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Tsai K, Zhou Z, Yang J, Xu Z, Xu S, Zandi R, Hao N, Chen W, Alber M. Study of Impacts of Two Types of Cellular Aging on the Yeast Bud Morphogenesis. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.02.29.582376. [PMID: 38464259 PMCID: PMC10925247 DOI: 10.1101/2024.02.29.582376] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/12/2024]
Abstract
Understanding the mechanisms of cellular aging processes is crucial for attempting to extend organismal lifespan and for studying age-related degenerative diseases. Yeast cells divide through budding, providing a classical biological model for studying cellular aging. With their powerful genetics, relatively short lifespan and well-established signaling pathways also found in animals, yeast cells offer valuable insights into the aging process. Recent experiments suggested the existence of two aging modes in yeast characterized by nucleolar and mitochondrial declines, respectively. In this study, by analyzing experimental data it was shown that cells evolving into those two aging modes behave differently when they are young. While buds grow linearly in both modes, cells that consistently generate spherical buds throughout their lifespan demonstrate greater efficacy in controlling bud size and growth rate at young ages. A three-dimensional chemical-mechanical model was developed and used to suggest and test hypothesized mechanisms of bud morphogenesis during aging. Experimentally calibrated simulations showed that tubular bud shape in one aging mode could be generated by locally inserting new materials at the bud tip guided by the polarized Cdc42 signal during the early stage of budding. Furthermore, the aspect ratio of the tubular bud could be stabilized during the late stage, as observed in experiments, through a reduction on the new cell surface material insertion or an expansion of the polarization site. Thus model simulations suggest the maintenance of new cell surface material insertion or chemical signal polarization could be weakened due to cellular aging in yeast and other cell types.
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Affiliation(s)
- Kevin Tsai
- Department of Mathematics, University of California, Riverside, CA, United States of America
- Interdisciplinary Center for Quantitative Modeling in Biology, University of California, Riverside, CA, United States of America
| | - Zhen Zhou
- Department of Molecular Biology, School of Biological Sciences, University of California, San Diego, CA, United States of America
| | - Jiadong Yang
- Department of Molecular, Cell and Systems Biology, University of California, Riverside, CA, United States of America
| | - Zhiliang Xu
- Applied and Computational Mathematics and Statistics Department, University of Notre Dame, Notre Dame, IN, United States of America
| | - Shixin Xu
- Duke Kunshan University, Kunshan, Jiangsu, China
| | - Roya Zandi
- Interdisciplinary Center for Quantitative Modeling in Biology, University of California, Riverside, CA, United States of America
- Department of Physics and Astronomy, University of California, Riverside, CA, United States of America
- Biophysics Graduate Program, University of California, Riverside, CA, United States of America
| | - Nan Hao
- Department of Molecular Biology, School of Biological Sciences, University of California, San Diego, CA, United States of America
| | - Weitao Chen
- Department of Mathematics, University of California, Riverside, CA, United States of America
- Interdisciplinary Center for Quantitative Modeling in Biology, University of California, Riverside, CA, United States of America
- Department of Molecular, Cell and Systems Biology, University of California, Riverside, CA, United States of America
- Biophysics Graduate Program, University of California, Riverside, CA, United States of America
| | - Mark Alber
- Department of Mathematics, University of California, Riverside, CA, United States of America
- Interdisciplinary Center for Quantitative Modeling in Biology, University of California, Riverside, CA, United States of America
- Department of Bioengineering, University of California, Riverside, CA, United States of America
- Biophysics Graduate Program, University of California, Riverside, CA, United States of America
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Lawson MJ, Drawert B, Petzold L, Yi TM. A positive feedback loop involving the Spa2 SHD domain contributes to focal polarization. PLoS One 2022; 17:e0263347. [PMID: 35134079 PMCID: PMC8824340 DOI: 10.1371/journal.pone.0263347] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2021] [Accepted: 01/16/2022] [Indexed: 11/18/2022] Open
Abstract
Focal polarization is necessary for finely arranged cell-cell interactions. The yeast mating projection, with its punctate polarisome, is a good model system for this process. We explored the critical role of the polarisome scaffold protein Spa2 during yeast mating with a hypothesis motivated by mathematical modeling and tested by in vivo experiments. Our simulations predicted that two positive feedback loops generate focal polarization, including a novel feedback pathway involving the N-terminal domain of Spa2. We characterized the latter using loss-of-function and gain-of-function mutants. The N-terminal region contains a Spa2 Homology Domain (SHD) which is conserved from yeast to humans, and when mutated largely reproduced the spa2Δ phenotype. Our work together with published data show that the SHD domain recruits Msb3/4 that stimulates Sec4-mediated transport of Bud6 to the polarisome. There, Bud6 activates Bni1-catalyzed actin cable formation, recruiting more Spa2 and completing the positive feedback loop. We demonstrate that disrupting this loop at any point results in morphological defects. Gain-of-function perturbations partially restored focal polarization in a spa2 loss-of-function mutant without restoring localization of upstream components, thus supporting the pathway order. Thus, we have collected data consistent with a novel positive feedback loop that contributes to focal polarization during pheromone-induced polarization in yeast.
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Affiliation(s)
- Michael J. Lawson
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA, United States of America
| | - Brian Drawert
- Department of Computer Science, University of North Carolina Asheville, Asheville, NC, United States of America
| | - Linda Petzold
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, CA, United States of America
| | - Tau-Mu Yi
- Molecular, Cellular, and Developmental Biology, 3131 Biological Sciences II, University of California, Santa Barbara, Santa Barbara, CA, United States of America
- * E-mail:
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3
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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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4
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Tian C, Shi Q, Cui X, Guo J, Yang Z, Shi J. Spatiotemporal dynamics of a reaction-diffusion model of pollen tube tip growth. J Math Biol 2019; 79:1319-1355. [PMID: 31280334 DOI: 10.1007/s00285-019-01396-7] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2018] [Revised: 06/06/2019] [Indexed: 11/28/2022]
Abstract
A reaction-diffusion model is proposed to describe the mechanisms underlying the spatial distributions of ROP1 and calcium on the pollen tube tip. The model assumes that the plasma membrane ROP1 activates itself through positive feedback loop, while the cytosolic calcium ions inhibit ROP1 via a negative feedback loop. Furthermore it is proposed that lateral movement of molecules on the plasma membrane are depicted by diffusion. It is shown that bistable or oscillatory dynamics could exist even in the non-spatial model, and stationary and oscillatory spatiotemporal patterns are found in the full spatial model which resemble the experimental data of pollen tube tip growth.
