1
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Gorin G, Vastola JJ, Pachter L. Studying stochastic systems biology of the cell with single-cell genomics data. Cell Syst 2023; 14:822-843.e22. [PMID: 37751736 PMCID: PMC10725240 DOI: 10.1016/j.cels.2023.08.004] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2023] [Revised: 08/16/2023] [Accepted: 08/25/2023] [Indexed: 09/28/2023]
Abstract
Recent experimental developments in genome-wide RNA quantification hold considerable promise for systems biology. However, rigorously probing the biology of living cells requires a unified mathematical framework that accounts for single-molecule biological stochasticity in the context of technical variation associated with genomics assays. We review models for a variety of RNA transcription processes, as well as the encapsulation and library construction steps of microfluidics-based single-cell RNA sequencing, and present a framework to integrate these phenomena by the manipulation of generating functions. Finally, we use simulated scenarios and biological data to illustrate the implications and applications of the approach.
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Affiliation(s)
- Gennady Gorin
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
| | - John J Vastola
- Department of Neurobiology, Harvard Medical School, Boston, MA 02115, USA
| | - Lior Pachter
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125, USA; Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125, USA.
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2
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Gorin G, Vastola JJ, Pachter L. Studying stochastic systems biology of the cell with single-cell genomics data. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.05.17.541250. [PMID: 37292934 PMCID: PMC10245677 DOI: 10.1101/2023.05.17.541250] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Recent experimental developments in genome-wide RNA quantification hold considerable promise for systems biology. However, rigorously probing the biology of living cells requires a unified mathematical framework that accounts for single-molecule biological stochasticity in the context of technical variation associated with genomics assays. We review models for a variety of RNA transcription processes, as well as the encapsulation and library construction steps of microfluidics-based single-cell RNA sequencing, and present a framework to integrate these phenomena by the manipulation of generating functions. Finally, we use simulated scenarios and biological data to illustrate the implications and applications of the approach.
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Affiliation(s)
- Gennady Gorin
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125
| | - John J. Vastola
- Department of Neurobiology, Harvard Medical School, Boston, MA, 02115
| | - Lior Pachter
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA, 91125
- Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, 91125
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3
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Fan R, Hilfinger A. The effect of microRNA on protein variability and gene expression fidelity. Biophys J 2023; 122:905-923. [PMID: 36698314 PMCID: PMC10027439 DOI: 10.1016/j.bpj.2023.01.027] [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: 08/13/2022] [Revised: 12/23/2022] [Accepted: 01/20/2023] [Indexed: 01/27/2023] Open
Abstract
Small regulatory RNA molecules such as microRNA modulate gene expression through inhibiting the translation of messenger RNA (mRNA). Such posttranscriptional regulation has been recently hypothesized to reduce the stochastic variability of gene expression around average levels. Here, we quantify noise in stochastic gene expression models with and without such regulation. Our results suggest that silencing mRNA posttranscriptionally will always increase, rather than decrease, gene expression noise when the silencing of mRNA also increases its degradation, as is expected for microRNA interactions with mRNA. In that regime, we also find that silencing mRNA generally reduces the fidelity of signal transmission from deterministically varying upstream factors to protein levels. These findings suggest that microRNA binding to mRNA does not generically confer precision to protein expression.
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Affiliation(s)
- Raymond Fan
- Department of Physics, University of Toronto, Toronto, Ontario, Canada; Department of Chemical & Physical Sciences, University of Toronto, Mississauga, Ontario, Canada.
