Polydispersity effects on head-to-tail polymerization of F-actin. A theoretical treatment

A theoretical description of the release of labeled subunits of F-actin that undergoes head-to-tail polymerization utilizing random-walk theory is extended to the case of a finite-length polymer. An exact expression is given for the number of released subunits in a suitable form for numerical calculation. By comparing the results for a finite-length polymer with that for an infinite-length case, the limitation of the infinite-length approximation is readily known. The results for finite-length polymers are applied to systems with polydispersity. It is shown that the number of labeled subunits released from F-actin depends strongly on the distribution functions of the polymer lengths and the values of the transition probabilities of the random walkers.