Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-19T11:09:11.562Z Has data issue: false hasContentIssue false
  • English
  • Français

A 3D Multi-Phase Hydrodynamic Model for Cytokinesis of Eukaryotic Cells

Part of: Two-phase and multiphase flows Mathematical modeling, applications of mathematics Physiological, cellular and medical topics

Published online by Cambridge University Press:  16 March 2016

Jia Zhao  and
Qi Wang
Jia Zhao
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA.
Qi Wang*
Affiliation:
Beijing Computational Science Research Center, Beijing, 100193, P.R. China. Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA. School of Mathematics, Nankai University, Tianjin, 300071, P.R. China.
*
*Corresponding author. Email addresses: zhao62@math.sc.edu (J. Zhao), qwang@math.sc.edu (Q.Wang)
Get access

Abstract

In the late stage of the mitotic cycle of eukaryotic cells, cytokinesis ensues during which a parent cell replicates its nucleus with the necessary genetical substances (i.e., DNAs and chromosomes) and splits into two similar offspring cells. This mitotic process involves complex chemical, biophysical andmechanical processes whose details are just beginning to be unfolded experimentally. In this paper, we propose a full 3-D hydrodynamical model using a phase field approach to study the cellular morphological change during cytokinesis. In this model, the force along the contracting ring induced by remodeling of actin-myosin filament on cell cortex layer at the division plane of the parent cell during cytokinesis, is approximated using a proxy force anchored on the newly formed nuclei. The symmetric or asymmetric cell division is simulated numerically with the model. Our numerical results show that the location of the division plane and the contracting force along the cytokinetic ring on the division plane are essential for the cell division. In addition, our numerical study also shows that, during cytokinesis, surface tension of the cell membrane also contributes to this process by retaining the morphological integrity of the offspring cells. This model and the accompanying numerical simulation tool provide a solid framework to build upon with more sophisticated whole cell models to probe the cell mitotic process.

