A mathematical model of microtubule assembly and polarity in dendrites

Abstract: In neurons, the microtubule cytoskeleton is responsible for long-range and long-term intracellular transport of mRNAs and proteins. Microtubules, comprised of tubulin dimers, are defined by their polarity and their highly dynamic assembly process, where each end of the microtubule can grow and depolymerize by stochastically switching between states of catastrophe and growth. The polarity and overall dynamics of neuronal microtubules are known to be stable throughout a lifetime. However, microtubule orientation and dynamics can change in the event of injury, and microtubule growth and catastrophe are known to be dependent on available tubulin. To understand how what mechanisms control the equilibrium microtubule length, we propose a spatially-explicit mathematical model of individual microtubule growth and catastrophe using parameters informed by experimental data. Several biologically relevant mechanisms are explored in the model, including availability of tubulin in the cell, dependence of catastrophe events on the microtubule length, and how severing proteins regulate microtubule length. This work is in close collaboration with biological experimentalists and fluorescence microscopy experiments are used to validate and support such mechanisms.

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