1
|
Szavits-Nossan J, Grima R. Solving stochastic gene-expression models using queueing theory: A tutorial review. Biophys J 2024; 123:1034-1057. [PMID: 38594901 PMCID: PMC11079947 DOI: 10.1016/j.bpj.2024.04.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Revised: 02/12/2024] [Accepted: 04/02/2024] [Indexed: 04/11/2024] Open
Abstract
Stochastic models of gene expression are typically formulated using the chemical master equation, which can be solved exactly or approximately using a repertoire of analytical methods. Here, we provide a tutorial review of an alternative approach based on queueing theory that has rarely been used in the literature of gene expression. We discuss the interpretation of six types of infinite-server queues from the angle of stochastic single-cell biology and provide analytical expressions for the stationary and nonstationary distributions and/or moments of mRNA/protein numbers and bounds on the Fano factor. This approach may enable the solution of complex models that have hitherto evaded analytical solution.
Collapse
Affiliation(s)
- Juraj Szavits-Nossan
- School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom.
| |
Collapse
|
2
|
Jiao F, Li J, Liu T, Zhu Y, Che W, Bleris L, Jia C. What can we learn when fitting a simple telegraph model to a complex gene expression model? PLoS Comput Biol 2024; 20:e1012118. [PMID: 38743803 PMCID: PMC11125521 DOI: 10.1371/journal.pcbi.1012118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2024] [Revised: 05/24/2024] [Accepted: 04/27/2024] [Indexed: 05/16/2024] Open
Abstract
In experiments, the distributions of mRNA or protein numbers in single cells are often fitted to the random telegraph model which includes synthesis and decay of mRNA or protein, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by crucial biological mechanisms such as feedback regulation, non-exponential gene inactivation durations, and multiple gene activation pathways. Here we investigate the dynamical properties of four relatively complex gene expression models by fitting their steady-state mRNA or protein number distributions to the simple telegraph model. We show that despite the underlying complex biological mechanisms, the telegraph model with three effective parameters can accurately capture the steady-state gene product distributions, as well as the conditional distributions in the active gene state, of the complex models. Some effective parameters are reliable and can reflect realistic dynamic behaviors of the complex models, while others may deviate significantly from their real values in the complex models. The effective parameters can also be applied to characterize the capability for a complex model to exhibit multimodality. Using additional information such as single-cell data at multiple time points, we provide an effective method of distinguishing the complex models from the telegraph model. Furthermore, using measurements under varying experimental conditions, we show that fitting the mRNA or protein number distributions to the telegraph model may even reveal the underlying gene regulation mechanisms of the complex models. The effectiveness of these methods is confirmed by analysis of single-cell data for E. coli and mammalian cells. All these results are robust with respect to cooperative transcriptional regulation and extrinsic noise. In particular, we find that faster relaxation speed to the steady state results in more precise parameter inference under large extrinsic noise.
Collapse
Affiliation(s)
- Feng Jiao
- Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou, China
| | - Jing Li
- Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou, China
| | - Ting Liu
- Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou, China
| | - Yifeng Zhu
- Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou, China
| | - Wenhao Che
- Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou, China
| | - Leonidas Bleris
- Bioengineering Department, The University of Texas at Dallas, Richardson, Texas, United States of America
- Center for Systems Biology, The University of Texas at Dallas, Richardson, Texas, United States of America
- Department of Biological Sciences, The University of Texas at Dallas, Richardson, Texas, United States of America
| | - Chen Jia
- Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing, China
| |
Collapse
|
3
|
Wang Z, Zhang Z, Luo S, Zhou T, Zhang J. Power-law behavior of transcriptional bursting regulated by enhancer-promoter communication. Genome Res 2024; 34:106-118. [PMID: 38171575 PMCID: PMC10903953 DOI: 10.1101/gr.278631.123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2023] [Accepted: 12/18/2023] [Indexed: 01/05/2024]
Abstract
Revealing how transcriptional bursting kinetics are genomically encoded is challenging because genome structures are stochastic at the organization level and are suggestively linked to gene transcription. To address this challenge, we develop a generic theoretical framework that integrates chromatin dynamics, enhancer-promoter (E-P) communication, and gene-state switching to study transcriptional bursting. The theory predicts that power law can be a general rule to quantitatively describe bursting modulations by E-P spatial communication. Specifically, burst frequency and burst size are up-regulated by E-P communication strength, following power laws with positive exponents. Analysis of the scaling exponents further reveals that burst frequency is preferentially regulated. Bursting kinetics are down-regulated by E-P genomic distance with negative power-law exponents, and this negative modulation desensitizes at large distances. The mutual information between burst frequency (or burst size) and E-P spatial distance further reveals essential characteristics of the information transfer from E-P communication to transcriptional bursting kinetics. These findings, which are in agreement with experimental observations, not only reveal fundamental principles of E-P communication in transcriptional bursting but also are essential for understanding cellular decision-making.