| | - Andreas Hilfinger
- Department of Physics, University of Toronto, Toronto, Ontario, Canada; Department of Chemical & Physical Sciences, University of Toronto, Mississauga, Ontario, Canada; Department of Cell & Systems Biology, University of Toronto, , Toronto, Ontario, Canada; Department of Mathematics, University of Toronto, Toronto, Ontario, Canada
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4
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Gorin G, Fang M, Chari T, Pachter L. RNA velocity unraveled. PLoS Comput Biol 2022; 18:e1010492. [PMID: 36094956 PMCID: PMC9499228 DOI: 10.1371/journal.pcbi.1010492] [Citation(s) in RCA: 49] [Impact Index Per Article: 24.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Revised: 09/22/2022] [Accepted: 08/14/2022] [Indexed: 11/24/2022] Open
Abstract
We perform a thorough analysis of RNA velocity methods, with a view towards understanding the suitability of the various assumptions underlying popular implementations. In addition to providing a self-contained exposition of the underlying mathematics, we undertake simulations and perform controlled experiments on biological datasets to assess workflow sensitivity to parameter choices and underlying biology. Finally, we argue for a more rigorous approach to RNA velocity, and present a framework for Markovian analysis that points to directions for improvement and mitigation of current problems. Single-cell sequencing data are snapshots of biological processes, making it challenging to infer dynamic relationships between cell types. RNA velocity attempts to bypass this challenge by treating the unspliced RNA content as a proxy for spliced RNA content in the near future, and using this “extrapolation” to build directional relationships. However, the method, as implemented in several software packages, is not yet reliable enough to be actionable, in part due to the large number of arbitrary, user-set hyperparameters, as well as fundamental incompatibilities between the biophysics of transcription in the living cell and the models used throughout the velocity workflows. In this study, we review these issues, and use existing results from the fields of stochastic modeling and fluorescence transcriptomics to develop an alternative theoretical framework. We show that our framework can facilitate the development and inference of physically consistent models for sequencing data, as well as the unification of single-cell analyses to self-consistently treat variation due to cell type dynamics and identities, the stochasticity inherent to single-molecule processes, and the uncertainty introduced by sequencing experiments.
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Affiliation(s)
- Gennady Gorin
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California, United States of America
| | - Meichen Fang
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, California, United States of America
| | - Tara Chari
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, California, United States of America
| | - Lior Pachter
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, California, United States of America
- Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California, United States of America
- * E-mail:
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5
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Joly-Smith E, Wang ZJ, Hilfinger A. Inferring gene regulation dynamics from static snapshots of gene expression variability. Phys Rev E 2021; 104:044406. [PMID: 34781497 DOI: 10.1103/physreve.104.044406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Accepted: 08/27/2021] [Indexed: 11/07/2022]
Abstract
Inferring functional relationships within complex networks from static snapshots of a subset of variables is a ubiquitous problem in science. For example, a key challenge of systems biology is to translate cellular heterogeneity data obtained from single-cell sequencing or flow-cytometry experiments into regulatory dynamics. We show how static population snapshots of covariability can be exploited to rigorously infer properties of gene expression dynamics when gene expression reporters probe their upstream dynamics on separate timescales. This can be experimentally exploited in dual-reporter experiments with fluorescent proteins of unequal maturation times, thus turning an experimental bug into an analysis feature. We derive correlation conditions that detect the presence of closed-loop feedback regulation in gene regulatory networks. Furthermore, we show how genes with cell-cycle-dependent transcription rates can be identified from the variability of coregulated fluorescent proteins. Similar correlation constraints might prove useful in other areas of science in which static correlation snapshots are used to infer causal connections between dynamically interacting components.
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Affiliation(s)
- Euan Joly-Smith
- Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7
| | - Zitong Jerry Wang
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Andreas Hilfinger
- Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7.,Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4.,Department of Cell & Systems Biology, University of Toronto, 25 Harbord Street, Toronto, Ontario, Canada M5S 3G5
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6
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Ham L, Jackson M, Stumpf MPH. Pathway dynamics can delineate the sources of transcriptional noise in gene expression. eLife 2021; 10:e69324. [PMID: 34636320 PMCID: PMC8608387 DOI: 10.7554/elife.69324] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2021] [Accepted: 10/11/2021] [Indexed: 11/25/2022] Open
Abstract
Single-cell expression profiling opens up new vistas on cellular processes. Extensive cell-to-cell variability at the transcriptomic and proteomic level has been one of the stand-out observations. Because most experimental analyses are destructive we only have access to snapshot data of cellular states. This loss of temporal information presents significant challenges for inferring dynamics, as well as causes of cell-to-cell variability. In particular, we typically cannot separate dynamic variability from within cells ('intrinsic noise') from variability across the population ('extrinsic noise'). Here, we make this non-identifiability mathematically precise, allowing us to identify new experimental set-ups that can assist in resolving this non-identifiability. We show that multiple generic reporters from the same biochemical pathways (e.g. mRNA and protein) can infer magnitudes of intrinsic and extrinsic transcriptional noise, identifying sources of heterogeneity. Stochastic simulations support our theory, and demonstrate that 'pathway-reporters' compare favourably to the well-known, but often difficult to implement, dual-reporter method.
