Microtubules are one of three cytoskeletal filaments found in eukaryotic cells, which exhibit a constant transition between growth and shrinkage states. This phenomenon, known as dynamic instability, is the focus of our study. We have investigated microtubule dynamics found in isotypically purified β-tubulin in order to understand how different microtubule protein compositions may affect growth and shrinkage rates. A deeper understanding of these dynamics allows us to calculate nanoscale mechanical properties of microtubules such as their force generation and rigidity. In this paper we analyze the differences between the polymerization and depolymerization rates of purified β-II, β-III, and β-IV microtubules. Each of these three isotypes displays varying behavior in terms of dynamic instability rates. We developed a model that describes the different growth and shrinkage behavior of each isotype in terms of a recursive map representation based on a modified random walk with four independent probabilistic variables describing the possible states of a microtubule. Using further probabilistic methods, we simulated the growth and shrinkage behavior of isotypically pure microtubules and determined their average growth and shrinkage rate constants and their probability distributions. The rate constants determined by our model were found to vary significantly between β-II, β-III, and β-IV microtubules. This variation in growth and shrinkage rates subsequently leads to a variation in the forces generated by isotypically purified microtubules that were calculated from a force-velocity relationship. This enables us to extrapolate these results to a model that can predict the dynamic instability of microtubules with an arbitrary isotype composition. This, in turn, gives us the ability to assemble microtubules with pre-determined β-tubulin isotype composition in order to generate a desired amount of force for a particular nano-engineering application. It has also been suggested that microtubule rigidity is directly related to the rate of growth, and that slower growing microtubules are stiffer. Here again, the β-tubulin isotype composition can be varied in order to produce a microtubule with a specific growth rate, in order to produce a microtubule of desired rigidity. In conclusion, by analyzing the experimental data for pure isotype microtubules we were able to determine varying nanoscale mechanical properties of these filaments such as force generation and rigidity.
This research was supported by funding from MITACS and NSERC
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