Morphology of cylindrical cell sheets with embedded contractile ring

doi:10.1007/s10483-019-2544-8

摘要/Abstract

摘要： The behavior of large deformations of cellular tissues is usually affected by the local properties of cells and their interactions, resulting in folding which acts as an important role in the embryonic development, as well as growing and spreading of a tumor, which can rapidly promote the stereo complexity of the architecture of the tissues. In the present study, a cylindrical vertex model is constructed to explore the morphology of the tubular cell sheets subject to an embedded contractile ring. It is found that an inner region of the contractile ring in equilibrium will protrude from the tube wall, and it will suddenly collapse when the contractile strength exceeds a threshold, indicating the occurrence of a bifurcation. These results on the effect of embedded contraction in the tubular shell are quite different from the planar cases, which can reveal the importance of the interaction between the geometric and material non-linearity in cylindrical geometry. The dependence of the large deformation on the bending modulus parameters and contraction strength is also analyzed for the cylindrical cell shell.

关键词: vertex model, cylindrical cell sheet, contractile ring, large deformation, protrusion

Abstract: The behavior of large deformations of cellular tissues is usually affected by the local properties of cells and their interactions, resulting in folding which acts as an important role in the embryonic development, as well as growing and spreading of a tumor, which can rapidly promote the stereo complexity of the architecture of the tissues. In the present study, a cylindrical vertex model is constructed to explore the morphology of the tubular cell sheets subject to an embedded contractile ring. It is found that an inner region of the contractile ring in equilibrium will protrude from the tube wall, and it will suddenly collapse when the contractile strength exceeds a threshold, indicating the occurrence of a bifurcation. These results on the effect of embedded contraction in the tubular shell are quite different from the planar cases, which can reveal the importance of the interaction between the geometric and material non-linearity in cylindrical geometry. The dependence of the large deformation on the bending modulus parameters and contraction strength is also analyzed for the cylindrical cell shell.

Key words: vertex model, cylindrical cell sheet, contractile ring, large deformation, protrusion

中图分类号:

92C10
92C05

Nan NAN, Guohui HU. Morphology of cylindrical cell sheets with embedded contractile ring[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(12): 1847-1860.

