The two-pathway model for the catch-slip transition in biological adhesion

Abstract

Some recently studied biological noncovalent bonds have shown increased lifetime when stretched by mechanical force. In each case these counterintuitive "catch-bonds" have transitioned into ordinary "slip-bonds" that become increasingly shorter lived as the tensile force on the bond is further increased. We describe analytically how these results are supported by a physical model whereby the ligand escapes the receptor binding site via two alternative routes, a catch-pathway that is opposed by the applied force and a slip-pathway that is promoted by force. The model predicts under what conditions and at what critical force the catch-to-slip transition would be observed, as well as the degree to which the bond lifetime is enhanced at the critical force. The model is applied to four experimentally studied systems taken from the literature, involving the binding of P- and L-selectins to sialyl Lewis(X) oligosaccharide-containing ligands. Good quantitative fit to the experimental data is obtained, both for experiments with a constant force and for experiments where the force increases linearly with time.

FIGURE 1

Potential energy profile projected onto the direction of force for a simple slip-bond. A simple catch-bond would have the opposite energy profile with respect to the direction of force.

FIGURE 2

Potential energy profile describing the catch-slip transition. The two planes are used to represent a section of the ligand binding pocket that is bent around the catch barrier maximum. For simplicity, the force f (dotted line) is drawn to form the same angle with the two planes. In order for an efficient catch-slip transition to occur from the bound state x₁, the catch-barrier “c” opposite to the applied force must be lower than the slip-barrier “s,” and preferably farther from the bound state when projected onto the direction of force as quantified in Eq. 8. Thus, the left barrier grows with force and is responsible for the catch-bond behavior, whereas the right barrier decreases with force, contributing the slip-bond behavior. The effect of force on the energy landscape is illustrated by the dashed line.

FIGURE 3

The inverse lifetime as a function of the applied force for bonds of L-selectin with sPSGL-1 (open symbols) and PSGL-1 (solid symbols). The inverse lifetimes are shown as determined by Sarangapani et al. (7) by the reciprocal mean lifetimes (squares), negative slopes for the off-rate (circles), and the reciprocal standard deviation of the lifetime (triangles). The data form a single trend supporting the expectation that both systems form single catch-bonds because L-selectin functions as a monomer. The solid line shows the theoretical fit to Eq. 6 using the parameters estimated from all six data sets using SAAM II software (19) as described in the text and reported in Table 1.

FIGURE 4

The bond lifetime as a function of the applied force for bonds of dimeric P-selectin with monomeric sPSGL-1 (solid symbols) and dimeric PSGL-1 (open symbols). The lifetimes are shown as determined by Marshall et al. (2003) by the mean lifetimes (squares), inverse negative slopes for the off-rate (circles), and the standard deviation of the lifetime (triangles) The left panel shows the data as previously published (6). The thin solid line shows the theoretical fit to Eq. 6 using the parameter estimates reported for P-selectin in Table 1, and this shows good fit to the monomeric sPSGL-1 data. The thick solid line shows the predicted behavior of the dimeric PSGL-1 bond, assuming the relationship of Eqs. A7 and 18, as described in the Appendix, and demonstrates good fit to the data. The thick dotted line shows the predicted behavior of the dimeric bond by the alternative model that is described by Eq. A6 and demonstrates poor fit to the data. The right panel shows the experimental data for PSGL-1 scaled according to Eq. 18, because this was shown to fit the model better in the left panel. The solid line (right) shows the theoretical fit to Eq. 6 using the parameters estimated from all six data sets (right) using SAAM II software (19) as described in the text and reported in Table 1.

FIGURE 5

The distribution of rupture forces in variable force experiments for binding of P-selectin to sPSGL-1. The squares show the “jump-ramp” experimental data from Evans et al. (9) where force was jumped to the indicated value and then ramped up at the indicated loading rate. The best fits are included for comparison for two models. The solid line shows the model fit for the two-pathway model described in this article with the parameters in the third line of Table 1. The heavy dotted line shows the fit of two-well two-pathway model used to describe the data by Evans et al. (9) () using the parameters k_1rup = 10, k_2rup = 0.36, f_b = 19.6, f₁₂ = 9.0, = 14.5.