  We study the stochastic dynamics of growth and shrinkage of single actin
filaments taking into account insertion, removal, and ATP hydrolysis of
subunits either according to the vectorial mechanism or to the random
mechanism. In a previous work, we developed a model for a single actin or
microtubule filament where hydrolysis occurred according to the vectorial
mechanism: the filament could grow only from one end, and was in contact with a
reservoir of monomers. Here we extend this approach in several ways, by
including the dynamics of both ends and by comparing two possible mechanisms of
ATP hydrolysis. Our emphasis is mainly on two possible limiting models for the
mechanism of hydrolysis within a single filament, namely the vectorial or the
random model. We propose a set of experiments to test the nature of the precise
mechanism of hydrolysis within actin filaments.
