Simulation of chemotactic migration of a crawling cell by finite elements in a two-dimensional framework

ilustraciones a color, tablas

Autores:
Hernández Aristizábal, David
Tipo de recurso:
Fecha de publicación:
2021
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
eng
OAI Identifier:
oai:repositorio.unal.edu.co:unal/79543
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/79543
https://repositorio.unal.edu.co/
Palabra clave:
620 - Ingeniería y operaciones afines::629 - Otras ramas de la ingeniería
Simulación (Informática)
Computer simulation
Quimiotaxis
Chemotaxis
Células Quimiorreceptoras
Chemoreceptor Cells
computational cell migration
ESFEM
Moving mesh
bulk-surface PDE
Migración celular computacional
Método de elementos finitos en superficies en evolución
Malla en movimiento
EDP de bulto y superficie
Rights
openAccess
License
Atribución-NoComercial-SinDerivadas 4.0 Internacional
id UNACIONAL2_e58342034310da322e0b09ce7e767baa
oai_identifier_str oai:repositorio.unal.edu.co:unal/79543
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.eng.fl_str_mv Simulation of chemotactic migration of a crawling cell by finite elements in a two-dimensional framework
dc.title.translated.spa.fl_str_mv Simulación del movimiento tipo arrastrado de una célula en migración tipo quimiotáctica por elementos finitos en un dominio bidimensional
title Simulation of chemotactic migration of a crawling cell by finite elements in a two-dimensional framework
spellingShingle Simulation of chemotactic migration of a crawling cell by finite elements in a two-dimensional framework
620 - Ingeniería y operaciones afines::629 - Otras ramas de la ingeniería
Simulación (Informática)
Computer simulation
Quimiotaxis
Chemotaxis
Células Quimiorreceptoras
Chemoreceptor Cells
computational cell migration
ESFEM
Moving mesh
bulk-surface PDE
Migración celular computacional
Método de elementos finitos en superficies en evolución
Malla en movimiento
EDP de bulto y superficie
title_short Simulation of chemotactic migration of a crawling cell by finite elements in a two-dimensional framework
title_full Simulation of chemotactic migration of a crawling cell by finite elements in a two-dimensional framework
title_fullStr Simulation of chemotactic migration of a crawling cell by finite elements in a two-dimensional framework
title_full_unstemmed Simulation of chemotactic migration of a crawling cell by finite elements in a two-dimensional framework
title_sort Simulation of chemotactic migration of a crawling cell by finite elements in a two-dimensional framework
dc.creator.fl_str_mv Hernández Aristizábal, David
dc.contributor.advisor.none.fl_str_mv Garzón Alvarado, Diego Alexánder
Madzvamuse, Anotida
dc.contributor.author.none.fl_str_mv Hernández Aristizábal, David
dc.contributor.researchgroup.spa.fl_str_mv GNUM - Grupo de Modelado y Métodos Numericos en Ingeniería
dc.subject.ddc.spa.fl_str_mv 620 - Ingeniería y operaciones afines::629 - Otras ramas de la ingeniería
topic 620 - Ingeniería y operaciones afines::629 - Otras ramas de la ingeniería
Simulación (Informática)
Computer simulation
Quimiotaxis
Chemotaxis
Células Quimiorreceptoras
Chemoreceptor Cells
computational cell migration
ESFEM
Moving mesh
bulk-surface PDE
Migración celular computacional
Método de elementos finitos en superficies en evolución
Malla en movimiento
EDP de bulto y superficie
dc.subject.other.none.fl_str_mv Simulación (Informática)
Computer simulation
dc.subject.decs.none.fl_str_mv Quimiotaxis
Chemotaxis
Células Quimiorreceptoras
Chemoreceptor Cells
dc.subject.proposal.eng.fl_str_mv computational cell migration
ESFEM
Moving mesh
bulk-surface PDE
dc.subject.proposal.spa.fl_str_mv Migración celular computacional
Método de elementos finitos en superficies en evolución
Malla en movimiento
EDP de bulto y superficie
description ilustraciones a color, tablas
publishDate 2021
dc.date.accessioned.none.fl_str_mv 2021-05-20T17:59:51Z
dc.date.available.none.fl_str_mv 2021-05-20T17:59:51Z
dc.date.issued.none.fl_str_mv 2021
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/79543
dc.identifier.instname.spa.fl_str_mv Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv https://repositorio.unal.edu.co/
url https://repositorio.unal.edu.co/handle/unal/79543
https://repositorio.unal.edu.co/
identifier_str_mv Universidad Nacional de Colombia
Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.references.spa.fl_str_mv Alberts, B., Johnson, A., Lewis, J., Morgan, D., Raff, M., Roberts, K., and Walter, P. (2015). The Cytoskeleton. In Molecular Biology of the Cell, chapter 16, pages 880-962. Garland Science, 6 edition.
Alhazmi, M. (2019). Exploring Mechanisms for Pattern Formation through Coupled Bulk-Surface PDEs in Case of Non-linear Reactions. International Journal of Advanced Computer Science and Applications, 10(3):556-568.
Allard, J. and Mogilner, A. (2013). Traveling waves in actin dynamics and cell motility. Current Opinion in Cell Biology, 25(1):107-115.
Alt, W. and Tranquillo, R. T. (1995). Basic morphogenetic system modeling shape changes of migrating cells, how to explain fluctuating lamellipodial dynamics. Journal of Biological Systems, 3(4):905-916.
