1
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Gorin G, Yoshida S, Pachter L. Assessing Markovian and Delay Models for Single-Nucleus RNA Sequencing. Bull Math Biol 2023; 85:114. [PMID: 37828255 DOI: 10.1007/s11538-023-01213-9] [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: 11/22/2022] [Accepted: 09/11/2023] [Indexed: 10/14/2023]
Abstract
The serial nature of reactions involved in the RNA life-cycle motivates the incorporation of delays in models of transcriptional dynamics. The models couple a transcriptional process to a fairly general set of delayed monomolecular reactions with no feedback. We provide numerical strategies for calculating the RNA copy number distributions induced by these models, and solve several systems with splicing, degradation, and catalysis. An analysis of single-cell and single-nucleus RNA sequencing data using these models reveals that the kinetics of nuclear export do not appear to require invocation of a non-Markovian waiting time.
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Affiliation(s)
- Gennady Gorin
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Shawn Yoshida
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA, 91125, 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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Kell B, Ripsman R, Hilfinger A. Noise properties of adaptation-conferring biochemical control modules. Proc Natl Acad Sci U S A 2023; 120:e2302016120. [PMID: 37695915 PMCID: PMC10515136 DOI: 10.1073/pnas.2302016120] [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: 02/05/2023] [Accepted: 06/12/2023] [Indexed: 09/13/2023] Open
Abstract
A key goal of synthetic biology is to develop functional biochemical modules with network-independent properties. Antithetic integral feedback (AIF) is a recently developed control module in which two control species perfectly annihilate each other's biological activity. The AIF module confers robust perfect adaptation to the steady-state average level of a controlled intracellular component when subjected to sustained perturbations. Recent work has suggested that such robustness comes at the unavoidable price of increased stochastic fluctuations around average levels. We present theoretical results that support and quantify this trade-off for the commonly analyzed AIF variant in the idealized limit with perfect annihilation. However, we also show that this trade-off is a singular limit of the control module: Even minute deviations from perfect adaptation allow systems to achieve effective noise suppression as long as cells can pay the corresponding energetic cost. We further show that a variant of the AIF control module can achieve significant noise suppression even in the idealized limit with perfect adaptation. This atypical configuration may thus be preferable in synthetic biology applications.
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Affiliation(s)
- Brayden Kell
- Department of Physics, University of Toronto, Toronto, ONM5S 1A7, Canada
- Department of Chemical and Physical Sciences, University of Toronto, Mississauga, ONL5L 1C6, Canada
- Department of Molecular Biosciences, Northwestern University, Evanston, IL60208
- National Science Foundation-Simons Center for Quantitative Biology, Northwestern University, Evanston, IL60208
| | - Ryan Ripsman
- Department of Physics, University of Toronto, Toronto, ONM5S 1A7, Canada
- Department of Laboratory Medicine and Pathobiology, University of Toronto, Toronto, ONM5S 1A8, Canada
| | - Andreas Hilfinger
- Department of Physics, University of Toronto, Toronto, ONM5S 1A7, Canada
- Department of Chemical and Physical Sciences, University of Toronto, Mississauga, ONL5L 1C6, Canada
- Department of Mathematics, University of Toronto, Toronto, ONM5S 2E4, Canada
- Department of Cell and Systems Biology, University of Toronto, Toronto, ONM5S 3G5, Canada
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3
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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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4
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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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5
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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: 1] [Impact Index Per Article: 1.0] [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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6
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Quantifying biochemical reaction rates from static population variability within incompletely observed complex networks. PLoS Comput Biol 2022; 18:e1010183. [PMID: 35731728 PMCID: PMC9216546 DOI: 10.1371/journal.pcbi.1010183] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 05/07/2022] [Indexed: 11/19/2022] Open
Abstract
Quantifying biochemical reaction rates within complex cellular processes remains a key challenge of systems biology even as high-throughput single-cell data have become available to characterize snapshots of population variability. That is because complex systems with stochastic and non-linear interactions are difficult to analyze when not all components can be observed simultaneously and systems cannot be followed over time. Instead of using descriptive statistical models, we show that incompletely specified mechanistic models can be used to translate qualitative knowledge of interactions into reaction rate functions from covariability data between pairs of components. This promises to turn a globally intractable problem into a sequence of solvable inference problems to quantify complex interaction networks from incomplete snapshots of their stochastic fluctuations.