[1]	ALT, S., GANGULY, P., and SALBREUX, G. Vertex models:from cell mechanics to tissue morphogenesis. Philosophical Transactions of the Royal Society B:Biological Sciences, 372(1720), 20150520(2017)
[2]	FLETCHER, A. G., COOPER, F., and BAKER, R. E. Mechanocellular models of epithelial morphogenesis. Philosophical Transactions of the Royal Society B:Biological Sciences, 372(1720), 20150519(2017)
[3]	MERKEL, M. and MANNING, M. L. Using cell deformation and motion to predict forces and collective behavior in morphogenesis. Seminars in Cell and Developmental Biology, 67, 161-169(2017)
[4]	LECUIT, T. and LENNE, P. F. Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis. Nature Reviews Molecular Cell Biology, 8(8), 633-644(2007)
[5]	LIN, S. Z., LI, B., LAN, G., and FENG, X. Q. Activation and synchronization of the oscillatory morphodynamics in multicellular monolayer. Proceedings of the National Academy of Sciences, 114(31), 8157-8162(2017)
[6]	POLYAKOV, O., HE, B., SWAN, M., SHAEVITZ, J. W., KASCHUBE, M., and WIESCHAUS, E. Passive mechanical forces control cell-shape change during drosophila ventral furrow formation. Biophysical Journal, 107(4), 998-1010(2014)
[7]	XIE, J. and HU, G. H. Hydrodynamic modeling of bicoid morphogen gradient formation in drosophila embryo. Biomechanics and Modeling in Mechanobiology, 15(6), 1765-1773(2016)
[8]	YU, J. C. and FERNANDEZ-GONZALEZ, R. Quantitative modelling of epithelial morphogenesis:integrating cell mechanics and molecular dynamics. Seminars in Cell and Developmental Biology, 67, 153-160(2017)
[9]	NAGAI, T. and HONDA, H. Computer simulation of wound closure in epithelial tissues:cellbasal-lamina adhesion. Physical Review E, 80(6), 061903(2009)
[10]	OSBORNE, J. M., WALTER, A., KERSHAW, S., MIRAMS, G., FLETCHER, A., PATHMANATHAN, P., GAVAGHAN, D., JENSEN, O., MAINI, P., and BYRNE, H. A hybrid approach to multi-scale modelling of cancer. Philosophical Transactions of the Royal Society A:Mathematical, Physical and Engineering Sciences, 368(1930), 5013-5028(2010)
[11]	REJNIAK, K. A., WANG, S. E., BRYCE, N. S., CHANG, H., PARVIN, B., JOURQUIN, J., ESTRADA, L., GRAY, J. W., ARTEAGA, C. L., and WEAVER, A. M. Linking changes in epithelial morphogenesis to cancer mutations using computational modeling. PLoS Computational Biology, 6(8), e1000900(2010)
[12]	OSTERFIELD, M., BERG, C. A., and SHVARTSMAN, S. Y. Epithelial patterning, morphogenesis, and evolution:drosophila eggshell as a model. Developmental Cell, 41(4), 337-348(2017)
[13]	GONZALEZ-RODRIGUEZ, D., GUEVORKIAN, K., DOUEZAN, S., and BROCHARDWYART, F. Soft matter models of developing tissues and tumors. Science, 338(6109), 910-917(2012)
[14]	MARCHETTI, M. C., JOANNY, J. F., RAMASWAMY, S., LIVERPOOL, T. B., PROST, J., RAO, M., and SIMHA, R. A. Hydrodynamics of soft active matter. Reviews of Modern Physics, 85(3), 1143-1189(2013)
[15]	RAMASWAMY, S. The mechanics and statistics of active matter. Annual Review of Condensed Matter Physics, 1(1), 323-345(2010)
[16]	NOJOOMI, A., ARSLAN, H., LEE, K., and YUM, K. Bioinspired 3D structures with programmable morphologies and motions. Nature Communications, 9(1), 3705(2018)
[17]	NAN, K., KANG, S. D., LI, K., YU, K. J., ZHU, F., WANG, J., DUNN, A. C., ZHOU, C., XIE, Z., AGNE, M. T., WANG, H., LUAN, H., ZHANG, Y., HUANG, Y., SNYDER, G. J., and ROGERS, J. A. Compliant and stretchable thermoelectric coils for energy harvesting in miniature exible devices. Science Advances, 4(11), eaau5849(2018)
[18]	LIU, W. K., LIU, Y., FARRELL, D., ZHANG, L., WANG, X. S., FUKUI, Y., PATANKAR, N., ZHANG, Y., BAJAJ, C., and LEE, J. Immersed finite element method and its applications to biological systems. Computer Methods in Applied Mechanics and Engineering, 195(13-16), 1722-1749(2006)
[19]	LEE, T. R., CHOI, M., KOPACZ, A. M., YUN, S. H., LIU, W. K., and DECUZZI, P. On the nearwall accumulation of injectable particles in the microcirculation:smaller is not better. Scientific Reports, 3, 2079(2013)
[20]	GUYOT, Y., SMEETS, B., ODENTHAL, T., SUBRAMANI, R., LUYTEN, F. P., RAMON, H., PAPANTONIOU, I., and GERIS, L. Immersed boundary models for quantifying flow-induced mechanical stimuli on stem cells seeded on 3D scaffolds in perfusion bioreactors. PLoS Computational Biology, 12(9), e1005108(2016)
[21]	SUBRAMANIAM, D. R., GEE, D. J., and KING, M. R. Deformable cell-cell and cell-substrate interactions in semi-infinite domain. Journal of Biomechanics, 46(6), 1067-1074(2013)
[22]	REJNIAK, K. A. An immersed boundary framework for modelling the growth of individual cells:an application to the early tumour development. Journal of Theoretical Biology, 247(1), 186-204(2007)
[23]	RANFT, J., BASAN, M., ELGETI, J., JOANNY, J. F., PROST, J., and JÜLICHER, F. Fluidization of tissues by cell division and apoptosis. Proceedings of the National Academy of Sciences, 107(49), 20863-20868(2010)