Baaijens, F. P., Trickey, W. R., Laursen, T. A., and Guilak, F. (2005). Large deformation finite element analysis of micropipette aspiration to determine the mechanical properties of the chondrocyte. Annals of Biomedical Engineering, 33(4):494-501.
Barreira, R., Elliott, C. M., and Madzvamuse, A. (2011). Mathematical Biology The surface finite element method for pattern formation on evolving biological surfaces. J Math Biol, 63:1095-1119.
Barrett, J. W., Garcke, H., and Nürnberg, R. (2020). Chapter 4 - Parametric finite element approximations of curvature-driven interface evolutions. In Bonito, A. and Nochetto, R. H. B. T. H. o. N. A., editors, Geometric Partial Differential Equations - Part I, volume 21, pages 275-423. Elsevier.
Bhattacharya, S. and Iglesias, P. A. (2016). The Regulation of Cell Motility Through an Excitable Network. IFAC PapersOnLine, 49(26):357-363.
Brezzi, F., Falk, R. S., and Donatella Marini, L. (2014). Basic principles of mixed Virtual Element Methods. ESAIM: Mathematical Modelling and Numerical Analysis, 48(4):1227-1240.
Calderwood, D. A., Campbell, I. D., and Critchley, D. R. (2013). Talins and kindlins: Partners in integrin-mediated adhesion. Nature Reviews Molecular Cell Biology, 14(8):503-517.
Camley, B. A., Zhao, Y., Li, B., Levine, H., and Rappel, W. J. (2017). Crawling and turning in a minimal reaction-diffusion cell motility model: Coupling cell shape and biochemistry. Physical Review E, 95(1):1-13.
Campbell, E. J., Bagchi, P., Campbell, E. J., and Bagchi, P. (2017). A computational model of amoeboid cell swimming A computational model of amoeboid cell swimming. Physics of Fluids, 29:101902:1-101902:16.
Chang, C. M. E., D, D. A. L. P., and D, T. I. M. P. (2003). Motile chondrocytes from newborn calf : migration properties and synthesis of collagen II. Osteoarthritis and Cartilage, 11:603-612.
Cheng, B., Lin, M., Huang, G., Li, Y., Ji, B., Genin, G. M., Deshpande, V. S., Lu, T. J., and Xu, F. (2017). Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses. Physics of Life Reviews, 22-23:88-119.
Cheng, Y. and Othmer, H. (2016). A Model for Direction Sensing in Dictyostelium discoideum: Ras Activity and Symmetry Breaking Driven by a Gβγ-Mediated, Gα2-Ric8 Dependent Signal Transduction Network. PLoS Computational Biology, 12(5):e1004900.
Cooper, G. M. (2000). Structure and Organization of Actin Filaments. In The Cell: A Molecular Approach. Sunderland (MA): Sinauer Associates, 2 edition.
Cotton, M. and Claing, A. (2009). G protein-coupled receptors stimulation and the control of cell migration. Cellular Signalling, 21(7):1045-1053.
Cusseddu, D., Edelstein-Keshet, L., Mackenzie, J. A., Portet, S., and Madzvamuse, A. (2019). A coupled bulk-surface model for cell polarisation. Journal of Theoretical Biology, 481:119-135.
Da Yang, T., Park, J. S., Choi, Y., Choi, W., Ko, T. W., and Lee, K. J. (2011). Zigzag turning preference of freely crawling cells. PLoS ONE, 6(6):e20255.
De Boor, C. (1973). Good approximation by splines with variable knot. In Numerical Solution of Differential Equations, pages 12-20, Dundee. Lecture Notes in Math. 363, Springer, 1974.
Devreotes, P. and Horwitz, A. R. (2015). Signaling Networks that Regulate Cell Migration. Cold Spring Harbor Perspectives in Biology, 7(8):a005959.
Durand, R., Pantoja-rosero, B. G., and Oliveira, V. (2019). A general mesh smoothing method for finite elements. Finite Elements in Analysis & Design, 158(February):17-30.
Dziuk, G. and Elliott, C. M. (2007). Finite elements on evolving surfaces. IMA Journal of Numerical Analysis, 27(2):262-292.
Dziuk, G. and Elliott, C. M. (2013). Finite element methods for surface PDEs. Acta Numerica, 22(April):289-396.
Elliott, C. M. and Ranner, T. (2013). Finite element analysis for a coupled bulk-surface partial differential equation. IMA Journal of Numerical Analysis, 33(2):377-402.
Elliott, C. M., Ranner, T., and Venkataraman, C. (2017). Coupled Bulk-Surface Free Boundary Problems Arising from a Mathematical Model of Receptor-Ligand Dynamics. SIAM Journal on Mathematical Analysis, 49(1):360-397.
Elliott, C. M., Stinner, B., and Venkataraman, C. (2012). Modelling cell motility and chemotaxis with evolving surface finite elements. J. R. Soc. Interface, 9(June):3027-3044.
Elliott, C. M. and Styles, V. (2012). An ALE ESFEM for solving PDEs on evolvoing surfaces. Milan J. Math., 80:469-501.
Engwirda, D. (2005). Unstructured mesh methods for the Navier-Stokes equations.
Engwirda, D. (2014). Locally-optimal Delaunay-refinement and optimisation-based mesh generation. PhD thesis, The University of Sydney.
Friedl, P. and Alexander, S. (2011). Cancer invasion and the microenvironment: Plasticity and reciprocity. Cell, 147(5):992-1009.
Frittelli, M., Madzvamuse, A., and Sgura, I. (2021). Bulk-surface virtual element method for systems of PDEs in two-space dimensions. Numerische Mathematik, 147(2):305-348.
