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A wave-pinning mechanism for eukaryotic cell polarization based on Rho GTPase dynamics Jilkine, Alexandra


In response to chemical stimulation, many eukaryotic cells are able to sense the direction of the stimulus and initiate movement. To do so, the cell must break symmetry and develop a front and back in a process known as polarization. During polarization, members of the Rho GTPase family (Cdc42, Rac, and Rho) are recruited to the plasma membrane and localize to form a front and a back of the polarizing cell. These proteins exist in both active forms (on the inner surface of the membrane of the cell), and inactive forms (in the cytosol). In earlier work, I have shown that the property of membrane-cytosol interconversion, together with appropriate feedbacks, endows the Rho proteins with the ability to initiate cell polarity, resulting in a high Cdc42/Rac region, which will become the front, and a high Rho region, which will become the back of the cell. Here I show that this property of polarizability can be explained using a simplified model system comprising of a single active/inactive protein pair with positive feedback. In this model, a travelling wave of GTPase activation is initiated at one end of the domain, moves across the cell, and eventually stops inside the domain, resulting in a stable polar distribution. The key requirements for the mechanism to work include conservation of total amount of protein, a sufficiently large difference in diffusion rates of the two forms, and nonlinear positive feedback that allows for multiple homogeneous steady states to exist. Using singular perturbation theory, I explain the mathematical basis of wave-pinning behaviour, and discuss its biological and mathematical implications. I show that this mechanism for generating a chemical pattern is distinct from Turing pattern formation. I also analyze the transition from a spatially heterogeneous solution to a spatially homogeneous solution as the diffusion coefficient of the active form is increased, and show the existence of other unstable stationary wavefronts. Finally, I argue that this wave-pinning mechanism can account for a number of features of cell polarization such as spatial amplification, maintenance of polarity, and the sensitivity to new stimuli that is typical of polarization of eukaryotic cells.

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