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Affiliation(s)
- Chenwei Tian
- Department of Statistics, University of California, Riverside, CA, 92521, USA
| | - Qingyan Shi
- Department of Mathematics, College of William and Mary, Williamsburg, VA, 23187-8795, USA.,School of Mathematical Sciences, Tongji University, Shanghai, 200092, China
| | - Xinping Cui
- Department of Statistics, University of California, Riverside, CA, 92521, USA
| | - Jingzhe Guo
- Department of Botany and Plant Sciences, Center for Plant Cell Biology, University of California, Riverside, CA, 92521, USA
| | - Zhenbiao Yang
- Department of Botany and Plant Sciences, Center for Plant Cell Biology, University of California, Riverside, CA, 92521, USA
| | - Junping Shi
- Department of Mathematics, College of William and Mary, Williamsburg, VA, 23187-8795, USA.
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Landeros A, Stutz T, Keys KL, Alekseyenko A, Sinsheimer JS, Lange K, Sehl ME. BioSimulator.jl: Stochastic simulation in Julia. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2018; 167:23-35. [PMID: 30501857 PMCID: PMC6388686 DOI: 10.1016/j.cmpb.2018.09.009] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2018] [Revised: 09/11/2018] [Accepted: 09/26/2018] [Indexed: 06/09/2023]
Abstract
BACKGROUND AND OBJECTIVES Biological systems with intertwined feedback loops pose a challenge to mathematical modeling efforts. Moreover, rare events, such as mutation and extinction, complicate system dynamics. Stochastic simulation algorithms are useful in generating time-evolution trajectories for these systems because they can adequately capture the influence of random fluctuations and quantify rare events. We present a simple and flexible package, BioSimulator.jl, for implementing the Gillespie algorithm, τ-leaping, and related stochastic simulation algorithms. The objective of this work is to provide scientists across domains with fast, user-friendly simulation tools. METHODS We used the high-performance programming language Julia because of its emphasis on scientific computing. Our software package implements a suite of stochastic simulation algorithms based on Markov chain theory. We provide the ability to (a) diagram Petri Nets describing interactions, (b) plot average trajectories and attached standard deviations of each participating species over time, and (c) generate frequency distributions of each species at a specified time. RESULTS BioSimulator.jl's interface allows users to build models programmatically within Julia. A model is then passed to the simulate routine to generate simulation data. The built-in tools allow one to visualize results and compute summary statistics. Our examples highlight the broad applicability of our software to systems of varying complexity from ecology, systems biology, chemistry, and genetics. CONCLUSION The user-friendly nature of BioSimulator.jl encourages the use of stochastic simulation, minimizes tedious programming efforts, and reduces errors during model specification.
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Affiliation(s)
- Alfonso Landeros
- Department of Biomathematics, David Geffen School of Medicine at UCLA, USA.
| | - Timothy Stutz
- Department of Biomathematics, David Geffen School of Medicine at UCLA, USA.
| | - Kevin L Keys
- Department of Medicine, University of California, San Francisco, CA, USA.
| | | | - Janet S Sinsheimer
- Department of Human Genetics, David Geffen School of Medicine at UCLA, USA.
| | - Kenneth Lange
- Department of Biomathematics, David Geffen School of Medicine at UCLA, USA.
| | - Mary E Sehl
- Department of Biomathematics, David Geffen School of Medicine at UCLA, USA.
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Trogdon M, Drawert B, Gomez C, Banavar SP, Yi TM, Campàs O, Petzold LR. The effect of cell geometry on polarization in budding yeast. PLoS Comput Biol 2018; 14:e1006241. [PMID: 29889845 PMCID: PMC6013239 DOI: 10.1371/journal.pcbi.1006241] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2017] [Revised: 06/21/2018] [Accepted: 05/29/2018] [Indexed: 11/19/2022] Open
Abstract
The localization (or polarization) of proteins on the membrane during the mating of budding yeast (Saccharomyces cerevisiae) is an important model system for understanding simple pattern formation within cells. While there are many existing mathematical models of polarization, for both budding and mating, there are still many aspects of this process that are not well understood. In this paper we set out to elucidate the effect that the geometry of the cell can have on the dynamics of certain models of polarization. Specifically, we look at several spatial stochastic models of Cdc42 polarization that have been adapted from published models, on a variety of tip-shaped geometries, to replicate the shape change that occurs during the growth of the mating projection. We show here that there is a complex interplay between the dynamics of polarization and the shape of the cell. Our results show that while models of polarization can generate a stable polarization cap, its localization at the tip of mating projections is unstable, with the polarization cap drifting away from the tip of the projection in a geometry dependent manner. We also compare predictions from our computational results to experiments that observe cells with projections of varying lengths, and track the stability of the polarization cap. Lastly, we examine one model of actin polarization and show that it is unlikely, at least for the models studied here, that actin dynamics and vesicle traffic are able to overcome this effect of geometry.