Frittelli, M., Madzvamuse, A., Sgura, I., and Venkataraman, C. (2018). Numerical Preservation of Velocity Induced Invariant Regions for Reaction-Diffusion Systems on Evolving Surfaces. J Sci Comput, 77(2):971-1000.
Fuhrmann, J., Käs, J., and Stevens, A. (2007). Initiation of cytoskeletal asymmetry for cell polarization and movement. Journal of Theoretical Biology, 249:278-288.
Garzón-Alvarado, D. A., Galeano, C., and Mantilla, J. (2012). Numerical tests on pattern formation in 2d heterogeneous mediums : An approach using the schnakenberg model. Dyna, 172:56-66.
Gau, D. and Roy, P. (2020). Single Cell Migration Assay Using Human Breast Cancer MDA-MB-231 Cell Line. Bio-protocol, 10(8):e3586.
George, U. Z., Stéphanou, A., and Madzvamuse, A. (2013). Mathematical modelling and numerical simulations of actin dynamics in the eukaryotic cell. Journal of Mathematical Biology, 66(3):547-593.
Gierer, A. and Meinhardt, H. (1972). A theory of biological pattern formation. Kybernetik, 12(1):30-39.
Goehring, N. W. and Grill, S. W. (2013). Cell polarity : mechanochemical patterning. Trends in Cell Biology, 23(2):72-80.
Harris, P. J. (2017). A simple mathematical model of cell clustering by chemotaxis. Mathematical Biosciences, 294(May):62-70.
Heine, C. J. (2004). Isoparametric finite element approximation of curvature on hypersurfaces.
Holmes, W. R., Park, J., Levchenko, A., and Edelstein-keshet, L. (2017). A mathematical model coupling polarity signaling to cell adhesion explains diverse cell migration patterns. PLoS Comput Biol, 13(5):1-22.
Jarrell, K. F. and McBride, M. J. (2008). The surprisingly diverse ways that prokaryotes move. Nature Reviews Microbiology, 6(6):466-476.
Jeong, H. J., Yoo, R. J., Kim, J. K., Kim, M. H., Park, S. H., Kim, H., Lim, J. W., Do, S. H., Lee, K. C., Lee, Y. J., and Kim, D. W. (2019). Macrophage cell tracking PET imaging using mesoporous silica nanoparticles via in vivo bioorthogonal F-18 labeling. Biomaterials, 199(January):32-39.
Jung, H. J., Park, J. Y., Jeon, H. S., and Kwon, T. H. (2011). Aquaporin-5: A marker protein for proliferation and migration of human breast cancer cells. PLoS ONE, 6(12).
Krause, M. and Gautreau, A. (2014). Steering cell migration: lamellipodium dynamics and the regulation of directional persistence. Nature Reviews Molecular Cell Biology, 15(9):577-590.
Lehtimäki, J., Hakala, M., and Lappalainen, P. (2016). Actin Filament Structures in Migrating Cells. In Jockush, B. M., editor, The Actin Cytoskeleton. Handbook of Experimental Pharmacology, vol. 235, pages 123-152. Springer, Cham.
Lodish, H., Berk, A., Kaiser, C. A., Krieger, M., Bretscher, A., Ploegh, H., Amon, A., and Scott, M. P. (2016). Organizaci´on y Movimiento Celular I: Microfilamentos. In Biolog´ıa Celular y Molecular, chapter 17, pages 773-820. Editorial Médica Panamericana, 7 edition.
Luxenburg, C. and Zaidel-bar, R. (2019). From cell shape to cell fate via the cytoskeleton | Insights from the epidermis. Experimental Cell Research, 378(2):232-237.
Mackenzie, J. A., Nolan, M., Rowlatt, C. F., and Insall, R. H. (2019). An Adaptive Moving Mesh Method for Forced Curve Shortening Flow. SIAM J. Sci. Comput., 41(2):1170-1200.
Madzvamuse, A. and George, U. Z. (2013). The moving grid finite element method applied to cell movement and deformation. Finite Elements in Analysis and Design, 74:76-92.
Madzvamuse, A., Maini, P. K., and Wathen, A. J. (2005). A moving grid finite element method for the simulation of pattern generation by turing models on growing domains. Journal of Scientific Computing, 24(2):247-262.
Meinhardt, H. (1999). Orientation of chemotactic cells and growth cones : models and mechanisms. Journal of Cell Science, 112:2867-2874.
Morales, T. (2007). Chondrocyte Moves : clever strategies ? Osteoarthritis Cartilage, 15(8):861-871.
Mori, Y., Jilkine, A., and Edelstein-Keshet, L. (2008). Wave-pinning and cell polarity from a bistable reaction-diffusion system. Biophysical Journal, 94(9):3684-3697.
Murray, J. D. (2002). Mathematical Biology : I . An Introduction. Springer, 3 edition.
Murray, J. D. (2003). Mathematical Biology II : Spatial Models and Biomedical Applications. Springer, 3 edition.
Neilson, M. P., Mackenzie, J. A., Webb, S. D., and Insall, R. H. (2011). Modeling cell movement and chemotaxis using pseudopod-based feedback. Computational Methods in Science and Engineering, 33(1):1035-1057.
Novak, I. L., Gao, F., Choi, Y.-S., Resasco, D., Schaff, J. C., and Slepchenko, B. M. (2007). Diffusion on a curved surface coupled to diffusion in the volume: Application to cell biology. Journal of Computational Physics, 226(2):1271-1290.
