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Mathematical Model of Contractile Ring-Driven Cytokinesis in a Three-Dimensional Domain

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Abstract

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.

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Acknowledgements

The author was supported by the National Institute for Mathematical Sciences (NIMS) grant funded by the Korean government (No. A21300000) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2017R1C1B1001937).

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Authors and Affiliations

  1. National Institute for Mathematical Sciences, Daejeon, 34047, Republic of Korea

    Seunggyu Lee

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  1. Seunggyu Lee
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Correspondence to Seunggyu Lee.

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Lee, S. Mathematical Model of Contractile Ring-Driven Cytokinesis in a Three-Dimensional Domain. Bull Math Biol 80, 583–597 (2018). https://doi.org/10.1007/s11538-018-0390-x

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  • DOI: https://doi.org/10.1007/s11538-018-0390-x

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