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Affiliation(s)
- Michael Trogdon
- Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, California, United States of America
- * E-mail:
| | - Brian Drawert
- Department of Computer Science, University of North Carolina, Asheville, Asheville, North Carolina, United States of America
| | - Carlos Gomez
- Department of Molecular, Cell and Developmental Biology, University of California, Santa Barbara, Santa Barbara, California, United States of America
- California NanoSystems Institute, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Samhita P. Banavar
- California NanoSystems Institute, University of California, Santa Barbara, Santa Barbara, California, United States of America
- Department of Physics, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Tau-Mu Yi
- Department of Molecular, Cell and Developmental Biology, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Otger Campàs
- Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, California, United States of America
- Department of Molecular, Cell and Developmental Biology, University of California, Santa Barbara, Santa Barbara, California, United States of America
- California NanoSystems Institute, University of California, Santa Barbara, Santa Barbara, California, United States of America
- Center for Bioengineering, University of California, Santa Barbara, Santa Barbara, California, United States of America
| | - Linda R. Petzold
- Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, California, United States of America
- Center for Bioengineering, University of California, Santa Barbara, Santa Barbara, California, United States of America
- Department of Computer Science, University of California, Santa Barbara, Santa Barbara, California, United States of America
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7
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Renardy M, Yi TM, Xiu D, Chou CS. Parameter uncertainty quantification using surrogate models applied to a spatial model of yeast mating polarization. PLoS Comput Biol 2018; 14:e1006181. [PMID: 29813055 PMCID: PMC5993324 DOI: 10.1371/journal.pcbi.1006181] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2018] [Revised: 06/08/2018] [Accepted: 05/07/2018] [Indexed: 11/19/2022] Open
Abstract
A common challenge in systems biology is quantifying the effects of unknown parameters and estimating parameter values from data. For many systems, this task is computationally intractable due to expensive model evaluations and large numbers of parameters. In this work, we investigate a new method for performing sensitivity analysis and parameter estimation of complex biological models using techniques from uncertainty quantification. The primary advance is a significant improvement in computational efficiency from the replacement of model simulation by evaluation of a polynomial surrogate model. We demonstrate the method on two models of mating in budding yeast: a smaller ODE model of the heterotrimeric G-protein cycle, and a larger spatial model of pheromone-induced cell polarization. A small number of model simulations are used to fit the polynomial surrogates, which are then used to calculate global parameter sensitivities. The surrogate models also allow rapid Bayesian inference of the parameters via Markov chain Monte Carlo (MCMC) by eliminating model simulations at each step. Application to the ODE model shows results consistent with published single-point estimates for the model and data, with the added benefit of calculating the correlations between pairs of parameters. On the larger PDE model, the surrogate models allowed convergence for the distribution of 15 parameters, which otherwise would have been computationally prohibitive using simulations at each MCMC step. We inferred parameter distributions that in certain cases peaked at values different from published values, and showed that a wide range of parameters would permit polarization in the model. Strikingly our results suggested different diffusion constants for active versus inactive Cdc42 to achieve good polarization, which is consistent with experimental observations in another yeast species S. pombe.
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Affiliation(s)
- Marissa Renardy
- Department of Mathematics, Ohio State University, Columbus, Ohio, United States of America
| | - Tau-Mu Yi
- Department of Molecular, Cellular, and Developmental Biology, University of California, Santa Barbara, California, United States of America
| | - Dongbin Xiu
- Department of Mathematics, Ohio State University, Columbus, Ohio, United States of America
| | - Ching-Shan Chou
- Department of Mathematics, Ohio State University, Columbus, Ohio, United States of America
- * E-mail:
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8
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Giese W, Milicic G, Schröder A, Klipp E. Spatial modeling of the membrane-cytosolic interface in protein kinase signal transduction. PLoS Comput Biol 2018; 14:e1006075. [PMID: 29630597 PMCID: PMC5908195 DOI: 10.1371/journal.pcbi.1006075] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2017] [Revised: 04/19/2018] [Accepted: 03/07/2018] [Indexed: 02/06/2023] Open
Abstract
The spatial architecture of signaling pathways and the interaction with cell size and morphology are complex, but little understood. With the advances of single cell imaging and single cell biology, it becomes crucial to understand intracellular processes in time and space. Activation of cell surface receptors often triggers a signaling cascade including the activation of membrane-attached and cytosolic signaling components, which eventually transmit the signal to the cell nucleus. Signaling proteins can form steep gradients in the cytosol, which cause strong cell size dependence. We show that the kinetics at the membrane-cytosolic interface and the ratio of cell membrane area to the enclosed cytosolic volume change the behavior of signaling cascades significantly. We suggest an estimate of average concentration for arbitrary cell shapes depending on the cell volume and cell surface area. The normalized variance, known from image analysis, is suggested as an alternative measure to quantify the deviation from the average concentration. A mathematical analysis of signal transduction in time and space is presented, providing analytical solutions for different spatial arrangements of linear signaling cascades. Quantification of signaling time scales reveals that signal propagation is faster at the membrane than at the nucleus, while this time difference decreases with the number of signaling components in the cytosol. Our investigations are complemented by numerical simulations of non-linear cascades with feedback and asymmetric cell shapes. We conclude that intracellular signal propagation is highly dependent on cell geometry and, thereby, conveys information on cell size and shape to the nucleus.
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Affiliation(s)
- Wolfgang Giese
- Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine, Berlin, Germany
| | - Gregor Milicic
- Department of Mathematics, University of Salzburg, Salzburg, Austria
| | - Andreas Schröder
- Department of Mathematics, University of Salzburg, Salzburg, Austria
| | - Edda Klipp
- Theoretische Biophysik, Humboldt-Universität zu Berlin, Berlin, Germany
- * E-mail:
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9
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Khatibi S, Rios KI, Nguyen LK. Computational Modeling of the Dynamics of Spatiotemporal Rho GTPase Signaling: A Systematic Review. Methods Mol Biol 2018; 1821:3-20. [PMID: 30062401 DOI: 10.1007/978-1-4939-8612-5_1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The Rho family of GTPases are known to play pivotal roles in the regulation of fundamental cellular processes, ranging from cell migration and polarity to wound healing and regulation of actin cytoskeleton. Over the past decades, accumulating experimental work has increasingly mapped out the mechanistic details and interactions between members of the family and their regulators, establishing detailed interaction circuits within the Rho GTPase signaling network. These circuits have served as a vital foundation based on which a multitude of mathematical models have been developed to explain experimental data, gain deeper insights into the biological phenomenon they describe, as well as make new testable predictions and hypotheses. Due to the diverse nature and purpose of these models, they often vary greatly in size, scope, complexity, and formulation. Here, we provide a systematic, categorical, and comprehensive account of the recent modeling studies of Rho family GTPases, with an aim to offer a broad perspective of the field. The modeling limitations and possible future research directions are also discussed.