Ojima, Y., Hakamada, K., Nishinoue, Y., Nguyen, M. H., Miyake, J., and Taya, M. (2012). Motility behavior of rpoS -deficient Escherichia coli analyzed by individual cell tracking. Journal of Bioscience and Bioengineering, 114(6):652-656.
Othmer, H. G. (2019). Eukaryotic cell dynamics from crawlers to swimmers. Wiley Interdisciplinary Reviews: Computational Molecular Science, 9(1):e1376.
Page, K., Maini, P. K., and Monk, N. A. M. (2003). Pattern formation in spatially heterogeneous Turing reaction - diffusion models. Physica D, 181:80-101.
Page, K. M., Maini, P. K., and Monk, N. A. M. (2005). Complex pattern formation in reaction-diffusion systems with spatially varying parameters. Physica D, 202:95-115.
Piltti, K. M., Cummings, B. J., Carta, K., Manughian-peter, A., Worne, C. L., Singh, K., Ong, D., Maksymyuk, Y., Khine, M., and Anderson, A. J. (2018). Live-cell time-lapse imaging and single-cell tracking of in vitro cultured neural stem cells - Tools for analyzing dynamics of cell cycle , migration , and lineage selection. Methods, 133:81-90.
Preziosi, L. and Tosin, A. (2009). Multiphase modelling of tumour growth and extracellular matrix interaction: Mathematical tools and applications. Journal of Mathematical Biology, 58(4-5):625-656.
Rätz, A. (2015). Turing-type instabilities in bulk-surface reaction-diffusion systems. Journal of Computational and Applied Mathematics, 289:142-152.
Rätz, A. and Röger, M. (2014). Symmetry breaking in a bulk-surface reaction-diffusion model for signalling networks. Nonlinearity, 27(8):1805-1827.
Ridley, A. J. (2015). Rho GTPase signalling in cell migration. Current Opinion in Cell Biology, 36:103-112.
Ridley, A. J., Schwartz, M. A., Burridge, K., Firtel, R. A., Ginsberg, M. H., Borisy, G., Parsons, J. T., and Horwitz, A. R. (2003). Cell Migration: Integrating Signals from Front to Back. Science, 302(5651):1704-1709.
Rodrigues, D., Barra, L. P., Lobosco, M., and Bastos, F. (2014). Analysis of Turing Instability in Biological Models. In ICCSA, Part VI, pages 576-591.
Salloum, G., Jaafar, L., and El-Sibai, M. (2020). Rho A and Rac1: Antagonists moving forward. Tissue and Cell, 65(March):101364.
Schnakenberg, J. (1979). Simple Chemical Reaction Systems with Limit Cycle Behaviour. J Theor Biol, 81:389-400.
Séguis, J.-C., Burrage, K., Erban, R., and Kay, D. (2012). Simulation of cell movement through evolving environment : a fictitious domain approach. Technical report, University of Oxford.
Sel’kov, E. E. (1968). Self-Oscillations in Glycolysis. European Journal of Biochemistry, 4(1):79-86.
Seydel, R. (2010). Practical Bifurcation and Stability Analysis. Springer, 3 edition. Shah, E. A. and Keren, K. (2013). Mechanical forces and feedbacks in cell motility. Current Opinion in Cell Biology, 25(5):550-557.
Steffen, A., Stradal, T. E. B., and Rottner, K. (2016). Signalling Pathways Controlling Cellular Actin Organization. In Jockush, B. M., editor, The Actin Cytoskeleton. Handbook of Experimental Pharmacology, vol. 235, pages 153-178. Springer, Cham.
Stéphanou, A. and Tracqui, P. (2002). Cytomechanics of cell deformations and migration : from models to experiments. C. R. Biologies, 325:295-308.
Ting, L. H., Jahn, J. R., Jung, J. I., Shuman, B. R., Feghhi, S., Han, S. J., Rodriguez, M. L., and Sniadecki, N. J. (2012). Flow mechanotransduction regulates traction forces , intercellular forces , and adherens junctions Flow mechanotransduction regulates traction forces , intercellular forces , and adherens junctions. Am J Physiol Heart Circ Physiol, 302(March):2220-2229.
Turing, A. M. (1952). The Chemical Basis of Morphogenesis. Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 237(641):37-72. Uriu, K., Morelli, L. G., and Oates, A. C. (2014). Interplay between intercellular signaling and cell movement in development. Seminars in Cell and Developmental Biology, 35:66-72.
Vu, H., Zhou, J., Huang, Y., Hakamivala, A., and Kyung, M. (2019). Development of a dual-wavelength fluorescent nanoprobe for in vivo and in vitro cell tracking consecutively. Bioorganic & Medicinal Chemistry, 27(9):1855-1862.
Warner, H., Wilson, B. J., and Caswell, P. T. (2019). Control of adhesion and protrusion in cell migration by Rho GTPases. Current Opinion in Cell Biology, 56:64-70.
Welf, E. S. and Haugh, J. M. (2011). Signaling pathways that control cell migration: models and analysis. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 3(2):231-240.
Zhao, J., Cao, Y., Dipietro, L. A., and Liang, J. (2017). Dynamic cellular finiteelement method for modelling large-scale cell migration and proliferation under the control of mechanical and biochemical cues : a study of reepithelialization. J. R. Soc. Interface, 14(129).
