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Cole J, Schulman R. Limiting the Broadcast Range of a Secreting Cell during Intercellular Signaling Using Protease-Mediated Degradation. ACS Synth Biol 2024; 13:2019-2028. [PMID: 38885472 DOI: 10.1021/acssynbio.4c00042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/20/2024]
Abstract
Synthetic biology is revolutionizing our approaches to biocomputing, diagnostics, and environmental monitoring through the use of designed genetic circuits that perform a function within a single cell. More complex functions can be performed by multiple cells that coordinate as they perform different subtasks. Cell-cell communication using molecular signals is particularly suited for aiding in this communication, but the number of molecules that can be used in different communication channels is limited. Here we investigate how proteases can limit the broadcast range of communicating cells. We find that adding barrierpepsin to Saccharomyces cerevisiae cells in two-dimensional multicellular networks that use α-factor signaling prevents cells beyond a specific radius from responding to α-factor signals. Such limiting of the broadcast range of cells could allow multiple cells to use the same signaling molecules to direct different communication processes and functions, provided that they are far enough from one another. These results suggest a means by which complex synthetic cellular networks using only a few signals for communication could be created by structuring a community of cells to create distinct broadcast environments.
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Affiliation(s)
- Joshua Cole
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Rebecca Schulman
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
- Department of Computer Science, Johns Hopkins University, Baltimore, Maryland 21218, United States
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States
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2
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Guan K, Curtis ER, Lew DJ, Elston TC. Particle-based simulations reveal two positive feedback loops allow relocation and stabilization of the polarity site during yeast mating. PLoS Comput Biol 2023; 19:e1011523. [PMID: 37782676 PMCID: PMC10569529 DOI: 10.1371/journal.pcbi.1011523] [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: 05/04/2023] [Revised: 10/12/2023] [Accepted: 09/17/2023] [Indexed: 10/04/2023] Open
Abstract
Many cells adjust the direction of polarized growth or migration in response to external directional cues. The yeast Saccharomyces cerevisiae orient their cell fronts (also called polarity sites) up pheromone gradients in the course of mating. However, the initial polarity site is often not oriented towards the eventual mating partner, and cells relocate the polarity site in an indecisive manner before developing a stable orientation. During this reorientation phase, the polarity site displays erratic assembly-disassembly behavior and moves around the cell cortex. The mechanisms underlying this dynamic behavior remain poorly understood. Particle-based simulations of the core polarity circuit revealed that molecular-level fluctuations are unlikely to overcome the strong positive feedback required for polarization and generate relocating polarity sites. Surprisingly, inclusion of a second pathway that promotes polarity site orientation generated relocating polarity sites with properties similar to those observed experimentally. This pathway forms a second positive feedback loop involving the recruitment of receptors to the cell membrane and couples polarity establishment to gradient sensing. This second positive feedback loop also allows cells to stabilize their polarity site once the site is aligned with the pheromone gradient.
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Affiliation(s)
- Kaiyun Guan
- Curriculum in Bioinformatics and Computational Biology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
| | - Erin R. Curtis
- Department of Biology, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - Daniel J. Lew
- Department of Biology, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - Timothy C. Elston
- Department of Pharmacology and Computational Medicine Program, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
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3
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Bernoff AJ, Jilkine A, Navarro Hernández A, Lindsay AE. Single-cell directional sensing from just a few receptor binding events. Biophys J 2023; 122:3108-3116. [PMID: 37355773 PMCID: PMC10432224 DOI: 10.1016/j.bpj.2023.06.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Revised: 06/08/2023] [Accepted: 06/20/2023] [Indexed: 06/26/2023] Open
Abstract
Identifying the directionality of signaling sources from noisy input to membrane receptors is an essential task performed by many cell types. A variety of models have been proposed to explain directional sensing in cells. However, many of these require significant computational and memory capacities for the cell. We propose and analyze a simple mechanism in which a cell adopts the direction associated with the first few membrane binding events. This model yields an accurate angular estimate to the source long before steady state is reached in biologically relevant scenarios. Our proposed mechanism allows for reliable estimates of the directionality of external signals using temporal information and assumes minimal computational capacities of the cell.
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Affiliation(s)
- Andrew J Bernoff
- Department of Mathematics, Harvey Mudd College, Claremont, California
| | - Alexandra Jilkine
- Department of Applied & Computational Mathematics & Statistics, University of Notre Dame, South Bend, Indiana
| | - Adrián Navarro Hernández
- Department of Applied & Computational Mathematics & Statistics, University of Notre Dame, South Bend, Indiana
| | - Alan E Lindsay
- Department of Applied & Computational Mathematics & Statistics, University of Notre Dame, South Bend, Indiana.
