1
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Wang W, Camley BA. Limits on the accuracy of contact inhibition of locomotion. Phys Rev E 2024; 109:054408. [PMID: 38907435 PMCID: PMC11193850 DOI: 10.1103/physreve.109.054408] [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: 11/10/2023] [Accepted: 03/25/2024] [Indexed: 06/24/2024]
Abstract
Cells that collide with each other repolarize away from contact, in a process called contact inhibition of locomotion (CIL), which is necessary for correct development of the embryo. CIL can occur even when cells make a micron-scale contact with a neighbor-much smaller than their size. How precisely can a cell sense cell-cell contact and repolarize in the correct direction? What factors control whether a cell recognizes it has contacted a neighbor? We propose a theoretical model for the limits of CIL where cells recognize the presence of another cell by binding the protein ephrin with the Eph receptor. This recognition is made difficult by the presence of interfering ligands that bind nonspecifically. Both theoretical predictions and simulation results show that it becomes more difficult to sense cell-cell contact when it is difficult to distinguish ephrin from the interfering ligands, or when there are more interfering ligands, or when the contact width decreases. However, the error of estimating contact position remains almost constant when the contact width changes. This happens because the cell gains spatial information largely from the boundaries of cell-cell contact. We study using statistical decision theory the likelihood of a false-positive CIL event in the absence of cell-cell contact, and the likelihood of a false negative where CIL does not occur when another cell is present. Our results suggest that the cell is more likely to make incorrect decisions when the contact width is very small or so large that it nears the cell's perimeter. However, in general, we find that cells have the ability to make reasonably reliable CIL decisions even for very narrow (micron-scale) contacts, even if the concentration of interfering ligands is ten times that of the correct ligands.
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Affiliation(s)
- Wei Wang
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Brian A Camley
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
- Department of Biophysics, Johns Hopkins University, Baltimore, Maryland 21218, USA
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2
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How does an organism extract relevant information from transcription factor concentrations? Biochem Soc Trans 2022; 50:1365-1376. [DOI: 10.1042/bst20220333] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2022] [Revised: 08/16/2022] [Accepted: 08/17/2022] [Indexed: 11/17/2022]
Abstract
How does an organism regulate its genes? The involved regulation typically occurs in terms of a signal processing chain: an externally applied stimulus or a maternally supplied transcription factor leads to the expression of some downstream genes, which, in turn, are transcription factors for further genes. Especially during development, these transcription factors are frequently expressed in amounts where noise is still important; yet, the signals that they provide must not be lost in the noise. Thus, the organism needs to extract exactly relevant information in the signal. New experimental approaches involving single-molecule measurements at high temporal precision as well as increased precision in manipulations directly on the genome are allowing us to tackle this question anew. These new experimental advances mean that also from the theoretical side, theoretical advances should be possible. In this review, I will describe, specifically on the example of fly embryo gene regulation, how theoretical approaches, especially from inference and information theory, can help in understanding gene regulation. To do so, I will first review some more traditional theoretical models for gene regulation, followed by a brief discussion of information-theoretical approaches and when they can be applied. I will then introduce early fly development as an exemplary system where such information-theoretical approaches have traditionally been applied and can be applied; I will specifically focus on how one such method, namely the information bottleneck approach, has recently been used to infer structural features of enhancer architecture.
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3
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Kirby D, Rothschild J, Smart M, Zilman A. Pleiotropy enables specific and accurate signaling in the presence of ligand cross talk. Phys Rev E 2021; 103:042401. [PMID: 34005921 DOI: 10.1103/physreve.103.042401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2020] [Accepted: 02/22/2021] [Indexed: 12/27/2022]
Abstract
Living cells sense their environment through the binding of extracellular molecular ligands to cell surface receptors. Puzzlingly, vast numbers of signaling pathways exhibit a high degree of cross talk between different signals whereby different ligands act through the same receptor or shared components downstream. It remains unclear how a cell can accurately process information from the environment in such cross-wired pathways. We show that a feature which commonly accompanies cross talk-signaling pleiotropy (the ability of a receptor to produce multiple outputs)-offers a solution to the cross-talk problem. In a minimal model we show that a single pleiotropic receptor can simultaneously identify and accurately sense the concentrations of arbitrary unknown ligands present individually or in a mixture. We calculate the fundamental limits of the signaling specificity and accuracy of such signaling schemes. The model serves as an elementary "building block" toward understanding more complex cross-wired receptor-ligand signaling networks.
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Affiliation(s)
- Duncan Kirby
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
| | - Jeremy Rothschild
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
| | - Matthew Smart
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
| | - Anton Zilman
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada.,Institute for Bioengineering, University of Toronto, Toronto, Ontario M5S 3G9, Canada
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4
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Malaguti G, ten Wolde PR. Theory for the optimal detection of time-varying signals in cellular sensing systems. eLife 2021; 10:e62574. [PMID: 33594978 PMCID: PMC7946427 DOI: 10.7554/elife.62574] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2020] [Accepted: 02/12/2021] [Indexed: 11/29/2022] Open
Abstract
Living cells often need to measure chemical concentrations that vary in time, yet how accurately they can do so is poorly understood. Here, we present a theory that fully specifies, without any adjustable parameters, the optimal design of a canonical sensing system in terms of two elementary design principles: (1) there exists an optimal integration time, which is determined by the input statistics and the number of receptors; and (2) in the optimally designed system, the number of independent concentration measurements as set by the number of receptors and the optimal integration time equals the number of readout molecules that store these measurements and equals the work to store these measurements reliably; no resource is then in excess and hence wasted. Applying our theory to the Escherichia coli chemotaxis system indicates that its integration time is not only optimal for sensing shallow gradients but also necessary to enable navigation in these gradients.