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Affiliation(s)
- Lucy Ham
- School of BioSciences, University of MelbourneMelbourneAustralia
| | - Marcel Jackson
- Department of Mathematics and Statistics, La Trobe UniversityMelbourneAustralia
| | - Michael PH Stumpf
- School of Mathematics and Statistics, University of MelbourneMelbourneAustralia
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7
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Yeung E, Kim J, Yuan Y, Gonçalves J, Murray RM. Data-driven network models for genetic circuits from time-series data with incomplete measurements. J R Soc Interface 2021; 18:20210413. [PMID: 34493091 PMCID: PMC8424335 DOI: 10.1098/rsif.2021.0413] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2021] [Accepted: 08/12/2021] [Indexed: 12/23/2022] Open
Abstract
Synthetic gene networks are frequently conceptualized and visualized as static graphs. This view of biological programming stands in stark contrast to the transient nature of biomolecular interaction, which is frequently enacted by labile molecules that are often unmeasured. Thus, the network topology and dynamics of synthetic gene networks can be difficult to verify in vivo or in vitro, due to the presence of unmeasured biological states. Here we introduce the dynamical structure function as a new mesoscopic, data-driven class of models to describe gene networks with incomplete measurements of state dynamics. We develop a network reconstruction algorithm and a code base for reconstructing the dynamical structure function from data, to enable discovery and visualization of graphical relationships in a genetic circuit diagram as time-dependent functions rather than static, unknown weights. We prove a theorem, showing that dynamical structure functions can provide a data-driven estimate of the size of crosstalk fluctuations from an idealized model. We illustrate this idea with numerical examples. Finally, we show how data-driven estimation of dynamical structure functions can explain failure modes in two experimentally implemented genetic circuits, a previously reported in vitro genetic circuit and a new E. coli-based transcriptional event detector.
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Affiliation(s)
- Enoch Yeung
- Center for Biological Engineering, Biomolecular Science and Engineering Program, Department of Mechanical Engineering, Center for Control, Dynamical Systems, and Computation, University of California, Santa Barbara, CA, USA
| | - Jongmin Kim
- Department of Life Sciences, POSTECH, Pohang, South Korea
| | - Ye Yuan
- School of Artificial Intelligence and Automation, Hua Zhong University of Science and Technology, Wuhan, People’s Republic of China
| | - Jorge Gonçalves
- Systems Biology Research Group, University of Luxembourg, Belvaux, Luxembourg
| | - Richard M. Murray
- Control and Dynamical Systems, California Institute of Technology, Pasadena, CA, USA
- Biology and Biological Engineering, California Institute of Technology, Pasadena, CA, USA
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8
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Gene Expression at a Single Molecule Level: Implications for MDS and AML. Blood 2021; 138:625-636. [PMID: 34157070 DOI: 10.1182/blood.2019004261] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 12/03/2020] [Indexed: 12/11/2022] Open
Abstract
Non-genetic heterogeneity, or gene expression stochasticity, is an important source of variability in biological systems. With the advent and improvement of single molecule resolution technologies, it has been shown that transcription dynamics and resultant transcript number fluctuations generate significant cell-to-cell variability that has important biological effects and may contribute substantially to both tissue homeostasis and disease. In this respect, the pathophysiology of stem cell-derived malignancies such as AML and MDS, which has historically been studied at the ensemble level, may require re-evaluation. To that end, it is our aim in this review to highlight the results of recent single-molecule, biophysical, and systems studies of gene expression dynamics, with the explicit purpose of demonstrating how the insights from these basic science studies may help inform and progress the field of leukemia biology and, ultimately, research into novel therapies.