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7
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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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8
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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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9
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Ren Y, Hiscock HG, Hore PJ. Angular Precision of Radical Pair Compass Magnetoreceptors. Biophys J 2021; 120:547-555. [PMID: 33421412 PMCID: PMC7896030 DOI: 10.1016/j.bpj.2020.12.023] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2020] [Revised: 12/17/2020] [Accepted: 12/30/2020] [Indexed: 11/19/2022] Open
Abstract
The light-dependent magnetic compass sense of night-migratory songbirds is thought to rely on magnetically sensitive chemical reactions of radical pairs in cryptochrome proteins located in the birds' eyes. Recently, an information theory approach was developed that provides a strict lower bound on the precision with which a bird could estimate its head direction using only geomagnetic cues and a cryptochrome-based radical pair sensor. By means of this lower bound, we show here how the performance of the compass sense could be optimized by adjusting the orientation of cryptochrome molecules within photoreceptor cells, the distribution of cells around the retina, and the effects of the geomagnetic field on the photochemistry of the radical pair.
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Affiliation(s)
- Yi Ren
- Department of Chemistry, University of Oxford, Oxford, United Kingdom
| | - Hamish G Hiscock
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts
| | - P J Hore
- Department of Chemistry, University of Oxford, Oxford, United Kingdom.
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10
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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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11
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Lederer AR, La Manno G. The emergence and promise of single-cell temporal-omics approaches. Curr Opin Biotechnol 2020; 63:70-78. [DOI: 10.1016/j.copbio.2019.12.005] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2019] [Revised: 12/03/2019] [Accepted: 12/08/2019] [Indexed: 12/13/2022]
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12
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Cardelli L, Laurenti L, Csikasz-Nagy A. Coupled membrane transporters reduce noise. Phys Rev E 2020; 101:012414. [PMID: 32069604 DOI: 10.1103/physreve.101.012414] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2019] [Indexed: 11/07/2022]
Abstract
Molecular systems are inherently probabilistic and operate in a noisy environment, yet, despite all these uncertainties, molecular functions are surprisingly reliable and robust. The principles used by natural systems to deal with noise are still not well understood, especially in a nonhomogeneous environment where molecules can diffuse across different compartments. In this paper we show that membrane transport mechanisms have very effective properties of noise reduction. In particular, we show that active transport mechanisms (those that can transport against a gradient of concentration by using energy or by means of the concentration gradient of other substances), such as symporters and antiporters, have surprising efficiency in noise reduction, which outperforms passive diffusion mechanisms and are well below Poisson levels. We link our results to the coupled transport of potassium, sodium, and glucose to show that the noise in internal glucose level can be greatly reduced. Our results show that compartmentalization can be a highly effective mechanism of noise reduction and suggests that membrane transport could give this extra benefit, contributing to the emergence of complex compartmentalization in eukaryotes.
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Affiliation(s)
- Luca Cardelli
- Department of Computer Science, University of Oxford, Oxford OX1 3QD, United Kingdom
| | - Luca Laurenti
- Department of Computer Science, University of Oxford, Oxford OX1 3QD, United Kingdom
| | - Attila Csikasz-Nagy
- Randall Division of Cell and Molecular Biophysics and Institute of Mathematical and Molecular Biomedicine, King's College London, London, United Kingdom and Pázmány Péter Catholic University, Faculty of Information Technology and Bionics Budapest, Hungary
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13
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Navigating at night: fundamental limits on the sensitivity of radical pair magnetoreception under dim light. Q Rev Biophys 2019; 52:e9. [DOI: 10.1017/s0033583519000076] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Abstract
Night-migratory songbirds appear to sense the direction of the Earth's magnetic field via radical pair intermediates formed photochemically in cryptochrome flavoproteins contained in photoreceptor cells in their retinas. It is an open question whether this light-dependent mechanism could be sufficiently sensitive given the low-light levels experienced by nocturnal migrants. The scarcity of available photons results in significant uncertainty in the signal generated by the magnetoreceptors distributed around the retina. Here we use results from Information Theory to obtain a lower bound estimate of the precision with which a bird could orient itself using only geomagnetic cues. Our approach bypasses the current lack of knowledge about magnetic signal transduction and processing in vivo by computing the best-case compass precision under conditions where photons are in short supply. We use this method to assess the performance of three plausible cryptochrome-derived flavin-containing radical pairs as potential magnetoreceptors.