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5
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Vennettilli M, Erez A, Mugler A. Multicellular sensing at a feedback-induced critical point. Phys Rev E 2020; 102:052411. [PMID: 33327087 DOI: 10.1103/physreve.102.052411] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2020] [Accepted: 10/06/2020] [Indexed: 11/07/2022]
Abstract
Feedback in sensory biochemical networks can give rise to bifurcations in cells' behavioral response. These bifurcations share many properties with thermodynamic critical points. Evidence suggests that biological systems may operate near these critical points, but the functional benefit of doing so remains poorly understood. Here we investigate a simple biochemical model with nonlinear feedback and multicellular communication to determine if criticality provides a functional benefit in terms of the ability to gain information about a stochastic chemical signal. We find that when signal fluctuations are slow, the mutual information between the signal and the intracellular readout is maximized at criticality, because the benefit of high signal susceptibility outweighs the detriment of high readout noise. When cells communicate, criticality gives rise to long-range correlations in readout molecule number among cells. Consequently, we find that communication increases the mutual information between a given cell's readout and the spatial average of the signal across the population. Finally, we find that both with and without communication, the sensory benefits of criticality compete with critical slowing down, such that the information rate, as opposed to the information itself, is minimized at the critical point. Our results reveal the costs and benefits of feedback-induced criticality for multicellular sensing.
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Affiliation(s)
- Michael Vennettilli
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Amir Erez
- Department of Molecular Biology, Princeton University, Princeton, New Jersey 08544, USA
- The Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel
| | - Andrew Mugler
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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6
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Abstract
The reliable detection of environmental molecules in the presence of noise is an important cellular function, yet the underlying computational mechanisms are not well understood. We introduce a model of two interacting sensors which allows for the principled exploration of signal statistics, cooperation strategies and the role of energy consumption in optimal sensing, quantified through the mutual information between the signal and the sensors. Here we report that in general the optimal sensing strategy depends both on the noise level and the statistics of the signals. For joint, correlated signals, energy consuming (nonequilibrium), asymmetric couplings result in maximum information gain in the low-noise, high-signal-correlation limit. Surprisingly we also find that energy consumption is not always required for optimal sensing. We generalise our model to incorporate time integration of the sensor state by a population of readout molecules, and demonstrate that sensor interaction and energy consumption remain important for optimal sensing. Cells exhibit exceptional chemical sensitivity, yet we haven’t fully understood how they achieve it. Here the authors consider the mutual information between signals and two coupled sensors as a proxy for sensing performance and show its optimisation depending on noise level and signal statistics.
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7
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Micali G, Endres RG. Maximal information transmission is compatible with ultrasensitive biological pathways. Sci Rep 2019; 9:16898. [PMID: 31729454 PMCID: PMC6858467 DOI: 10.1038/s41598-019-53273-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2018] [Accepted: 10/29/2019] [Indexed: 11/16/2022] Open
Abstract
Cells are often considered input-output devices that maximize the transmission of information by converting extracellular stimuli (input) via signaling pathways (communication channel) to cell behavior (output). However, in biological systems outputs might feed back into inputs due to cell motility, and the biological channel can change by mutations during evolution. Here, we show that the conventional channel capacity obtained by optimizing the input distribution for a fixed channel may not reflect the global optimum. In a new approach we analytically identify both input distributions and input-output curves that optimally transmit information, given constraints from noise and the dynamic range of the channel. We find a universal optimal input distribution only depending on the input noise, and we generalize our formalism to multiple outputs (or inputs). Applying our formalism to Escherichia coli chemotaxis, we find that its pathway is compatible with optimal information transmission despite the ultrasensitive rotary motors.
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Affiliation(s)
- Gabriele Micali
- Department of Life Sciences, Imperial College, London, UK.,Centre for Integrative Systems Biology and Bioinformatics, Imperial College, London, UK.,Department of Environmental Microbiology, Eawag, Dübendorf, Switzerland.,Department of Environmental Systems Science, ETH Zürich, Zürich, Switzerland
| | - Robert G Endres
- Department of Life Sciences, Imperial College, London, UK. .,Centre for Integrative Systems Biology and Bioinformatics, Imperial College, London, UK.
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8
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Byrd TA, Erez A, Vogel RM, Peterson C, Vennettilli M, Altan-Bonnet G, Mugler A. Critical slowing down in biochemical networks with feedback. Phys Rev E 2019; 100:022415. [PMID: 31574667 PMCID: PMC8499154 DOI: 10.1103/physreve.100.022415] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2019] [Indexed: 06/10/2023]
Abstract
Near a bifurcation point, the response time of a system is expected to diverge due to the phenomenon of critical slowing down. We investigate critical slowing down in well-mixed stochastic models of biochemical feedback by exploiting a mapping to the mean-field Ising universality class. We analyze the responses to a sudden quench and to continuous driving in the model parameters. In the latter case, we demonstrate that our class of models exhibits the Kibble-Zurek collapse, which predicts the scaling of hysteresis in cellular responses to gradual perturbations. We discuss the implications of our results in terms of the tradeoff between a precise and a fast response. Finally, we use our mapping to quantify critical slowing down in T cells, where the addition of a drug is equivalent to a sudden quench in parameter space.
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Affiliation(s)
- Tommy A. Byrd
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Amir Erez
- Department of Molecular Biology, Princeton University, Princeton, New Jersey 08544, USA
| | - Robert M. Vogel
- IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - Curtis Peterson
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Department of Physics and School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, USA
| | - Michael Vennettilli
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Grégoire Altan-Bonnet
- Immunodynamics Group, Cancer and Inflammation Program, National Cancer Institute, National Institutes of Health, Bethesda, Maryland 20814, USA
| | - Andrew Mugler
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
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9
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Carballo-Pacheco M, Desponds J, Gavrilchenko T, Mayer A, Prizak R, Reddy G, Nemenman I, Mora T. Receptor crosstalk improves concentration sensing of multiple ligands. Phys Rev E 2019; 99:022423. [PMID: 30934315 DOI: 10.1103/physreve.99.022423] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2018] [Indexed: 06/09/2023]
Abstract
Cells need to reliably sense external ligand concentrations to achieve various biological functions such as chemotaxis or signaling. The molecular recognition of ligands by surface receptors is degenerate in many systems, leading to crosstalk between ligand-receptor pairs. Crosstalk is often thought of as a deviation from optimal specific recognition, as the binding of noncognate ligands can interfere with the detection of the receptor's cognate ligand, possibly leading to a false triggering of a downstream signaling pathway. Here we quantify the optimal precision of sensing the concentrations of multiple ligands by a collection of promiscuous receptors. We demonstrate that crosstalk can improve precision in concentration sensing and discrimination tasks. To achieve superior precision, the additional information about ligand concentrations contained in short binding events of the noncognate ligand should be exploited. We present a proofreading scheme to realize an approximate estimation of multiple ligand concentrations that reaches a precision close to the derived optimal bounds. Our results help rationalize the observed ubiquity of receptor crosstalk in molecular sensing.
