieve growth, replication, or locomotion. Given time series observations of intra-, inter-, or multicellular processes, a key challenge is to detect nonequilibrium behavior and quantify the rate of free energy consumption. Obtaining reliable bounds on energy consumption and entropy production directly from experimental data remains difficult in practice, as many degrees of freedom typically are hidden to the observer, so that the accessible coarse-grained dynamics may not obviously violate detailed balance. Here, we introduce a novel method for bounding the entropy production of physical and living systems which uses only the waiting time statistics of hidden Markov processes and, hence, can be directly applied to experimental data. By determining a universal limiting curve, we infer entropy production bounds from experimental data for gene regulatory networks, mammalian behavioral dynamics, and numerous other biological processes. Further considering the asymptotic limit of increasingly precise biological timers, we estimate the necessary entropic cost of heartbeat regulation in humans, dogs, and mice.
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Affiliation(s)
- Dominic J Skinner
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
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8
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Klindziuk A, Kolomeisky AB. Understanding the molecular mechanisms of transcriptional bursting. Phys Chem Chem Phys 2021; 23:21399-21406. [PMID: 34550142 DOI: 10.1039/d1cp03665c] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
In recent years, it has been experimentally established that transcription, a fundamental biological process that involves the synthesis of messenger RNA molecules from DNA templates, does not proceed continuously as was expected. Rather, it exhibits a distinct dynamic behavior of alternating between productive phases when RNA molecules are actively synthesized and inactive phases when there is no RNA production at all. The bimodal transcriptional dynamics is now confirmed to be present in most living systems. This phenomenon is known as transcriptional bursting and it attracts significant amounts of attention from researchers in different fields. However, despite multiple experimental and theoretical investigations, the microscopic origin and biological functions of the transcriptional bursting remain unclear. Here we discuss the recent developments in uncovering the underlying molecular mechanisms of transcriptional bursting and our current understanding of them. Our analysis presents a physicochemical view of the processes that govern transcriptional bursting in living cells.
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Affiliation(s)
- Alena Klindziuk
- Department of Chemistry, Center for Theoretical Biological Physics and Applied Physics Graduate Program, Rice University, Houston, TX 77005-1892, USA.
| | - Anatoly B Kolomeisky
- Department of Chemistry, Department of Physics and Astronomy, Department of Chemical and Biomolecular Engineering and Center for Theoretical Biological Physics, Rice University, Houston, TX 77005-1892, USA.
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9
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Shiraga K, Urabe M, Matsui T, Kikuchi S, Ogawa Y. Highly precise characterization of the hydration state upon thermal denaturation of human serum albumin using a 65 GHz dielectric sensor. Phys Chem Chem Phys 2020; 22:19468-19479. [PMID: 32761010 DOI: 10.1039/d0cp02265a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
The biological functions of proteins depend on harmonization with hydration water surrounding them. Indeed, the dynamical transition of proteins, such as thermal denaturation, is dependent on the changes in the mobility of hydration water. However, the role of hydration water during dynamical transition is yet to be fully understood due to technical limitations in precisely characterizing the amount of hydration water. A state-of-the-art CMOS dielectric sensor consisting of 65 GHz LC resonators addressed this issue by utilizing the feature that oscillation frequency sensitively shifts in response to the complex dielectric constant at 65 GHz with extremely high precision. This study aimed to establish an analytical algorithm to derive the hydration number from the measured frequency shift and to demonstrate the transition of hydration number upon the thermal denaturation of human serum albumin. The determined hydration number in the native state drew a "global" hydration picture beyond the first solvation shell, with substantially reduced uncertainty of the hydration number (about ±1%). This allowed the detection of a rapid increase in the hydration number at about 55 °C during the heating process, which was in excellent phase with the irreversible rupture of the α-helical structure into solvent-exposed extended chains, whereas the hydration number did not trace the forward path in the subsequent cooling process. Our result indicates that the weakening of water hydrogen bonds trigger the unfolding of the protein structure first, followed by the changes in the number of hydration water as a consequence of thermal denaturation.
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Affiliation(s)
- Keiichiro Shiraga
- RIKEN Center for Integrative Medical Sciences (IMS), Tsurumi, Yokohama, Kanagawa 230-0045, Japan.
