An effective theory is formulated for the dynamics of the guanosine triphosphate (GTP) cap believed to stabilize growing microtubules. The theory provides a ‘coarse-grained’ description of the cap’s dynamics. ‘Microscopic’ details, such as the microtubule lattice structure and the fate of its individual tubulin dimers, are ignored. In this cap model, GTP hydrolysis is assumed to be stochastic and uncoupled to microtubule growth. Different rates of hydrolysis are assumed for GTP in the cap’s interior and for GTP at its boundary with hydrolyzed parts of the microtubule. Expectation values and probability distributions relating to available experimental data are derived. Caps are found to be short and the total rate of hydrolysis at a microtubule end is found to be dynamically coupled to growth. The so-called catastrophe rate is a simple function of the microtubule growth rate and fits experimental data. A constant nonzero catastrophe rate, identical for both microtubule ends, is predicted at large growth rates. The delay time for dilution-induced catastrophes is stochastic with a simple distribution that fits the experimental one and, like the experimental one, does not depend on the rate of microtubule growth before dilution. The GTP content of microtubules is found and its rate of hydrolysis is determined under the circumstances created in an experiment designed to measure this GTP content. It is concluded that this experiment’s failure to register any GTP content is consistent with the model. A recent experimental result for the size of the minimal cap that can stabilize a microtubule is shown to agree with the result predicted by the cap model, after its parameters have been extracted from previous experimental results. Thus the effective theory and cap model presented here provide a unified description of several apparently contradictory experimental data. Experimental results for the catastrophe rate at different concentrations of magnesium ions and of microtubule associated proteins are discussed in terms of the model. Feasible experiments are suggested that can provide decisive tests of the model and determine its three parameters with higher precision.
|Number of pages||23|
|Journal||Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|State||Published - 1996|