Analysis of spontaneous emergence of cell polarity with delayed negative feedback

Yue Liu; Wing-Cheong Lo; Yue Liu; Wing-Cheong Lo

doi:10.3934/mbe.2019068

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 3: 1392-1413. doi: 10.3934/mbe.2019068

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Research article Special Issues

Analysis of spontaneous emergence of cell polarity with delayed negative feedback

Yue Liu ,
Wing-Cheong Lo ^,

Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR.

Received: 29 October 2018 Accepted: 24 January 2019 Published: 20 February 2019

Cell polarity refers to spatial di erences in the shape and structure of cells, which leads to the generation of diverse cell types playing di erent roles in biological processes. Cell polarization usually involves the localization of some specific signaling molecules to a proper location of the cell membrane. Recent studies proposed that delayed negative feedback may be important for maintaining the robustness of cell polarization and the observed oscillating behavior of signaling cluster. However, the fundamental mechanisms for achieving cell polarization under negative feedback remain controversial. In this paper, we formulate the cell polarization system as a non-local reaction di usion equation with positive and delayed negative feedback loops. Through the Turing stability analysis, we identify the parameter conditions, including the range of the time delay constant, for achieving cell polarization without any inhomogeneous spatial cues. Also, our numerical results support that by controlling the length of the time delay in negative feedback and the magnitude of positive feedback, the oscillating behavior of signaling cluster can be observed in our simulations.
- cell polarization,
- delayed feedback control,
- mathematical modeling,
- Turing stability analysis,
- systems biology
Citation: Yue Liu, Wing-Cheong Lo. Analysis of spontaneous emergence of cell polarity with delayed negative feedback[J]. Mathematical Biosciences and Engineering, 2019, 16(3): 1392-1413. doi: 10.3934/mbe.2019068

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Abstract

Cell polarity refers to spatial di erences in the shape and structure of cells, which leads to the generation of diverse cell types playing di erent roles in biological processes. Cell polarization usually involves the localization of some specific signaling molecules to a proper location of the cell membrane. Recent studies proposed that delayed negative feedback may be important for maintaining the robustness of cell polarization and the observed oscillating behavior of signaling cluster. However, the fundamental mechanisms for achieving cell polarization under negative feedback remain controversial. In this paper, we formulate the cell polarization system as a non-local reaction di usion equation with positive and delayed negative feedback loops. Through the Turing stability analysis, we identify the parameter conditions, including the range of the time delay constant, for achieving cell polarization without any inhomogeneous spatial cues. Also, our numerical results support that by controlling the length of the time delay in negative feedback and the magnitude of positive feedback, the oscillating behavior of signaling cluster can be observed in our simulations.

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