Prolonging assembly through dissociation:A self assembly paradigm in microtubules

We study a one-dimensional model of microtubule assembly/disassembly in which GTP bound to tubulins within the microtubule undergoes stochastic hydrolysis. In contrast to models that only consider a cap of GTP-bound tubulin, stochastic hydrolysis allows GTP-bound tubulin remnants to exist within the microtubule. We find that these buried GTP remnants enable an alternative mechanism of recovery from shrinkage, and enhances fluctuations of filament lengths. Under conditions for which this alternative mechanism dominates, an increasing depolymerization rate leads to a decrease in dissociation rate and thus a net increase in assembly.

💡 Research Summary

The paper presents a one‑dimensional stochastic model of microtubule (MT) dynamics that explicitly incorporates random GTP hydrolysis of tubulin subunits already incorporated into the filament. Traditional “GTP‑cap” models assume that only the terminal GTP‑tubulin protects the MT from rapid depolymerization; once the cap is lost, the filament undergoes a catastrophic shrinkage until a new cap is re‑established. In contrast, the present model allows each incorporated subunit to hydrolyze GTP to GDP with a constant probability per unit time, irrespective of its position. Consequently, GTP‑tubulin “remnants” can be buried deep inside the lattice.

The authors formulate the dynamics on a linear lattice of length L. Tubulin addition occurs at rate k_on·