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9
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Phillips NE, Hugues A, Yeung J, Durandau E, Nicolas D, Naef F. The circadian oscillator analysed at the single-transcript level. Mol Syst Biol 2021; 17:e10135. [PMID: 33719202 PMCID: PMC7957410 DOI: 10.15252/msb.202010135] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Revised: 01/05/2021] [Accepted: 01/19/2021] [Indexed: 12/31/2022] Open
Abstract
The circadian clock is an endogenous and self-sustained oscillator that anticipates daily environmental cycles. While rhythmic gene expression of circadian genes is well-described in populations of cells, the single-cell mRNA dynamics of multiple core clock genes remain largely unknown. Here we use single-molecule fluorescence in situ hybridisation (smFISH) at multiple time points to measure pairs of core clock transcripts, Rev-erbα (Nr1d1), Cry1 and Bmal1, in mouse fibroblasts. The mean mRNA level oscillates over 24 h for all three genes, but mRNA numbers show considerable spread between cells. We develop a probabilistic model for multivariate mRNA counts using mixtures of negative binomials, which accounts for transcriptional bursting, circadian time and cell-to-cell heterogeneity, notably in cell size. Decomposing the mRNA variability into distinct noise sources shows that clock time contributes a small fraction of the total variability in mRNA number between cells. Thus, our results highlight the intrinsic biological challenges in estimating circadian phase from single-cell mRNA counts and suggest that circadian phase in single cells is encoded post-transcriptionally.
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Affiliation(s)
- Nicholas E Phillips
- Institute of BioengineeringSchool of Life SciencesEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
| | - Alice Hugues
- Institute of BioengineeringSchool of Life SciencesEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
- Master de BiologieÉcole Normale Supérieure de LyonUniversité Claude Bernard Lyon IUniversité de LyonLyonFrance
| | - Jake Yeung
- Institute of BioengineeringSchool of Life SciencesEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
| | - Eric Durandau
- Institute of BioengineeringSchool of Life SciencesEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
| | - Damien Nicolas
- Institute of BioengineeringSchool of Life SciencesEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
| | - Felix Naef
- Institute of BioengineeringSchool of Life SciencesEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
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10
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Hsu IS, Moses AM. Stochastic models for single-cell data: Current challenges and the way forward. FEBS J 2021; 289:647-658. [PMID: 33570798 DOI: 10.1111/febs.15760] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2020] [Revised: 12/22/2020] [Accepted: 02/10/2021] [Indexed: 11/28/2022]
Abstract
Although the quantity and quality of single-cell data have progressed rapidly, making quantitative predictions with single-cell stochastic models remains challenging. The stochastic nature of cellular processes leads to at least three challenges in building models with single-cell data: (a) because variability in single-cell data can be attributed to multiple different sources, it is difficult to rule out conflicting mechanistic models that explain the same data equally well; (b) the distinction between interesting biological variability and experimental variability is sometimes ambiguous; (c) the nonstandard distributions of single-cell data can lead to violations of the assumption of symmetric errors in least-squares fitting. In this review, we first discuss recent studies that overcome some of the challenges or set up a promising direction and then introduce some powerful statistical approaches utilized in these studies. We conclude that applying and developing statistical approaches could lead to further progress in building stochastic models for single-cell data.
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Affiliation(s)
- Ian S Hsu
- Department of Cell & Systems Biology, University of Toronto, ON, Canada
| | - Alan M Moses
- Department of Cell & Systems Biology, University of Toronto, ON, Canada
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11
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Hou XF, Zhou BQ, Zhou YF, Apata CO, Jiang L, Pei QM. Noisy signal propagation and amplification in phenotypic transition cascade of colonic cells. Phys Rev E 2021; 102:062411. [PMID: 33466057 DOI: 10.1103/physreve.102.062411] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2020] [Accepted: 11/10/2020] [Indexed: 11/07/2022]
Abstract
Like genes and proteins, cells can use biochemical networks to sense and process information. The differentiation of the cell state in colonic crypts forms a typical unidirectional phenotypic transitional cascade, in which stem cells differentiate into the transit-amplifying cells (TACs), and TACs continue to differentiate into fully differentiated cells. In order to quantitatively describe the relationship between the noise of each compartment and the amplification of signals, the gain factor is introduced, and the gain-fluctuation relation is obtained by using the linear noise approximation of the master equation. Through the simulation of these theoretical formulas, the characters of noise propagation and amplification are studied. It is found that the transmitted noise is an important part of the total noise in each downstream cell. Therefore, a small number of downstream cells can only cause its small inherent noise, but the total noise may be very large due to the transmitted noise. The influence of the transmitted noise may be the indirect cause of colon cancer. In addition, the total noise of the downstream cells always has a minimum value. As long as a reasonable value of the gain factor is selected, the number of cells in colonic crypts will be controlled within the normal range. This may be a good method to intervene the uncontrollable growth of tumor cells and effectively control the deterioration of colon cancer.
