Mean lifetime of microtubules attached to nucleating sites

A simple two-phase (cap; no cap) macroscopic model describing the kinetic behavior at a labile tip of a microtubule has been proposed [Hill, T. L. (1984) Proc. Natl. Acad. Sci. USA 81, 6728-6732]. In the model, a microtubule exists either in a slowly growing phase (first-order rate constant, alpha) characterized by the existence of a GTP-tubulin cap at the growing tip; or the same microtubule exists in a rapidly shrinking phase (first-order rate constant, beta), which is entered if/when the GTP-tubulin cap is lost through a fluctuation, thus exposing GDP-tubulin subunits, which constitute the body of the microtubule. Transition between the two phases--i.e., loss of a cap (first-order rate constant, k) or formation of a new cap (first-order rate constant, k') occurs very infrequently and in a stochastic manner. In vitro experiments with centrosome-nucleated microtubules by Mitchison and Kirschner and Monte Carlo kinetic simulations, based on a realistic set of microscopic rate constants that apply to the end of a microtubule, suggest this alternation between two "quasimacroscopic" phases. In this paper, I outline the calculation of the mean lifetime of a microtubule nucleated on a centrosome by using Hill's model. For a microtubule M units long in the slowly growing phase, the mean lifetime for complete depolymerization is [M(k + k') + alpha + beta](beta k - alpha k')-1, provided that beta k greater than alpha k'. If the microtubule is in the rapidly shrinking phase, then the mean lifetime is M(k + k')(beta k - alpha k')-1, provided that beta k greater than alpha k'. In case beta k less than alpha k', the microtubule grows indefinitely, and the mean lifetime is infinite.