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Affiliation(s)
- Martín Carballo-Pacheco
- School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom
| | - Jonathan Desponds
- Department of Physics, University of California San Diego, La Jolla, CA 92093, USA
| | - Tatyana Gavrilchenko
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Andreas Mayer
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA
| | - Roshan Prizak
- Institute of Science and Technology Austria, Am Campus 1, A-3400, Klosterneuburg, Austria
| | - Gautam Reddy
- Department of Physics, University of California San Diego, La Jolla, CA 92093, USA
| | - Ilya Nemenman
- Department of Physics, Department of Biology, and Initiative in Theory and Modeling of Living Systems, Emory University, Atlanta, GA 30322, USA
| | - Thierry Mora
- Laboratoire de physique de l'École normale supérieure (PSL university), CNRS, Sorbonne University, and University Paris-Diderot, 75005 Paris, France
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10
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Precision in a rush: Trade-offs between reproducibility and steepness of the hunchback expression pattern. PLoS Comput Biol 2018; 14:e1006513. [PMID: 30307984 PMCID: PMC6198997 DOI: 10.1371/journal.pcbi.1006513] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Revised: 10/23/2018] [Accepted: 09/14/2018] [Indexed: 11/19/2022] Open
Abstract
Fly development amazes us by the precision and reproducibility of gene expression, especially since the initial expression patterns are established during very short nuclear cycles. Recent live imaging of hunchback promoter dynamics shows a stable steep binary expression pattern established within the three minute interphase of nuclear cycle 11. Considering expression models of different complexity, we explore the trade-off between the ability of a regulatory system to produce a steep boundary and minimize expression variability between different nuclei. We show how a limited readout time imposed by short developmental cycles affects the gene’s ability to read positional information along the embryo’s anterior posterior axis and express reliably. Comparing our theoretical results to real-time monitoring of the hunchback transcription dynamics in live flies, we discuss possible regulatory strategies, suggesting an important role for additional binding sites, gradients or non-equilibrium binding and modified transcription factor search strategies. Despite very limited time, organisms develop in reproducible ways. In the early stages of fly development the information about maternal signals is read out in a few minutes to produce steep and precise gene expression patterns. Motivated by recent live imaging experiments in fly embryos, we explore the consequences of the trade-off between a rushed but reproducible readout and a steep expression pattern on the regulatory modules of gene expression. We show that the current view of one anterior gradient morphogen binding to six binding sites is quantitatively inconsistent with the experimental data given the short readout time, suggesting other regulatory features.
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11
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Namba T, Shibata T. Propagation of regulatory fluctuations induces coordinated switching of flagellar motors in chemotaxis signaling pathway of single bacteria. J Theor Biol 2018; 454:367-375. [PMID: 29969599 DOI: 10.1016/j.jtbi.2018.06.023] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2018] [Revised: 06/25/2018] [Accepted: 06/27/2018] [Indexed: 01/14/2023]
Abstract
The random motion of E. coli is driven by multiple flagella motors. When all motors rotate in the counter clockwise direction, the bacteria swims smoothly. A recent experimental report by Terasawa et al. [Biophys J,100,2193,(2011)] demonstrated that a coordination of the motors can occur through signaling pathways, and perturbation of a regulatory molecule disrupted the coordination. Here, we develop a mathematical model to show that a large temporal fluctuation in the regulator concentration can induce a correlated switching of the multiple motors. Such a large fluctuation is generated by a chemotaxis receptor cluster in unilateral cell pole, which then exhibits a spatial propagation through the cytoplasm from the receptor position to the motor around cell periphery. Our numerical simulation successfully reproduces synchronized switching and the lag time in the motions of two distant motors, which has been observed experimentally. We further show that the large fluctuation in the regulator concentration at the motor positions can expand the dynamic range that the motor can respond, which confers robustness to the signaling system.
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Affiliation(s)
- Toshinori Namba
- Department of Mathematical and Life Sciences, Hiroshima University, Higashihiroshima, Japan; Research Center for the Mathematics on Chromatin Live Dynamics (RcMcD), Hiroshima University, Higashihiroshima, Japan
| | - Tatsuo Shibata
- Laboratory for Physical Biology, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan.
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12
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Waite AJ, Frankel NW, Emonet T. Behavioral Variability and Phenotypic Diversity in Bacterial Chemotaxis. Annu Rev Biophys 2018; 47:595-616. [PMID: 29618219 DOI: 10.1146/annurev-biophys-062215-010954] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Living cells detect and process external signals using signaling pathways that are affected by random fluctuations. These variations cause the behavior of individual cells to fluctuate over time (behavioral variability) and generate phenotypic differences between genetically identical individuals (phenotypic diversity). These two noise sources reduce our ability to predict biological behavior because they diversify cellular responses to identical signals. Here, we review recent experimental and theoretical advances in understanding the mechanistic origin and functional consequences of such variation in Escherichia coli chemotaxis-a well-understood model of signal transduction and behavior. After briefly summarizing the architecture and logic of the chemotaxis system, we discuss determinants of behavior and chemotactic performance of individual cells. Then, we review how cell-to-cell differences in protein abundance map onto differences in individual chemotactic abilities and how phenotypic variability affects the performance of the population. We conclude with open questions to be addressed by future research.
