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MATHEMATICAL MODELS OF PATTERN FORMATION IN CELL BIOLOGY

Yang, Xige
http://rave.ohiolink.edu/etdc/view?acc_num=osu1542236214346341

Abstract Details

2018, Doctor of Philosophy, Ohio State University, Mathematics.
This thesis provides a study of mathematical models about pattern formation phenomena in cell biology. Chapter 2 introduces the necessary background on mathematical methods of developing and analyzing mathematical models at the cellular and molecular scales. I then considered two detailed cases related to pattern formation in cell biology, chemotaxis of bacterial populations which generates wave-like patterns, and axonal cytoskeleton segregation which exhibits peak-valley patterns. In Chapter 3, we derived a PDE model for E. coli chemotaxis that incorporates detailed intracellular signaling. Unlike previous PDE models, the new model can approximate the population dynamics accurately even if the external signal changes rapidly. In Chapter 4, we developed and analyzed a nonlocal PDE model for the polymer segregation phenomena. Reaction-diffusion equations have been widely used to describe biological pattern formation. In Chapter 5, we developed numerical methods for computing multiple steady-state patterns of reaction-diffusion models. For that we combined homotopy tracking method in numerical algebraic geometry and multigrid method, and as an example, we computed multiple patterns for the Gray-Scott model.
Chuan Xue (Advisor)
Avner Friedman (Committee Member)
Janet Best (Committee Member)
Yi Zhao (Committee Member)
170 p.
Mathematics
Mathematical modeling, Computational PDE, Chemotaxis, Axonal transport, Bifurcation theory, Asymptotic analysis, Dynamical system

Recommended Citations

Citations

  • Yang, X. (2018). MATHEMATICAL MODELS OF PATTERN FORMATION IN CELL BIOLOGY [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1542236214346341

    APA Style (7th edition)

  • Yang, Xige. MATHEMATICAL MODELS OF PATTERN FORMATION IN CELL BIOLOGY. 2018. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1542236214346341.

    MLA Style (8th edition)

  • Yang, Xige. "MATHEMATICAL MODELS OF PATTERN FORMATION IN CELL BIOLOGY." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1542236214346341

    Chicago Manual of Style (17th edition)

osu1542236214346341
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© 2018, some rights reserved.Creative Commons License MATHEMATICAL MODELS OF PATTERN FORMATION IN CELL BIOLOGY by Xige Yang is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.