Mechanisms for facilitated target location and the optimal number of molecules in the diffusion search process

Abstract

We investigate the number N of molecules needed to perform independent diffusions in order to achieve bonding of a single molecule to a specific site in time t [subscript] 0. For a certain range of values of t [subscript] 0, an increase from N to k · N molecules (k > 1) results in the decrease of search time from t [subscript] 0 to (t [subscript] 0)/k. In this regime, increasing the number of molecules is an effective way of speeding up the search process. However when N [is greater than or equal to] N [subscript] 0 (optimal number of N) the reduction of time from t [subscript] 0 to (t [subscript] 0)/k can be achieved only by an exponentially large increase of the number of molecules (from N to N exp(ck) for some c > 0).