Figure 3.

Dependence of 2D association kinetics on the gap distance. (A) The natural log of waiting frequency P_w, calculated as the fraction of measurements with a waiting time >t_w, was plotted versus t_w for the indicated values of gap distance and fitted by our model. (B) Plots of the average waiting time 〈t_w〉 and the negative reciprocal of slope of the linear-fit in (A) versus gap distance d. (C) Apparent 2D on-rate $\langle A_{\text{c}}\rangle k_{\text{on}}^{\text{m}}$, calculated from the negative slope of the linear-fit in (A), was plotted against the gap distance d. $\langle A_{\text{c}}\rangle k_{\text{on}}^{\text{m}}$ was calculated by dividing the cellular on-rate $k_{\text{on}}^{\text{c}}$ by the product of the protein densities on the probe (A1) and target (GC) beads, e.g., m_rm_l = 1.95 × 10⁵μm⁻⁴ determined by flow cytometry (cf. Materials and Methods). The p-values for model fit to experiment data were indicated accordingly from the χ² goodness-of-fit tests. (D) Plots of average bond lifetimes 〈t_b〉 versus bond force. Gap distances corresponding to forces are indicated. The error bars represent SEM. All the data of experiments (symbols) and models (curves) were obtained at a fixed value of BFP spring constant (κ = 0.25 pN/nm). Each data point was derived from 20∼40 measurements.