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Affiliation(s)
- Shabnam Khatibi
- Department of Biochemistry and Molecular Biology, Monash University, Melbourne, VIC, Australia
| | - Karina Islas Rios
- Department of Biochemistry and Molecular Biology, Monash University, Melbourne, VIC, Australia
| | - Lan K Nguyen
- Department of Biochemistry and Molecular Biology, Monash University, Melbourne, VIC, Australia.
- Cancer Program, Biomedicine Discovery Institute, Monash University, Melbourne, VIC, Australia.
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10
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Chen W, Nie Q, Yi TM, Chou CS. Modelling of Yeast Mating Reveals Robustness Strategies for Cell-Cell Interactions. PLoS Comput Biol 2016; 12:e1004988. [PMID: 27404800 PMCID: PMC4942089 DOI: 10.1371/journal.pcbi.1004988] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2016] [Accepted: 05/16/2016] [Indexed: 11/18/2022] Open
Abstract
Mating of budding yeast cells is a model system for studying cell-cell interactions. Haploid yeast cells secrete mating pheromones that are sensed by the partner which responds by growing a mating projection toward the source. The two projections meet and fuse to form the diploid. Successful mating relies on precise coordination of dynamic extracellular signals, signaling pathways, and cell shape changes in a noisy background. It remains elusive how cells mate accurately and efficiently in a natural multi-cell environment. Here we present the first stochastic model of multiple mating cells whose morphologies are driven by pheromone gradients and intracellular signals. Our novel computational framework encompassed a moving boundary method for modeling both a-cells and α-cells and their cell shape changes, the extracellular diffusion of mating pheromones dynamically coupled with cell polarization, and both external and internal noise. Quantification of mating efficiency was developed and tested for different model parameters. Computer simulations revealed important robustness strategies for mating in the presence of noise. These strategies included the polarized secretion of pheromone, the presence of the α-factor protease Bar1, and the regulation of sensing sensitivity; all were consistent with data in the literature. In addition, we investigated mating discrimination, the ability of an a-cell to distinguish between α-cells either making or not making α-factor, and mating competition, in which multiple a-cells compete to mate with one α-cell. Our simulations were consistent with previous experimental results. Moreover, we performed a combination of simulations and experiments to estimate the diffusion rate of the pheromone a-factor. In summary, we constructed a framework for simulating yeast mating with multiple cells in a noisy environment, and used this framework to reproduce mating behaviors and to identify strategies for robust cell-cell interactions. One of the riddles of Nature is how cells interact with one another to create complex cellular networks such as the neural networks in the brain. Forming precise connections between irregularly shaped cells is a challenge for biology. We developed computational methods for simulating these complex cell-cell interactions. We applied these methods to investigate yeast mating in which two yeast cells grow projections that meet and fuse guided by pheromone attractants. The simulations described molecules both inside and outside of the cell, and represented the continually changing shapes of the cells. We found that positioning the secretion and sensing of pheromones at the same location on the cell surface was important. Other key factors for robust mating included secreting a protein that removed excess pheromone from outside of the cell so that the signal would not be too strong. An important advance was being able to simulate as many as five cells in complex mating arrangements. Taken together we used our novel computational methods to describe in greater detail the yeast mating process, and more generally, interactions among cells changing their shapes in response to their neighbors.
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Affiliation(s)
- Weitao Chen
- Department of Mathematics, University of California, Irvine, Irvine, California, United States of America
| | - Qing Nie
- Department of Mathematics, University of California, Irvine, Irvine, California, United States of America
| | - Tau-Mu Yi
- Molecular, Cellular, and Developmental Biology, University of California, Santa Barbara, Santa Barbara, California, United States of America
- * E-mail: (TMY); (CSC)
| | - Ching-Shan Chou
- Department of Mathematics, The Ohio State University, Columbus, Ohio, United States of America
- * E-mail: (TMY); (CSC)
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11
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Muller N, Piel M, Calvez V, Voituriez R, Gonçalves-Sá J, Guo CL, Jiang X, Murray A, Meunier N. A Predictive Model for Yeast Cell Polarization in Pheromone Gradients. PLoS Comput Biol 2016; 12:e1004795. [PMID: 27077831 PMCID: PMC4831791 DOI: 10.1371/journal.pcbi.1004795] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2015] [Accepted: 02/08/2016] [Indexed: 11/18/2022] Open
Abstract
Budding yeast cells exist in two mating types, a and α, which use peptide pheromones to communicate with each other during mating. Mating depends on the ability of cells to polarize up pheromone gradients, but cells also respond to spatially uniform fields of pheromone by polarizing along a single axis. We used quantitative measurements of the response of a cells to α-factor to produce a predictive model of yeast polarization towards a pheromone gradient. We found that cells make a sharp transition between budding cycles and mating induced polarization and that they detect pheromone gradients accurately only over a narrow range of pheromone concentrations corresponding to this transition. We fit all the parameters of the mathematical model by using quantitative data on spontaneous polarization in uniform pheromone concentration. Once these parameters have been computed, and without any further fit, our model quantitatively predicts the yeast cell response to pheromone gradient providing an important step toward understanding how cells communicate with each other.