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Affiliation(s)
- Adam James Waite
- Department of Molecular, Cellular, and Developmental Biology, Yale University, New Haven, Connecticut 06520; .,Current affiliation: Calico Life Sciences, LLC, South San Francisco, California 94080
| | - Nicholas W Frankel
- Department of Molecular, Cellular, and Developmental Biology, Yale University, New Haven, Connecticut 06520; .,Department of Cellular and Molecular Pharmacology, University of California, San Francisco, California 94158
| | - Thierry Emonet
- Department of Molecular, Cellular, and Developmental Biology, Yale University, New Haven, Connecticut 06520; .,Department of Physics, Yale University, New Haven, Connecticut 06520
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13
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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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14
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Samanta S, Layek R, Kar S, Raj MK, Mukhopadhyay S, Chakraborty S. Predicting Escherichia coli's chemotactic drift under exponential gradient. Phys Rev E 2017; 96:032409. [PMID: 29346905 DOI: 10.1103/physreve.96.032409] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2017] [Indexed: 06/07/2023]
Abstract
Bacterial species are known to show chemotaxis, i.e., the directed motions in the presence of certain chemicals, whereas the motion is random in the absence of those chemicals. The bacteria modulate their run time to induce chemotactic drift towards the attractant chemicals and away from the repellent chemicals. However, the existing theoretical knowledge does not exhibit a proper match with experimental validation, and hence there is a need for developing alternate models and validating experimentally. In this paper a more robust theoretical model is proposed to investigate chemotactic drift of peritrichous Escherichia coli under an exponential nutrient gradient. An exponential gradient is used to understand the steady state behavior of drift because of the logarithmic functionality of the chemosensory receptors. Our theoretical estimations are validated through the experimentation and simulation results. Thus, the developed model successfully delineates the run time, run trajectory, and drift velocity as measured from the experiments.
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Affiliation(s)
- Sibendu Samanta
- Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Kharagpur WB-721302, India
| | - Ritwik Layek
- Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Kharagpur WB-721302, India
| | - Shantimoy Kar
- Advanced Technology Development Centre, Indian Institute of Technology, Kharagpur WB-721302, India
| | - M Kiran Raj
- Advanced Technology Development Centre, Indian Institute of Technology, Kharagpur WB-721302, India
| | - Sudipta Mukhopadhyay
- Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Kharagpur WB-721302, India
| | - Suman Chakraborty
- Advanced Technology Development Centre, Indian Institute of Technology, Kharagpur WB-721302, India
- Department of Mechanical Engineering, Microfluidic Laboratory, Indian Institute of Technology, Kharagpur WB-721302, India
- School of Medical Science and Technology, Indian Institute of Technology, Kharagpur WB-721302, India
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15
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Deshpande A, Samanta S, Das H, Layek RK. A Boolean approach to bacterial chemotaxis. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2017; 2016:6125-6129. [PMID: 28269650 DOI: 10.1109/embc.2016.7592126] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Bacterium such as Escherichia coli (E. coli) show biased Brownian motion in different chemical concentration gradients. This chemical sensitive motility or chemotaxis has gained considerable interest among scientists for some remarkable features such as chemo-sensory dynamic range, adaptation, diffusion and drift. A Boolean model of the whole chemotaxis process has been developed in this manuscript. The response of the circuit is in accordance with the experimental results available in the literature, providing indirect validation of the model. This simple Boolean network (BN) can be easily integrated into the paradigm of modular whole cell modelling. Another crucial application is in designing bio-inspired micro-robots to detect certain spatio-temporal chemical signatures.
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16
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Topologically protected modes in non-equilibrium stochastic systems. Nat Commun 2017; 8:13881. [PMID: 28071644 PMCID: PMC5234070 DOI: 10.1038/ncomms13881] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2016] [Accepted: 11/08/2016] [Indexed: 12/02/2022] Open
Abstract
Non-equilibrium driving of biophysical processes is believed to enable their robust functioning despite the presence of thermal fluctuations and other sources of disorder. Such robust functions include sensory adaptation, enhanced enzymatic specificity and maintenance of coherent oscillations. Elucidating the relation between energy consumption and organization remains an important and open question in non-equilibrium statistical mechanics. Here we report that steady states of systems with non-equilibrium fluxes can support topologically protected boundary modes that resemble similar modes in electronic and mechanical systems. Akin to their electronic and mechanical counterparts, topological-protected boundary steady states in non-equilibrium systems are robust and are largely insensitive to local perturbations. We argue that our work provides a framework for how biophysical systems can use non-equilibrium driving to achieve robust function. Energy dissipation characterizes the states far from equilibrium, whilst how it affects the local organization remains elusive. Here, Murugan et al. show that the non-equilibrium systems exhibit topologically protected boundary modes that have been known in electronic and mechanical systems.
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17
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Roob E, Trendel N, Rein Ten Wolde P, Mugler A. Cooperative Clustering Digitizes Biochemical Signaling and Enhances its Fidelity. Biophys J 2016; 110:1661-1669. [PMID: 27074690 DOI: 10.1016/j.bpj.2016.02.031] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2015] [Revised: 02/04/2016] [Accepted: 02/22/2016] [Indexed: 10/21/2022] Open
Abstract
Many membrane-bound molecules in cells form small clusters. It has been hypothesized that these clusters convert an analog extracellular signal into a digital intracellular signal and that this conversion increases signaling fidelity. However, the mechanism by which clusters digitize a signal and the subsequent effects on fidelity remain poorly understood. Here we demonstrate using a stochastic model of cooperative cluster formation that sufficient cooperation leads to digital signaling. We show that despite reducing the number of output states, which decreases fidelity, digitization also reduces noise in the system, which increases fidelity. The tradeoff between these effects leads to an optimal cluster size that agrees with experimental measurements.
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Affiliation(s)
- Edward Roob
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana
| | - Nicola Trendel
- Systems Biology Doctoral Training Centre, University of Oxford, Oxford, United Kingdom; FOM Institute AMOLF, Amsterdam, the Netherlands
| | | | - Andrew Mugler
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana; FOM Institute AMOLF, Amsterdam, the Netherlands.
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18
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19
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Fundamental constraints on the abundances of chemotaxis proteins. Biophys J 2016; 108:1293-305. [PMID: 25762341 DOI: 10.1016/j.bpj.2015.01.024] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2014] [Revised: 01/25/2015] [Accepted: 01/28/2015] [Indexed: 01/01/2023] Open
Abstract
Flagellated bacteria, such as Escherichia coli, perform directed motion in gradients of concentration of attractants and repellents in a process called chemotaxis. The E. coli chemotaxis signaling pathway is a model for signal transduction, but it has unique features. We demonstrate that the need for fast signaling necessitates high abundances of the proteins involved in this pathway. We show that further constraints on the abundances of chemotaxis proteins arise from the requirements of self-assembly both of flagellar motors and of chemoreceptor arrays. All these constraints are specific to chemotaxis, and published data confirm that chemotaxis proteins tend to be more highly expressed than their homologs in other pathways. Employing a chemotaxis pathway model, we show that the gain of the pathway at the level of the response regulator CheY increases with overall chemotaxis protein abundances. This may explain why, at least in one E. coli strain, the abundance of all chemotaxis proteins is higher in media with lower nutrient content. We also demonstrate that the E. coli chemotaxis pathway is particularly robust to abundance variations of the motor protein FliM.