Collapse
Affiliation(s)
- Zihao Wang
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, P.R. China
- School of Mathematics, Sun Yat-sen University, Guangzhou 510275, P.R. China
| | - Zhenquan Zhang
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, P.R. China
- School of Mathematics, Sun Yat-sen University, Guangzhou 510275, P.R. China
| | - Songhao Luo
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, P.R. China
- School of Mathematics, Sun Yat-sen University, Guangzhou 510275, P.R. China
| | - Tianshou Zhou
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, P.R. China;
- School of Mathematics, Sun Yat-sen University, Guangzhou 510275, P.R. China
| | - Jiajun Zhang
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, P.R. China;
- School of Mathematics, Sun Yat-sen University, Guangzhou 510275, P.R. China
| |
Collapse
|
4
|
Grima R, Esmenjaud PM. Quantifying and correcting bias in transcriptional parameter inference from single-cell data. Biophys J 2024; 123:4-30. [PMID: 37885177 PMCID: PMC10808030 DOI: 10.1016/j.bpj.2023.10.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Revised: 09/12/2023] [Accepted: 10/19/2023] [Indexed: 10/28/2023] Open
Abstract
The snapshot distribution of mRNA counts per cell can be measured using single-molecule fluorescence in situ hybridization or single-cell RNA sequencing. These distributions are often fit to the steady-state distribution of the two-state telegraph model to estimate the three transcriptional parameters for a gene of interest: mRNA synthesis rate, the switching on rate (the on state being the active transcriptional state), and the switching off rate. This model assumes no extrinsic noise, i.e., parameters do not vary between cells, and thus estimated parameters are to be understood as approximating the average values in a population. The accuracy of this approximation is currently unclear. Here, we develop a theory that explains the size and sign of estimation bias when inferring parameters from single-cell data using the standard telegraph model. We find specific bias signatures depending on the source of extrinsic noise (which parameter is most variable across cells) and the mode of transcriptional activity. If gene expression is not bursty then the population averages of all three parameters are overestimated if extrinsic noise is in the synthesis rate; underestimation occurs if extrinsic noise is in the switching on rate; both underestimation and overestimation can occur if extrinsic noise is in the switching off rate. We find that some estimated parameters tend to infinity as the size of extrinsic noise approaches a critical threshold. In contrast when gene expression is bursty, we find that in all cases the mean burst size (ratio of the synthesis rate to the switching off rate) is overestimated while the mean burst frequency (the switching on rate) is underestimated. We estimate the size of extrinsic noise from the covariance matrix of sequencing data and use this together with our theory to correct published estimates of transcriptional parameters for mammalian genes.
Collapse
Affiliation(s)
- Ramon Grima
- School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom.
| | - Pierre-Marie Esmenjaud
- Biology Department, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
| |
Collapse
|
5
|
Hong H, Cortez MJ, Cheng YY, Kim HJ, Choi B, Josić K, Kim JK. Inferring delays in partially observed gene regulation processes. Bioinformatics 2023; 39:btad670. [PMID: 37935426 PMCID: PMC10660296 DOI: 10.1093/bioinformatics/btad670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Revised: 10/25/2023] [Accepted: 11/02/2023] [Indexed: 11/09/2023] Open
Abstract
MOTIVATION Cell function is regulated by gene regulatory networks (GRNs) defined by protein-mediated interaction between constituent genes. Despite advances in experimental techniques, we can still measure only a fraction of the processes that govern GRN dynamics. To infer the properties of GRNs using partial observation, unobserved sequential processes can be replaced with distributed time delays, yielding non-Markovian models. Inference methods based on the resulting model suffer from the curse of dimensionality. RESULTS We develop a simulation-based Bayesian MCMC method employing an approximate likelihood for the efficient and accurate inference of GRN parameters when only some of their products are observed. We illustrate our approach using a two-step activation model: an activation signal leads to the accumulation of an unobserved regulatory protein, which triggers the expression of observed fluorescent proteins. With prior information about observed fluorescent protein synthesis, our method successfully infers the dynamics of the unobserved regulatory protein. We can estimate the delay and kinetic parameters characterizing target regulation including transcription, translation, and target searching of an unobserved protein from experimental measurements of the products of its target gene. Our method is scalable and can be used to analyze non-Markovian models with hidden components. AVAILABILITY AND IMPLEMENTATION Our code is implemented in R and is freely available with a simple example data at https://github.com/Mathbiomed/SimMCMC.
