Microtubule dynamic instability: Numerical simulation of microtubule transition properties using a lateral cap model

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Abstract
We present a numerical formulation for the dynamic instability of microtubules involving the stabilisation of growing microtubules by a single layer of tubulin-GTP, with GTP hydrolysis effectively coupled to tubulin-GTP addition. This Lateral Cap model provides a readily visualised, working mechanism for the co-existence and interconversion of growing and shrinking microtubules. This class of model is specified in terms of a hydrolysis rule, whereby the addition of tubulin-GTP causes hydrolysis of GTP on a previously terminal tubulin-GTP molecule as it becomes incorporated into the microtubule lattice. A specific formulation is illustrated, though this is not unique. A limited set of parameters defines the kinetics and affinity for tubulin-GTP at the binding sites at a given end of the microtubule. The rate constants are a function of the nucleotide composition of the binding site, principally comprising the two tubulin molecules, which interact laterally and longitudinally with the incoming tubulin-GTP molecule. The Lateral Cap formulation demonstrates that a single terminal layer of tubulin-GTP is sufficient to reproduce the apparently complex behaviour of a dynamic population of microtubules. It differs significantly from the fluctuating tubulin-GTP cap model of Chen and Hill (1985). It gives a molecular description to the switching of individual microtubules between growing and shrinking states in terms of the composition of the multi-start terminal layer of the microtubule, and provides a general mechanism for the differential kinetic behaviour at opposite ends of dynamic microtubules. It reproduces the essential features of microtubule length excursions, and predicts detailed characteristics of microtubule dynamics, including the basis of the apparently cooperative nature of the transition behaviour as a function of the concentration of tubulin-GTP. It is readily amenable to further experimental test and refinement.