Figure 6.

Association rate for the hopping + sliding model of Berg, Blomberg, Winter and von Hippel, normalized to the diffusion limit (k/Da), as a function of sliding length in units of the specific target size (l_sl/a). The case where sliding and 3-D diffusion occur at equal rates (D₁/D = 1) is presented. Two specific target concentration cases are shown: (upper line) low target concentration (a²Lc = 10^–6); (lower line) high target concentration (a²Lc = 10^–2). The total association rate shows a maximum at a certain optimal sliding length. For the optimal sliding length, 3-D motion keeps the protein from spending too long ‘oversampling’ any particular region of the DNA contour by 1-D diffusion. The optimal sliding length becomes shorter for higher target concentrations.