Regulation of catch binding by allosteric transitions

Abstract

An allosteric model is used to describe changes in lifetimes of biological receptor-ligand bonds subjected to an external force. Force-induced transitions between the two states of the allosteric site lead to changes in the receptor conformation. The ligand bound to the receptor fluctuates between two different potentials formed by the two receptor conformations. The effect of the force on the receptor-ligand interaction potential is described by the Bell mechanism. The probability of detecting the ligand in the bound state is found to depend on the relaxation times of both ligand and allosteric sites. An analytic expression for the bond lifetime is derived as a function of force. The formal theoretical results are used to explain the anomalous force and time dependences of the integrin-fibronectin bond lifetimes measured by atomic force microscopy (Kong, F.; et al J. Cell Biol. 2009, 185, 1275-1284). The analytic expression and model parameters describe very well all anomalous dependences identified in the experiments.

Figure 1

Schematic of the potential energy profiles of the allosteric site (bottom) and the ligand-binding site (top). The allosteric site can exist in two distinct states, corresponding to the potential energy minima a1 and a2. The conformation of the ligand site, l1 and l2 respectively, depends on the allosteric state. An applied force f (red arrow) transforms the potential energy profiles from the black solid curves to the dashed red curves.

Figure 2

Force dependence of the lifetimes of the FN/α₅β₁ − Fc/GG − 7 complex with the following cations: A) Ca²⁺/Mg²⁺, B) Mg²⁺/EGTA, and C) Mn²⁺. The orange circles depict the experimental data, Figs. 3A–C of Ref. . The blue solid curves are obtained using the exact equation, Eq. 9. The green dashed curves show the approximate result, Eq. 11. The six parameters of the model obtained by fitting Eq. 9 to the experimental data are shown in Table 1.

Figure 3

The force dependence of the relaxation time of the allosteric site τ_a(f) (black-dashed line), the lifetime of the receptor/ligand complex τ_c(f) (red-solid line), and the dimentionless function h(f) (green-dotted line) for case A in Table 1 and Fig. 2.

Figure 4

Time-dependence of the logarithm of the number of bonds surviving by time t for the FN/α₅β₁ − Fc/GG − 7 complex with the Ca²⁺/Mg²⁺ cations. The solid lines are obtained using Eq. 13 with the parameters listed in Table 1. The initial values for the logarithms of the number of bonds at t = 0 are taken from experiment, Fig. S5A of Ref. (12). The green circles show the experimental points for f = 30pN taken from the above reference.

Figure 5

Force dependence of the lifetimes of the complexes involving transacted integrins (A, C) and monoclonical antibody (B,C). The orange circles represent the experimental data taken from Figs. 5A, 6A, and 6C of Ref. . The solid blue curves are obtained using Eq. 9 with the parameters presented in Table 2.