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Affiliation(s)
- Nicolas Muller
- MAP5, CNRS UMR 8145, Université Paris Descartes, Paris, France
| | - Matthieu Piel
- Institut Curie, CNRS UMR 144, Paris, France
- * E-mail: (MP); (AM); (NM)
| | - Vincent Calvez
- Unité de Mathématiques Pures et Appliquées, CNRS UMR 5669 and équipe-projet INRIA NUMED, École Normale Supérieure de Lyon, Lyon, France
| | - Raphaël Voituriez
- Laboratoire Jean Perrin and Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS /UPMC, Paris, France
| | - Joana Gonçalves-Sá
- Molecular and Cell Biology and FAS Center for Systems Biology, Harvard University, Cambridge, Massachusetts, United States of America
| | - Chin-Lin Guo
- Molecular and Cell Biology and FAS Center for Systems Biology, Harvard University, Cambridge, Massachusetts, United States of America
- Institute of Physics, Academia Sinica, Taiwan
| | - Xingyu Jiang
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts, United States of America
- CAS Key Laboratory for Biological Effects of Nanomaterials and Nanosafety, National Center for Nanoscience and Technology, Beijing, People’s Republic of China
| | - Andrew Murray
- Molecular and Cell Biology and FAS Center for Systems Biology, Harvard University, Cambridge, Massachusetts, United States of America
- * E-mail: (MP); (AM); (NM)
| | - Nicolas Meunier
- MAP5, CNRS UMR 8145, Université Paris Descartes, Paris, France
- * E-mail: (MP); (AM); (NM)
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12
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Ismael A, Tian W, Waszczak N, Wang X, Cao Y, Suchkov D, Bar E, Metodiev MV, Liang J, Arkowitz RA, Stone DE. Gβ promotes pheromone receptor polarization and yeast chemotropism by inhibiting receptor phosphorylation. Sci Signal 2016; 9:ra38. [PMID: 27072657 DOI: 10.1126/scisignal.aad4376] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Gradient-directed cell migration (chemotaxis) and growth (chemotropism) are processes that are essential to the development and life cycles of all species. Cells use surface receptors to sense the shallow chemical gradients that elicit chemotaxis and chemotropism. Slight asymmetries in receptor activation are amplified by downstream signaling systems, which ultimately induce dynamic reorganization of the cytoskeleton. During the mating response of budding yeast, a model chemotropic system, the pheromone receptors on the plasma membrane polarize to the side of the cell closest to the stimulus. Although receptor polarization occurs before and independently of actin cable-dependent delivery of vesicles to the plasma membrane (directed secretion), it requires receptor internalization. Phosphorylation of pheromone receptors by yeast casein kinase 1 or 2 (Yck1/2) stimulates their internalization. We showed that the pheromone-responsive Gβγ dimer promotes the polarization of the pheromone receptor by interacting with Yck1/2 and locally inhibiting receptor phosphorylation. We also found that receptor phosphorylation is essential for chemotropism, independently of its role in inducing receptor internalization. A mathematical model supports the idea that the interaction between Gβγ and Yck1/2 results in differential phosphorylation and internalization of the pheromone receptor and accounts for its polarization before the initiation of directed secretion.
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Affiliation(s)
- Amber Ismael
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL 60607, USA
| | - Wei Tian
- Department of Bioengineering, University of Illinois at Chicago, Chicago, IL 60607, USA
| | - Nicholas Waszczak
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL 60607, USA
| | - Xin Wang
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL 60607, USA
| | - Youfang Cao
- Department of Bioengineering, University of Illinois at Chicago, Chicago, IL 60607, USA
| | - Dmitry Suchkov
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL 60607, USA
| | - Eli Bar
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL 60607, USA
| | - Metodi V Metodiev
- School of Biological Sciences, University of Essex, Essex CO4 3SQ, UK
| | - Jie Liang
- Department of Bioengineering, University of Illinois at Chicago, Chicago, IL 60607, USA
| | - Robert A Arkowitz
- CNRS UMR7277/INSERM UMR1091/Université Nice-Sophia Antipolis, Institute of Biology Valrose, 06108 Nice Cedex 2, France
| | - David E Stone
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL 60607, USA.
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13
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Giese W, Eigel M, Westerheide S, Engwer C, Klipp E. Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models. Phys Biol 2015; 12:066014. [DOI: 10.1088/1478-3975/12/6/066014] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
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14
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Chou CS, Moore TI, Nie Q, Yi TM. Alternative cell polarity behaviours arise from changes in G-protein spatial dynamics. IET Syst Biol 2015; 9:52-63. [PMID: 26029251 DOI: 10.1049/iet-syb.2013.0018] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
Yeast cells form a single mating projection when exposed to mating pheromone, a classic example of cell polarity. Prolonged treatment with pheromone or specific mutations results in alternative cell polarity behaviours. The authors performed mathematical modelling to investigate these unusual cell morphologies from the perspective of balancing spatial amplification (i.e. positive feedback that localises components) with spatial tracking (i.e. negative feedback that allows sensing of gradient). First, they used generic models of cell polarity to explore different cell polarity behaviours that arose from changes in the model spatial dynamics. By exploring the positive and negative feedback loops in each stage of a two-stage model, they simulated a variety of cell morphologies including single bending projections, single straight projections, periodic multiple projections and simultaneous double projections. In the second half of the study, they used a two-stage mechanistic model of yeast cell polarity focusing on G-protein signalling to integrate the modelling results more closely with the authors' previously published experimental observations. In summary, the combination of modelling and experiments describes how yeast cells exhibit a diversity of cell morphologies arising from two-stage G-protein signalling dynamics modulated by positive and negative feedbacks.