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4
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Lindsay AE, Bernoff AJ, Navarro Hernández A. Short-time diffusive fluxes over membrane receptors yields the direction of a signalling source. ROYAL SOCIETY OPEN SCIENCE 2023; 10:221619. [PMID: 37122946 PMCID: PMC10130716 DOI: 10.1098/rsos.221619] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/19/2022] [Accepted: 03/31/2023] [Indexed: 05/03/2023]
Abstract
An essential ability of many cell types is to detect stimuli in the form of shallow chemical gradients. Such cues may indicate the direction that new growth should occur, or the location of a mate. Amplification of these faint signals is due to intra-cellular mechanisms, while the cue itself is generated by the noisy arrival of signalling molecules to surface bound membrane receptors. We employ a new hybrid numerical-asymptotic technique coupling matched asymptotic analysis and numerical inverse Laplace transform to rapidly and accurately solve the parabolic exterior problem describing the dynamic diffusive fluxes to receptors. We observe that equilibration occurs on long timescales, potentially limiting the usefulness of steady-state quantities for localization at practical biological timescales. We demonstrate that directional information is encoded primarily in early arrivals to the receptors, while equilibrium quantities inform on source distance. We develop a new homogenization result showing that complex receptor configurations can be replaced by a uniform effective condition. In the extreme scenario where the cell adopts the angular direction of the first impact, we show this estimate to be surprisingly accurate.
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Affiliation(s)
- Alan E. Lindsay
- Department of Applied and Computational Math and Statistics, University of Notre Dame, Notre Dame, IN 46617, USA
| | - Andrew J. Bernoff
- Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA
| | - Adrián Navarro Hernández
- Department of Applied and Computational Math and Statistics, University of Notre Dame, Notre Dame, IN 46617, USA
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5
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Abstract
Accurate decoding of spatial chemical landscapes is critical for many cell functions. Eukaryotic cells decode local chemical gradients to orient growth or movement in productive directions. Recent work on yeast model systems, whose gradient sensing pathways display much less complexity than those in animal cells, has suggested new paradigms for how these very small cells successfully exploit information in noisy and dynamic pheromone gradients to identify their mates. Pheromone receptors regulate a polarity circuit centered on the conserved Rho-family GTPase, Cdc42. The polarity circuit contains both positive and negative feedback pathways, allowing spontaneous symmetry breaking and also polarity site disassembly and relocation. Cdc42 orients the actin cytoskeleton, leading to focused vesicle traffic that promotes movement of the polarity site and also reshapes the cortical distribution of receptors at the cell surface. In this article, we review the advances from work on yeasts and compare them with the excitable signaling pathways that have been revealed in chemotactic animal cells. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Debraj Ghose
- Department of Pharmacology and Cancer Biology, Duke University Medical Center, Durham, North Carolina, USA;
| | - Timothy Elston
- Department of Pharmacology, University of North Carolina at Chapel Hill, North Carolina, USA
| | - Daniel Lew
- Department of Pharmacology and Cancer Biology, Duke University Medical Center, Durham, North Carolina, USA;
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6
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Ghose D, Jacobs K, Ramirez S, Elston T, Lew D. Chemotactic movement of a polarity site enables yeast cells to find their mates. Proc Natl Acad Sci U S A 2021; 118:e2025445118. [PMID: 34050026 PMCID: PMC8179161 DOI: 10.1073/pnas.2025445118] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Abstract
How small eukaryotic cells can interpret dynamic, noisy, and spatially complex chemical gradients to orient growth or movement is poorly understood. We address this question using Saccharomyces cerevisiae, where cells orient polarity up pheromone gradients during mating. Initial orientation is often incorrect, but polarity sites then move around the cortex in a search for partners. We find that this movement is biased by local pheromone gradients across the polarity site: that is, movement of the polarity site is chemotactic. A bottom-up computational model recapitulates this biased movement. The model reveals how even though pheromone-bound receptors do not mimic the shape of external pheromone gradients, nonlinear and stochastic effects combine to generate effective gradient tracking. This mechanism for gradient tracking may be applicable to any cell that searches for a target in a complex chemical landscape.