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20
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Abstract
Specific conformations of signaling proteins can serve as “signals” in signal transduction by being recognized by receptors.
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Affiliation(s)
- Peter Tompa
- VIB Structural Biology Research Center (SBRC)
- Brussels
- Belgium
- Vrije Universiteit Brussel
- Brussels
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21
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Barato AC, Seifert U. Dispersion for two classes of random variables: general theory and application to inference of an external ligand concentration by a cell. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032127. [PMID: 26465446 DOI: 10.1103/physreve.92.032127] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2015] [Indexed: 06/05/2023]
Abstract
We derive expressions for the dispersion for two classes of random variables in Markov processes. Random variables such as current and activity pertain to the first class, which is composed of random variables that change whenever a jump in the stochastic trajectory occurs. The second class corresponds to the time the trajectory spends in a state (or cluster of states). While the expression for the first class follows straightforwardly from known results in the literature, we show that a similar formalism can be used to derive an expression for the second class. As an application, we use this formalism to analyze a cellular two-component network estimating an external ligand concentration. The uncertainty related to this external concentration is calculated by monitoring different random variables related to an internal protein. We show that, inter alia, monitoring the time spent in the phosphorylated state of the protein leads to a finite uncertainty only if there is dissipation, whereas the uncertainty obtained from the activity of the transitions of the internal protein can reach the Berg-Purcell limit even in equilibrium.
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Affiliation(s)
- Andre C Barato
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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22
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Yaron T, Cordova Y, Sprinzak D. Juxtacrine signaling is inherently noisy. Biophys J 2015; 107:2417-24. [PMID: 25418310 DOI: 10.1016/j.bpj.2014.10.006] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2014] [Revised: 09/28/2014] [Accepted: 10/01/2014] [Indexed: 10/24/2022] Open
Abstract
Juxtacrine signaling is an important class of signaling systems that plays a crucial role in various developmental processes ranging from coordination of differentiation between neighboring cells to guiding axon growth during neurogenesis. Such signaling systems rely on the interaction between receptors on one cell and trans-membrane ligands on the membrane of a neighboring cell. Like other signaling systems, the ability of signal-receiving cells to accurately determine the concentration of ligands, is affected by stochastic diffusion processes. However, it is not clear how restriction of ligand movement to the two-dimensional (2D) cell membrane in juxtacrine signaling affects the accuracy of ligand sensing. In this study, we use a statistical mechanics approach, to show that long integration times, from around one second to several hours, are required to reach high-sensing accuracy (better than 10%). Surprisingly, the accuracy of sensing cannot be significantly improved, neither by increasing the number of receptors above three to five receptors per contact area, nor by increasing the contact area between cells. We show that these results impose stringent constraints on the dynamics of processes relying on juxtacrine signaling systems, such as axon guidance mediated by Ephrins and developmental patterns mediated by the Notch pathway.
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Affiliation(s)
- Tomer Yaron
- Department of Biochemistry and Molecular Biology, Faculty of Life Sciences, Tel-Aviv University, Tel Aviv, Israel
| | - Yossi Cordova
- Department of Biochemistry and Molecular Biology, Faculty of Life Sciences, Tel-Aviv University, Tel Aviv, Israel; Hemda Center for Science Education, 7 Ha Pardes St., Tel Aviv, Israel
| | - David Sprinzak
- Department of Biochemistry and Molecular Biology, Faculty of Life Sciences, Tel-Aviv University, Tel Aviv, Israel.
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23
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Sevier SA, Levine H. Properties of cooperatively induced phases in sensing models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052707. [PMID: 26066199 DOI: 10.1103/physreve.91.052707] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2014] [Indexed: 06/04/2023]
Abstract
A large number of eukaryotic cells are able to directly detect external chemical gradients with great accuracy and the ultimate limit to their sensitivity has been a topic of debate for many years. Previous work has been done to understand many aspects of this process but little attention has been paid to the possibility of emergent sensing states. Here we examine how cooperation between sensors existing in a two-dimensional network, as they do on the cell's surface, can both enhance and fundamentally alter the response of the cell to a spatially varying signal. We show that weakly interacting sensors linearly amplify the cell's response to an external gradient while a network of strongly interacting sensors form a collective nonlinear response with two separate domains of active and inactive sensors forming what have called a "1/2-state." In our analysis we examine the cell's ability to sense the direction of a signal and pay special attention to the substantially different behavior realized in the strongly interacting regime.
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Affiliation(s)
- Stuart A Sevier
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Herbert Levine
- Department of Bioengineering, Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
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24
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Zamparo M, Chianale F, Tebaldi C, Cosentino-Lagomarsino M, Nicodemi M, Gamba A. Dynamic membrane patterning, signal localization and polarity in living cells. SOFT MATTER 2015; 11:838-849. [PMID: 25563791 DOI: 10.1039/c4sm02157f] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We review the molecular and physical aspects of the dynamic localization of signaling molecules on the plasma membranes of living cells. At the nanoscale, clusters of receptors and signaling proteins play an essential role in the processing of extracellular signals. At the microscale, "soft" and highly dynamic signaling domains control the interaction of individual cells with their environment. At the multicellular scale, individual polarity patterns control the forces that shape multicellular aggregates and tissues.
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Affiliation(s)
- M Zamparo
- Human Genetics Foundation - Torino, Italy.
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25
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Chemodetection in fluctuating environments: receptor coupling, buffering, and antagonism. Proc Natl Acad Sci U S A 2015; 112:1898-903. [PMID: 25624502 DOI: 10.1073/pnas.1420903112] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Variability in the chemical composition of the extracellular environment can significantly degrade the ability of cells to detect rare cognate ligands. Using concepts from statistical detection theory, we formalize the generic problem of detection of small concentrations of ligands in a fluctuating background of biochemically similar ligands binding to the same receptors. We discover that in contrast with expectations arising from considerations of signal amplification, inhibitory interactions between receptors can improve detection performance in the presence of substantial environmental variability, providing an adaptive interpretation to the phenomenon of ligand antagonism. Our results suggest that the structure of signaling pathways responsible for chemodetection in fluctuating and heterogeneous environments might be optimized with respect to the statistics and dynamics of environmental composition. The developed formalism stresses the importance of characterizing nonspecific interactions to understand function in signaling pathways.