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial-SinDerivadas 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nd/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial-SinDerivadas 4.0 Internacional
http://creativecommons.org/licenses/by-nd/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.spa.fl_str_mv 1 recurso en línea (77 páginas)
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv Bogotá - Ingeniería - Maestría en Ingeniería - Ingeniería Mecánica
dc.publisher.faculty.spa.fl_str_mv Facultad de Ingeniería
dc.publisher.place.spa.fl_str_mv Bogotá
dc.publisher.branch.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/79543/1/license.txt
https://repositorio.unal.edu.co/bitstream/unal/79543/4/1019106364%20DOCUMENTO%20FINAL%20DE%20TESIS.pdf
https://repositorio.unal.edu.co/bitstream/unal/79543/5/license_rdf
https://repositorio.unal.edu.co/bitstream/unal/79543/6/1019106364%20DOCUMENTO%20FINAL%20DE%20TESIS.pdf.jpg
bitstream.checksum.fl_str_mv cccfe52f796b7c63423298c2d3365fc6
dac15f43a94df74269e68e24820918cd
f7d494f61e544413a13e6ba1da2089cd
9abc4254f6370f9fa7f81d72d701a451
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv repositorio_nal@unal.edu.co
_version_ 1814089563823407104
spelling Atribución-NoComercial-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Garzón Alvarado, Diego Alexánderef8db986d1dadd6d652bfa455a45ec38Madzvamuse, Anotida0008bcc27fe989d0d29bb8097ea44041Hernández Aristizábal, David32e5e1b17ce54f0f7c57cb026973feb5GNUM - Grupo de Modelado y Métodos Numericos en Ingeniería2021-05-20T17:59:51Z2021-05-20T17:59:51Z2021https://repositorio.unal.edu.co/handle/unal/79543Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones a color, tablasLa migración celular es un proceso presente en todas las etapas de la vida que es accionado principalmente por la dinámica del citoesqueleto de actina. Los trabajos experimentales y computacionales han sido clave para elucidar los mecanismos presentes en este fenómeno. Los primeros permiten modelar interacciones intra y extracelulares de forma realística y los segundos permiten aislar y analizar tales interacciones. En este trabajo se presenta un marco computacional capaz de copiar algunas características de la migración celular en dos dimensiones. Se consideran dinámicas membranales y citosólicas que pueden ser activadas o modificadas por señales externas. Los resultados muestran que la implementación computacional es capaz de reproducir las siguientes características fundamentales: (i) polarización en la membrana, (ii) polarización en el citosol y (iii) protusiones dependientes de actina.Cell migration is a process ubiquitous in life that is mainly trigger by the dynamics of the actin cytoskeleton. Experimental and computational works have been key to elucidate the mechanisms underlying this phenomenon. The former allow modelling realistic interactions both at the intra and extracellular level while the later allow the isolation and analysis of such interactions. Here, we present a computational framework able to mimic some two-dimensional cell-migration features considering membrane and cytosolic activities that may be triggered by external cues. The results show that the computational implementation is able to deal with the following fundamental characteristics: (i) membrane polarisation, (ii) cytosolic polarisation, and (iii) actin-dependent protrusions.MaestríaMagíster en Ingeniería - Ingeniería MecánicaModelación computacional1 recurso en línea (77 páginas)application/pdfengUniversidad Nacional de ColombiaBogotá - Ingeniería - Maestría en Ingeniería - Ingeniería MecánicaFacultad de IngenieríaBogotáUniversidad Nacional de Colombia - Sede Bogotá620 - Ingeniería y operaciones afines::629 - Otras ramas de la ingenieríaSimulación (Informática)Computer simulationQuimiotaxisChemotaxisCélulas QuimiorreceptorasChemoreceptor Cellscomputational cell migrationESFEMMoving meshbulk-surface PDEMigración celular computacionalMétodo de elementos finitos en superficies en evoluciónMalla en movimientoEDP de bulto y superficieSimulation of chemotactic migration of a crawling cell by finite elements in a two-dimensional frameworkSimulación del movimiento tipo arrastrado de una célula en migración tipo quimiotáctica por elementos finitos en un dominio bidimensionalTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAlberts, B., Johnson, A., Lewis, J., Morgan, D., Raff, M., Roberts, K., and Walter, P. (2015). The Cytoskeleton. In Molecular Biology of the Cell, chapter 16, pages 880-962. Garland Science, 6 edition.Alhazmi, M. (2019). Exploring Mechanisms for Pattern Formation through Coupled Bulk-Surface PDEs in Case of Non-linear Reactions. International Journal of Advanced Computer Science and Applications, 10(3):556-568.Allard, J. and Mogilner, A. (2013). Traveling waves in actin dynamics and cell motility. Current Opinion in Cell Biology, 25(1):107-115.Alt, W. and Tranquillo, R. T. (1995). Basic morphogenetic system modeling shape changes of migrating cells, how to explain fluctuating lamellipodial dynamics. Journal of Biological