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14
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Yan J, Hilfinger A, Vinnicombe G, Paulsson J. Kinetic Uncertainty Relations for the Control of Stochastic Reaction Networks. PHYSICAL REVIEW LETTERS 2019; 123:108101. [PMID: 31573304 DOI: 10.1103/physrevlett.123.108101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2019] [Revised: 06/27/2019] [Indexed: 06/10/2023]
Abstract
Nonequilibrium stochastic reaction networks are commonly found in both biological and nonbiological systems, but have remained hard to analyze because small differences in rate functions or topology can change the dynamics drastically. Here, we conjecture exact quantitative inequalities that relate the extent of fluctuations in connected components, for various network topologies. Specifically, we find that regardless of how two components affect each other's production rates, it is impossible to suppress fluctuations below the uncontrolled equivalents for both components: one must increase its fluctuations for the other to be suppressed. For systems in which components control each other in ringlike structures, it appears that fluctuations can only be suppressed in one component if all other components instead increase fluctuations, compared to the case without control. Even the general N-component system-with arbitrary connections and parameters-must have at least one component with increased fluctuations to reduce fluctuations in others. In connected reaction networks it thus appears impossible to reduce the statistical uncertainty in all components, regardless of the control mechanisms or energy dissipation.
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Affiliation(s)
- Jiawei Yan
- Department of Systems Biology, Harvard University, 200 Longwood Avenue, Boston, Massachusetts 02115, USA
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Andreas Hilfinger
- Department of Chemical & Physical Sciences, University of Toronto, Mississauga, Ontario L5L 1C6, Canada
- Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario M5S 2E4, Canada
- Department of Cell & Systems Biology, University of Toronto, 25 Harbord Street, Toronto, Ontario M5S 3G5, Canada
| | - Glenn Vinnicombe
- Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom
| | - Johan Paulsson
- Department of Systems Biology, Harvard University, 200 Longwood Avenue, Boston, Massachusetts 02115, USA
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15
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A universal biomolecular integral feedback controller for robust perfect adaptation. Nature 2019; 570:533-537. [PMID: 31217585 DOI: 10.1038/s41586-019-1321-1] [Citation(s) in RCA: 138] [Impact Index Per Article: 27.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2018] [Accepted: 05/22/2019] [Indexed: 11/09/2022]
Abstract
Homeostasis is a recurring theme in biology that ensures that regulated variables robustly-and in some systems, completely-adapt to environmental perturbations. This robust perfect adaptation feature is achieved in natural circuits by using integral control, a negative feedback strategy that performs mathematical integration to achieve structurally robust regulation1,2. Despite its benefits, the synthetic realization of integral feedback in living cells has remained elusive owing to the complexity of the required biological computations. Here we prove mathematically that there is a single fundamental biomolecular controller topology3 that realizes integral feedback and achieves robust perfect adaptation in arbitrary intracellular networks with noisy dynamics. This adaptation property is guaranteed both for the population-average and for the time-average of single cells. On the basis of this concept, we genetically engineer a synthetic integral feedback controller in living cells4 and demonstrate its tunability and adaptation properties. A growth-rate control application in Escherichia coli shows the intrinsic capacity of our integral controller to deliver robustness and highlights its potential use as a versatile controller for regulation of biological variables in uncertain networks. Our results provide conceptual and practical tools in the area of cybergenetics3,5, for engineering synthetic controllers that steer the dynamics of living systems3-9.
