Abstract
Cell motility is an essential phenomenon in almost all living organisms. It is natural to think that behavioral or shape changes of a cell bear information about the underlying mechanisms that generate these changes. Reading cell motion, namely, understanding the underlying biophysical and mechanochemical processes, is of paramount importance. The mathematical model developed in this paper determines some physical features and material properties of the cells locally through analysis of live cell image sequences and uses this information to make further inferences about the molecular structures, dynamics, and processes within the cells, such as the actin network, microdomains, chemotaxis, adhesion, and retrograde flow. The generality of the principals used in formation of the model ensures its wide applicability to different phenomena at various levels. Based on the model outcomes, we hypothesize a novel biological model for collective biomechanical and molecular mechanism of cell motion.
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Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., & Walter, P. (2002). Molecular biology of the cell. New York: Garland.
Alt, W., & Dembo, M. (1999). Cytoplasm dynamics and cell motion: two-phase flow models. Math. Biosci., 156, 207–228.
Bottino, D., Mogilner, A., Roberts, T., Stewart, M., & Oster, G. (2002). How nematode sperm crawl. J. Cell Sci., 115, 367–384.
Bray, D. (2001). Cell movements. New York: Garland.
Caille, N., Thoumine, O., Tardy, Y., & Meister, J. J. (2002). Contribution of the nucleus to the mechanical properties of endothelial cells. J. Biomech., 35(2), C177–C188.
Campi, G., Varma, R., & Dustin, M. L. (2005). Actin and agonist mhc-peptide complex-dependent t cell receptor microclusters as scaffolds for signaling. J. Exp. Med., 202(8), 1031–1036.
Coskun, H. (2006). Mathematical models for cell movements and model based inverse problems. Ph.D. thesis, University of Iowa.
Coskun, H. (2009). A continuum model with free boundary formulation and the inverse problem for ameboid cell motility. Preprint.
Coskun, H., Li, Y., & Mackey, M. A. (2007). Ameboid cell motility: A model and inverse problem, with an application to live cell imaging data. J. Theor. Biol., 244(2), 169–179.
Dobereiner, H. G., Dubin-Thaler, B. J., Hofman, J. M., Xenias, H. S., Sims, T. N., Giannone, G., Dustin, M. L., Wiggins, C. H., & Sheetz, M. P. (2006). Lateral membrane waves constitute a universal dynamic pattern of motile cells. Phys. Rev. Lett., 97(3), 038102.
Defilippi, P., Olivo, C., Venturino, M., Dolce, L., Silengo, L., & Tarone, G. (1999). Actin cytoskeleton organization in response to integrin-mediated adhesion. Microsc. Res. Tech., 47, 67–78.
DiMilla, P. A., Barbee, K., & Lauffenburger, D. A. (1991). Mathematical model for the effects of adhesion and mechanics on cell migration speed. Biophys. J., 60, 15–37.
Dong, C., & Skalak, R. (1992). Leukocyte deformability: finite-element modeling of large viscoelastic deformation. J. Theor. Biol., 158, 173–193.
Fournier, M. F., Sauser, R., Ambrosi, D., Meister, J. J., & Verkhovsky, A. B. (2010). Force transmission in migrating cells. J. Cell Biol., 188(2), 287–297.
Giannone, G., Dubin-Thaler, B. J., Rossier, O., Cai, Y., Chaga, O., Jiang, G., Beaver, W., Dobereiner, H. G., Freund, Y., Borisy, G., & Sheetz, M. P. (2007). Lamellipodial actin mechanically links myosin activity with adhesion-site formation. Cell, 128(3), 561–575.
Glading, A., Lauffenburger, D. A., & Wells, A. (2002). Cutting to the chase: calpain proteases in cell motility. Trends Cell Biol., 12(1), 46–54.
Gupton, S. L., Anderson, K. L., Kole, T. P., Fischer, R. S., Ponti, A., Hitchcock-DeGregori, S. E., Danuser, G., Fowler, V. M., Wirtz, D., Hanein, D., & Waterman-Storer, C. M. (2005). Cell migration without a lamellipodium. J. Cell Biol., 168(4), 619–631.
Kass, M., Witkin, A., & Terzopoulos, D. (1987). Snakes: Active contour models. Int. J. Comput. Vis., 1, 321–331.
Koestler, S. A., Auinger, S., Vinzenz, M., Rottner, K., & Small, J. V. (2008). Differentially oriented populations of actin filaments generated in lamellipodia collaborate in pushing and pausing at the cell front. Nat. Cell Biol., 10(3), 306–313.
Krauss, K., & Altevogt, P. (1999). Integrin leukocyte function-associated antigen-1-mediated cell binding can be activated by clustering of membrane rafts. J. Biol. Chem., 274(52), 36,921–36,927.
Kuusela, E., & Alt, W. (2009). Continuum model of cell adhesion and migration. J. Math. Biol., 58(1), 135–161.
Laude, A. J., & Prior, I. A. (2004). Plasma membrane microdomains: Organization, function and trafficking (review). Mol. Membr. Biol., 21(3), 193–205.
Lee, J., Leonard, M., Oliver, T., Ishihara, A., & Jacobson, K. (1994). Traction forces generated by locomoting keratocytes. J. Cell Biol., 127(6), 1957–1964.
Lekka, M., Laidler, P., Gil, D., Lekki, J., Stachura, Z., & Hrynkiewicz, A. Z. (1999). Elasticity of normal and cancerous human bladder cells studied by scanning force microscopy. Eur. Biophys. J., 28(4), 312–316.
