Organization of the cytokeratin network in an epithelial cell. (English) Zbl 1464.92090
Summary: The cytoskeleton is a dynamic three-dimensional structure mainly located in the cytoplasm. It is involved in many cell functions such as mechanical signal transduction and maintenance of cell integrity. Among the three cytoskeletal components, intermediate filaments (the cytokeratin in epithelial cells) are the best candidates for this mechanical role. A model of the establishment of the cytokeratin network of an epithelial cell is proposed to study the dependence of its structural organization on extracellular mechanical environment. To implicitly describe the latter and its effects on the intracellular domain, we use mechanically regulated protein synthesis. Our model is a hybrid of a partial differential equation of parabolic type, governing the evolution of the concentration of cytokeratin, and a set of stochastic differential equations describing the dynamics of filaments. Each filament is described by a stochastic differential equation that reflects both the local interactions with the environment and the non-local interactions via the past history of the filament. A three-dimensional simulation model is derived from this mathematical model. This simulation model is then used to obtain examples of cytokeratin network architectures under given mechanical conditions, and to study the influence of several parameters.
References:
| [1] | Boal, D., Mechanics of the Cell (2002), Cambridge University Press: Cambridge University Press Cambridge |
| [2] | Bolterauer, H.; Limbach, H.-J.; Tuszynski, J., From stochastic to coherent assembly of microtubulesModels and new results, Bioelectrochem. Bioenergetics, 41, 71-76 (1996) |
| [3] | Bray, D., Cell Movements (1992), Garland Publishing, INC: Garland Publishing, INC New York |
| [4] | Chicurel, M.; Singer, R.; Meyer, C.; Ingber, D., Recruitment of mRNA and ribosomes to focal adhesions triggered by integrin binding and mechanical tension, Nature, 392, 730-733 (1998) |
| [5] | Chou, Y.; Goldman, R., Intermediate filaments on the move, J. Cell Biol., 150, 101-105 (2000) |
| [6] | Chou, C.; Riopel, C.; Rott, L.; Omary, M., A significant soluble keratin fraction in ‘simple’ epithelial cells. Lack of an apparent phosphorylation and glycosylation role in keratin solubility, J. Cell Sci., 105, 433-444 (1993) |
| [7] | Civelekoglu, G.; Edelstein-Keshet, L., Modelling the dynamics of F-actin in the cell, Bull. Math. Biol., 56, 587-616 (1994) · Zbl 0805.92004 |
| [8] | Coulombe, P.; Bousquet, O.; Ma, L.; Yamada, S.; Wirtz, D., The ‘ins’ and ‘outs’ of intermediate filament organization, Trends Cell Biol., 10, 420-428 (2000) |
| [9] | Dallon, J.; Sherratt, J. A., A mathematical model for spatially varying extracellular matrix alignment, SIAM J. Appl. Math., 61, 506-527 (2000) · Zbl 1012.92019 |
| [10] | Dallon, J.; Sherratt, J.; Maini, P., Mathematical modelling of extracellular matrix dynamics using discrete cellsFibers orientation and tissue regeneration, J. Theor. Biol., 199, 449-471 (1999) |
| [11] | Dufort, P. A.; Lumsden, C., Cellular automaton model of the actin cytoskeleton, Cell Motility Cytoskeleton, 25, 87-104 (1993) |
| [12] | Eckes, B.; Dogic, D.; Colucci-Guyon, E.; Wang, N.; Maniotis, A.; Ingber, D.; Merckling, A.; Langa, M.; Aumailley, F.; Delouvée, A.; Koteliansky, V.; Babinet, C.; Krieg, T., Impaired mechanical stability, migration and contractile capacity in vimentin-deficient fibroblast, J. Cell Sci., 111, 1897-1907 (1998) |