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16
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Olsman N, Paulsson J. A universal control system for synthetic gene networks. Nature 2019; 570:452-453. [DOI: 10.1038/d41586-019-01772-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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17
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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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18
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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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19
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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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Park SJ, Song S, Yang GS, Kim PM, Yoon S, Kim JH, Sung J. The Chemical Fluctuation Theorem governing gene expression. Nat Commun 2018; 9:297. [PMID: 29352116 PMCID: PMC5775451 DOI: 10.1038/s41467-017-02737-0] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2017] [Accepted: 12/20/2017] [Indexed: 11/20/2022] Open
Abstract
Gene expression is a complex stochastic process composed of numerous enzymatic reactions with rates coupled to hidden cell-state variables. Despite advances in single-cell technologies, the lack of a theory accurately describing the gene expression process has restricted a robust, quantitative understanding of gene expression variability among cells. Here we present the Chemical Fluctuation Theorem (CFT), providing an accurate relationship between the environment-coupled chemical dynamics of gene expression and gene expression variability. Combined with a general, accurate model of environment-coupled transcription processes, the CFT provides a unified explanation of mRNA variability for various experimental systems. From this analysis, we construct a quantitative model of transcription dynamics enabling analytic predictions for the dependence of mRNA noise on the mRNA lifetime distribution, confirmed against stochastic simulation. This work suggests promising new directions for quantitative investigation into cellular control over biological functions by making complex dynamics of intracellular reactions accessible to rigorous mathematical deductions. A unified framework to understand gene expression noise is still lacking. Here the authors derive a universal theorem relating the biological noise with dynamics of birth and death processes and present a model of transcription dynamics, allowing analytical prediction of the dependence of mRNA noise on mRNA lifetime variability.
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Affiliation(s)
- Seong Jun Park
- Creative Research Initiative Center for Chemical Dynamics in Living Cells, Chung-Ang University, Seoul, 06974, Korea.,Department of Chemistry, Chung-Ang University, Seoul, 06974, Korea.,National Institute of Innovative Functional Imaging, Chung-Ang University, Seoul, 06974, Korea
| | - Sanggeun Song
- Creative Research Initiative Center for Chemical Dynamics in Living Cells, Chung-Ang University, Seoul, 06974, Korea.,Department of Chemistry, Chung-Ang University, Seoul, 06974, Korea.,National Institute of Innovative Functional Imaging, Chung-Ang University, Seoul, 06974, Korea
| | - Gil-Suk Yang
- Creative Research Initiative Center for Chemical Dynamics in Living Cells, Chung-Ang University, Seoul, 06974, Korea
| | - Philip M Kim
- Terrence Donnelly Center for Cellular and Biomolecular Research, Department of Molecular Genetics and Department of Computer Science, University of Toronto, Toronto, M5S 3E1, ON, Canada
| | - Sangwoon Yoon
- Department of Chemistry, Chung-Ang University, Seoul, 06974, Korea.
| | - Ji-Hyun Kim
- Creative Research Initiative Center for Chemical Dynamics in Living Cells, Chung-Ang University, Seoul, 06974, Korea.
| | - Jaeyoung Sung
- Creative Research Initiative Center for Chemical Dynamics in Living Cells, Chung-Ang University, Seoul, 06974, Korea. .,Department of Chemistry, Chung-Ang University, Seoul, 06974, Korea. .,National Institute of Innovative Functional Imaging, Chung-Ang University, Seoul, 06974, Korea.
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Keegstra JM, Kamino K, Anquez F, Lazova MD, Emonet T, Shimizu TS. Phenotypic diversity and temporal variability in a bacterial signaling network revealed by single-cell FRET. eLife 2017; 6:e27455. [PMID: 29231170 PMCID: PMC5809149 DOI: 10.7554/elife.27455] [Citation(s) in RCA: 44] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2017] [Accepted: 11/17/2017] [Indexed: 11/13/2022] Open
Abstract
We present in vivo single-cell FRET measurements in the Escherichia coli chemotaxis system that reveal pervasive signaling variability, both across cells in isogenic populations and within individual cells over time. We quantify cell-to-cell variability of adaptation, ligand response, as well as steady-state output level, and analyze the role of network design in shaping this diversity from gene expression noise. In the absence of changes in gene expression, we find that single cells demonstrate strong temporal fluctuations. We provide evidence that such signaling noise can arise from at least two sources: (i) stochastic activities of adaptation enzymes, and (ii) receptor-kinase dynamics in the absence of adaptation. We demonstrate that under certain conditions, (ii) can generate giant fluctuations that drive signaling activity of the entire cell into a stochastic two-state switching regime. Our findings underscore the importance of molecular noise, arising not only in gene expression but also in protein networks.
