Mathematical and Experimental Studies of Pollen Tube Tip Growth and Guidance

Tip growth is an extreme form of polar growth and involves highly polarized cellular activities, such as vesicular trafficking and cell surface extension. In the presence of environmental signals, tip growing cells are able to reestablish the axis of polarity and growth in a process called growth guidance. Previous studies showed that in various cell systems, tip growth and growth guidance depend on polarized Rho GTPase signaling and exocytosis. In this study, we combined mathematical modeling and biological experimentation to study the molecular mechanisms underlying the tip growth and guidance of Arabidopsis pollen tubes. Firstly, a mathematical model integrating the intracellular signaling and the cell surface mechanics in pollen tube tip growth is presented. The predictions of the model were confirmed by phenotypic characterization of mutants defective in the ROP1 signaling, exocytosis or cell wall modification. The results supported the hypothesis that in pollen tube tip growth, exocytosis is the central player that couples ROP1 GTPase signaling pathways with cell wall mechanical properties. Secondly, a mathematical model of pollen tube guidance was developed based on the framework of the tip growth model using the Finite Element Method. In this model, the distribution of active ROP1 is biased by the gradient of the extracellular guidance signal, leading to asymmetric growth towards the source of the guidance signal. This model is validated by observing the dynamics of ROP1 activity and cell morphology in pollen tube guidance using the semi-in vitro assay. Finally, a novel method of measuring the exocytosis rate of cell membrane or cell wall proteins is presented. In this method, the protein-of-interest is tagged with Dendra2, a photo-convertible fluorescent protein. Following photoconversion, both exocytosis and other processes that affect fluorescence recovery such as endocytosis and cell surface extension can be tracked simultaneously. We developed an algorithm for data processing and calculation, and applied this method in measuring the exocytosis rate of PRK1 in Arabidopsis pollen tubes. Overall, this study provided a platform for the application of mathematics in the study of plant cell signaling and morphogenesis