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

dc.contributor.advisorGarzón Alvarado, Diego Alexánder
dc.contributor.advisorMadzvamuse, Anotida
dc.contributor.authorHernández Aristizábal, David
dc.contributor.researchgroupGNUM - Grupo de Modelado y Métodos Numericos en Ingenieríaspa
dc.date.accessioned2021-05-20T17:59:51Z
dc.date.available2021-05-20T17:59:51Z
dc.date.issued2021
dc.descriptionilustraciones a color, tablasspa
dc.description.abstractLa 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.spa
dc.description.abstractCell 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.eng
dc.description.degreelevelMaestríaspa
dc.description.degreenameMagíster en Ingeniería - Ingeniería Mecánicaspa
dc.description.researchareaModelación computacionalspa
dc.format.extent1 recurso en línea (77 páginas)spa
dc.format.mimetypeapplication/pdfspa
dc.identifier.instnameUniversidad Nacional de Colombiaspa
dc.identifier.reponameRepositorio Institucional Universidad Nacional de Colombiaspa
dc.identifier.repourlhttps://repositorio.unal.edu.co/spa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/79543
dc.language.isoengspa
dc.publisherUniversidad Nacional de Colombiaspa
dc.publisher.branchUniversidad Nacional de Colombia - Sede Bogotáspa
dc.publisher.facultyFacultad de Ingenieríaspa
dc.publisher.placeBogotáspa
dc.publisher.programBogotá - Ingeniería - Maestría en Ingeniería - Ingeniería Mecánicaspa
dc.relation.referencesAlberts, 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.spa
dc.relation.referencesAlhazmi, 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.spa
dc.relation.referencesAllard, J. and Mogilner, A. (2013). Traveling waves in actin dynamics and cell motility. Current Opinion in Cell Biology, 25(1):107-115.spa
dc.relation.referencesAlt, 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.spa
dc.relation.referencesBaaijens, 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.spa
dc.relation.referencesBarreira, 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.spa
dc.relation.referencesBarrett, 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.spa
dc.relation.referencesBhattacharya, S. and Iglesias, P. A. (2016). The Regulation of Cell Motility Through an Excitable Network. IFAC PapersOnLine, 49(26):357-363.spa
dc.relation.referencesBrezzi, 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.spa
dc.relation.referencesCalderwood, 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.spa
dc.relation.referencesCamley, 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.spa
dc.relation.referencesCampbell, 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.spa
dc.relation.referencesChang, 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.spa
dc.relation.referencesCheng, 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.spa
dc.relation.referencesCheng, 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.spa
dc.relation.referencesCooper, G. M. (2000). Structure and Organization of Actin Filaments. In The Cell: A Molecular Approach. Sunderland (MA): Sinauer Associates, 2 edition.spa
dc.relation.referencesCotton, M. and Claing, A. (2009). G protein-coupled receptors stimulation and the control of cell migration. Cellular Signalling, 21(7):1045-1053.spa
dc.relation.referencesCusseddu, 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.spa
dc.relation.referencesDa 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.spa
dc.relation.referencesDe 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.spa
dc.relation.referencesDevreotes, P. and Horwitz, A. R. (2015). Signaling Networks that Regulate Cell Migration. Cold Spring Harbor Perspectives in Biology, 7(8):a005959.spa
dc.relation.referencesDurand, 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.spa
dc.relation.referencesDziuk, G. and Elliott, C. M. (2007). Finite elements on evolving surfaces. IMA Journal of Numerical Analysis, 27(2):262-292.spa
dc.relation.referencesDziuk, G. and Elliott, C. M. (2013). Finite element methods for surface PDEs. Acta Numerica, 22(April):289-396.spa
dc.relation.referencesElliott, 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.spa
dc.relation.referencesElliott, 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.spa
