Hierarchic Crossing through the Energy Barriers
For almost all molecular complexes investigated so far, the dependence between the unbinding force and the logarithm of the loading rate is represented by a single line, indicating the presence of only one energy barrier in the interaction energy landscape. However, the unbinding that involves single molecules with complex unbinding sites may exhibit multiple local maxima and minima in the interaction potential along the reaction coordinate. In such cases, the plot of the most probable unbinding force and logarithm of the loading rate shows a sequence of lines with different slopes, each corresponding to the position of a particular energy barrier. Apart from biotin-(strept)avidin complex [15, 16], the hierarchic crossing through energy barriers has been shown, for instance, for individual a5@1 integrin- fibronectin complexes . Another example showing two linear regions in the dependence of the unbinding force on the loading rate is presented in Fig. 5.5.
Figure 5.5 (A) The force versus loading rate dependence measured
for BSA-EDTA complex showing two segments of linear dependencies corresponding to two energy barriers (outer and inner one). Reprinted with permission from .
The measurements were carried out for two molecules: albumin and ethylene-di-amine tetraacetic acid (EDTA). The observed two linear segments indicated existence of two barriers (inner and outer ones) in the corresponding energy landscape. For each of them a separate set of the Bell-Evans model parameters could be determined. The region A (Fig. 5.5) corresponds to the outermost energy barrier characterized by the dissociation rate constant of k01 = 6.4 ± 3.5 s-1. Passing through inner energy barrier (region B, Fig. 5.5) is described by the dissociation rate constant of k02 = 49.1 ± 35.0 s-1. The extrapolation of the different linear segments to F = 0 differs by the amount related to the relative differences in the magnitude of the individual energy (the absolute values of multiple activation barriers can no longer be calculated directly). During the unbinding, the complex stays for 0.020 s in the first transition state (inner barrier) and for 0.156 s in the second transition state (outer barrier).
From the theory, for a hierarchic crossing, each z'-th barrier is described by its own dissociation rate constant (k0) and a position of the energy barrier (xb). In such case, the force-induced unbinding is modeled as the crossing over a series of barriers . Then, the overall unbinding rate (koff) is a sum of a specific dissociation rates:
When the system must overcome a series of activation barriers, the dissociation kinetics at low loading rate is dominated by properties of the outermost barrier. With increase of the loading rate, the outermost barriers are suppressed, and the dissociation is governed by the inner activation barriers .