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15
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Tian W, Cao Y, Ismael A, Stone D, Liang J. Roles of regulated internalization in the polarization of cell surface receptors. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2015; 2014:1166-9. [PMID: 25570171 DOI: 10.1109/embc.2014.6943803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Cell polarization, the generation of cellular asymmetries, is a fundamental biological process. Polarity of different molecules can arise through several mechanisms. Among these, internalization has been shown to play an important role in the polarization of cell surface receptors. The internalization of cell surface receptors can be upregulated upon ligand binding. Additional regulatory mechanism can downregulate the internalization process. Here we describe a general model, which incorporates these two opposing processes, to study the role of internalization in the establishment of cell polarity. We find that the competition between these two processes is sufficient to induce receptor polarization. Our results show that regulated internalization provides additional regulation on polarization as well. In addition, we discuss applications of our model to the yeast system, which shows the capability and potential of the model.
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16
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Chen M, Wang L, Liu CC, Nie Q. Noise attenuation in the ON and OFF states of biological switches. ACS Synth Biol 2013; 2:587-93. [PMID: 23768065 PMCID: PMC3805451 DOI: 10.1021/sb400044g] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2013] [Indexed: 11/28/2022]
Abstract
Biological switches must sense changes in signal concentration and at the same time buffer against signal noise. While many studies have focused on the response of switching systems to noise in the ON state, how systems buffer noise at both ON and OFF states is poorly understood. Through analytical and computational approaches, we find that switching systems require different dynamics at the OFF state than at the ON state in order to have good noise buffering capability. Specifically, we introduce a quantity called the input-associated Signed Activation Time (iSAT) that concisely captures an intrinsic temporal property at either the ON or OFF state. We discover a trade-off between achieving good noise buffering in the ON versus the OFF states: a large iSAT corresponds to noise amplification in the OFF state in contrast to noise buffering in the ON state. To search for biological circuits that can buffer noise in both ON and OFF states, we systematically analyze all three-node circuits and identify mutual activation as a central motif. We also study connections among signal sensitivity, iSAT, and noise amplification. We find that a large iSAT at the ON state maintains signaling sensitivity while minimizing noise propagation. Taken together, the analysis of iSATs helps reveal the noise properties of biological networks and should aid in the design of robust switches that can both repress noise at the OFF state and maintain a reliable ON state.
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Affiliation(s)
- Meng Chen
- Department
of Mathematics and Department of Biomedical Engineering, University
of California at Irvine, Irvine, California 92697, United
States
| | - Liming Wang
- Department of Mathematics, California State University, Los Angeles, California
90032, United States
| | - Chang C. Liu
- Department
of Mathematics and Department of Biomedical Engineering, University
of California at Irvine, Irvine, California 92697, United
States
| | - Qing Nie
- Department
of Mathematics and Department of Biomedical Engineering, University
of California at Irvine, Irvine, California 92697, United
States
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17
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Lawson MJ, Drawert B, Khammash M, Petzold L, Yi TM. Spatial stochastic dynamics enable robust cell polarization. PLoS Comput Biol 2013; 9:e1003139. [PMID: 23935469 PMCID: PMC3723497 DOI: 10.1371/journal.pcbi.1003139] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2012] [Accepted: 05/31/2013] [Indexed: 11/18/2022] Open
Abstract
Although cell polarity is an essential feature of living cells, it is far from being well-understood. Using a combination of computational modeling and biological experiments we closely examine an important prototype of cell polarity: the pheromone-induced formation of the yeast polarisome. Focusing on the role of noise and spatial heterogeneity, we develop and investigate two mechanistic spatial models of polarisome formation, one deterministic and the other stochastic, and compare the contrasting predictions of these two models against experimental phenotypes of wild-type and mutant cells. We find that the stochastic model can more robustly reproduce two fundamental characteristics observed in wild-type cells: a highly polarized phenotype via a mechanism that we refer to as spatial stochastic amplification, and the ability of the polarisome to track a moving pheromone input. Moreover, we find that only the stochastic model can simultaneously reproduce these characteristics of the wild-type phenotype and the multi-polarisome phenotype of a deletion mutant of the scaffolding protein Spa2. Significantly, our analysis also demonstrates that higher levels of stochastic noise results in increased robustness of polarization to parameter variation. Furthermore, our work suggests a novel role for a polarisome protein in the stabilization of actin cables. These findings elucidate the intricate role of spatial stochastic effects in cell polarity, giving support to a cellular model where noise and spatial heterogeneity combine to achieve robust biological function. Cell polarity is the fundamental process of breaking symmetry to create asymmetric cellular structures. It is an open question how randomness (stochasticity) in the cell hinders or helps cell polarity. In this work, we focus on the ability of yeast cells to sense a spatial gradient of mating pheromone and respond by forming a projection in the direction of the mating partner. A key element is the polarisome, which is at the tip of the mating projection. We introduce the first model of polarisome formation in yeast. The model is well-supported by experimental data. We perform modeling to explore the role of noise in the formation of the polarisome. By running simulations with and without noise, we arrive at the surprising conclusion, that gradient-dependent polarization is enhanced by stochasticity. Both the tight localization (amplification) and the ability to respond to directional change of the input (tracking) are enhanced by stochastic dynamics, resulting in a more robust behavior. Mutants in which key polarisome proteins have been deleted exhibit broader, noisier polarisome than the wild type. The mutant phenotype is accurately captured by our stochastic simulations. These results demonstrate the importance of stochasticity in the study of cell polarity.
