zbMATH — the first resource for mathematics

Mathematical model of contractile ring-driven cytokinesis in a three-dimensional domain. (English) Zbl 1391.92013
Summary: In this paper, a mathematical model of contractile ring-driven cytokinesis is presented by using both phase-field and immersed-boundary methods in a three-dimensional domain. It is one of the powerful hypotheses that cytokinesis happens driven by the contractile ring; however, there are only few mathematical models following the hypothesis, to the author’s knowledge. I consider a hybrid method to model the phenomenon. First, a cell membrane is represented by a zero-contour of a phase-field implicitly because of its topological change. Otherwise, immersed-boundary particles represent a contractile ring explicitly based on the author’s previous work. Here, the multi-component (or vector-valued) phase-field equation is considered to avoid the emerging of each cell membrane right after their divisions. Using a convex splitting scheme, the governing equation of the phase-field method has unique solvability. The numerical convergence of contractile ring to cell membrane is proved. Several numerical simulations are performed to validate the proposed model.

92C37 Cell biology
92C35 Physiological flow
76Z05 Physiological flows
Full Text: DOI
[1] Alberts B, Johnson A, Lewis J, Raff M, Roberts P (2002) Molecular biology of the cell, 4th edn. Garland Science, New York
[2] Bathe, M; Chang, F, Cytokinesis and the contractile ring in fission yeast: towards a systems-level understanding, Trends Microbiol, 18, 38-45, (2010)
[3] Bertozzi, A; Esedoglu, S; Gilette, A, Inpainting of binary images using the Cahn-Hilliard equation, IEEE Trans Image Process, 16, 285-291, (2007) · Zbl 1279.94008
[4] Bi, E; Maddox, P; Lew, D; Salmon, E; McMilland, E; Yeh, E; Prihngle, J, Involvement of an actomyosin contractile ring in saccharomyces cerevisiae cytokinesis, J Cell Biol, 142, 1301-1312, (1998)
[5] Botella, O; Ait-Messaoud, M; Pertat, A; Cheny, Y; Rigal, C, The LS-STAG immersed boundary method for non-Newtonian flows in irregular geometries: flow of shear-thinning liquids between eccentric rotating cylinders, Theor Comput Fluid Dyn, 29, 93-110, (2015)
[6] Britton N (2003) Essential mathematical biology. Springer, Berlin · Zbl 1037.92001
[7] Cahn, J; Hilliard, J, Free energy of a nonuniform system. I. interfacial free energy, J Chem Phys, 28, 258-267, (1958)
[8] Calvert, M; Wright, G; Lenong, F; Chiam, K; Chen, Y; Jedd, G; Balasubramanian, M, Myosin concentration underlies cell size-dependent scalability of actomyosin ring constriction, J Cell Biol, 195, 799-813, (2011)
[9] Carvalgo, A; Oegema, ADK, Structural memory in the contractile ring makes the duration of cytokinesis independent of cell size, Cell, 137, 926-937, (2009)
[10] Celton-Morizur, S; Dordes, N; Fraisier, V; Tran, P; Paoletti, A, C-terminal anchoring of mid1p to membranes stabilized cytokinetic ring position in early mitosis in fission yeast, Mol Cellul Biol, 24, 10621-10635, (2004)
[11] Chang, F; Drubin, D; Nurse, P, Cdc12p, a protein required for cytokineses in fission yeast, is a component of the cell division ring and interacts with profilin, J Cell Biol, 137, 169-182, (1997)
[12] Chen, Y; Wise, S; Shenoy, V; Lowengrub, J, A stable scheme for a nonlinear multiphase tumor growth model with an elastic membrane, Int J Numer Methods Biomed Eng, 30, 726-754, (2014)
[13] Chen, Z; Hickel, S; Devesa, A; Berland, J; Adams, N, Wall modeling for implicit large-eddy simulation and immersed-interface methods, Theor Comput Fluid Dyn, 28, 1-21, (2014)
[14] Chorin, A, Numerical solution of the Navier-Stokes equation, Math Comput, 22, 745-762, (1968) · Zbl 0198.50103
[15] Daniels, M; Wang, Y; Lee, M; Venkitaraman, A, Abnormal cytokinesis in cells deficient in the breast cancer susceptibility protein brca2, Science, 306, 876-879, (2004)
[16] de Fontaine D (1967) A computer simulation of the evolution of coherent composition variations in solid solutions. Ph.D. thesis, Northwestern University
[17] Eyer, D, Unconditionally gradient stable scheme marching the Cahn-Hilliard equation, MRS Proc, 529, 39-46, (1998)
[18] Gisselsson, D; Jin, Y; Lindgren, D; Persson, J; Gisselsson, L; Hanks, S; Sehic, D; Mengelbier, L; Øra, I; Rahman, N; etal., Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis, Proc Natl Acad Sci, 107, 20489-20493, (2010)
[19] Gompper, G; Zschoke, S, Elastic properties of interfaces in a Ginzburg-Landau theory of swollen micelles, droplet crystals and lamellar phases, Europhys Lett, 16, 731-736, (1991)
[20] Harlow, E; Welch, J, Numerical calculation of time dependent viscous incompressible flow with free surface, Phys Fluid, 8, 2182-2189, (1965) · Zbl 1180.76043