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Affiliation(s)
- Xue-Fen Hou
- School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China
| | - Bin-Qian Zhou
- School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China
| | - Yi-Fan Zhou
- School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China
| | - Charles Omotomide Apata
- School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China
| | - Long Jiang
- School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China
| | - Qi-Ming Pei
- School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China
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12
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Abstract
Mathematical models play an important role in the design of synthetic gene circuits, by guiding the choice of biological components and their assembly into novel gene networks. Here, we present a guide for biologists to build and utilize models of gene networks (synthetic or natural) to analyze dynamical properties of these networks while considering the low numbers of molecules inside cells that results in stochastic gene expression. We start by describing how to write down a model and discussing the level of details to include. We then briefly demonstrate how to simulate a network's dynamics using deterministic differential equations that assume high numbers of molecules. To consider the role of stochastic gene expression in single cells, we provide a detailed tutorial on running stochastic Gillespie simulations of a network, including instructions on coding the Gillespie algorithm with example code. Finally, we illustrate how using a combination of quantitative experimental characterization of a synthetic circuit and mathematical modeling can guide the iterative redesign of a synthetic circuit to achieve the desired properties. This is shown using a classic synthetic oscillator, the repressilator, which we recently redesigned into the most precise and robust synthetic oscillator to date. We thus provide a toolkit for synthetic biologists to build more precise and robust synthetic circuits, which should lead to a deeper understanding of the dynamics of gene regulatory networks.
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Affiliation(s)
- Giselle McCallum
- Department of Biology, Concordia University, Montreal, QC, Canada
| | - Laurent Potvin-Trottier
- Department of Biology, Concordia University, Montreal, QC, Canada.
- Center for Applied Synthetic Biology, Concordia University, Montreal, QC, Canada.
- Department of Physics, Concordia University, Montreal, QC, Canada.
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13
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Li G, Neuert G. Multiplex RNA single molecule FISH of inducible mRNAs in single yeast cells. Sci Data 2019; 6:94. [PMID: 31209217 PMCID: PMC6572782 DOI: 10.1038/s41597-019-0106-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2019] [Accepted: 05/17/2019] [Indexed: 12/31/2022] Open
Abstract
Transcript levels powerfully influence cell behavior and phenotype and are carefully regulated at several steps. Recently developed single cell approaches such as RNA single molecule fluorescence in-situ hybridization (smFISH) have produced advances in our understanding of how these steps work within the cell. In comparison to single-cell sequencing, smFISH provides more accurate quantification of RNA levels. Additionally, transcript subcellular localization is directly visualized, enabling the analysis of transcription (initiation and elongation), RNA export and degradation. As part of our efforts to investigate how this type of analysis can generate improved models of gene expression, we used smFISH to quantify the kinetic expression of STL1 and CTT1 mRNAs in single Saccharomyces cerevisiae cells upon 0.2 and 0.4 M NaCl osmotic stress. In this Data Descriptor, we outline our procedure along with our data in the form of raw images and processed mRNA counts. We discuss how these data can be used to develop single cell modelling approaches, to study fundamental processes in transcription regulation and develop single cell image processing approaches.
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Affiliation(s)
- Guoliang Li
- Department of Molecular Physiology and Biophysics, School of Medicine, Vanderbilt University, Nashville, TN, 37232, USA
| | - Gregor Neuert
- Department of Molecular Physiology and Biophysics, School of Medicine, Vanderbilt University, Nashville, TN, 37232, USA.
- Department of Biomedical Engineering, School of Engineering, Vanderbilt University, Nashville, TN, 37232, USA.
- Department of Pharmacology, School of Medicine, Vanderbilt University, Nashville, TN, 37232, USA.
