Dynamic instability of microtubules: Monte Carlo simulation and application to different types of microtubule lattice

Abstract

Dynamic instability is the term used to describe the transition of an individual microtubule, apparently at random, between extended periods of slow growth and brief periods of rapid shortening. The typical sawtooth growth and shortening transition behavior has been successfully simulated numerically for the 13-protofilament microtubule A-lattice by a lateral cap model (Bayley, P. M., M. J. Schilstra, and S. R. Martin. 1990. J. Cell Sci. 95:33-48). This kinetic model is now extended systematically to other related lattice geometries, namely the 13-protofilament B-lattice and the 14-protofilament A-lattice, which contain structural "seams". The treatment requires the assignment of the free energies of specific protein-protein interactions in terms of the basic microtubule lattice. It is seen that dynamic instability is not restricted to the helically symmetric 13-protofilament A-lattice but is potentially a feature of all A- and B-lattices, irrespective of protofilament number. The advantages of this general energetic approach are that it allows a consistent treatment to be made for both ends of any microtubule lattice. Important features are the predominance of longitudinal interactions between tubulin molecules within the same protofilament and the implication of a relatively favorable interaction of tubulin-GDP with the growing microtubule end. For the three lattices specifically considered, the treatment predicts the dependence of the transition behavior upon tubulin concentration as a cooperative process, in good agreement with recent experimental observations. The model rationalizes the dynamic properties in terms of a metastable microtubule lattice of tubulin-GDP, stabilized by the kinetic process of tubulin-GTP addition. It provides a quantitative basis for the consideration of in vitro microtubule behaviour under both steady-state and non-steady-state conditions, for comparison with experimental data on the dilution-induced disassembly of microtubules. Similarly, the effects of small tubulin-binding molecules such as GDP and nonhydrolyzable GTP analogues are readily treated. An extension of the model allows a detailed quantitative examination of possible modes of substoichiometric action of a number of antimitotic drugs relevant to cancer chemotherapy.