Collapse
Affiliation(s)
- Hyukpyo Hong
- Department of Mathematical Sciences, KAIST, Daejeon 34141, Korea
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Korea
| | - Mark Jayson Cortez
- Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, Laguna 4031, Philippines
| | - Yu-Yu Cheng
- Department of Biochemistry, University of Wisconsin–Madison, Madison, WI 53706, United States
| | - Hang Joon Kim
- Division of Statistics and Data Science, University of Cincinnati, Cincinnati, OH 45221, United States
| | - Boseung Choi
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Korea
- Division of Big Data Science, Korea University Sejong Campus, Sejong 30019, Korea
- College of Public Health, The Ohio State University, Columbus, OH 43210, United States
| | - Krešimir Josić
- Department of Mathematics, University of Houston, Houston, TX 77204, United States
- Department of Biology and Biochemistry, University of Houston, Houston, TX 77204, United States
| | - Jae Kyoung Kim
- Department of Mathematical Sciences, KAIST, Daejeon 34141, Korea
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Korea
| |
Collapse
|
6
|
Szavits-Nossan J, Grima R. Uncovering the effect of RNA polymerase steric interactions on gene expression noise: Analytical distributions of nascent and mature RNA numbers. Phys Rev E 2023; 108:034405. [PMID: 37849194 DOI: 10.1103/physreve.108.034405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2023] [Accepted: 08/24/2023] [Indexed: 10/19/2023]
Abstract
The telegraph model is the standard model of stochastic gene expression, which can be solved exactly to obtain the distribution of mature RNA numbers per cell. A modification of this model also leads to an analytical distribution of nascent RNA numbers. These solutions are routinely used for the analysis of single-cell data, including the inference of transcriptional parameters. However, these models neglect important mechanistic features of transcription elongation, such as the stochastic movement of RNA polymerases and their steric (excluded-volume) interactions. Here we construct a model of gene expression describing promoter switching between inactive and active states, binding of RNA polymerases in the active state, their stochastic movement including steric interactions along the gene, and their unbinding leading to a mature transcript that subsequently decays. We derive the steady-state distributions of the nascent and mature RNA numbers in two important limiting cases: constitutive expression and slow promoter switching. We show that RNA fluctuations are suppressed by steric interactions between RNA polymerases, and that this suppression can in some instances even lead to sub-Poissonian fluctuations; these effects are most pronounced for nascent RNA and less prominent for mature RNA, since the latter is not a direct sensor of transcription. We find a relationship between the parameters of our microscopic mechanistic model and those of the standard models that ensures excellent consistency in their prediction of the first and second RNA number moments over vast regions of parameter space, encompassing slow, intermediate, and rapid promoter switching, provided the RNA number distributions are Poissonian or super-Poissonian. Furthermore, we identify the limitations of inference from mature RNA data, specifically showing that it cannot differentiate between highly distinct RNA polymerase traffic patterns on a gene.
