  Polymerization dynamics of single actin filaments is investigated
theoretically using a stochastic model that takes into account the hydrolysis
of ATP-actin subunits, the geometry of actin filament tips, the lateral
interactions between the monomers as well as the processes at both ends of the
polymer. Exact analytical expressions are obtained for a mean growth velocity
and for dispersion in length fluctuations. It is found that the ATP hydrolysis
has a strong effect on dynamic properties of single actin filaments. At high
concentrations of free actin monomers the mean size of unhydrolyzed ATP-cap is
very large, and the dynamics is governed by association/dissociation of
ATP-actin subunits. However, at low concentrations the size of the cap becomes
finite, and the dissociation of ADP-actin subunits makes a significant
contribution to overall dynamics. Actin filament length fluctuations reach the
maximum at the boundary between two dynamic regimes, and this boundary is
always larger than the critical concentration. Random and vectorial mechanisms
of hydrolysis are compared, and it is found that they predict qualitatively
similar dynamic properties. The possibility of attachment and detachment of
oligomers is also discussed. Our theoretical approach is successfully applied
to analyze the latest experiments on the growth and length fluctuations of
individual actin filaments.