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Affiliation(s)
- Debraj Ghose
- Computational Biology and Bioinformatics, Duke University, Durham, NC 27710
- Department of Pharmacology and Cancer Biology, Duke University Medical Center, Durham, NC 27710
| | - Katherine Jacobs
- Department of Pharmacology and Cancer Biology, Duke University Medical Center, Durham, NC 27710
| | - Samuel Ramirez
- Department of Pharmacology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599
| | - Timothy Elston
- Department of Pharmacology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599
| | - Daniel Lew
- Department of Pharmacology and Cancer Biology, Duke University Medical Center, Durham, NC 27710;
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7
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Lawley SD, Lindsay AE, Miles CE. Receptor Organization Determines the Limits of Single-Cell Source Location Detection. PHYSICAL REVIEW LETTERS 2020; 125:018102. [PMID: 32678664 DOI: 10.1103/physrevlett.125.018102] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2019] [Accepted: 06/09/2020] [Indexed: 06/11/2023]
Abstract
Many types of cells require the ability to pinpoint the location of an external stimulus from the arrival of diffusing signaling molecules at cell-surface receptors. How does the organization (number and spatial configuration) of these receptors shape the limit of a cell's ability to infer the source location? In the idealized scenario of a spherical cell, we apply asymptotic analysis to compute splitting probabilities between individual receptors and formulate an information-theoretic framework to quantify the role of receptor organization. Clustered configurations of receptors provide an advantage in detecting sources aligned with the clusters, suggesting a possible multiscale mechanism for single-cell source inference.
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Affiliation(s)
- Sean D Lawley
- Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA
| | - Alan E Lindsay
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, South Bend, Indiana 46556, USA
| | - Christopher E Miles
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10005, USA
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Henderson NT, Pablo M, Ghose D, Clark-Cotton MR, Zyla TR, Nolen J, Elston TC, Lew DJ. Ratiometric GPCR signaling enables directional sensing in yeast. PLoS Biol 2019; 17:e3000484. [PMID: 31622333 PMCID: PMC6818790 DOI: 10.1371/journal.pbio.3000484] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2019] [Revised: 10/29/2019] [Accepted: 09/25/2019] [Indexed: 11/19/2022] Open
Abstract
Accurate detection of extracellular chemical gradients is essential for many cellular behaviors. Gradient sensing is challenging for small cells, which can experience little difference in ligand concentrations on the up-gradient and down-gradient sides of the cell. Nevertheless, the tiny cells of the yeast Saccharomyces cerevisiae reliably decode gradients of extracellular pheromones to find their mates. By imaging the behavior of polarity factors and pheromone receptors, we quantified the accuracy of initial polarization during mating encounters. We found that cells bias the orientation of initial polarity up-gradient, even though they have unevenly distributed receptors. Uneven receptor density means that the gradient of ligand-bound receptors does not accurately reflect the external pheromone gradient. Nevertheless, yeast cells appear to avoid being misled by responding to the fraction of occupied receptors rather than simply the concentration of ligand-bound receptors. Such ratiometric sensing also serves to amplify the gradient of active G protein. However, this process is quite error-prone, and initial errors are corrected during a subsequent indecisive phase in which polarity clusters exhibit erratic mobile behavior. Cells use surface receptors to decode spatial information from chemical gradients, but accurate decoding is hampered by small cell size and the presence of molecular noise. This study shows that yeast cells decode pheromone gradients by measuring the local ratio of bound to unbound receptors. This mechanism corrects for uneven receptor density at the surface and amplifies the gradient transmitted to downstream components.