Collapse
Affiliation(s)
- Juraj Szavits-Nossan
- School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3JH, United Kingdom
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3JH, United Kingdom
| |
Collapse
|
7
|
Weidemann DE, Holehouse J, Singh A, Grima R, Hauf S. The minimal intrinsic stochasticity of constitutively expressed eukaryotic genes is sub-Poissonian. SCIENCE ADVANCES 2023; 9:eadh5138. [PMID: 37556551 PMCID: PMC10411910 DOI: 10.1126/sciadv.adh5138] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2023] [Accepted: 07/07/2023] [Indexed: 08/11/2023]
Abstract
Gene expression inherently gives rise to stochastic variation ("noise") in the production of gene products. Minimizing noise is crucial for ensuring reliable cellular functions. However, noise cannot be suppressed below a certain intrinsic limit. For constitutively expressed genes, this limit is typically assumed to be Poissonian noise, wherein the variance in mRNA numbers is equal to their mean. Here, we demonstrate that several cell division genes in fission yeast exhibit mRNA variances significantly below this limit. The reduced variance can be explained by a gene expression model incorporating multiple transcription and mRNA degradation steps. Notably, in this sub-Poissonian regime, distinct from Poissonian or super-Poissonian regimes, cytoplasmic noise is effectively suppressed through a higher mRNA export rate. Our findings redefine the lower limit of eukaryotic gene expression noise and uncover molecular requirements for achieving ultralow noise, which is expected to be important for vital cellular functions.
Collapse
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
| | - James Holehouse
- The Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87510, 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, UK
| | - Silke Hauf
- Department of Biological Sciences, Virginia Tech, Blacksburg, VA 24061, USA
- Fralin Life Sciences Institute, Virginia Tech, Blacksburg, VA 24061, USA
| |
Collapse
|
8
|
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: 0] [Impact Index Per Article: 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.
Collapse
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
| |
Collapse
|
9
|
Luo S, Zhang Z, Wang Z, Yang X, Chen X, Zhou T, Zhang J. Inferring transcriptional bursting kinetics from single-cell snapshot data using a generalized telegraph model. ROYAL SOCIETY OPEN SCIENCE 2023; 10:221057. [PMID: 37035293 PMCID: PMC10073913 DOI: 10.1098/rsos.221057] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/15/2022] [Accepted: 03/13/2023] [Indexed: 06/19/2023]
Abstract
Gene expression has inherent stochasticity resulting from transcription's burst manners. Single-cell snapshot data can be exploited to rigorously infer transcriptional burst kinetics, using mathematical models as blueprints. The classical telegraph model (CTM) has been widely used to explain transcriptional bursting with Markovian assumptions. However, growing evidence suggests that the gene-state dwell times are generally non-exponential, as gene-state switching is a multi-step process in organisms. Therefore, interpretable non-Markovian mathematical models and efficient statistical inference methods are urgently required in investigating transcriptional burst kinetics. We develop an interpretable and tractable model, the generalized telegraph model (GTM), to characterize transcriptional bursting that allows arbitrary dwell-time distributions, rather than exponential distributions, to be incorporated into the ON and OFF switching process. Based on the GTM, we propose an inference method for transcriptional bursting kinetics using an approximate Bayesian computation framework. This method demonstrates an efficient and scalable estimation of burst frequency and burst size on synthetic data. Further, the application of inference to genome-wide data from mouse embryonic fibroblasts reveals that GTM would estimate lower burst frequency and higher burst size than those estimated by CTM. In conclusion, the GTM and the corresponding inference method are effective tools to infer dynamic transcriptional bursting from static single-cell snapshot data.
Collapse
Affiliation(s)
- Songhao Luo
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China
- School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China
| | - Zhenquan Zhang
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China
- School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China
| | - Zihao Wang
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China
- School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China
| | - Xiyan Yang
- School of Financial Mathematics and Statistics, Guangdong University of Finance, Guangzhou 510521, People's Republic of China
| | - Xiaoxuan Chen
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China
- School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China
| | - Tianshou Zhou
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China
- School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China
| | - Jiajun Zhang
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China
- School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China
| |
Collapse
|
10
|
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.
Collapse
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
| |
Collapse
|
11
|
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.
Collapse
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
| |
Collapse
|
12
|
Kilic Z, Schweiger M, Moyer C, Shepherd D, Pressé S. Gene expression model inference from snapshot RNA data using Bayesian non-parametrics. NATURE COMPUTATIONAL SCIENCE 2023; 3:174-183. [PMID: 38125199 PMCID: PMC10732567 DOI: 10.1038/s43588-022-00392-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2022] [Accepted: 12/15/2022] [Indexed: 12/23/2023]
Abstract
Gene expression models, which are key towards understanding cellular regulatory response, underlie observations of single-cell transcriptional dynamics. Although RNA expression data encode information on gene expression models, existing computational frameworks do not perform simultaneous Bayesian inference of gene expression models and parameters from such data. Rather, gene expression models-composed of gene states, their connectivities and associated parameters-are currently deduced by pre-specifying gene state numbers and connectivity before learning associated rate parameters. Here we propose a method to learn full distributions over gene states, state connectivities and associated rate parameters, simultaneously and self-consistently from single-molecule RNA counts. We propagate noise from fluctuating RNA counts over models by treating models themselves as random variables. We achieve this within a Bayesian non-parametric paradigm. We demonstrate our method on the Escherichia coli lacZ pathway and the Saccharomyces cerevisiae STL1 pathway, and verify its robustness on synthetic data.
