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 , by comparing two possible mechanisms of ATP hydrolysis , and by introducing mass conservation for the monomers . Our emphasis is mainly on the role and mechanism of hydrolysis within a single filament  . We propose a set of experiments to test the nature of the precise mechanism of hydrolysis within actin filaments.
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.
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and
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, and by introducing mass conservation for the monomers
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the role and
two possible limiting models for the
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, namely the vectorial or the random model