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Affiliation(s)
- Nicholas T. Henderson
- Department of Pharmacology and Cancer Biology, Duke University, Durham, North Carolina, United States of America
| | - Michael Pablo
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
- Program in Molecular and Cellular Biophysics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
| | - Debraj Ghose
- Department of Pharmacology and Cancer Biology, Duke University, Durham, North Carolina, United States of America
| | - Manuella R. Clark-Cotton
- Department of Pharmacology and Cancer Biology, Duke University, Durham, North Carolina, United States of America
| | - Trevin R. Zyla
- Department of Pharmacology and Cancer Biology, Duke University, Durham, North Carolina, United States of America
| | - James Nolen
- Department of Mathematics, Duke University, Durham, North Carolina, United States of America
| | - Timothy C. Elston
- Department of Pharmacology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
| | - Daniel J. Lew
- Department of Pharmacology and Cancer Biology, Duke University, Durham, North Carolina, United States of America
- * E-mail:
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9
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Wang X, Tian W, Banh BT, Statler BM, Liang J, Stone DE. Mating yeast cells use an intrinsic polarity site to assemble a pheromone-gradient tracking machine. J Cell Biol 2019; 218:3730-3752. [PMID: 31570500 PMCID: PMC6829655 DOI: 10.1083/jcb.201901155] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2019] [Revised: 06/06/2019] [Accepted: 08/08/2019] [Indexed: 12/12/2022] Open
Abstract
The mating of budding yeast depends on chemotropism, a fundamental cellular process. The two yeast mating types secrete peptide pheromones that bind to GPCRs on cells of the opposite type. Cells find and contact a partner by determining the direction of the pheromone source and polarizing their growth toward it. Actin-directed secretion to the chemotropic growth site (CS) generates a mating projection. When pheromone-stimulated cells are unable to sense a gradient, they form mating projections where they would have budded in the next cell cycle, at a position called the default polarity site (DS). Numerous models have been proposed to explain yeast gradient sensing, but none address how cells reliably switch from the intrinsically determined DS to the gradient-aligned CS, despite a weak spatial signal. Here we demonstrate that, in mating cells, the initially uniform receptor and G protein first polarize to the DS, then redistribute along the plasma membrane until they reach the CS. Our data indicate that signaling, polarity, and trafficking proteins localize to the DS during assembly of what we call the gradient tracking machine (GTM). Differential activation of the receptor triggers feedback mechanisms that bias exocytosis upgradient and endocytosis downgradient, thus enabling redistribution of the GTM toward the pheromone source. The GTM stabilizes when the receptor peak centers at the CS and the endocytic machinery surrounds it. A computational model simulates GTM tracking and stabilization and correctly predicts that its assembly at a single site contributes to mating fidelity.
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Affiliation(s)
- Xin Wang
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL
| | - Wei Tian
- Department of Bioengineering, University of Illinois at Chicago, Chicago, IL
| | - Bryan T Banh
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL
| | | | - Jie Liang
- Department of Bioengineering, University of Illinois at Chicago, Chicago, IL
| | - David E Stone
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL
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10
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Di Nardo AA, Fuchs J, Joshi RL, Moya KL, Prochiantz A. The Physiology of Homeoprotein Transduction. Physiol Rev 2019; 98:1943-1982. [PMID: 30067157 DOI: 10.1152/physrev.00018.2017] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
The homeoprotein family comprises ~300 transcription factors and was long seen as primarily involved in developmental programs through cell autonomous regulation. However, recent evidence reveals that many of these factors are also expressed in the adult where they exert physiological functions not yet fully deciphered. Furthermore, the DNA-binding domain of most homeoproteins contains two signal sequences allowing their secretion and internalization, thus intercellular transfer. This review focuses on this new-found signaling in cell migration, axon guidance, and cerebral cortex physiological homeostasis and speculates on how it may play important roles in early arealization of the neuroepithelium. It also describes the use of homeoproteins as therapeutic proteins in mouse models of diseases affecting the central nervous system, in particular Parkinson disease and glaucoma.
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Affiliation(s)
- Ariel A Di Nardo
- Centre for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS UMR 7241, INSERM U1050, Labex MemoLife, PSL Research University , Paris , France
| | - Julia Fuchs
- Centre for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS UMR 7241, INSERM U1050, Labex MemoLife, PSL Research University , Paris , France
| | - Rajiv L Joshi
- Centre for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS UMR 7241, INSERM U1050, Labex MemoLife, PSL Research University , Paris , France
| | - Kenneth L Moya
- Centre for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS UMR 7241, INSERM U1050, Labex MemoLife, PSL Research University , Paris , France
| | - Alain Prochiantz
- Centre for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS UMR 7241, INSERM U1050, Labex MemoLife, PSL Research University , Paris , France
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11