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26
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Govern CC, ten Wolde PR. Energy dissipation and noise correlations in biochemical sensing. PHYSICAL REVIEW LETTERS 2014; 113:258102. [PMID: 25554909 DOI: 10.1103/physrevlett.113.258102] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2014] [Indexed: 05/18/2023]
Abstract
To measure chemical concentrations, cells need to extract information from stochastic receptor signals via signaling networks which are also inherently stochastic. Here, we study how the accuracy of sensing depends on the correlations between these extrinsic and intrinsic sources of noise. We find that the sensing precision of signaling networks that are not driven out of equilibrium is fundamentally limited by the fluctuation-dissipation theorem, which generates a tradeoff between the removal of extrinsic and intrinsic noise. As a result, the sensing precision of equilibrium systems is limited by the number of receptors; the downstream network can never improve sensing. To lift the tradeoff, energy dissipation is essential. This allows the receptor to transduce the signal as a catalyst and enables time integration of the receptor state. To beat the sensing limit of equilibrium systems, a canonical nonequilibrium signaling network based on the push-pull motif needs to dissipate at least 1k_{B}T per receptor.
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27
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Haselwandter CA, Wingreen NS. The role of membrane-mediated interactions in the assembly and architecture of chemoreceptor lattices. PLoS Comput Biol 2014; 10:e1003932. [PMID: 25503274 PMCID: PMC4263354 DOI: 10.1371/journal.pcbi.1003932] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2014] [Accepted: 09/22/2014] [Indexed: 01/04/2023] Open
Abstract
In vivo fluorescence microscopy and electron cryo-tomography have revealed that chemoreceptors self-assemble into extended honeycomb lattices of chemoreceptor trimers with a well-defined relative orientation of trimers. The signaling response of the observed chemoreceptor lattices is remarkable for its extreme sensitivity, which relies crucially on cooperative interactions among chemoreceptor trimers. In common with other membrane proteins, chemoreceptor trimers are expected to deform the surrounding lipid bilayer, inducing membrane-mediated anisotropic interactions between neighboring trimers. Here we introduce a biophysical model of bilayer-chemoreceptor interactions, which allows us to quantify the role of membrane-mediated interactions in the assembly and architecture of chemoreceptor lattices. We find that, even in the absence of direct protein-protein interactions, membrane-mediated interactions can yield assembly of chemoreceptor lattices at very dilute trimer concentrations. The model correctly predicts the observed honeycomb architecture of chemoreceptor lattices as well as the observed relative orientation of chemoreceptor trimers, suggests a series of “gateway” states for chemoreceptor lattice assembly, and provides a simple mechanism for the localization of large chemoreceptor lattices to the cell poles. Our model of bilayer-chemoreceptor interactions also helps to explain the observed dependence of chemotactic signaling on lipid bilayer properties. Finally, we consider the possibility that membrane-mediated interactions might contribute to cooperativity among neighboring chemoreceptor trimers. The chemotaxis system allows bacteria to respond to minute changes in chemical concentration, and serves as a paradigm for biological signal processing and the self-assembly of large protein lattices in living cells. The sensitivity of the chemotaxis system relies crucially on cooperative interactions among chemoreceptor trimers, which are organized into intricate honeycomb lattices. Chemoreceptors are membrane proteins and, hence, are expected to deform the surrounding lipid bilayer, leading to membrane-mediated interactions between chemoreceptor trimers. Using a biophysical model of bilayer-chemoreceptor interactions we show that the membrane-mediated interactions induced by chemoreceptor trimers provide a mechanism for the observed self-assembly of chemoreceptor lattices. We find that the directionality of membrane-mediated interactions between trimers complements protein-protein interactions in the stabilization of the observed honeycomb architecture of chemoreceptor lattices. Our results suggest that the symmetry of membrane protein complexes such as chemoreceptor trimers is reflected in the anisotropy of membrane-mediated interactions, yielding a general mechanism for the self-assembly of ordered protein lattices in cell membranes.
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Affiliation(s)
- Christoph A. Haselwandter
- Departments of Physics & Astronomy and Biological Sciences, University of Southern California, Los Angeles, California, United States of America
- * E-mail: (CAH); (NSW)
| | - Ned S. Wingreen
- Department of Molecular Biology, Princeton University, Princeton, New Jersey, United States of America
- * E-mail: (CAH); (NSW)
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28
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Clausznitzer D, Micali G, Neumann S, Sourjik V, Endres RG. Predicting chemical environments of bacteria from receptor signaling. PLoS Comput Biol 2014; 10:e1003870. [PMID: 25340783 PMCID: PMC4207464 DOI: 10.1371/journal.pcbi.1003870] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2014] [Accepted: 08/19/2014] [Indexed: 11/19/2022] Open
Abstract
Sensory systems have evolved to respond to input stimuli of certain statistical properties, and to reliably transmit this information through biochemical pathways. Hence, for an experimentally well-characterized sensory system, one ought to be able to extract valuable information about the statistics of the stimuli. Based on dose-response curves from in vivo fluorescence resonance energy transfer (FRET) experiments of the bacterial chemotaxis sensory system, we predict the chemical gradients chemotactic Escherichia coli cells typically encounter in their natural environment. To predict average gradients cells experience, we revaluate the phenomenological Weber's law and its generalizations to the Weber-Fechner law and fold-change detection. To obtain full distributions of gradients we use information theory and simulations, considering limitations of information transmission from both cell-external and internal noise. We identify broad distributions of exponential gradients, which lead to log-normal stimuli and maximal drift velocity. Our results thus provide a first step towards deciphering the chemical nature of complex, experimentally inaccessible cellular microenvironments, such as the human intestine. Outside the laboratory, bacteria live in complex microenvironments characterized by competition for space and available nutrients. Although often inaccessible by experiments, understanding the spatio-temporal dynamics of bacterial microenvironments is biomedically important. For instance, the chemical environment that symbiotic Escherichia coli encounter in the human gut relates to health of the gastrointestinal tract, gut metabolism, immune response, and tissue homeostasis. Other complex microenvironments include soil and biofilms. Assuming that bacterial sensory systems have evolved to optimally sense typical gradients, we treat signaling data, the signaling pathway with its architecture and reaction rates, and computer simulations of swimming bacteria in different gradients as “prior knowledge” to “reverse engineer” E. coli's habitat. Our identified gradients are exponentially shaped with wide-ranging rate values. These microenvironments most likely stem from local fluctuating nutrient sources and degradation by competing species, in which bacteria have evolved to swim with optimal performance.