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Affiliation(s)
| | | | | | | | - Thierry Emonet
- Department of Molecular, Cellular and Developmental BiologyYale UniversityNew HavenUnited States
- Department of PhysicsYale UniversityNew HavenUnited States
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Jia C, Xie P, Chen M, Zhang MQ. Stochastic fluctuations can reveal the feedback signs of gene regulatory networks at the single-molecule level. Sci Rep 2017; 7:16037. [PMID: 29167445 PMCID: PMC5700158 DOI: 10.1038/s41598-017-15464-9] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2017] [Accepted: 10/23/2017] [Indexed: 01/17/2023] Open
Abstract
Understanding the relationship between spontaneous stochastic fluctuations and the topology of the underlying gene regulatory network is of fundamental importance for the study of single-cell stochastic gene expression. Here by solving the analytical steady-state distribution of the protein copy number in a general kinetic model of stochastic gene expression with nonlinear feedback regulation, we reveal the relationship between stochastic fluctuations and feedback topology at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations. Based on such relationship, we also develop an effective method to extract the topological information of a gene regulatory network from single-cell gene expression data. The theory is demonstrated by numerical simulations and, more importantly, validated quantitatively by single-cell data analysis of a synthetic gene circuit integrated in human kidney cells.
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Affiliation(s)
- Chen Jia
- Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75080, USA
| | - Peng Xie
- Department of Biological Sciences, Center for Systems Biology, University of Texas at Dallas, Richardson, TX 75080, USA
| | - Min Chen
- Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75080, USA.
| | - Michael Q Zhang
- Department of Biological Sciences, Center for Systems Biology, University of Texas at Dallas, Richardson, TX 75080, USA.
- MOE Key Lab and Division of Bioinformatics, CSSB, TNLIST, Tsinghua University, Beijing, 100084, China.
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Janes KA, Chandran PL, Ford RM, Lazzara MJ, Papin JA, Peirce SM, Saucerman JJ, Lauffenburger DA. An engineering design approach to systems biology. Integr Biol (Camb) 2017; 9:574-583. [PMID: 28590470 PMCID: PMC6534349 DOI: 10.1039/c7ib00014f] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Measuring and modeling the integrated behavior of biomolecular-cellular networks is central to systems biology. Over several decades, systems biology has been shaped by quantitative biologists, physicists, mathematicians, and engineers in different ways. However, the basic and applied versions of systems biology are not typically distinguished, which blurs the separate aspirations of the field and its potential for real-world impact. Here, we articulate an engineering approach to systems biology, which applies educational philosophy, engineering design, and predictive models to solve contemporary problems in an age of biomedical Big Data. A concerted effort to train systems bioengineers will provide a versatile workforce capable of tackling the diverse challenges faced by the biotechnological and pharmaceutical sectors in a modern, information-dense economy.
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Affiliation(s)
- Kevin A Janes
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA 22908, USA.
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24
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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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Hilfinger A, Norman TM, Paulsson J. Exploiting Natural Fluctuations to Identify Kinetic Mechanisms in Sparsely Characterized Systems. Cell Syst 2016; 2:251-9. [PMID: 27135537 DOI: 10.1016/j.cels.2016.04.002] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2015] [Revised: 02/26/2016] [Accepted: 04/06/2016] [Indexed: 11/29/2022]
Abstract
From biochemistry to ecology, many biological systems are stochastic, complex, and sparsely characterized. In such systems, each component may respond to changes in any directly or indirectly connected components, thus requiring knowledge of the whole to predict the dynamics of the parts. Here, we address this challenge by deriving relations between properties of fluctuations that only reflect local interactions between a subset of components but are invariant to all indirectly connected dynamics. This greatly reduces the number of assumptions when evaluating dynamic models experimentally. We illustrate the approach by revisiting systematic single-cell gene expression data, and we show that the observed fluctuations contradict the assumptions made in most published models of stochastic gene expression, even when accounting for the possibility of systematic experimental artifacts.
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Affiliation(s)
- Andreas Hilfinger
- Department of Systems Biology, Harvard Medical School, 200 Longwood Avenue, Boston, MA 02115, USA.
| | - Thomas M Norman
- Department of Systems Biology, Harvard Medical School, 200 Longwood Avenue, Boston, MA 02115, USA
| | - Johan Paulsson
- Department of Systems Biology, Harvard Medical School, 200 Longwood Avenue, Boston, MA 02115, USA.
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