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Affiliation(s)
- Michael J. Lawson
- Department of BioMolecular Science and Engineering, University of California, Santa Barbara, California, United States of America
| | - Brian Drawert
- Department of Computer Science, University of California, Santa Barbara, California, United States of America
| | - Mustafa Khammash
- Department of Mechanical Engineering, University of California, Santa Barbara, California, United States of America
- Department of Biosystems Science and Engineering, ETH-Zürich, Basel, Switzerland
| | - Linda Petzold
- Department of Computer Science, University of California, Santa Barbara, California, United States of America
- Department of Mechanical Engineering, University of California, Santa Barbara, California, United States of America
| | - Tau-Mu Yi
- Department of Molecular, Cellular, and Developmental Biology, University of California, Santa Barbara, California, United States of America
- * E-mail:
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18
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Signaling regulated endocytosis and exocytosis lead to mating pheromone concentration dependent morphologies in yeast. FEBS Lett 2012; 586:4208-4214. [PMID: 23108052 DOI: 10.1016/j.febslet.2012.10.024] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2012] [Revised: 10/01/2012] [Accepted: 10/14/2012] [Indexed: 11/22/2022]
Abstract
Polarized cell morphogenesis requires actin cytoskeleton rearrangement for polarized transport of proteins, organelles and secretory vesicles, which fundamentally underlies cell differentiation and behavior. During yeast mating, Saccharomyces cerevisiae responds to extracellular pheromone gradients by extending polarized projections, which are likely maintained through vesicle transport to (exocytosis) and from (endocytosis) the membrane. We experimentally demonstrate that the projection morphology is pheromone concentration-dependent, and propose the underlying mechanism through mathematical modeling. The inclusion of membrane flux and dynamically evolving cell boundary into our yeast mating signaling model shows good agreement with experimental measurements, and provides a plausible explanation for pheromone-induced cell morphology.
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19
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Chou CS, Bardwell L, Nie Q, Yi TM. Noise filtering tradeoffs in spatial gradient sensing and cell polarization response. BMC SYSTEMS BIOLOGY 2011; 5:196. [PMID: 22166067 PMCID: PMC3268761 DOI: 10.1186/1752-0509-5-196] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/30/2011] [Accepted: 12/13/2011] [Indexed: 12/29/2022]
Abstract
BACKGROUND Cells sense chemical spatial gradients and respond by polarizing internal components. This process can be disrupted by gradient noise caused by fluctuations in chemical concentration. RESULTS We investigated how external gradient noise affects spatial sensing and response focusing on noise-filtering and the resultant tradeoffs. First, using a coarse-grained mathematical model of gradient-sensing and cell polarity, we characterized three negative consequences of noise: Inhibition of the extent of polarization, degradation of directional accuracy, and production of a noisy output polarization. Next, we explored filtering strategies and discovered that a combination of positive feedback, multiple signaling stages, and time-averaging produced good results. There was an important tradeoff, however, because filtering resulted in slower polarization. Simulations demonstrated that a two-stage filter-amplifier resulted in a balanced outcome. Then, we analyzed the effect of noise on a mechanistic model of yeast cell polarization in response to gradients of mating pheromone. This analysis showed that yeast cells likely also combine the above three filtering mechanisms into a filter-amplifier structure to achieve impressive spatial-noise tolerance, but with the consequence of a slow response time. Further investigation of the amplifier architecture revealed two positive feedback loops, a fast inner and a slow outer, both of which contributed to noise-tolerant polarization. This model also made specific predictions about how orientation performance depended upon the ratio between the gradient slope (signal) and the noise variance. To test these predictions, we performed microfluidics experiments measuring the ability of yeast cells to orient to shallow gradients of mating pheromone. The results of these experiments agreed well with the modeling predictions, demonstrating that yeast cells can sense gradients shallower than 0.1% μm-1, approximately a single receptor-ligand molecule difference between front and back, on par with motile eukaryotic cells. CONCLUSIONS Spatial noise impedes the extent, accuracy, and smoothness of cell polarization. A combined filtering strategy implemented by a filter-amplifier architecture with slow dynamics was effective. Modeling and experimental data suggest that yeast cells employ these elaborate mechanisms to filter gradient noise resulting in a slow but relatively accurate polarization response.
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Affiliation(s)
- Ching-Shan Chou
- Center for Complex Biological Systems, Department of Developmental and Cell Biology, University of California-Irvine, CA 92697, USA
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20
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Vanderlei B, Feng JJ, Edelstein-Keshet L. A computational model of cell polarization and motility coupling mechanics and biochemistry. MULTISCALE MODELING & SIMULATION : A SIAM INTERDISCIPLINARY JOURNAL 2011; 9:1420-1443. [PMID: 22904684 PMCID: PMC3419594 DOI: 10.1137/100815335] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
The motion of a eukaryotic cell presents a variety of interesting and challenging problems from both a modeling and a computational perspective. The processes span many spatial scales (from molecular to tissue) as well as disparate time scales, with reaction kinetics on the order of seconds, and the deformation and motion of the cell occurring on the order of minutes. The computational difficulty, even in 2D, resides in the fact that the problem is inherently one of deforming, non-stationary domains, bounded by an elastic perimeter, inside of which there is redistribution of biochemical signaling substances. Here we report the results of a computational scheme using the immersed boundary method to address this problem. We adopt a simple reaction-diffusion system that represents an internal regulatory mechanism controlling the polarization of a cell, and determining the strength of protrusion forces at the front of its elastic perimeter. Using this computational scheme we are able to study the effect of protrusive and elastic forces on cell shapes on their own, the distribution of the reaction-diffusion system in irregular domains on its own, and the coupled mechanical-chemical system. We find that this representation of cell crawling can recover important aspects of the spontaneous polarization and motion of certain types of crawling cells.