Collapse
Affiliation(s)
- Zeliha Kilic
- Department of Structural Biology, St. Jude Children’s Research Hospital, Memphis, TN, USA
- These authors contributed equally: Zeliha Kilic, Max Schweiger
| | - Max Schweiger
- Center for Biological Physics, ASU, Tempe, AZ, USA
- Department of Physics, ASU, Tempe, AZ, USA
- These authors contributed equally: Zeliha Kilic, Max Schweiger
| | - Camille Moyer
- Center for Biological Physics, ASU, Tempe, AZ, USA
- School of Mathematics and Statistical Sciences, ASU, Tempe, AZ, USA
| | - Douglas Shepherd
- Center for Biological Physics, ASU, Tempe, AZ, USA
- Department of Physics, ASU, Tempe, AZ, USA
| | - Steve Pressé
- Center for Biological Physics, ASU, Tempe, AZ, USA
- Department of Physics, ASU, Tempe, AZ, USA
- School of Molecular Sciences, ASU, Tempe, AZ, USA
| |
Collapse
|
13
|
Ramanayake S, Moulding DA, Tanaka Y, Singh A, Bangham CRM. Dynamics and consequences of the HTLV-1 proviral plus-strand burst. PLoS Pathog 2022; 18:e1010774. [PMID: 36441826 PMCID: PMC9731428 DOI: 10.1371/journal.ppat.1010774] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2022] [Revised: 12/08/2022] [Accepted: 11/15/2022] [Indexed: 11/30/2022] Open
Abstract
Expression of the transcriptional transactivator protein Tax, encoded on the proviral plus-strand of human T-cell leukaemia virus type 1 (HTLV-1), is crucial for the replication of the virus, but Tax-expressing cells are rarely detected in fresh blood ex vivo. The dynamics and consequences of the proviral plus-strand transcriptional burst remain insufficiently characterised. We combined time-lapse live-cell imaging, single-cell tracking and mathematical modelling to study the dynamics of Tax expression at single-cell resolution in two naturally-infected, non-malignant T-cell clones transduced with a short-lived enhanced green fluorescent protein (d2EGFP) Tax reporter system. Five different patterns of Tax expression were observed during the 30-hour observation period; the distribution of these patterns differed between the two clones. The mean duration of Tax expression in the two clones was 94 and 417 hours respectively, estimated from mathematical modelling of the experimental data. Tax expression was associated with a transient slowing in cell-cycle progression and proliferation, increased apoptosis, and enhanced activation of the DNA damage response pathways. Longer-term follow-up (14 days) revealed an increase in the proportion of proliferating cells and a decrease in the fraction of apoptotic cells as the cells ceased Tax expression, resulting in a greater net expansion of the initially Tax-positive population. Time-lapse live-cell imaging showed enhanced cell-to-cell adhesion among Tax-expressing cells, and decreased cell motility of Tax-expressing cells at the single-cell level. The results demonstrate the within-clone and between-clone heterogeneity in the dynamics and patterns of HTLV-1 plus-strand transcriptional bursts and the balance of positive and negative consequences of the burst for the host cell.