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10
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Jia C, Grima R. Dynamical phase diagram of an auto-regulating gene in fast switching conditions. J Chem Phys 2020; 152:174110. [DOI: 10.1063/5.0007221] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Chen Jia
- Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100193, China
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom
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11
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Holehouse J, Cao Z, Grima R. Stochastic Modeling of Autoregulatory Genetic Feedback Loops: A Review and Comparative Study. Biophys J 2020; 118:1517-1525. [PMID: 32155410 PMCID: PMC7136347 DOI: 10.1016/j.bpj.2020.02.016] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Revised: 01/27/2020] [Accepted: 02/11/2020] [Indexed: 02/08/2023] Open
Abstract
Autoregulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic parameters of the main biochemical steps. These models differ according to 1) which subcellular processes are explicitly modeled, 2) the modeling methodology employed (discrete, continuous, or hybrid), and 3) whether they can be analytically solved for the steady-state distribution of protein numbers. We discuss the assumptions and properties of the main models in the literature, summarize our current understanding of the relationship between them, and highlight some of the insights gained through modeling.
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Affiliation(s)
- James Holehouse
- School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom
| | - Zhixing Cao
- School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom; The Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai, People's Republic of China
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom.
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12
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Jia C, Grima R. Small protein number effects in stochastic models of autoregulated bursty gene expression. J Chem Phys 2020; 152:084115. [DOI: 10.1063/1.5144578] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Chen Jia
- Division of Applied and Computational Mathematics, Beijing Computational Science Research Center, Beijing 100193, China
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom
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13
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Limit theorems for generalized density-dependent Markov chains and bursty stochastic gene regulatory networks. J Math Biol 2019; 80:959-994. [DOI: 10.1007/s00285-019-01445-1] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2019] [Revised: 08/22/2019] [Indexed: 11/26/2022]
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14
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Jia C, Wang LY, Yin GG, Zhang MQ. Single-cell stochastic gene expression kinetics with coupled positive-plus-negative feedback. Phys Rev E 2019; 100:052406. [PMID: 31869986 DOI: 10.1103/physreve.100.052406] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2019] [Indexed: 06/10/2023]
Abstract
Here we investigate single-cell stochastic gene expression kinetics in a minimal coupled gene circuit with positive-plus-negative feedback. A triphasic stochastic bifurcation is observed upon increasing the ratio of the positive and negative feedback strengths, which reveals a strong synergistic interaction between positive and negative feedback loops. We discover that coupled positive-plus-negative feedback amplifies gene expression mean but reduces gene expression noise over a wide range of feedback strengths when promoter switching is relatively slow, stabilizing gene expression around a relatively high level. In addition, we study two types of macroscopic limits of the discrete chemical master equation model: the Kurtz limit applies to proteins with large burst frequencies and the Lévy limit applies to proteins with large burst sizes. We derive the analytic steady-state distributions of the protein abundance in a coupled gene circuit for both the discrete model and its two macroscopic limits, generalizing the results obtained by Liu et al. [Chaos 26, 043108 (2016)CHAOEH1054-150010.1063/1.4947202]. We also obtain the analytic time-dependent protein distribution for the classical Friedman-Cai-Xie random bursting model [Friedman, Cai, and Xie, Phys. Rev. Lett. 97, 168302 (2006)PRLTAO0031-900710.1103/PhysRevLett.97.168302]. Our analytic results are further applied to study the structure of gene expression noise in a coupled gene circuit, and a complete decomposition of noise in terms of five different biophysical origins is provided.