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14
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Xing J, Tian XJ. Investigating epithelial-to-mesenchymal transition with integrated computational and experimental approaches. Phys Biol 2019; 16:031001. [PMID: 30665206 PMCID: PMC6609444 DOI: 10.1088/1478-3975/ab0032] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
The transition between epithelial and mesenchymal (EMT) is a fundamental cellular process that plays critical roles in development, cancer metastasis, and tissue wound healing. EMT is not a binary process but involves multiple partial EMT states that give rise to a high degree of cell state plasticity. Here, we first reviewed several studies on theoretical predictions and experimental verification of these intermediate states, the role of partial EMT on kidney fibrosis development, and how quantitative signaling information controls cell commitment to partial or full EMT upon transient signals. Next, we summarized existing knowledge and open questions on the coupling between EMT and other biological processes, such as the cell cycle, epigenetic regulation, stemness, and apoptosis. Taken together, EMT is a model system that has attracted increasing interests for quantitative experimental and theoretical studies.
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Affiliation(s)
- Jianhua Xing
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, Pennsylvania, 15261, United States of America. UPMC-Hillman Cancer Center, University of Pittsburgh, Pittsburgh, PA, United States of America. To whom correspondence should be addressed
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15
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Propagation of Extrinsic Fluctuations in Biochemical Birth–Death Processes. Bull Math Biol 2018; 81:800-829. [DOI: 10.1007/s11538-018-00538-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2018] [Accepted: 11/28/2018] [Indexed: 01/07/2023]
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16
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Lin J, Amir A. Homeostasis of protein and mRNA concentrations in growing cells. Nat Commun 2018; 9:4496. [PMID: 30374016 PMCID: PMC6206055 DOI: 10.1038/s41467-018-06714-z] [Citation(s) in RCA: 84] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2018] [Accepted: 09/17/2018] [Indexed: 12/27/2022] Open
Abstract
Many experiments show that the numbers of mRNA and protein are proportional to the cell volume in growing cells. However, models of stochastic gene expression often assume constant transcription rate per gene and constant translation rate per mRNA, which are incompatible with these experiments. Here, we construct a minimal gene expression model to fill this gap. Assuming ribosomes and RNA polymerases are limiting in gene expression, we show that the numbers of proteins and mRNAs both grow exponentially during the cell cycle and that the concentrations of all mRNAs and proteins achieve cellular homeostasis; the competition between genes for the RNA polymerases makes the transcription rate independent of the genome number. Furthermore, by extending the model to situations in which DNA (mRNA) can be saturated by RNA polymerases (ribosomes) and becomes limiting, we predict a transition from exponential to linear growth of cell volume as the protein-to-DNA ratio increases.
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Affiliation(s)
- Jie Lin
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Ariel Amir
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA.
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17
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Abstract
Systems biology seeks to combine experiments with computation to predict biological behaviors. However, despite tremendous data and knowledge, biological models make less-accurate predictions compared with other fields. By analyzing single-cell, single-molecule measurements of mRNA during yeast stress response, we explore why and how the shapes of experimental distributions control prediction accuracy. We show how asymmetric data distributions with long tails cause standard modeling approaches to yield excellent fits but make meaningless predictions. We show how these biases arise from the violation of fundamental assumptions in standard modeling approaches. We demonstrate how advanced computational tools solve this dilemma and achieve predictive understanding of spatiotemporal mechanisms of transcription control including RNA polymerase initiation and elongation and mRNA accumulation, transport, and decay. Despite substantial experimental and computational efforts, mechanistic modeling remains more predictive in engineering than in systems biology. The reason for this discrepancy is not fully understood. One might argue that the randomness and complexity of biological systems are the main barriers to predictive understanding, but these issues are not unique to biology. Instead, we hypothesize that the specific shapes of rare single-molecule event distributions produce substantial yet overlooked challenges for biological models. We demonstrate why modern statistical tools to disentangle complexity and stochasticity, which assume normally distributed fluctuations or enormous datasets, do not apply to the discrete, positive, and nonsymmetric distributions that characterize mRNA fluctuations in single cells. As an example, we integrate single-molecule measurements and advanced computational analyses to explore mitogen-activated protein kinase induction of multiple stress response genes. Through systematic analyses of different metrics to compare the same model to the same data, we elucidate why standard modeling approaches yield nonpredictive models for single-cell gene regulation. We further explain how advanced tools recover precise, reproducible, and predictive understanding of transcription regulation mechanisms, including gene activation, polymerase initiation, elongation, mRNA accumulation, spatial transport, and decay.