dc.relation.referencesElliott, 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.spa
dc.relation.referencesElliott, C. M. and Styles, V. (2012). An ALE ESFEM for solving PDEs on evolvoing surfaces. Milan J. Math., 80:469-501.spa
dc.relation.referencesEngwirda, D. (2005). Unstructured mesh methods for the Navier-Stokes equations.spa
dc.relation.referencesEngwirda, D. (2014). Locally-optimal Delaunay-refinement and optimisation-based mesh generation. PhD thesis, The University of Sydney.spa
dc.relation.referencesFriedl, P. and Alexander, S. (2011). Cancer invasion and the microenvironment: Plasticity and reciprocity. Cell, 147(5):992-1009.spa
dc.relation.referencesFrittelli, 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.spa
dc.relation.referencesFrittelli, 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.spa
dc.relation.referencesFuhrmann, J., Käs, J., and Stevens, A. (2007). Initiation of cytoskeletal asymmetry for cell polarization and movement. Journal of Theoretical Biology, 249:278-288.spa
dc.relation.referencesGarzón-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.spa
dc.relation.referencesGau, D. and Roy, P. (2020). Single Cell Migration Assay Using Human Breast Cancer MDA-MB-231 Cell Line. Bio-protocol, 10(8):e3586.spa
dc.relation.referencesGeorge, 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.spa
dc.relation.referencesGierer, A. and Meinhardt, H. (1972). A theory of biological pattern formation. Kybernetik, 12(1):30-39.spa
dc.relation.referencesGoehring, N. W. and Grill, S. W. (2013). Cell polarity : mechanochemical patterning. Trends in Cell Biology, 23(2):72-80.spa
dc.relation.referencesHarris, P. J. (2017). A simple mathematical model of cell clustering by chemotaxis. Mathematical Biosciences, 294(May):62-70.spa
dc.relation.referencesHeine, C. J. (2004). Isoparametric finite element approximation of curvature on hypersurfaces.spa
dc.relation.referencesHolmes, 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.spa
dc.relation.referencesJarrell, K. F. and McBride, M. J. (2008). The surprisingly diverse ways that prokaryotes move. Nature Reviews Microbiology, 6(6):466-476.spa
dc.relation.referencesJeong, 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.spa
dc.relation.referencesJung, 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).spa
dc.relation.referencesKrause, 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.spa
dc.relation.referencesLehtimäki, 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.spa
dc.relation.referencesLodish, 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.spa
dc.relation.referencesLuxenburg, 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.spa
dc.relation.referencesMackenzie, 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.spa
dc.relation.referencesMadzvamuse, 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.spa
dc.relation.referencesMadzvamuse, 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.spa
dc.relation.referencesMeinhardt, H. (1999). Orientation of chemotactic cells and growth cones : models and mechanisms. Journal of Cell Science, 112:2867-2874.spa
dc.relation.referencesMorales, T. (2007). Chondrocyte Moves : clever strategies ? Osteoarthritis Cartilage, 15(8):861-871.spa
dc.relation.referencesMori, 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.spa
dc.relation.referencesMurray, J. D. (2002). Mathematical Biology : I . An Introduction. Springer, 3 edition.spa
dc.relation.referencesMurray, J. D. (2003). Mathematical Biology II : Spatial Models and Biomedical Applications. Springer, 3 edition.spa
dc.relation.referencesNeilson, 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.spa
dc.relation.referencesNovak, 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.spa
dc.relation.referencesOjima, 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.spa
dc.relation.referencesOthmer, H. G. (2019). Eukaryotic cell dynamics from crawlers to swimmers. Wiley Interdisciplinary Reviews: Computational Molecular Science, 9(1):e1376.spa
dc.relation.referencesPage, K., Maini, P. K., and Monk, N. A. M. (2003). Pattern formation in spatially heterogeneous Turing reaction - diffusion models. Physica D, 181:80-101.spa
dc.relation.referencesPage, 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.spa
