Microtubules are semiflexible polymers that serve as structural components inside the eukaryotic cell and are involved in many cellular processes such as mitosis, cytokinesis, and vesicular transport. In order to perform these functions, microtubules continually rearrange through a process known as dynamic instability, in which they switch from a phase of slow elongation to rapid shortening (catastrophe), and from rapid shortening to growth (rescue). The basic self-assembly mechanism underlying this process, assembly mediated by nucleotide phosphate activity, is omnipresent in biological systems. A recent paper, Prolonging assembly through dissociation: A self-assembly paradigm in microtubules , published in the May 3 issue of Physical Review E, presents a new paradigm for such self-assembly in which increasing depolymerization rate can enhance assembly. Such a scenario can occur only out of equilibrium. Brandeis Physics postdoc Sumedha, working with Chakraborty and Hagan, carried out theoretical analysis of a stochastic hydrolysis model to demonstrate the effect and predict features of growth fluctuations, which should be measurable in experiments that probe microtubule dynamics at the nanoscale.
Model for microtuble dynamics. All activity is assumed to occur at the right end of the microtubule (denoted as ">")
The essential features of the model that leads to the counterintuitive result of depolymerization helping assembly are (a) stochastic hydrolysis that allows GTP to transform into GDP in any part of the microtubule, and (b) a much higher rate of GTP attachment if the end of the microtubule has a GTP-bound tubulin dimer, compared to a GDP-bound tubulin dimer. Process (a) leads to islands of GTP-bound tubulins to be buried deep in the microtubule. Depolymerization from the end reveals these islands and enhances assembly because of the biased attachment rate (b). The simplicity of the model lent itself to analytical results for various aspects of the growth statistics in particular parameter regimes. Simulations of the model supported these analytical results, and extended them to regimes where it was not possible to solve the model analytically. The statistics of the growth fluctuations in this stochastic hydrolysis model are very different from “cap models” which do not have GTP remnants buried inside a growing microtubule. Testing the predictions in experiments could, therefore, lead to a better understanding of the processes underlying dynamical instability in-vivo and in-vitro. An interesting question to explore is whether the bias in the attachment rates is different under different conditions of microtubule growth.