Keywords

Cell biologymathematical modelmulti-phase field

MSC classification

Secondary: 92C37: Cell biology 97M10: Modeling and interdisciplinarity 76T30: Three or more component flows
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 3 , March 2016 , pp. 663 - 681
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Akiyama, Masakazu, Tero, Atsushi, and Kobayashi, Ryo. A mathematical model of cleavage. Journal of Theoretical Biology, 264:84–94, 2010.CrossRefGoogle ScholarPubMed
[2]Barr, Francis A. and Gruneberg, Ulrike. Cytokinesis: placing and making the final cut. Cell, 131:847–860, 2007.CrossRefGoogle ScholarPubMed
[3]Bell, Nathan and Garland, Michael. Cusp: Generic parallel algorithms for sparse matrix and graph computations. preprint, 0:0, 2012.Google Scholar
[4]Caginalp, Gunduz and Chen, Xinfu. Convergence of the phase field model to its sharp interface limit. European Journal of Applied Mathematics, 4:417–445, 1998.CrossRefGoogle Scholar
[5]Canman, Julie C., Cameron, Lisa A., Maddox, Paul S., Straight, Aaron, and etc. Determining the position of the cell division plane. Nature, 424:1074–1078, August 2003.CrossRefGoogle ScholarPubMed
[6]Chircop, Megan. Rho gtpases as regulators of mitosis and cytokinesis in mammalian cells. 2014 Special Focus on Rho GTPases, page e29770, 2014.Google ScholarPubMed
[7]Dodd, Michael S. and Ferrante, Antonino. A fast pressure correction method for incompressible two-fluid flows. Journal of Computational Physics, 273:416–437, 2014.CrossRefGoogle Scholar
[8]Dong, Song and Shen, Jie. A time stepping scheme involving constant coefficient matrices for pahse field simulations of two phase incompressible flows with large density ratios. Journal of Computational Physics, 231:5788–5804, 2012.CrossRefGoogle Scholar
[9]Eggert, Ulrike S., Mitchison, Timothy J., and Field, Christine M.. Animal cytokinesis: from parts list to mechanisms. The Annual Review of Biochemistry, 75:543–566, 2006.CrossRefGoogle ScholarPubMed
[10]Errington, Jeffery, Daniel, Richard A., and Scheffers, Dirk-Jan. Cytokinesis in bacteria. Microbiology and Molecular Biology Reviews, 67(1):52–65, March 2003.CrossRefGoogle ScholarPubMed
[11]Glotzer, Michael. The molecular requirements for cytokinesis. Science, 307:1735–1739, 2005.CrossRefGoogle ScholarPubMed
[12]Grover, William H., Bryan, Andrea K., Diez-Silva, Monica, Suresh, Subra, Higgins, John M., and Manalis, Scott R.. Measuring single-cell density. PNAS, 108(27):10992–10996, 2011.CrossRefGoogle ScholarPubMed
[13]Guertin, David A., Trautmann, Susanne, and McCollum, Dannel. Cytokinesis in eukaryotes. Microbiology and Molecular Biology Reviews, 66(2):155–178, June 2002.CrossRefGoogle ScholarPubMed
[14]Hoberock, Jared and Bell, Nathan. Thrust: a parallel template library. preprint, 0:0, 2010.Google Scholar
[15]Kalwarczyk, Tomasz, Ziebacz, Natalia, Bielejewska, Anna, Zaboklicka, Ewa, Koynov, Kaloian, and etc. Comparative analysis of viscosity of complex liquids and cytoplasm of mammalian cells at the nanoscale. Nano Letters, 11(5):2157–2163, 2011.CrossRefGoogle ScholarPubMed
[16]Li, Yibao, Yun, Ana, and Kim, Junseok. An immersed boundary method for simulating a single axisymmetric cell growth and division. Journal of Mathematical Biology, 65:653–675, 2012.CrossRefGoogle ScholarPubMed
[17]Lindley, Brandon, Wang, Qi, and Zhang, Tianyu. A multicomponent model for biofilm-drug interaction. Discrete and Continuous Dynamical Systems Series B, 15:417–456, March 2011.CrossRefGoogle Scholar
[18]Lindley, Brandon, Wang, Qi, and Zhang, Tianyu. Multicomponent hydrodynamic model for heterogeneous biofilms: Two-dimensional numerical simulations of growth and interaction with flows. Physical Review E, 85:031908, March 2012.CrossRefGoogle ScholarPubMed
[19]Miller, Ann L.. The contractile ring. Current Biology, 21(24):976–978, 2011.CrossRefGoogle ScholarPubMed
[20]Minc, Nicolas, Burgess, David, and Chang, Fred. Influence of cell geometry on division-plane positioning. Cell, 144:414–426, February 2011.CrossRefGoogle ScholarPubMed
[21]Mogilner, Alex, Wollman, Roy, Civelekoglu-Scholey, Gul, and Scholey, Jonathan M.. Modeling mitosis. Trends in Microbiology, 16(2):88–96, February 2006.Google ScholarPubMed
[22]Mohan, Krithika, IgIesias, Pablo A., and Robinson, Douglas N.. Separation anxiety: stress tension and cytokinesis. Experimental Cell Research, 318:1428–1434, 2012.CrossRefGoogle ScholarPubMed
[23]Nigg, Erich A.. Mitotic kinases as regulators of cell division and its checkpoints. Nature Reviews Molecular Cell Biology, 2:21–32, January 2001.CrossRefGoogle ScholarPubMed
[24]Poirier, Christopher C., Ng, Win Pin, Robinson, Douglas N., and IgIesias, Pablo A.. Deconvolution of the cellular force-generating subsystems that govern cytokinesis furrow ingression. PLOS Computational Biology, 8(4), 2012.CrossRefGoogle ScholarPubMed
[25]Pyo, Jae-Hong and Shen, Jie. Gauge-uzawa methods for incompressible flows with variable density. Journal of Computational Physics, 221:181–197, 2007.CrossRefGoogle Scholar
[26]Rankin, Kathleen E. and Wordeman, Linda. Long astral microtubules uncouple mitotic spindles from the cytokinetic furrow. The Journal of Cell Biology, 190(1):35–43, July 2010.CrossRefGoogle ScholarPubMed
[27]Rechl, Elizabeth M., Effler, Janet C., and Robinson, Douglas N.. The stress and strain of cytokinesis. Trends in Microbiology, 15(4):200–206, April 2005.Google Scholar
[28]Rejniak, Katarzyna A.. A single-cell approach in modeling the dynamics of tumor microregions. Mathematical Biosciences and Engineering, 2(3):643–655, August 2005.CrossRefGoogle ScholarPubMed
[29]Scholey, Jonathan M., Brust-Mascher, Ingrid, and Mogilner, Alex. Cell division. Nature, 422:746–752, April 2003.CrossRefGoogle ScholarPubMed
[30]Gregory Somers, W. and Saint, Robert. A rhogef and rho family grpase-activating protein compelx links the contractile ring to cortical microtubules at the onset of cytokinesis. Developmental Cell, 4:29–39, 2003.CrossRefGoogle Scholar
[31]Sun, Y. and Beckermann, C.. Sharp interface tracking using the phase-field equation. Journal of Computational Physics, 220:626–653, 2007.CrossRefGoogle Scholar
[32]Thery, Manuel and Bornens, Michel. Cell shape and cell division. Current Opinion in Cell Biology, 18:648–657, 2006.CrossRefGoogle ScholarPubMed
[33]Vasquez, Paula A. and Bloom, Kerry. Polymer models of interphase chromesomes. Nucleus, 5(5), 2014.CrossRefGoogle Scholar
[34]Zhang, Tianyu, Cogan, Nick G., and Wang, Qi. Phase-field models for biofilms i. theory and simulations. SIAM Journal of Applied Mathematics, 69:641–669, 2008.CrossRefGoogle Scholar