dc.relation.referencesPiltti, 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.spa
dc.relation.referencesPreziosi, 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.spa
dc.relation.referencesRätz, A. (2015). Turing-type instabilities in bulk-surface reaction-diffusion systems. Journal of Computational and Applied Mathematics, 289:142-152.spa
dc.relation.referencesRätz, A. and Röger, M. (2014). Symmetry breaking in a bulk-surface reaction-diffusion model for signalling networks. Nonlinearity, 27(8):1805-1827.spa
dc.relation.referencesRidley, A. J. (2015). Rho GTPase signalling in cell migration. Current Opinion in Cell Biology, 36:103-112.spa
dc.relation.referencesRidley, 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.spa
dc.relation.referencesRodrigues, D., Barra, L. P., Lobosco, M., and Bastos, F. (2014). Analysis of Turing Instability in Biological Models. In ICCSA, Part VI, pages 576-591.spa
dc.relation.referencesSalloum, G., Jaafar, L., and El-Sibai, M. (2020). Rho A and Rac1: Antagonists moving forward. Tissue and Cell, 65(March):101364.spa
dc.relation.referencesSchnakenberg, J. (1979). Simple Chemical Reaction Systems with Limit Cycle Behaviour. J Theor Biol, 81:389-400.spa
dc.relation.referencesSéguis, 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.spa
dc.relation.referencesSel’kov, E. E. (1968). Self-Oscillations in Glycolysis. European Journal of Biochemistry, 4(1):79-86.spa
dc.relation.referencesSeydel, 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.spa
dc.relation.referencesSteffen, 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.spa
dc.relation.referencesStéphanou, A. and Tracqui, P. (2002). Cytomechanics of cell deformations and migration : from models to experiments. C. R. Biologies, 325:295-308.spa
dc.relation.referencesTing, 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.spa
dc.relation.referencesTuring, 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.spa
dc.relation.referencesVu, 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.spa
dc.relation.referencesWarner, 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.spa
dc.relation.referencesWelf, 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.spa
dc.relation.referencesZhao, 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).spa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.licenseAtribución-NoComercial-SinDerivadas 4.0 Internacionalspa
dc.rights.urihttp://creativecommons.org/licenses/by-nd/4.0/spa
dc.subject.ddc620 - Ingeniería y operaciones afines::629 - Otras ramas de la ingenieríaspa
dc.subject.decsQuimiotaxis
dc.subject.decsChemotaxis
dc.subject.decsCélulas Quimiorreceptoras
dc.subject.decsChemoreceptor Cells
dc.subject.otherSimulación (Informática)
dc.subject.otherComputer simulation
dc.subject.proposalcomputational cell migrationeng
dc.subject.proposalESFEMeng
dc.subject.proposalMoving mesheng
dc.subject.proposalbulk-surface PDEeng
dc.subject.proposalMigración celular computacionalspa
dc.subject.proposalMétodo de elementos finitos en superficies en evoluciónspa
dc.subject.proposalMalla en movimientospa
dc.subject.proposalEDP de bulto y superficiespa
dc.titleSimulation of chemotactic migration of a crawling cell by finite elements in a two-dimensional frameworkeng
dc.title.translatedSimulación del movimiento tipo arrastrado de una célula en migración tipo quimiotáctica por elementos finitos en un dominio bidimensionalspa
dc.typeTrabajo de grado - Maestríaspa
dc.type.coarhttp://purl.org/coar/resource_type/c_bdccspa
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aaspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/masterThesisspa
dc.type.redcolhttp://purl.org/redcol/resource_type/TMspa
dc.type.versioninfo:eu-repo/semantics/acceptedVersionspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa

Archivos

Bloque original

Mostrando 1 - 1 de 1
Cargando...
Miniatura
Nombre:
1019106364 DOCUMENTO FINAL DE TESIS.pdf
Tamaño:
3.85 MB
Formato:
Adobe Portable Document Format
Descripción:
Tesis de Maestría en Ingeniería - Ingeniería Mecánica

Bloque de licencias

Mostrando 1 - 1 de 1
Cargando...
Miniatura
Nombre:
license.txt
Tamaño:
3.87 KB
Formato:
Item-specific license agreed upon to submission
Descripción: