Document Type



Doctor of Philosophy



First Adviser

Vavylonis, Dimitrios

Other advisers/committee members

Gunton, Jim; Ou-Yang, Daniel; Toulouse, Jean; Cassimeris, Lynne


Fission yeast is a pill-shaped unicellular organism, and before dividing it grows by extension at the tips to double the original length. This work consists of mathematical models for how fission yeast controls this growth process. The models presented are either developed in collaboration with experimentalists or using published experimental work on this organism.First, in collaboration with experimentalists Maitreyi Das and Fulvia Verde, we examine the organization of the signaling protein Cdc42, which we implicate as a central part of a control system for polarized growth. Cdc42, a member of the Rho family of proteins, binds to the inner membrane of the cell tips where growth occurs. In collaboration, we find that the fraction of Cdc42 bound to a given cell tip correlates to its growth rate, and that the amount of bound Cdc42 undergoes anti-correlated oscillations between the cell tips. We present a model that describes how Cdc42 and related proteins effect this organization, and shows how the oscillations could function as an exploratory mechanism to help the system overcome a kinetic barrier. Experimental results from our collaborators, such as a loss of correlation in very long cells and a reorganization after disruptive drug treatment, validate the model.Next, using experimental results from literature, we turn to the patterned remodeling of the cell wall. We make a hypothesis that extends the result that Cdc42 marks cell tips for growth from previous work: that Cdc42 marks sites for growth on a microscopic level. A model for the fission yeast cell as an elastic shell being remodeled under turgor pressure at a rate that depends on cortical Cdc42 levels reproduces essential experimental results, namely the ratio of signal width to cell diameter and a linear relation between growth rate and pressure, and gives an estimation of the wall remodeling rate at the cell tips. Since this model predicts that cell diameter depends crucially on the width of a Cdc42 signal, we consider the plausibility of mechanisms for establishing the width of that signal. We find that stronger-than-linear feedback from cell diameter to signal width leads to unstable width regulation, and propose an independent length scale such as from a reaction-diffusion-type mechanism for a cell-diameter-independent Cdc42 signal width. Finally, we describe a mathematical model consisting of Cdc42-signal-dependent cell growth, diffusing Cdc42 growth zones with native width, and an axis-sensing microtubule-based system capable of delivering landmark proteins to the cell tips that bias the diffusion of the growth zones. Parameter dependence of the model is explored, and we show that such a model can give straight, bent, and wide cells, all of which have been observed by experimentalists. We argue that such a model is consistent with the roles of cytoskeleton- and signal-related proteins and known aberrant shapes of mutant cells.As a whole, this work provides mechanistic insight into the system regulating shape and growth in one important model organism.

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