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Affiliation(s)
- Chen Jia
- Division of Applied and Computational Mathematics, Beijing Computational Science Research Center, Beijing 100193, China
- Department of Mathematics, Wayne State University, Detroit, Michigan 48202, USA
| | - Le Yi Wang
- Department of Electrical and Computer Engineering, Wayne State University, Detroit, Michigan 48202, USA
| | - George G Yin
- Department of Mathematics, Wayne State University, Detroit, Michigan 48202, USA
| | - Michael Q Zhang
- Department of Biological Sciences, Center for Systems Biology, University of Texas at Dallas, Richardson, Texas 75080, USA
- MOE Key Laboratory of Bioinformatics, Center for Synthetic and Systems Biology, Tsinghua University, Beijing 100084, China
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15
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VÁZQUEZ-JIMÉNEZ AARÓN, SANTILLÁN MOISÉS, RODRÍGUEZ-GONZÁLEZ JESÚS. CHARACTERIZATION OF INTRINSIC AND EXTRINSIC NOISE EFFECTS IN POSITIVELY REGULATED GENES. J BIOL SYST 2019. [DOI: 10.1142/s0218339019500165] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Gene regulation is fundamental for cell survival. This regulation must be both robust to noise and sensitive enough to external stimuli to elicit the proper responses. In this work, we study, through stochastic numerical simulations, how a gene regulatory network with a positive feedback loop responds to environmental changes in the presence of intrinsic and extrinsic noises. Noise effects were characterized by measuring the statistical differences between two protein time series resulting from identical systems subject to the same source of extrinsic noise. A robust analysis was implemented by modifying the kinetic system parameters. We found that the common source of time-varying extrinsic fluctuations leads to a correlation in the systems it affects. The correlation and the extrinsic and intrinsic noise components are modulated by the update period and noise intensity parameters. Our results suggest that noise perception is controlled through the parameters associated with the response time: degradation rates and promoter dissociation constant.
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Affiliation(s)
- AARÓN VÁZQUEZ-JIMÉNEZ
- Centro de Investigación y Estudios Avanzados del IPN, Unidad Monterrey, Vía del Conocimiento 201, Parque PIIT, CP 66600 Apodaca NL, México
| | - MOISÉS SANTILLÁN
- Centro de Investigación y Estudios Avanzados del IPN, Unidad Monterrey, Vía del Conocimiento 201, Parque PIIT, CP 66600 Apodaca NL, México
| | - JESÚS RODRÍGUEZ-GONZÁLEZ
- Centro de Investigación y Estudios Avanzados del IPN, Unidad Monterrey, Vía del Conocimiento 201, Parque PIIT, CP 66600 Apodaca NL, México
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16
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Jędrak J, Kwiatkowski M, Ochab-Marcinek A. Exactly solvable model of gene expression in a proliferating bacterial cell population with stochastic protein bursts and protein partitioning. Phys Rev E 2019; 99:042416. [PMID: 31108597 DOI: 10.1103/physreve.99.042416] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2018] [Indexed: 06/09/2023]
Abstract
Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not concentration, the decay term may also approximate the loss of protein molecules due to cell division as a continuous degradation process. The seminal model of that kind leads to gamma distributions of protein levels, whose parameters are defined by the mean frequency of protein bursts and mean burst size. However, such models (whether interpreted in terms of molecule numbers or concentrations) do not correctly account for the noise due to protein partitioning between daughter cells. We present an exactly solvable stochastic model of gene expression in cells dividing at random times, where we assume description in terms of molecule numbers with a constant mean protein burst size. The model is based on a population balance equation supplemented with protein production in random bursts. If protein molecules are partitioned equally between daughter cells, we obtain at steady state the analytical expressions for probability distributions similar in shape to gamma distributions, yet with quite different values of mean burst size and mean burst frequency than would result from fitting of the classical continuous-decay model to these distributions. For random partitioning of protein molecules between daughter cells, we obtain the moment equations for the protein number distribution and thus the analytical formulas for the squared coefficient of variation.
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Affiliation(s)
- Jakub Jędrak
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | | | - Anna Ochab-Marcinek
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
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17
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Klindziuk A, Kolomeisky AB. Theoretical Investigation of Transcriptional Bursting: A Multistate Approach. J Phys Chem B 2018; 122:11969-11977. [DOI: 10.1021/acs.jpcb.8b09676] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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18
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Jia C, Qian H, Chen M, Zhang MQ. Relaxation rates of gene expression kinetics reveal the feedback signs of autoregulatory gene networks. J Chem Phys 2018. [DOI: 10.1063/1.5009749] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Affiliation(s)
- Chen Jia
- Department of Mathematical Sciences, University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Hong Qian
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA
| | - Min Chen
- Department of Mathematical Sciences, University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Michael Q. Zhang
- Department of Biological Sciences, Center for Systems Biology, University of Texas at Dallas, Richardson, Texas 75080, USA
- MOE Key Lab and Division of Bioinformatics, CSSB, TNLIST, Tsinghua University, Beijing 100084, China
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