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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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Gómez-Schiavon M, El-Samad H. Complexity-aware simple modeling. Curr Opin Microbiol 2018; 45:47-52. [PMID: 29494832 DOI: 10.1016/j.mib.2018.01.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2017] [Accepted: 01/07/2018] [Indexed: 11/19/2022]
Abstract
Mathematical models continue to be essential for deepening our understanding of biology. On one extreme, simple or small-scale models help delineate general biological principles. However, the parsimony of detail in these models as well as their assumption of modularity and insulation make them inaccurate for describing quantitative features. On the other extreme, large-scale and detailed models can quantitatively recapitulate a phenotype of interest, but have to rely on many unknown parameters, making them often difficult to parse mechanistically and to use for extracting general principles. We discuss some examples of a new approach-complexity-aware simple modeling-that can bridge the gap between the small-scale and large-scale approaches.
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Affiliation(s)
- Mariana Gómez-Schiavon
- Department of Biochemistry and Biophysics, University of California San Francisco, San Francisco CA 94158, United States
| | - Hana El-Samad
- Department of Biochemistry and Biophysics, University of California San Francisco, San Francisco CA 94158, United States; Chan Zuckerberg Biohub, San Francisco, CA 94158, United States.
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20
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Cole J, Luthey-Schulten Z. Careful accounting of extrinsic noise in protein expression reveals correlations among its sources. Phys Rev E 2017; 95:062418. [PMID: 28709241 PMCID: PMC5669626 DOI: 10.1103/physreve.95.062418] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2017] [Indexed: 11/07/2022]
Abstract
In order to grow and replicate, living cells must express a diverse array of proteins, but the process by which proteins are made includes a great deal of inherent randomness. Understanding this randomness-whether it arises from the discrete stochastic nature of chemical reactivity ("intrinsic" noise), or from cell-to-cell variability in the concentrations of molecules involved in gene expression, or from the timings of important cell-cycle events like DNA replication and cell division ("extrinsic" noise)-remains a challenge. In this article we analyze a model of gene expression that accounts for several extrinsic sources of noise, including those associated with chromosomal replication, cell division, and variability in the numbers of RNA polymerase, ribonuclease E, and ribosomes. We then attempt to fit our model to a large proteomics and transcriptomics data set and find that only through the introduction of a few key correlations among the extrinsic noise sources can we accurately recapitulate the experimental data. These include significant correlations between the rate of mRNA degradation (mediated by ribonuclease E) and the rates of both transcription (RNA polymerase) and translation (ribosomes) and, strikingly, an anticorrelation between the transcription and the translation rates themselves.
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Affiliation(s)
- John Cole
- Department of Physics, University of Illinois, Urbana-Champaign
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21
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Determining the Limitations and Benefits of Noise in Gene Regulation and Signal Transduction through Single Cell, Microscopy-Based Analysis. J Mol Biol 2017; 429:1143-1154. [PMID: 28288800 DOI: 10.1016/j.jmb.2017.03.007] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2016] [Revised: 03/02/2017] [Accepted: 03/06/2017] [Indexed: 12/22/2022]
Abstract
Stochastic fluctuations, termed "noise," in the level of biological molecules can greatly impact cellular functions. While biological noise can sometimes be detrimental, recent studies have provided an increasing number of examples in which biological noise can be functionally beneficial. Rather than provide an exhaustive review of the growing literature in this field, in this review, we focus on single-cell studies based on quantitative microscopy that have generated a deeper understanding of the sources, characteristics, limitations, and benefits of biological noise. Specifically, we highlight studies showing how noise can help coordinate the expression of multiple downstream target genes, impact the channel capacity of signaling networks, and interact synergistically with oscillatory dynamics to enhance the sensitivity of signal processing. We conclude with a discussion of current challenges and future opportunities.
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Abstract
A new, game-changing approach makes it possible to rigorously disprove models without making assumptions about the unknown parts of the biological system.
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