Systems, 3(4):905-916.Baaijens, F. P., Trickey, W. R., Laursen, T. A., and Guilak, F. (2005). Large deformation finite element analysis of micropipette aspiration to determine the mechanical properties of the chondrocyte. Annals of Biomedical Engineering, 33(4):494-501.Barreira, R., Elliott, C. M., and Madzvamuse, A. (2011). Mathematical Biology The surface finite element method for pattern formation on evolving biological surfaces. J Math Biol, 63:1095-1119.Barrett, J. W., Garcke, H., and Nürnberg, R. (2020). Chapter 4 - Parametric finite element approximations of curvature-driven interface evolutions. In Bonito, A. and Nochetto, R. H. B. T. H. o. N. A., editors, Geometric Partial Differential Equations - Part I, volume 21, pages 275-423. Elsevier.Bhattacharya, S. and Iglesias, P. A. (2016). The Regulation of Cell Motility Through an Excitable Network. IFAC PapersOnLine, 49(26):357-363.Brezzi, F., Falk, R. S., and Donatella Marini, L. (2014). Basic principles of mixed Virtual Element Methods. ESAIM: Mathematical Modelling and Numerical Analysis, 48(4):1227-1240.Calderwood, D. A., Campbell, I. D., and Critchley, D. R. (2013). Talins and kindlins: Partners in integrin-mediated adhesion. Nature Reviews Molecular Cell Biology, 14(8):503-517.Camley, B. A., Zhao, Y., Li, B., Levine, H., and Rappel, W. J. (2017). Crawling and turning in a minimal reaction-diffusion cell motility model: Coupling cell shape and biochemistry. Physical Review E, 95(1):1-13.Campbell, E. J., Bagchi, P., Campbell, E. J., and Bagchi, P. (2017). A computational model of amoeboid cell swimming A computational model of amoeboid cell swimming. Physics of Fluids, 29:101902:1-101902:16.Chang, C. M. E., D, D. A. L. P., and D, T. I. M. P. (2003). Motile chondrocytes from newborn calf : migration properties and synthesis of collagen II. Osteoarthritis and Cartilage, 11:603-612.Cheng, B., Lin, M., Huang, G., Li, Y., Ji, B., Genin, G. M., Deshpande, V. S., Lu, T. J., and Xu, F. (2017). Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses. Physics of Life Reviews, 22-23:88-119.Cheng, Y. and Othmer, H. (2016). A Model for Direction Sensing in Dictyostelium discoideum: Ras Activity and Symmetry Breaking Driven by a Gβγ-Mediated, Gα2-Ric8 Dependent Signal Transduction Network. PLoS Computational Biology, 12(5):e1004900.Cooper, G. M. (2000). Structure and Organization of Actin Filaments. In The Cell: A Molecular Approach. Sunderland (MA): Sinauer Associates, 2 edition.Cotton, M. and Claing, A. (2009). G protein-coupled receptors stimulation and the control of cell migration. Cellular Signalling, 21(7):1045-1053.Cusseddu, D., Edelstein-Keshet, L., Mackenzie, J. A., Portet, S., and Madzvamuse, A. (2019). A coupled bulk-surface model for cell polarisation. Journal of Theoretical Biology, 481:119-135.Da Yang, T., Park, J. S., Choi, Y., Choi, W., Ko, T. W., and Lee, K. J. (2011). Zigzag turning preference of freely crawling cells. PLoS ONE, 6(6):e20255.De Boor, C. (1973). Good approximation by splines with variable knot. In Numerical Solution of Differential Equations, pages 12-20, Dundee. Lecture Notes in Math. 363, Springer, 1974.Devreotes, P. and Horwitz, A. R. (2015). Signaling Networks that Regulate Cell Migration. Cold Spring Harbor Perspectives in Biology, 7(8):a005959.Durand, R., Pantoja-rosero, B. G., and Oliveira, V. (2019). A general mesh smoothing method for finite elements. Finite Elements in Analysis & Design, 158(February):17-30.Dziuk, G. and Elliott, C. M. (2007). Finite elements on evolving surfaces. IMA Journal of Numerical Analysis, 27(2):262-292.Dziuk, G. and Elliott, C. M. (2013). Finite element methods for surface PDEs. Acta Numerica, 22(April):289-396.Elliott, C. M. and Ranner, T. (2013). Finite element analysis for a coupled bulk-surface partial differential equation. IMA Journal of Numerical Analysis, 33(2):377-402.Elliott, C. M., Ranner, T., and Venkataraman, C. (2017). Coupled Bulk-Surface Free Boundary Problems Arising from a Mathematical Model of Receptor-Ligand Dynamics. SIAM Journal on Mathematical Analysis, 49(1):360-397.Elliott, C. M., Stinner, B., and Venkataraman, C. (2012). Modelling cell motility and chemotaxis with evolving surface finite elements. J. R. Soc. Interface, 9(June):3027-3044.Elliott, C. M. and Styles, V. (2012). An ALE ESFEM for solving PDEs on evolvoing surfaces. Milan J. Math., 80:469-501.Engwirda, D. (2005). Unstructured mesh methods for the Navier-Stokes equations.Engwirda, D. (2014). Locally-optimal Delaunay-refinement and optimisation-based mesh generation. PhD thesis, The University of Sydney.Friedl, P. and Alexander, S. (2011). Cancer invasion and the microenvironment: Plasticity and reciprocity. Cell, 147(5):992-1009.Frittelli, M., Madzvamuse, A., and Sgura, I. (2021). Bulk-surface virtual element method for systems of PDEs in two-space dimensions. Numerische Mathematik, 147(2):305-348.Frittelli, M., Madzvamuse, A., Sgura, I., and Venkataraman, C. (2018). Numerical Preservation of Velocity Induced Invariant Regions for Reaction-Diffusion Systems on Evolving Surfaces. J