Machacek, M., & Danuser, G. (2006). Morphodynamic profiling of protrusion phenotypes. Biophys. J., 90(4), 1439–1452.
Marella, S. V., & Udaykumar, H. S. (2004). Computational analysis of the deformability of leukocytes modeled with viscous and elastic structural components. Phys. Fluids, 16(2), 244–264.
Mitchell, J. S., Kanca, O., & McIntyre, B. W. (2002). Lipid microdomain clustering induces a redistribution of antigen recognition and adhesion molecules on human t lymphocytes. J. Immunol., 168(6), 2737–2744.
Mogilner, A., & Edelstein-Keshet, L. (2002). Regulation of actin dynamics in rapidly moving cells: a quantitative analysis. Biophys. J., 83, 1237–1258.
Mogilner, A., Marland, E., & Bottino, D. (2000). A minimal model of locomotion applied to the steady gliding movement of fish keratocyte cells. In P. K. Maini & H. G. Othmer (Eds.), IMA vol. math. appl., Frontiers in application of mathematics : Vol. 121. Mathematical models for biological pattern formation (pp. 269–294). New York: Springer.
Mogilner, A., & Verzi, D. (2003). A simple 1-D physical model for the crawling nematode sperm cell. J. Stat. Phys., 110, 1169–1189.
Pollard, T., Blanchoin, L., & Mullins, R. D. (2000). Biophysics of actin filament dynamics in nonmuscle cells. Ann. Rev. Biophys. Biomol. Struct., 29, 545–576.
Ponti, A., Machacek, M., Gupton, S. L., Waterman-Storer, C. M., & Danuser, G. (2004). Two distinct actin networks drive the protrusion of migrating cells. Science, 305(5691), 1782–1786.
Ream, R. A., Theriot, J. A., & Somero, G. N. (2003). Influences of thermal acclimation and acute temperature change on the motility of epithelial wound-healing cells (keratocytes) of tropical, temperate and antarctic fish. J. Exp. Biol., 206(24), 4539–4551.
Reynolds, A. R., Tischer, C., Verveer, P. J., Rocks, O., & Bastiaens, P. I. H. (2003). Egfr activation coupled to inhibition of tyrosine phosphatases causes lateral signal propagation. Nat. Cell Biol., 5(5), 447–453.
Rubinstein, B., Fournier, M. F., Jacobson, K., Verkhovsky, A. B., & Mogilner, A. (2009). Actin-myosin viscoelastic flow in the keratocyte lamellipod. Biophys. J., 97(7), 1853–1863.
Sacan, A., Ferhatosmanoglu, H., & Coskun, H. (2008). Celltrack: an open-source software for cell tracking and motility analysis. Bioinformatics, 24(14), 1647–1649.
Schmid-Schönbein, G., Kosawada, T., Skalak, R., & Chien, S. (1995). Membrane model of endothelial cells and leukocytes. A proposal for the origin of a cortical stress. J. Biomech. Eng., 117, 171–178.
Simons, K., & Toomre, D. (2000). Lipid rafts and signal transduction. Nat. Rev. Mol. Cell Biol., 1(1), 31–39.
Vallotton, P., & Small, J. V. (2009). Shifting views on the leading role of the lamellipodium in cell migration: speckle tracking revisited. J. Cell Sci., 122(12), 1955–1958.
Vallotton, P., Danuser, G., Bohnet, S., Meister, J. J., & Verkhovsky, A. B. (2005). Tracking retrograde flow in keratocytes: News from the front. Mol. Biol. Cell, 16(3), 1223–1231.
Ward, K., Li, W., Zimmer, S., & Davis, T. (1991). Viscoelastic properties of transformed cells: role in tumor cell progression and metastasis formation. Biorheology, 28(3–4), 301–313.
Wottawah, F., Schinkinger, S., Lincoln, B., Ebert, S., Mooller, K., Sauer, F., Travis, K., & Guck, J. (2005). Characterizing single suspended cells by optorheology. Acta Biomater., 1(3), 263–271.
Yanai, M., Butler, J. P., Suzuki, T., Sasaki, H., & Higuchi, H. (2004). Regional rheological differences in locomoting neutrophils. Am. J. Physiol. Cell Physiol., 287, C603–C611.
Yeung, A., & Evans, E. (1989). Cortical shell-liquid core model for passive flow of liquid-like spherical cells into micropipets. Biophys. J., 56, 139–149.
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Annotated PtK1 epithelial cell membrane motion shows the relation between displacement and polymerization or depolymerization (MOV 794 KB)
Annotated PtK1 epithelial cell membrane local motion (i=47,…,53) shows the relation between displacement and polymerization or depolymerization (MOV 457 KB)
Annotated PtK1 epithelial cell (lamellipodium) membrane motion (MOV 1.26 MB)
Annotated PtK1 epithelial cell lamella (transition) line motion (MOV 1.06 MB)
Annotated PtK1 epithelial cell treated with CytD (MOV 1.05 MB)
Annotated movie of a neutrophil chasing bacteria (MOV 703 KB)
Annotated movie of a keratocyte (MOV 319 KB)
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Coskun, H., Coskun, H. Cell Physician: Reading Cell Motion. Bull Math Biol 73, 658–682 (2011). https://doi.org/10.1007/s11538-010-9580-x
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DOI: https://doi.org/10.1007/s11538-010-9580-x