Theoretical description of release, uptake, and pulse chase of labeled subunits of actin or a microtubule that undergoes head-to-tail polymerization.

The notion of the number of once-visited sites by a one-dimensional random walker is used to describe the amount of release, uptake, and pulse chase of labeled subunits of actin, or a microtubule that undergoes head-to-tail polymerization or treadmilling. Exact formulae for any number of steps are given as well as all the possible asymptotic forms of these quantities. Numerical calculations are carried out using hypothetical and experimentally measured values of rate constants.