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Pablo M, Ramirez SA, Elston TC. Particle-based simulations of polarity establishment reveal stochastic promotion of Turing pattern formation. PLoS Comput Biol 2018. [PMID: 29529021 PMCID: PMC5864077 DOI: 10.1371/journal.pcbi.1006016] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Polarity establishment, the spontaneous generation of asymmetric molecular distributions, is a crucial component of many cellular functions. Saccharomyces cerevisiae (yeast) undergoes directed growth during budding and mating, and is an ideal model organism for studying polarization. In yeast and many other cell types, the Rho GTPase Cdc42 is the key molecular player in polarity establishment. During yeast polarization, multiple patches of Cdc42 initially form, then resolve into a single front. Because polarization relies on strong positive feedback, it is likely that the amplification of molecular-level fluctuations underlies the generation of multiple nascent patches. In the absence of spatial cues, these fluctuations may be key to driving polarization. Here we used particle-based simulations to investigate the role of stochastic effects in a Turing-type model of yeast polarity establishment. In the model, reactions take place either between two molecules on the membrane, or between a cytosolic and a membrane-bound molecule. Thus, we developed a computational platform that explicitly simulates molecules at and near the cell membrane, and implicitly handles molecules away from the membrane. To evaluate stochastic effects, we compared particle simulations to deterministic reaction-diffusion equation simulations. Defining macroscopic rate constants that are consistent with the microscopic parameters for this system is challenging, because diffusion occurs in two dimensions and particles exchange between the membrane and cytoplasm. We address this problem by empirically estimating macroscopic rate constants from appropriately designed particle-based simulations. Ultimately, we find that stochastic fluctuations speed polarity establishment and permit polarization in parameter regions predicted to be Turing stable. These effects can operate at Cdc42 abundances expected of yeast cells, and promote polarization on timescales consistent with experimental results. To our knowledge, our work represents the first particle-based simulations of a model for yeast polarization that is based on a Turing mechanism. Many cells need to generate and maintain biochemical signals in specific subcellular regions. This phenomenon is broadly called polarity establishment, and is important in fundamental processes such as cell migration and differentiation. A key polarity factor found in diverse organisms, including yeast and humans, is the protein Cdc42. In yeast, Cdc42-dependent polarization occurs through a self-reinforcing biochemical signaling loop. Directional cues can guide polarity establishment, but interestingly, yeast can polarize in the absence of such a cue. The mechanism thought to underlie this symmetry breaking involves the amplification of inhomogeneities in molecular distributions that arise from molecular-level fluctuations. We investigated the effects of random fluctuations on polarization by performing particle-based simulations of the Cdc42 signaling network. We found that fluctuations can facilitate polarization, allowing faster polarization, and polarization over a broader range of concentrations. Our observations may help understand how polarity works in other systems.
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Affiliation(s)
- Michael Pablo
- Department of Chemistry, The University of North Carolina, Chapel Hill, NC, United States of America
- Program in Molecular and Cellular Biophysics, The University of North Carolina, Chapel Hill, NC, United States of America
| | - Samuel A. Ramirez
- Department of Pharmacology, The University of North Carolina, Chapel Hill, NC, United States of America
| | - Timothy C. Elston
- Department of Pharmacology, The University of North Carolina, Chapel Hill, NC, United States of America
- * E-mail:
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12
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Dobramysl U, Holcman D. Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows. JOURNAL OF COMPUTATIONAL PHYSICS 2018; 355:22-36. [PMID: 29456262 PMCID: PMC5765848 DOI: 10.1016/j.jcp.2017.10.058] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Is it possible to recover the position of a source from the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a domain? To address this question, we develop a numerical procedure to avoid tracking Brownian trajectories in the entire infinite space. Instead, we generate particles near the absorbing windows, computed from the analytical expression of the exit probability. When the Brownian particles are generated by a steady-state gradient at a single point, we compute asymptotically the fluxes to small absorbing holes distributed on the boundary of half-space and on a disk in two dimensions, which agree with stochastic simulations. We also derive an expression for the splitting probability between small windows using the matched asymptotic method. Finally, when there are more than two small absorbing windows, we show how to reconstruct the position of the source from the diffusion fluxes. The present approach provides a computational first principle for the mechanism of sensing a gradient of diffusing particles, a ubiquitous problem in cell biology.
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Affiliation(s)
- U. Dobramysl
- Wellcome Trust/Cancer Research UK Gurdon Institute, University of Cambridge, Tennis Court Rd, Cambridge CB2 1QN, United Kingdom
| | - D. Holcman
- Ecole Normale Supérieure, 46 rue d'Ulm, 75005 Paris, France
- Mathematical Institute, University of Oxford, Woodstock Rd, Oxford OX2 6GG, United Kingdom
- Corresponding author.
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13
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Cherstvy AG, Nagel O, Beta C, Metzler R. Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells. Phys Chem Chem Phys 2018; 20:23034-23054. [DOI: 10.1039/c8cp04254c] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
What is the underlying diffusion process governing the spreading dynamics and search strategies employed by amoeboid cells?
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Affiliation(s)
- Andrey G. Cherstvy
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Oliver Nagel
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Carsten Beta
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
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