Sci Comput, 77(2):971-1000.Fuhrmann, J., Käs, J., and Stevens, A. (2007). Initiation of cytoskeletal asymmetry for cell polarization and movement. Journal of Theoretical Biology, 249:278-288.Garzón-Alvarado, D. A., Galeano, C., and Mantilla, J. (2012). Numerical tests on pattern formation in 2d heterogeneous mediums : An approach using the schnakenberg model. Dyna, 172:56-66.Gau, D. and Roy, P. (2020). Single Cell Migration Assay Using Human Breast Cancer MDA-MB-231 Cell Line. Bio-protocol, 10(8):e3586.George, U. Z., Stéphanou, A., and Madzvamuse, A. (2013). Mathematical modelling and numerical simulations of actin dynamics in the eukaryotic cell. Journal of Mathematical Biology, 66(3):547-593.Gierer, A. and Meinhardt, H. (1972). A theory of biological pattern formation. Kybernetik, 12(1):30-39.Goehring, N. W. and Grill, S. W. (2013). Cell polarity : mechanochemical patterning. Trends in Cell Biology, 23(2):72-80.Harris, P. J. (2017). A simple mathematical model of cell clustering by chemotaxis. Mathematical Biosciences, 294(May):62-70.Heine, C. J. (2004). Isoparametric finite element approximation of curvature on hypersurfaces.Holmes, W. R., Park, J., Levchenko, A., and Edelstein-keshet, L. (2017). A mathematical model coupling polarity signaling to cell adhesion explains diverse cell migration patterns. PLoS Comput Biol, 13(5):1-22.Jarrell, K. F. and McBride, M. J. (2008). The surprisingly diverse ways that prokaryotes move. Nature Reviews Microbiology, 6(6):466-476.Jeong, H. J., Yoo, R. J., Kim, J. K., Kim, M. H., Park, S. H., Kim, H., Lim, J. W., Do, S. H., Lee, K. C., Lee, Y. J., and Kim, D. W. (2019). Macrophage cell tracking PET imaging using mesoporous silica nanoparticles via in vivo bioorthogonal F-18 labeling. Biomaterials, 199(January):32-39.Jung, H. J., Park, J. Y., Jeon, H. S., and Kwon, T. H. (2011). Aquaporin-5: A marker protein for proliferation and migration of human breast cancer cells. PLoS ONE, 6(12).Krause, M. and Gautreau, A. (2014). Steering cell migration: lamellipodium dynamics and the regulation of directional persistence. Nature Reviews Molecular Cell Biology, 15(9):577-590.Lehtimäki, J., Hakala, M., and Lappalainen, P. (2016). Actin Filament Structures in Migrating Cells. In Jockush, B. M., editor, The Actin Cytoskeleton. Handbook of Experimental Pharmacology, vol. 235, pages 123-152. Springer, Cham.Lodish, H., Berk, A., Kaiser, C. A., Krieger, M., Bretscher, A., Ploegh, H., Amon, A., and Scott, M. P. (2016). Organizaci´on y Movimiento Celular I: Microfilamentos. In Biolog´ıa Celular y Molecular, chapter 17, pages 773-820. Editorial Médica Panamericana, 7 edition.Luxenburg, C. and Zaidel-bar, R. (2019). From cell shape to cell fate via the cytoskeleton | Insights from the epidermis. Experimental Cell Research, 378(2):232-237.Mackenzie, J. A., Nolan, M., Rowlatt, C. F., and Insall, R. H. (2019). An Adaptive Moving Mesh Method for Forced Curve Shortening Flow. SIAM J. Sci. Comput., 41(2):1170-1200.Madzvamuse, A. and George, U. Z. (2013). The moving grid finite element method applied to cell movement and deformation. Finite Elements in Analysis and Design, 74:76-92.Madzvamuse, A., Maini, P. K., and Wathen, A. J. (2005). A moving grid finite element method for the simulation of pattern generation by turing models on growing domains. Journal of Scientific Computing, 24(2):247-262.Meinhardt, H. (1999). Orientation of chemotactic cells and growth cones : models and mechanisms. Journal of Cell Science, 112:2867-2874.Morales, T. (2007). Chondrocyte Moves : clever strategies ? Osteoarthritis Cartilage, 15(8):861-871.Mori, Y., Jilkine, A., and Edelstein-Keshet, L. (2008). Wave-pinning and cell polarity from a bistable reaction-diffusion system. Biophysical Journal, 94(9):3684-3697.Murray, J. D. (2002). Mathematical Biology : I . An Introduction. Springer, 3 edition.Murray, J. D. (2003). Mathematical Biology II : Spatial Models and Biomedical Applications. Springer, 3 edition.Neilson, M. P., Mackenzie, J. A., Webb, S. D., and Insall, R. H. (2011). Modeling cell movement and chemotaxis using pseudopod-based feedback. Computational Methods in Science and Engineering, 33(1):1035-1057.Novak, I. L., Gao, F., Choi, Y.-S., Resasco, D., Schaff, J. C., and Slepchenko, B. M. (2007). Diffusion on a curved surface coupled to diffusion in the volume: Application to cell biology. Journal of Computational Physics, 226(2):1271-1290.Ojima, Y., Hakamada, K., Nishinoue, Y., Nguyen, M. H., Miyake, J., and Taya, M. (2012). Motility behavior of rpoS -deficient Escherichia coli analyzed by individual cell tracking. Journal of Bioscience and Bioengineering, 114(6):652-656.Othmer, H. G. (2019). Eukaryotic cell dynamics from crawlers to swimmers. Wiley Interdisciplinary Reviews: Computational Molecular Science, 9(1):e1376.Page, K., Maini, P. K., and Monk, N. A. M. (2003). Pattern formation in spatially heterogeneous Turing reaction - diffusion models. Physica D, 181:80-101.Page, K. M., Maini, P. K., and Monk, N. A. M. (2005). Complex pattern formation in reaction-diffusion systems with spatially