Probabilistic approach for estimation of binding rate constants for clusters of targets

The binding rate constant for a target within a cluster of targets is smaller than for an isolated target due to competition between the targets; and the magnitude of this decrease in the binding rate constant depends upon the shape and the size of the cluster. We obtain a general formula for binding rate constants for clusters of arbitrary shapes and sizes using an approach based upon probabilities to visit a certain domain in space by a searching particle. We applied this result to various shapes of clusters including a spherical shell, a straight line, a random coil, and a random "cloud." Our results could be applicable for targets localized on natural and artificial particles (e.g., receptors on the surfaces of living cells, and macro- and small molecules attached to magnetic beads) and to the target localized on polymers (e.g., DNA or RNA).