Figure 2.

Validation of the VK model-based analytical form of k_app (Eq. 12) for systems involving competitor DNA but with no intersegment transfer. (A) Rate constant k_app for target association as a function of the total number of sites L. The position of the target was set to m = 2. The dashed lines were obtained from the ODE-based numerical kinetics simulations. The solid lines were obtained using Eq. 12. k_sl,N = 10³, 10⁴, 10⁵, and 10⁶ s⁻¹ and k_off,N = 10 s⁻¹ were used. Under these conditions, effective sliding lengths λ are 10 (black), 32 (red), 100 (magenta), and 316 (blue) bp. (B) Rate constants k_app as a function of the target position m for probe DNA with L = 90. For this panel, k_sl,N = 10⁴ s⁻¹ and k_off,N = 10 s⁻¹ (an effective sliding length λ = 32 bp) were used. The dotted line is from the ODE-based numerical simulations; the solid line, from the VK model-based analytical form of k_app (Eq. 12); and the dashed line, from the modified Berg’s approximation (Eq. 16). For both panels A and B, D_tot = 2.5 nM; P_tot = 50 nM, K_d,N = 4 μM; K_d,S = 0.1 nM; C_tot = 2 μM; ϕ = 1; and M = 20.