varying parameters. Physica D, 202:95-115.Piltti, K. M., Cummings, B. J., Carta, K., Manughian-peter, A., Worne, C. L., Singh, K., Ong, D., Maksymyuk, Y., Khine, M., and Anderson, A. J. (2018). Live-cell time-lapse imaging and single-cell tracking of in vitro cultured neural stem cells - Tools for analyzing dynamics of cell cycle , migration , and lineage selection. Methods, 133:81-90.Preziosi, L. and Tosin, A. (2009). Multiphase modelling of tumour growth and extracellular matrix interaction: Mathematical tools and applications. Journal of Mathematical Biology, 58(4-5):625-656.Rätz, A. (2015). Turing-type instabilities in bulk-surface reaction-diffusion systems. Journal of Computational and Applied Mathematics, 289:142-152.Rätz, A. and Röger, M. (2014). Symmetry breaking in a bulk-surface reaction-diffusion model for signalling networks. Nonlinearity, 27(8):1805-1827.Ridley, A. J. (2015). Rho GTPase signalling in cell migration. Current Opinion in Cell Biology, 36:103-112.Ridley, A. J., Schwartz, M. A., Burridge, K., Firtel, R. A., Ginsberg, M. H., Borisy, G., Parsons, J. T., and Horwitz, A. R. (2003). Cell Migration: Integrating Signals from Front to Back. Science, 302(5651):1704-1709.Rodrigues, D., Barra, L. P., Lobosco, M., and Bastos, F. (2014). Analysis of Turing Instability in Biological Models. In ICCSA, Part VI, pages 576-591.Salloum, G., Jaafar, L., and El-Sibai, M. (2020). Rho A and Rac1: Antagonists moving forward. Tissue and Cell, 65(March):101364.Schnakenberg, J. (1979). Simple Chemical Reaction Systems with Limit Cycle Behaviour. J Theor Biol, 81:389-400.Séguis, J.-C., Burrage, K., Erban, R., and Kay, D. (2012). Simulation of cell movement through evolving environment : a fictitious domain approach. Technical report, University of Oxford.Sel’kov, E. E. (1968). Self-Oscillations in Glycolysis. European Journal of Biochemistry, 4(1):79-86.Seydel, R. (2010). Practical Bifurcation and Stability Analysis. Springer, 3 edition. Shah, E. A. and Keren, K. (2013). Mechanical forces and feedbacks in cell motility. Current Opinion in Cell Biology, 25(5):550-557.Steffen, A., Stradal, T. E. B., and Rottner, K. (2016). Signalling Pathways Controlling Cellular Actin Organization. In Jockush, B. M., editor, The Actin Cytoskeleton. Handbook of Experimental Pharmacology, vol. 235, pages 153-178. Springer, Cham.Stéphanou, A. and Tracqui, P. (2002). Cytomechanics of cell deformations and migration : from models to experiments. C. R. Biologies, 325:295-308.Ting, L. H., Jahn, J. R., Jung, J. I., Shuman, B. R., Feghhi, S., Han, S. J., Rodriguez, M. L., and Sniadecki, N. J. (2012). Flow mechanotransduction regulates traction forces , intercellular forces , and adherens junctions Flow mechanotransduction regulates traction forces , intercellular forces , and adherens junctions. Am J Physiol Heart Circ Physiol, 302(March):2220-2229.Turing, A. M. (1952). The Chemical Basis of Morphogenesis. Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 237(641):37-72. Uriu, K., Morelli, L. G., and Oates, A. C. (2014). Interplay between intercellular signaling and cell movement in development. Seminars in Cell and Developmental Biology, 35:66-72.Vu, H., Zhou, J., Huang, Y., Hakamivala, A., and Kyung, M. (2019). Development of a dual-wavelength fluorescent nanoprobe for in vivo and in vitro cell tracking consecutively. Bioorganic & Medicinal Chemistry, 27(9):1855-1862.Warner, H., Wilson, B. J., and Caswell, P. T. (2019). Control of adhesion and protrusion in cell migration by Rho GTPases. Current Opinion in Cell Biology, 56:64-70.Welf, E. S. and Haugh, J. M. (2011). Signaling pathways that control cell migration: models and analysis. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 3(2):231-240.Zhao, J., Cao, Y., Dipietro, L. A., and Liang, J. (2017). Dynamic cellular finiteelement method for modelling large-scale cell migration and proliferation under the control of mechanical and biochemical cues : a study of reepithelialization. J. R. Soc. Interface, 14(129).LICENSElicense.txtlicense.txttext/plain; charset=utf-83964https://repositorio.unal.edu.co/bitstream/unal/79543/1/license.txtcccfe52f796b7c63423298c2d3365fc6MD51ORIGINAL1019106364 DOCUMENTO FINAL DE TESIS.pdf1019106364 DOCUMENTO FINAL DE TESIS.pdfTesis de Maestría en Ingeniería - Ingeniería Mecánicaapplication/pdf4041953https://repositorio.unal.edu.co/bitstream/unal/79543/4/1019106364%20DOCUMENTO%20FINAL%20DE%20TESIS.pdfdac15f43a94df74269e68e24820918cdMD54CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8799https://repositorio.unal.edu.co/bitstream/unal/79543/5/license_rdff7d494f61e544413a13e6ba1da2089cdMD55THUMBNAIL1019106364 DOCUMENTO FINAL DE TESIS.pdf.jpg1019106364 DOCUMENTO FINAL DE TESIS.pdf.jpgGenerated Thumbnailimage/jpeg5633https://repositorio.unal.edu.co/bitstream/unal/79543/6/1019106364%20DOCUMENTO%20FINAL%20DE%20TESIS.pdf.jpg9abc4254f6370f9fa7f81d72d701a451MD56unal/79543oai:repositorio.unal.edu.co:unal/795432023-07-19 23:03:29.373Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.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