UC Riverside

Cell polarity is a fundamental feature of almost all cells. An excellent example for studying cell polarity is pollen tube tip growth, which is a specialized form of cell growth, in which growth is limited to the apical end of the cell, allowing the cell to rapidly elongate and penetrate tissues. The key of pollen tube tip growth is polarized distribution on plasma membrane of a particle named ROP1 and Calcium. The oscillated distribution is the result of a feedback loop between ROP1 and Calcium.

This dissertation takes a multidisciplinary approach by combining knowledge of cell biology, mathematics, and statistics in order to quantitatively study the full system for the interaction between ROP1 and Calcium in pollen tube tip growth. In the first part of the dissertation, we propose a mechanistic reaction-diffusion equation derived model of cell polarity, and analytically study the spatiotemporal dynamic of proposed model. In the second part, we first introduce parameter estimation procedure of linear reaction-diffusion equation, then extend it to nonlinear case. Our approach can be seen as an extension of gradient matching procedure. Moreover, consistency and asymptotic normality of proposed method will be discussed in linear case. And simulation study will be conducted in both cases. In the end, we will apply proposed method on the pollen tube tip growth model to predict ROP1 and Calcium concentration on plasma membrane. And guidance of refining proposed model is given based on predication of ROP1 and Calcium.