Analysis of pattern formation in reaction-diffusion models for cell polarization
department or school: Science, Faculty of
department or school: Mathematics, Department of
data provider: DSpace
degree campus: UBCV
creator: Liu, Yue
issued: 2019-04-18T21:10:41Z
issued: 2019
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: Small GTPases are a family of signalling proteins that regulates cell shape through actin assembly. Actin filaments are a major component of the cellular cytoskeleton, a supporting structure of the cell. Patterns of GTPase activity are related to a variety of cell behaviors, including cell polarization, formation of protrusions such as filopodia, and actin waves. These phenomena are in turn related to cell migration, cancer metastasis and viral infection. We seek to investigate pattern formation in the context of GTPase activity through a variant of the reaction-diffusion partial differential equation model, known as the Wave Pinning Model. By determining the possible spatio-temporal patterns, as well as their required conditions, we can better understand the cellular behaviors corresponding to these patterns. We first introduce and motivate the wave pinning model and its extensions involving F-actin feedback and source-sink terms. Next, we explore the behavior of the model with numerical simulations. We have identified patterns of localized spots, travelling waves, pulses, and others. We interpret some of these patterns as cell polarization, filopodia formation, and actin waves, as well as other complex behaviors that do not closely resemble common experimental observations. Next, we delineate distinct parameter regimes with Turing analysis and local perturbation analysis (LPA). Turing analysis is a classical method for determining linear stability of homogeneous steady states. LPA is a recently developed technique that is able to detect instabilities to perturbations of finite size that cannot be detected by Turing analysis. LPA has the caveat that it describes only the limiting behavior of the system as the ratio of diffusion coefficient of the two forms of GTPase goes to zero. We also study the effects stemming from the interaction of GTPase dynamics and the deforming cell boundary with a simplified wave pinning model coupled with cell size, and with Cellular Po…
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/69812
note: Analysis of pattern formation inreaction-diffusion models for cellpolarizationbyYue LiuB.Math. Hons., University of Waterloo, 2017A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Mathematics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)April 2019c© Yue Liu 2019The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis/dissertation entitled: Analysis of pattern formation in reaction-diffusion models for cell polarization submitted by Yue Liu in partial fulfillment of the requirements for the degree of Master of Science in Mathematics Examining Committee: Leah Edelstein-Keshet, Mathematics Supervisor Eric Cytrynbaum, Mathematics Supervisory Committee Member Wayne Nagata, Mathematics Supervisory Committee Member iiAbstractSmall GTPases are a family of signalling proteins that regulates cell shapethrough actin assembly. Actin filaments are a major component of the cel-lular cytoskeleton, a supporting structure of the cell. Patterns of GTPaseactivity are related to a variety of cell behaviors, including cell polariza-tion, formation of protrusions such as filopodia, and actin waves. Thesephenomena are in turn related to cell migration, cancer metastasis and viralinfection. We seek to investigate pattern formation in the context of GTPaseactivity through a variant of the reaction-diffusion partial differential equa-tion model, known as the Wave Pinning Model. By determining the possiblespatio-temporal patterns, as well as their required conditions, we can betterunderstand the cellular behaviors corresponding to these patterns.We first introduce and motivate the wave pinning model and its exten-sions involving F-actin feedback and source-sink terms. Next, we explorethe behavior of the model with numerical simulations. We have identifiedpatterns of localized spots, travelling waves, pulses, an…
has type: Thesis/Dissertation
date issued: 2019-05
is shown at: 10.14288/1.0378329
language: eng
degree discipline: Mathematics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
type: Text
identifier URI: http://hdl.handle.net/2429/69812