Deterministic and Stochastic Analysis for the Spontaneous Emergence of Cell Polarity in Budding Yeast with Different Regulations

不同調控下芽殖酵母的自發極性的確定性和隨機性分析

Student thesis: Doctoral Thesis

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Award date25 Jun 2021

Abstract

This thesis is concerned with the mechanisms for the spontaneous emergence of cell polarity in budding yeast with different regulations. We mainly focus on the roles of delayed negative feedback and stochasticity for maintaining the robustness of cell polarization.

In the first part, we describe the cell polarization system as a non-local reaction-diffusion equation with positive and delayed negative feedback loops. The model is formulated to study the polarizing behavior under negative feedback. Through the Turing instability analysis, we identify the parameter conditions, including the range of the time delay constant, for achieving cell polarization without any spatial cues. Moreover, 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.

In the second part, we extend the model to a two-equation system with a general positive feedback function which could be linear, quadratic, Hill form. Turing instability analysis provides us the conditions for achieving the polarity and suggests that the linear positive feedback is insufficient to establish the localization. Numerical simulations of reaction-diffusion equations provide us the localization profile when polarity establishes.

In the final part, we describe the polarization process stochastically and establish chemical master equations. Numerical simulations by Stochastic Simulation Algorithm (SSA) suggest that stochastic method leads to a broader parameter region for the emergence of cell polarity compared to deterministic method. To analytically investigate the stochastic effect, the intrinsic noise in polarization process is studied through approximating the power spectrum which can help to find the frequency distribution and predict the behavior of inherent fluctuations near the steady state. We apply linear noise approximation to obtain a Langevin equation for chemical reactions and diffusions and then utilize the Fourier transform to derive the theoretical approximation for power spectrum. A good agreement between the prediction of the power spectrum and the simulations of SSA is observed, and this result allows us to use the power spectrum to effectively predict the regimes instead of implementing the time-consuming SSA.

In conclusion, the analysis in present study provides detailed insights on the robustness of cell polarization process in budding yeast. Such a robust emergence of cell polarity is essential for ensuring the generation of diverse cell types in biological processes. These analysis can be extended to higher dimensional domain where dynamical cell geometries can be involved and help to understand other similar biological systems in which cell polarity is established.