| [13] | Edelstein-Keshet, L.; Ermentrout, G., Models for spatial polymerization dynamics of rod-like polymers, J. Math. Biol., 40, 64-96 (2000) · Zbl 0998.92015 |
| [14] | Geisler, N.; Schunemann, J.; Weber, K.; Haner, M.; Aebi, U., Assembly and architecture of invertebrate cytoplasmic intermediate filaments reconcile features of vertebrate cytoplasmic and nuclear lamin-type intermediate filaments, J. Mol. Biol., 282, 601-617 (1998) |
| [15] | Goldman, R.; Khuon, S.; Chou, Y.; Opal, P.; Steinert, P., The function of intermediate filaments in cell shape and cytoskeletal integrity, J. Cell Biol., 134, 971-983 (1996) |
| [16] | Harris, J.; Stocker, H., Handbook of Mathematics and Computational Science (1998), Springer: Springer Berlin · Zbl 0962.00507 |
| [17] | Hatzfeld, M.; Burba, M., Function of type I and type II keratin head domainstheir role in dimer, tetramer and filament formation, J. Cell Sci., 107, 1959-1972 (1994) |
| [18] | Herrmann, H.; Aebi, U., Intermediate filaments and their associatesmulti-talented structural elements specifying cytoarchitecture and cytodynamics, Curr. Opin. Cell Biol., 12, 79-90 (2000) |
| [19] | Howard, J., Mechanics of Motor Proteins and the Cytoskeleton (2001), Sinauer Associated Inc |
| [20] | Ingber, D., Cellular tensegritydefining new rules of biological design that govern the cytoskeleton, J. Cell Sci., 104, 613-627 (1993) |
| [21] | Ingber, D., Tensegritythe architectural basis of cellular mechanotransduction, Annu. Rev. Physiol., 59, 575-599 (1997) |
| [22] | Janosi, I.; Chretien, D.; Flyvbjerg, H., Modeling elastic properties of microtubule tips and walls, Eur. Biophys. J., 27, 501-513 (1998) |
| [23] | Jansen, R., RNA-cytoskeletal associations, FASEB J., 13, 455-466 (1999) |
| [24] | Ma, L.; Xu, J.; Coulombe, P.; Wirtz, D., Keratin filament suspensions show unique micromechanical properties, J. Biol. Chem., 274, 19145-19151 (1999) |
| [25] | McGrath, J.; Tardy, Y.; Dewey, C.; Meister, J.; Hartwig, J., Simultaneous measurements of actin filament turnover, filament fraction, and monomer diffusion in endothelial cells, Biophys. J., 75, 2070-2078 (1998) |
| [26] | Mech, R., Prusinkiewicz, P., 1996. Visual models of plants interacting with their environment. In: Proceedings of SIGGRAPH 96, New Orleans, Louisiana, August 4-9, 1996, In Computer Graphics. ACM SIGGRAPH, New York.; Mech, R., Prusinkiewicz, P., 1996. Visual models of plants interacting with their environment. In: Proceedings of SIGGRAPH 96, New Orleans, Louisiana, August 4-9, 1996, In Computer Graphics. ACM SIGGRAPH, New York. |
| [27] | Mogilner, A.; Edelstein-Keshet, L., Spatio-angular order in populations of self-aligning objectsformation of oriented patches, Physica D, 89, 346-367 (1996) · Zbl 0885.92007 |
| [28] | Mogilner, A.; Oster, G., The polymerization ratchet model explains the force-velocity relation for growing microtubules, Eur. Biophys. J., 28, 235-242 (1999) |
| [29] | Portet, S.; Vassy, J.; Beil, M.; Millot, G.; Hebbache, A.; Rigaut, J.; Schoevaert, D., Quantitative analysis of cytokeratin network topology in the MCF7 cell line, Cytometry, 35, 203-213 (1999) |
| [30] | Potard, U.; Butler, J. P.; Wang, N., Cytoskeletal mechanics in confluent epithelial cells probed through integrins and E-cadherins, AJP—Cell Physiol., 272, C1654-C1663 (1997) |
