Estimation of the diffusion-limited rate of microtubule assembly
Microtubule assembly is a complex process with individual microtubules alternating stochastically between extended periods of assembly and disassembly, a phenomenon known as dynamic instability. Since the discovery of dynamic instability, molecular models of assembly have generally assumed that tubulin incorporation into the microtubule lattice is primarily reaction-limited. Recently this assumption has been challenged and the importance of diffusion in microtubule assembly dynamics asserted on the basis of scaling arguments, with tubulin gradients predicted to extend over length scales exceeding a cell diameter, ~50 μm. To assess whether individual microtubules in vivo assemble at diffusion-limited rates and to predict the theoretical upper limit on the assembly rate, a steady-state mean-field model for the concentration of tubulin about a growing microtubule tip was developed. Using published parameter values for microtubule assembly in vivo (growth rate = 7 μm/min, diffusivity = 6 x 10-12 m2/s, tubulin concentration = 10 μM), the model predicted that the tubulin concentration at the microtubule tip was ~ 89% of the concentration far from the tip, indicating that microtubule self-assembly is not diffusion-limited. Furthermore, the gradients extended less than ~50 nm (the equivalent of about two microtubule diameters) from the microtubule tip, a distance much less than a cell diameter. In addition, a general relation was developed to predict the diffusion-limited assembly rate from the diffusivity and bulk tubulin concentration. Using this relation, it was estimated that the maximum theoretical assembly rate is ~65 μm/min, above which tubulin can no longer diffuse rapidly enough to support faster growth.
Estimation of the diffusion-limited rate of microtubule assembly.
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