[24]	BUDDAY, S., STEINMANN, P., GORIELY, A., and KUHL, E. Size and curvature regulate pattern selection in the mammalian brain. Extreme Mechanics Letters, 4, 193-198(2015)
[25]	ALLENA, R. and AUBRY, D. An extensive numerical simulation of the cephalic furrow formation in drosophila embryo. Computer Methods in Biomechanics and Biomedical Engineering, 15(5), 445-455(2012)
[26]	STREICHAN, S. J., LEFEBVRE, M. F., NOLL, N., WIESCHAUS, E. F., and SHRAIMAN, B. I. Global morphogenetic flow is accurately predicted by the spatial distribution of myosin motors. Elife, 7, e27454(2018)
[27]	MURISIC, N., HAKIM, V., KEVREKIDIS, I. G., SHVARTSMAN, S. Y., and AUDOLY, B. From discrete to continuum models of three-dimensional deformations in epithelial sheets. Biophysical Journal, 109(1), 154-163(2015)
[28]	BARTON, D. L., HENKES, S., WEIJER, C. J., and SKNEPNEK, R. Active vertex model for cellresolution description of epithelial tissue mechanics. PLoS Computational Biology, 13(6), e1005569(2017)
[29]	FARHADIFAR, R., RÖPER, J. C., AIGOUY, B., EATON, S., and JÜLICHER, F. The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing. Current Biology, 17(24), 2095-2104(2007)
[30]	HANNEZO, E., PROST, J., and JOANNY, J. F. Theory of epithelial sheet morphology in three dimensions. Proceedings of the National Academy of Sciences, 111(1), 27-32(2014)
[31]	BREZAVŠČEK, A. H., RAUZI, M., LEPTIN, M., and ZIHERL, P. A model of epithelial invagination driven by collective mechanics of identical cells. Biophysical Journal, 103(5), 1069-1077(2012)
[32]	LANDSBERG, K. P., FARHADIFAR, R., RANFT, J., UMETSU, D., WIDMANN, T. J., BITTIG, T., SAID, A., JÜLICHER, F., and DAHMANN, C. Increased cell bond tension governs cell sorting at the drosophila anteroposterior compartment boundary. Current Biology, 19(22), 1950-1955(2009)
[33]	OSTERFIELD, M., DU, X., SCHÜPBACH, T., WIESCHAUS, E., and SHVARTSMAN, S. Y. Three-dimensional epithelial morphogenesis in the developing drosophila egg. Developmental Cell, 24(4), 400-410(2013)
[34]	RAUZI, M., BREZAVŠČEK, A. H., ZIHERL, P., and LEPTIN, M. Physical models of mesoderm invagination in drosophila embryo. Biophysical Journal, 105(1), 3-10(2013)
[35]	XU, G. K., LIU, Y., and ZHENG, Z. Oriented cell division affects the global stress and cell packing geometry of a monolayer under stretch. Journal of Biomechanics, 49(3), 401-407(2016)
[36]	EIRAKU, M., TAKATA, N., ISHIBASHI, H., KAWADA, M., SAKAKURA, E., OKUDA, S., SEKIGUCHI, K., ADACHI, T., and SASAI, Y. Self-organizing optic-cup morphogenesis in threedimensional culture. nature, 472(7341), 51-56(2011)
[37]	DU, X., OSTERFIELD, M., and SHVARTSMAN, S. Y. Computational analysis of three dimensional epithelial morphogenesis using vertex models. Physical Biology, 11(6), 066007(2014)
[38]	TRICHAS, G., SMITH, A. M., WHITE, N., WILKINS, V., WATANABE, T., MOORE, A., JOYCE, B., SUGNASEELAN, J., RODRIGUEZ, T. A., KAY, D., BAKER, R. E., MAINI, P. K., and SRINIVAS, S. Multi-cellular rosettes in the mouse visceral endoderm facilitate the ordered migration of anterior visceral endoderm cells. PLoS Biology, 10(2), e1001256(2012)
[39]	OKUDA, S., INOUE, Y., EIRAKU, M., ADACHI, T., and SASAI, Y. Vertex dynamics simulations of viscosity-dependent deformation during tissue morphogenesis. Biomechanics and Modeling in Mechanobiology, 14(2), 413-425(2015)
[40]	SUSSMAN, D. M., PAOLUZZI, M., MARCHETTI, M. C., and MANNING, M. L. Anomalous glassy dynamics in simple models of dense biological tissue. Europhysics Letters, 121(3), 36001(2018)
[41]	YANG, X., BI, D., CZAJKOWSKI, M., MERKEL, M., MANNING, M. L., and MARCHETTI, M. C. Correlating cell shape and cellular stress in motile confluent tissues. Proceedings of the National Academy of Sciences, 114(48), 12663-12668(2017)
[42]	SUSSMAN, D. M., SCHWARZ, J. M., MARCHETTI, M. C., and MANNING, M. L. Soft yet sharp interfaces in a vertex model of confluent tissue. Physical Review Letters, 120(5), 058001(2018)
[43]	OKUYAMA, R., IZUMIDA, W., and ETO, M. Topological phase transition in metallic single-wall carbon nanotube. Journal of the Physical Society of Japan, 86(1), 013702(2016)
[44]	DIAS, E. S., CASTONGUAY, D., LONGO, H., and JRADI, W. A. R. Efficient enumeration of all chordless cycles in graphs. arXiv, arXiv:1309.1051(2013)
[45]	JIANG, X., PEZZULLA, M., SHAO, H., GHOSH, T. K., and HOLMES, D. P. Snapping of bistable, prestressed cylindrical shells. Europhysics Letters, 122(6), 64003(2018)
[46]	AUDOLY, B. and POMEAU, Y. Elasticity and Geometry, World Scientific Publishing, Singapore (2000)
[47]	QIN, L. C. Determination of the chiral indices (n, m) of carbon nanotubes by electron diffraction. Physical Chemistry Chemical Physics, 9(1), 31-48(2007)