| [31] | Robert, C.; Bouchiba, M.; Robert, R.; Margolis, R.; Job, D., Self organization of the microtubule network. A diffusion based model, Biol. Cell, 68, 177-181 (1990) |
| [32] | Sarria, A.; Lieber, J.; Nordeen, S.; Evans, R., The presence or absence of a vimentin-type intermediate filament network affects the shape of the nucleus in human SW-13 cells, J. Cell Sci., 107, 1593-1607 (1994) |
| [33] | Sept, D.; Limbach, H.; Bolterauer, H.; Tuszynski, J., A chemical kinetics model for microtubule oscillations, J. Theor. Biol., 197, 77-88 (1999) |
| [34] | Sherratt, J. A.; Lewis, J., Stress-induced alignment of actin filaments and the mechanics of cytogel, Bull. Math. Biol., 55, 637-654 (1993) · Zbl 0765.92008 |
| [35] | Smith, E.; Fuchs, E., Defining the interactions between intermediate filaments and desmosomes, J. Cell Biol., 141, 1229-1241 (1998) |
| [36] | Sonnenberg, A.; de Melker, A.; Martinez de Velasco, A.; Janssen, H.; Calafat, J.; Niessen, C., Formation of hemidesmosomes in cells of a transformed murine mammary tumor cell line and mechanisms involved in adherence of these cells to laminin and kalinin, J. Cell Sci., 106, 1083-1102 (1993) |
| [37] | Spiros, A.; Edelstein-Keshet, L., Testing a model for the dynamics of actin structures with biological parameter values, Bull. Math. Biol., 60, 275-305 (1998) · Zbl 1053.92505 |
| [38] | Stokes, C.; Lauffenburger, D., Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis, J. Theor. Biol., 152, 377-403 (1991) |
| [39] | Strikwerda, J., Finite Difference Schemes and Partial Differential Equations (1989), Wadsworth and Brooks: Wadsworth and Brooks California · Zbl 0681.65064 |
| [40] | Suciu, A.; Civelekoglu, G.; Tardy, Y.; Meister, J., Model for the alignment of actin filaments in endothelial cells subjected to fluid shear stress, Bull. Math. Biol., 59, 1029-1046 (1997) · Zbl 0894.92014 |
| [41] | Thoumine, O.; Ziegler, T.; Girard, P.; Nerem, R., Elongation of confluent endothelial cells in culture: The importance of fields of force in the associated alterations of their cytoskeletal structure, Exp. Cell Res., 219, 427-441 (1995) |
| [42] | Vaario, J.; Onitsuka, A.; Shimohara, K., Formation of neural structures, (Husbands, P.; Harvey, I., The Proceedings of the Fourth European Conference on Artificial Life (1997), The MIT Press: The MIT Press Boston) |
| [43] | Vassy, J.; Portet, S.; Beil, M.; Millot, G.; Fauvel-Lafeve, F.; Karniguian, A.; Gasset, G.; Irinopoulou, T.; Calvo, F.; Rigaut, J.; Schoevaert, D., The effect of weightlessness on cytoskeleton architecture and proliferation of human breast cancer cell line MCF-7, FASEB J. Express, 15, 1104-1106 (2001) |
| [44] | Wang, J., Substrate deformation determines actin cytoskeleton reorganizationa mathematical modeling and experimental study, J. Theor. Biol., 202, 33-41 (2000) |
| [45] | Wang, N.; Ingber, D., Control of cytoskeletal mechanics by extracellular matrix, cell shape, and mechanical tension, Biophys. J., 66, 2181-2189 (1994) |
| [46] | Wang, N.; Stamenovic, D., Contribution of intermediate filaments to cell stiffness, stiffening and growth, Am. J. Physiol. Cell Physiol., 279, 188-194 (2000) |
| [47] | Wendling, S.; Oddou, C.; Isabey, D., Stiffening response of a cellular tensegrity model, J. Theor. Biol., 196, 309-325 (1999) |
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