[21] Helfrich, W, Elastic properties of lipid bilayers: theory and possible experiments, Z Naturforschung C, 28, 693-703, (1973)
[22] Jochova, J; Rupes, I; Streiblova, E, F-actin contractile rings in protoplasts of the yeast schizosaccharomyces, Cell Biol Int Rep, 15, 607-610, (1991)
[23] Kamasaki, T; Osumi, M; Mabuchi, I, Three-dimensional arrangement of f-actin in the contractile ring of fission yeast, J Cell Biol, 178, 765-771, (2007)
[24] Kang, B; Mackey, M; El-Sayed, M, Nuclear targeting of gold nanoparticles in cancer cells induces DNA damage, causing cytokinesis arrest and apoptosis, J Am Chem Soc, 132, 1517-1519, (2010)
[25] Kim, J, A continuous surface tension force formulation for diffuse-interface models, J Comput Phys, 204, 784-804, (2005) · Zbl 1329.76103
[26] Koudehi, M; Tang, H; Vavylonis, D, Simulation of the effect of confinement in actin ring formation, Biophys J, 110, 126a, (2016)
[27] Lee, H; Kim, J, A second-order accurate non-linear difference scheme for the n-component Cahn-Hilliard system, Physica A, 387, 4787-4799, (2008)
[28] Lee, H; Choi, J; Kim, J, A practically unconditionally gradient stable scheme for the n-component Cahn-Hilliard system, Physica A, 391, 1009-1019, (2012)
[29] Lee, S; Jeong, D; Choi, Y; Kim, J, Comparison of numerical methods for ternary fluid flows: immersed boundary, level-set, and phase-field methods, J KSIAM, 20, 83-106, (2016) · Zbl 1338.76018
[30] Lee, S; Jeong, D; Lee, W; Kim, J, An immersed boundary method for a contractile elastic ring in a three-dimensional Newtonian fluid, J Sci Comput, 67, 909-925, (2016) · Zbl 1383.76363
[31] Li, Y; Kim, J, Three-dimensional simulations of the cell growth and cytokinesis using the immersed boundary method, Math Biosci, 271, 118-127, (2016) · Zbl 1364.92009
[32] Li, Y; Yun, A; Kim, J, An immersed boundary method for simulating a single axisymmetric cell growth and division, J Math Biol, 65, 653-675, (2012) · Zbl 1252.92017
[33] Li, Y; Jeong, D; Choi, J; Lee, S; Kim, J, Fast local image inpainting based on the local Allen-Cahn model, Digital Signal Process, 37, 65-74, (2015)
[34] Lim, S, Dynamics of an open elastic rod with intrinsic curvature and twist in a viscous fluid, Phys Fluids, 22, 024104, (2010) · Zbl 1183.76313
[35] Lim, S; Ferent, A; Wang, X; Peskin, C, Dynamics of a closed rod with twist and bend in fluid, SIAM J Sci Comput, 31, 273-302, (2008) · Zbl 1404.92138
[36] Mandato, C; Berment, W, Contraction and polymerization cooperate to assemble and close actomyosin rings round xenopus oocyte wounds, J Cell Biol, 154, 785-797, (2001)
[37] Miller, A, The contractile ring, Curr Biol, 21, r976-r978, (2011)
[38] Pelham, R; Chang, F, Actin dynamics in the contractile ring during cytokinesis in fission yeast, Nature, 419, 82-86, (2002)
[39] Peskin, C, Flow patterns around heart valves: a numerical method, J Comput Phys, 10, 252-271, (1972) · Zbl 0244.92002
[40] Pollard, T; Cooper, J, Actin, a central player in cell shape and movement, Science, 326, 1208-1212, (2008)
[41] Posa, A; Balaras, E, Model-based near-wall reconstructions for immersed-boundary methods, Theor Comput Fluid Dyn, 28, 473-483, (2014)
[42] Shlomovitz, R; Gov, N, Physical model of contractile ring initiation in dividing cells, Biophys J, 94, 1155-1168, (2008)
[43] Trottenberg U, Oosterlee C, Schüller A (2001) Multigrid. Academic Press, London · Zbl 0976.65106
[44] Vahidkhah, K; Abdollahi, V, Numerical simulation of a flexible fiber deformation in a viscous flow by the immersed boundary-lattice Boltzmann method, Commun Nonlinear Sci Numer Simul, 17, 1475-1484, (2012) · Zbl 1364.76191
[45] Vavylonis, D; Wu, J; Hao, S; O’Shaughnessy, B; Pollard, T, Assembly mechanism of the contractile ring for cytokinesis by fission yeast, Science, 319, 97-100, (2008)
[46] Wang, MZY, Distinct pathways for the early recruitment of myosin ii and actin to the cytokinetic furrow, Mol Biol Cell, 19, 318-326, (2008)
[47] Wheeler, A; Boettinger, W; McFadden, G, Phase-field model for isothermal phase transitions in binary alloys, Phys Rev A, 45, 7424-7439, (1992)
[48] Zang, J; Spudich, J, Myosin ii localization during cytokinesis occurs by a mechanism that does not require its motor domain, Proc Natl Acad Sci, 95, 13652-13657, (1998)
[49] Zhao, J; Wang, Q, A 3d multi-phase hydrodynamic model for cytokinesis of eukaryotic cells, Commun Comput Phys, 19, 663-681, (2016) · Zbl 1373.92036
[50] Zhao J, Wang Q (2016b) Modeling cytokinesis of eukaryotic cells driven by the actomyosin contractile ring. Int J Numer Methods Biomed Eng 32(12):e027774
[51] Zhou, Z; Munteanu, E; He, J; Ursell, T; Bathe, M; Huang, K; Chang, F, The contractile ring coordinates curvature-dependent septum assembly during fission yeast cytokinesis, Mol Biol Cell, 26, 78-90, (2015)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.