Collapse
Affiliation(s)
- Saumya Ramanayake
- Department of Infectious Diseases, Faculty of Medicine, Imperial College London, London, United Kingdom
| | - Dale A. Moulding
- Light Microscopy Core Facility, Great Ormond Street Institute of Child Health, University College London, London, United Kingdom
| | - Yuetsu Tanaka
- Department of Infectious Disease and Immunology, Okinawa-Asia Research Center of Medical Science, Faculty of Medicine, University of the Ryukyus, Nishihara, Okinawa, Japan
| | - Abhyudai Singh
- Department of Electrical and Computer Engineering, University of Delaware, Newark, Delaware, United States of America
| | - Charles R. M. Bangham
- Department of Infectious Diseases, Faculty of Medicine, Imperial College London, London, United Kingdom
- * E-mail:
| |
Collapse
|
14
|
Sukys A, Öcal K, Grima R. Approximating Solutions of the Chemical Master Equation using Neural Networks. iScience 2022; 25:105010. [PMID: 36117994 PMCID: PMC9474291 DOI: 10.1016/j.isci.2022.105010] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Revised: 06/13/2022] [Accepted: 08/18/2022] [Indexed: 10/27/2022] Open
|
15
|
Öcal K, Gutmann MU, Sanguinetti G, Grima R. Inference and uncertainty quantification of stochastic gene expression via synthetic models. JOURNAL OF THE ROYAL SOCIETY, INTERFACE 2022; 19:20220153. [PMID: 35858045 PMCID: PMC9277240 DOI: 10.1098/rsif.2022.0153] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
Estimating uncertainty in model predictions is a central task in quantitative biology. Biological models at the single-cell level are intrinsically stochastic and nonlinear, creating formidable challenges for their statistical estimation which inevitably has to rely on approximations that trade accuracy for tractability. Despite intensive interest, a sweet spot in this trade-off has not been found yet. We propose a flexible procedure for uncertainty quantification in a wide class of reaction networks describing stochastic gene expression including those with feedback. The method is based on creating a tractable coarse-graining of the model that is learned from simulations, a synthetic model, to approximate the likelihood function. We demonstrate that synthetic models can substantially outperform state-of-the-art approaches on a number of non-trivial systems and datasets, yielding an accurate and computationally viable solution to uncertainty quantification in stochastic models of gene expression.
Collapse
Affiliation(s)
- Kaan Öcal
- School of Informatics, University of Edinburgh, Edinburgh EH9 3JH, UK.,School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3JH, UK
| | - Michael U Gutmann
- School of Informatics, University of Edinburgh, Edinburgh EH9 3JH, UK
| | - Guido Sanguinetti
- Scuola Internazionale Superiore di Studi Avanzati, 34136 Trieste, Italy
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3JH, UK
| |
Collapse
|
16
|
Holehouse J, Pollitt H. Non-equilibrium time-dependent solution to discrete choice with social interactions. PLoS One 2022; 17:e0267083. [PMID: 35617345 PMCID: PMC9135261 DOI: 10.1371/journal.pone.0267083] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2022] [Accepted: 04/02/2022] [Indexed: 12/30/2022] Open
Abstract
We solve the binary decision model of Brock and Durlauf (2001) in time using a method reliant on the resolvent of the master operator of the stochastic process. Our solution is valid when not at equilibrium and can be used to exemplify path-dependent behaviours of the binary decision model. The solution is computationally fast and is indistinguishable from Monte Carlo simulation. Well-known metastable effects are observed in regions of the model’s parameter space where agent rationality is above a critical value, and we calculate the time scale at which equilibrium is reached using a highly accurate method based on first passage time theory. In addition to considering selfish agents, who only care to maximise their own utility, we consider altruistic agents who make decisions on the basis of maximising global utility. Curiously, we find that although altruistic agents coalesce more strongly on a particular decision, thereby increasing their utility in the short-term, they are also more prone to being subject to non-optimal metastable regimes as compared to selfish agents. The method used for this solution can be easily extended to other binary decision models, including Kirman’s model of ant recruitment Kirman (1993), and under reinterpretation also provides a time-dependent solution to the mean-field Ising model. Finally, we use our time-dependent solution to construct a likelihood function that can be used on non-equilibrium data for model calibration. This is a rare finding, since often calibration in economic agent based models must be done without an explicit likelihood function. From simulated data, we show that even with a well-defined likelihood function, model calibration is difficult unless one has access to data representative of the underlying model.
Collapse
Affiliation(s)
- James Holehouse
- School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom
- * E-mail:
| | - Hector Pollitt
- The World Bank, Washington, DC, United States of America
| |
Collapse
|
17
|
Filatova T, Popović N, Grima R. Modulation of nuclear and cytoplasmic mRNA fluctuations by time-dependent stimuli: Analytical distributions. Math Biosci 2022; 347:108828. [DOI: 10.1016/j.mbs.2022.108828] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2022] [Revised: 04/15/2022] [Accepted: 04/15/2022] [Indexed: 10/18/2022]
|