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21
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Zheng Z, Chou CS, Yi TM, Nie Q. Mathematical analysis of steady-state solutions in compartment and continuum models of cell polarization. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2011; 8:1135-1168. [PMID: 21936604 PMCID: PMC3806509 DOI: 10.3934/mbe.2011.8.1135] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Cell polarization, in which substances previously uniformly distributed become asymmetric due to external or/and internal stimulation, is a fundamental process underlying cell mobility, cell division, and other polarized functions. The yeast cell S. cerevisiae has been a model system to study cell polarization. During mating, yeast cells sense shallow external spatial gradients and respond by creating steeper internal gradients of protein aligned with the external cue. The complex spatial dynamics during yeast mating polarization consists of positive feedback, degradation, global negative feedback control, and cooperative effects in protein synthesis. Understanding such complex regulations and interactions is critical to studying many important characteristics in cell polarization including signal amplification, tracking dynamic signals, and potential trade-off between achieving both objectives in a robust fashion. In this paper, we study some of these questions by analyzing several models with different spatial complexity: two compartments, three compartments, and continuum in space. The step-wise approach allows detailed characterization of properties of the steady state of the system, providing more insights for biological regulations during cell polarization. For cases without membrane diffusion, our study reveals that increasing the number of spatial compartments results in an increase in the number of steady-state solutions, in particular, the number of stable steady-state solutions, with the continuum models possessing infinitely many steady-state solutions. Through both analysis and simulations, we find that stronger positive feedback, reduced diffusion, and a shallower ligand gradient all result in more steady-state solutions, although most of these are not optimally aligned with the gradient. We explore in the different settings the relationship between the number of steady-state solutions and the extent and accuracy of the polarization. Taken together these results furnish a detailed description of the factors that influence the tradeoff between a single correctly aligned but poorly polarized stable steady-state solution versus multiple more highly polarized stable steady-state solutions that may be incorrectly aligned with the external gradient.
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Affiliation(s)
- Zhenzhen Zheng
- Department of Mathematics, Center for Complex Biological Systems and Center for Mathematical and Computational Biology, University of California-Irvine, CA 92697, United States.
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22
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Tanaka H, Yi TM. The effects of replacing Sst2 with the heterologous RGS4 on polarization and mating in yeast. Biophys J 2010; 99:1007-17. [PMID: 20712983 DOI: 10.1016/j.bpj.2010.04.078] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2009] [Revised: 04/16/2010] [Accepted: 04/30/2010] [Indexed: 11/30/2022] Open
Abstract
RGS proteins stimulate the deactivation of heterotrimeric G-proteins. The yeast RGS protein Sst2 is regulated at both the transcriptional and posttranscriptional levels. We replaced the SST2 gene with the distantly related human RGS4 gene, which consists of the catalytic domain and an N-terminal membrane attachment peptide, and replaced the native promoter (P(SST2)) with the heterologous tetracycline-repressible promoter (P(TET)). We then measured the effect of the substitutions on pheromone sensitivity, mating, and polarization. Although the pheromone sensitivity was essentially normal, there were differences in mating and polarization. In particular, the RGS4-substituted strains did not form multiple mating projections at high levels of alpha-factor, but instead formed a single malformed projection, which frequently gave rise to a bud. We provide evidence that this phenotype arose because unlike Sst2, RGS4 did not localize to the projection. We use mathematical modeling to argue that localization of Sst2 to the projection prevents excess G-protein activation during the pheromone response. In addition, modeling and experiments demonstrate that the dose of Sst2 influences the frequency of mating projection formation.
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Affiliation(s)
- Hiromasa Tanaka
- Department of Developmental and Cell Biology, University of California, Irvine, California, USA
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23
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Wang L, Xin J, Nie Q. A critical quantity for noise attenuation in feedback systems. PLoS Comput Biol 2010; 6:e1000764. [PMID: 20442870 PMCID: PMC2861702 DOI: 10.1371/journal.pcbi.1000764] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2009] [Accepted: 03/25/2010] [Indexed: 11/19/2022] Open
Abstract
Feedback modules, which appear ubiquitously in biological regulations, are often subject to disturbances from the input, leading to fluctuations in the output. Thus, the question becomes how a feedback system can produce a faithful response with a noisy input. We employed multiple time scale analysis, Fluctuation Dissipation Theorem, linear stability, and numerical simulations to investigate a module with one positive feedback loop driven by an external stimulus, and we obtained a critical quantity in noise attenuation, termed as "signed activation time". We then studied the signed activation time for a system of two positive feedback loops, a system of one positive feedback loop and one negative feedback loop, and six other existing biological models consisting of multiple components along with positive and negative feedback loops. An inverse relationship is found between the noise amplification rate and the signed activation time, defined as the difference between the deactivation and activation time scales of the noise-free system, normalized by the frequency of noises presented in the input. Thus, the combination of fast activation and slow deactivation provides the best noise attenuation, and it can be attained in a single positive feedback loop system. An additional positive feedback loop often leads to a marked decrease in activation time, decrease or slight increase of deactivation time and allows larger kinetic rate variations for slow deactivation and fast activation. On the other hand, a negative feedback loop may increase the activation and deactivation times. The negative relationship between the noise amplification rate and the signed activation time also holds for the six other biological models with multiple components and feedback loops. This principle may be applicable to other feedback systems.
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Affiliation(s)
- Liming Wang
- Center for Mathematical and Computational Biology, Center for Complex Biological Systems, and Department of Mathematics, University of California at Irvine, Irvine, California, United States of America
| | - Jack Xin
- Center for Mathematical and Computational Biology, Center for Complex Biological Systems, and Department of Mathematics, University of California at Irvine, Irvine, California, United States of America
| | - Qing Nie
- Center for Mathematical and Computational Biology, Center for Complex Biological Systems, and Department of Mathematics, University of California at Irvine, Irvine, California, United States of America
- * E-mail:
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24
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Drawert B, Lawson MJ, Petzold L, Khammash M. The diffusive finite state projection algorithm for efficient simulation of the stochastic reaction-diffusion master equation. J Chem Phys 2010; 132:074101. [PMID: 20170209 PMCID: PMC2905448 DOI: 10.1063/1.3310809] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2009] [Accepted: 01/16/2010] [Indexed: 11/14/2022] Open
Abstract
We have developed a computational framework for accurate and efficient simulation of stochastic spatially inhomogeneous biochemical systems. The new computational method employs a fractional step hybrid strategy. A novel formulation of the finite state projection (FSP) method, called the diffusive FSP method, is introduced for the efficient and accurate simulation of diffusive transport. Reactions are handled by the stochastic simulation algorithm.
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Affiliation(s)
- Brian Drawert
- Department of Computer Science, University of California-Santa Barbara, Santa Barbara, California 93106, USA.
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