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Affiliation(s)
- Diana Clausznitzer
- Department of Life Sciences, Imperial College, London, United Kingdom
- Centre for Integrative Systems Biology and Bioinformatics, Imperial College, London, United Kingdom
- BioQuant, Heidelberg University, Heidelberg, Germany
- Institute for Medical Informatics and Biometry, Technische Universität Dresden, Dresden, Germany
| | - Gabriele Micali
- Department of Life Sciences, Imperial College, London, United Kingdom
- Centre for Integrative Systems Biology and Bioinformatics, Imperial College, London, United Kingdom
| | - Silke Neumann
- Centre of Molecular Biology, Heidelberg University, DKFZ-ZMBH Alliance, Heidelberg, Germany
| | - Victor Sourjik
- Centre of Molecular Biology, Heidelberg University, DKFZ-ZMBH Alliance, Heidelberg, Germany
- Max Planck Institute for Terrestrial Microbiology, Marburg, Germany
| | - Robert G. Endres
- Department of Life Sciences, Imperial College, London, United Kingdom
- Centre for Integrative Systems Biology and Bioinformatics, Imperial College, London, United Kingdom
- * E-mail:
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29
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Hu B, Rappel WJ, Levine H. How input noise limits biochemical sensing in ultrasensitive systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032702. [PMID: 25314468 PMCID: PMC4457451 DOI: 10.1103/physreve.90.032702] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2014] [Indexed: 06/04/2023]
Abstract
Many biological processes are regulated by molecular devices that respond in an ultrasensitive fashion to upstream signals. An important question is whether such ultrasensitivity improves or limits its ability to read out the (noisy) input stimuli. Here, we develop a simple model to study the statistical properties of ultrasensitive signaling systems. We demonstrate that the output sensory noise is always bounded, in contrast to earlier theories using the small noise approximation, which tends to overestimate the impact of noise in ultrasensitive pathways. Our analysis also shows that the apparent sensitivity of the system is ultimately constrained by the input signal-to-noise ratio. Thus, ultrasensitivity can improve the precision of biochemical sensing only to a finite extent. This corresponds to a new limit for ultrasensitive signaling systems, which is strictly tighter than the Berg-Purcell limit.
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Affiliation(s)
- Bo Hu
- IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598, USA
| | - Wouter-Jan Rappel
- Center for Theoretical Biological Physics, University of California San Diego, La Jolla, California 92093-0319, USA
| | - Herbert Levine
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
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30
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Chang Q, Zuo L. The biophysical model for accuracy of cellular sensing spatial gradients of multiple chemoattractants. Phys Biol 2013; 10:056014. [PMID: 24104469 DOI: 10.1088/1478-3975/10/5/056014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Spatial gradients of surrounding chemoattractants are the key factors in determining the directionality of eukaryotic cell movement. Thus, it is important for cells to accurately measure the spatial gradients of surrounding chemoattractants. Here, we study the precision of sensing the spatial gradients of multiple chemoattractants using cooperative receptor clusters. Cooperative receptors on cells are modeled as an Ising chain of Monod-Wyman-Changeux clusters subject to multiple chemical-gradient fields to study the physical limits of multiple chemoattractants spatial gradients sensing. We found that eukaryotic cells cannot sense each chemoattractant gradient individually. Instead, cells can only sense a weighted sum of surrounding chemical gradients. Moreover, the precision of sensing one chemical gradient is signicantly affected by coexisting chemoattractant concentrations. These findings can provide a further insight into the role of chemoattractants in immune response and help develop novel treatments for inflammatory diseases.
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Affiliation(s)
- Qiang Chang
- Chinese Academy of Sciences-Max Plank Society Partner Institute for Computational Biology Shanghai Institute for Biological Sciences, Shanghai 200031, People's Republic of China. Department of Chemistry, University of Virginia, Charlottesville, VA 22904, USA
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31
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Skoge M, Naqvi S, Meir Y, Wingreen NS. Chemical sensing by nonequilibrium cooperative receptors. PHYSICAL REVIEW LETTERS 2013; 110:248102. [PMID: 25165963 PMCID: PMC4114058 DOI: 10.1103/physrevlett.110.248102] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2012] [Indexed: 05/25/2023]
Abstract
Cooperativity arising from local interactions in equilibrium receptor systems provides gain, but does not increase sensory performance, as measured by the signal-to-noise ratio (SNR) due to a fundamental tradeoff between gain and intrinsic noise. Here we allow sensing to be a nonequilibrium process and show that energy dissipation cannot circumvent the fundamental tradeoff, so that the SNR is still optimal for independent receptors. For systems requiring high gain, nonequilibrium 2D-coupled receptors maximize the SNR, revealing a new design principle for biological sensors.
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Affiliation(s)
- Monica Skoge
- Department of Biology, University of California, San Diego, La Jolla, California 92093-0319, USA
| | - Sahin Naqvi
- Department of Molecular Biology, Princeton University, Princeton, New Jersey 08544, USA
| | - Yigal Meir
- Department of Physics, Ben-Gurion University, Beer Sheva 84105, Israel
| | - Ned S. Wingreen
- Department of Molecular Biology, Princeton University, Princeton, New Jersey 08544, USA
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32
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Piasta KN, Ulliman CJ, Slivka PF, Crane BR, Falke JJ. Defining a key receptor-CheA kinase contact and elucidating its function in the membrane-bound bacterial chemosensory array: a disulfide mapping and TAM-IDS Study. Biochemistry 2013; 52:3866-80. [PMID: 23668882 DOI: 10.1021/bi400385c] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The three core components of the ubiquitous bacterial chemosensory array - the transmembrane chemoreceptor, the histidine kinase CheA, and the adaptor protein CheW - assemble to form a membrane-bound, hexagonal lattice in which receptor transmembrane signals regulate kinase activity. Both the regulatory domain of the kinase and the adaptor protein bind to overlapping sites on the cytoplasmic tip of the receptor (termed the protein interaction region). Notably, the kinase regulatory domain and the adaptor protein share the same fold constructed of two SH3-like domains. The present study focuses on the structural interface between the receptor and the kinase regulatory domain. Two models have been proposed for this interface: Model 1 is based on the crystal structure of a homologous Thermotoga complex between a receptor fragment and the CheW adaptor protein. This model has been used in current models of chemosensory array architecture to build the receptor-CheA kinase interface. Model 2 is based on a newly determined crystal structure of a homologous Thermotoga complex between a receptor fragment and the CheA kinase regulatory domain. Both models present unique strengths and weaknesses, and current evidence is unable to resolve which model best describes contacts in the native chemosensory arrays of Escherichia coli, Salmonella typhimurium, and other bacteria. Here we employ disulfide mapping and tryptophan and alanine mutation to identify docking sites (TAM-IDS) to test Models 1 and 2 in well-characterized membrane-bound arrays formed from E. coli and S. typhimurium components. The results reveal that the native array interface between the receptor protein interaction region and the kinase regulatory domain is accurately described by Model 2, but not by Model 1. In addition, the results show that the interface possesses both a structural function that contributes to stable CheA kinase binding in the array and a regulatory function central to transmission of the activation signal from receptor to CheA kinase. On-off switching alters the disulfide formation rates of specific Cys pairs at the interface, but not most Cys pairs, indicating that signaling perturbs localized regions of the interface. The findings suggest a simple model for the rearrangement of the interface triggered by the attractant signal and for longer range transmission of the signal in the chemosensory array.
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Affiliation(s)
- Kene N Piasta
- Department of Chemistry and Biochemistry and the Molecular Biophysics Program, University of Colorado , Boulder, Colorado 80309-0215, United States
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33
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Spatial partitioning improves the reliability of biochemical signaling. Proc Natl Acad Sci U S A 2013; 110:5927-32. [PMID: 23530194 DOI: 10.1073/pnas.1218301110] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
Spatial heterogeneity is a hallmark of living systems, even at the molecular scale in individual cells. A key example is the partitioning of membrane-bound proteins via lipid domain formation or cytoskeleton-induced corralling. However, the impact of this spatial heterogeneity on biochemical signaling processes is poorly understood. Here, we demonstrate that partitioning improves the reliability of biochemical signaling. We exactly solve a stochastic model describing a ubiquitous motif in membrane signaling. The solution reveals that partitioning improves signaling reliability via two effects: it moderates the nonlinearity of the switching response, and it reduces noise in the response by suppressing correlations between molecules. An optimal partition size arises from a trade-off between minimizing the number of proteins per partition to improve signaling reliability and ensuring sufficient proteins per partition to maintain signal propagation. The predicted optimal partition size agrees quantitatively with experimentally observed systems. These results persist in spatial simulations with explicit diffusion barriers. Our findings suggest that molecular partitioning is not merely a consequence of the complexity of cellular substructures, but also plays an important functional role in cell signaling.
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34
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Berezhkovskii AM, Dagdug L, Vazquez MV, Lizunov VA, Zimmerberg J, Bezrukov SM. Trapping of diffusing particles by clusters of absorbing disks on a reflecting wall with disk centers on sites of a square lattice. J Chem Phys 2013; 138:064105. [PMID: 23425459 DOI: 10.1063/1.4790370] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A simple approximate formula is derived for the rate constant that describes steady-state flux of diffusing particles through a cluster of perfectly absorbing disks on the otherwise reflecting flat wall, assuming that the disk centers occupy neighboring sites of a square lattice. A distinctive feature of trapping by a disk cluster is that disks located at the cluster periphery shield the disks in the center of the cluster. This competition of the disks for diffusing particles makes it impossible to find an exact analytical solution for the rate constant in the general case. To derive the approximate formula, we use a recently suggested approach [A. M. Berezhkovskii, L. Dagdug, V. A. Lizunov, J. Zimmerberg, and S. M. Bezrukov, J. Chem. Phys. 136, 211102 (2012)], which is based on the replacement of the disk cluster by an effective uniform partially absorbing spot. The formula shows how the rate constant depends on the size and shape of the cluster. To check the accuracy of the formula, we compare its predictions with the values of the rate constant obtained from Brownian dynamics simulations. The comparison made for 18 clusters of various shapes and sizes shows good agreement between the theoretical predictions and numerical results.
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Affiliation(s)
- Alexander M Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Division for Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA
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35
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Govern CC, ten Wolde PR. Fundamental limits on sensing chemical concentrations with linear biochemical networks. PHYSICAL REVIEW LETTERS 2012; 109:218103. [PMID: 23215617 DOI: 10.1103/physrevlett.109.218103] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2012] [Indexed: 06/01/2023]
Abstract
Living cells often need to extract information from biochemical signals that are noisy. We study how accurately cells can measure chemical concentrations with signaling networks that are linear. For stationary signals of long duration, they can reach, but not beat, the Berg-Purcell limit, which relies on uniformly averaging in time the fluctuations in the input signal. For short times or nonstationary signals, however, they can beat the Berg-Purcell limit, by nonuniformly time averaging the input. We derive the optimal weighting function for time averaging and use it to provide the fundamental limit of measuring chemical concentrations with linear signaling networks.
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36
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Berezhkovskii AM, Dagdug L, Lizunov VA, Zimmerberg J, Bezrukov SM. Communication: Clusters of absorbing disks on a reflecting wall: competition for diffusing particles. J Chem Phys 2012; 136:211102. [PMID: 22697521 DOI: 10.1063/1.4726015] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Trapping of diffusing particles by a cluster of absorbing disks on the otherwise reflecting wall is a manifestly many-body problem because of the disk competition for the particles. By replacing the cluster with an effective uniformly absorbing spot, we derive a simple formula for the rate constant that characterizes the trapping. The formula shows how the rate constant depends on the size and shape of the cluster.
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Affiliation(s)
- Alexander M Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Division for Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA
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