The two-pathway model of the biological catch-bond as a limit of the allosteric model

Abstract

Catch-binding is a counterintuitive phenomenon in which the lifetime of a receptor/ligand bond increases when a force is applied to break the bond. Several mechanisms have been proposed to rationalize catch-binding. In the two-pathway model, the force drives the system away from its native dissociation pathway into an alternative pathway involving a higher energy barrier. Here, we analyze an allosteric model suggesting that a force applied to the complex alters the distribution of receptor conformations, and as a result, induces changes in the ligand-binding site. The model assumes explicitly that the allosteric transitions govern the properties of the ligand site. We demonstrate that the dynamics of the ligand is described by two relaxation times, one of which arises from the allosteric site. Therefore, we argue that one can characterize the allosteric transitions by studying the receptor/ligand binding. We show that the allosteric description reduces to the two-pathway model in the limit when the allosteric transitions are faster than the bond dissociation. The formal results are illustrated with two systems, P-selectin/PSGL-1 and FimH/mannose, subjected to both constant and time-dependent forces. The report advances our understanding of catch-binding by combining alternative physical models into a unified description and makes the problem more tractable for the bond mechanics community.

Figure 1

Binding and dissociation of a receptor/ligand catch-bond complex. The diagram is based most directly on the FimH/mannose system (27,44); however, it also represents other catch-bonds. The two-domain fragment of the receptor protein, composed of the pilin (black) and lectin (green) domains, exists in either bent or extended state. (Solid lines) More stable conformation; (dashes) less stable conformation. The bent state is more favorable in the free receptor. Binding to mannose (circle) shifts the conformational equilibrium toward the extended state. The interaction between lectin's binding site (angle made of two thin black lines) and mannose is stronger for the extended state (angle holding the circle) than the bent state (angle releasing the circle). The applied force (red arrows) lowers the bond dissociation barrier and favors the extended conformation. The control of the receptor conformation by force, combined with the correlation between the receptor conformation and the receptor/ligand binding strength, forms the basis for the allosteric model (19); see also Fig. 2a. The bond dissociations via the bent and extended channels represent the catch- and slip-pathways in the two-pathway model (12); see also Fig. 2b.

Figure 2

Energy profiles in the bound receptor/ligand complex for (a) allosteric (19) and (b) two-pathway (12) models of catch-binding. Minima a1 and a2 in panel a describe the bent and extended states of the two-domain receptor fragment, in accordance with the central part of Fig. 1. States a1 and a2 of the receptor allosteric fragment correlate with the free energy profiles l1 and l2 characterizing the ligand binding site. For a certain relationship between the model parameters, the allosteric model of panel a transforms into the two-pathway model of panel b, in which the ligand escapes from the binding site l via either the catch-barrier (left) or the slip-barrier (right). Application of the force (vector arrow) modifies the energy profiles for the allosteric and ligand interactions in panels a and b (from solid to dashed curves). All barriers are characterized by their widths x, as labeled in the figure. The barrier width is defined as the distance from the minimum to the maximum.

Figure 3

Lifetime of the P-selectin/PSGL-1 complex as a function of force in the constant force experiments. (Dots) Experimental data (2). (Curve) Theoretical results for the allosteric and two-pathway models, Eqs. 4, 5, and 6 and Eq. 1, respectively, with the parameters presented in the text.

Figure 4

Dependence of the probability P₁(f) (see Eq. 6) to find the allosteric fragment in the bent state a1 (see Fig 2b) as a function of force for P-selectin/PSGL-1 (solid line) and FimH/mannose (dashes). Ligand binding favors the extended state (44), defining the initial value P₁(0). The applied force stabilizes the extended state further. The small values of P₁(f) justify the approximation leading to Eq. 7.

Figure 5

Probability density of the bond rupture force for the P-selectin/PSGL-1 complex, normalized to the total number of pulls for the ramp rate r = 1400 pN s⁻¹. (Dots) Experimental data (10). (Curve) Theoretical results from Eqs. 11 and 12 with the model parameters presented in the text.

Figure 6

Same as Fig. 3, but for the FimH/mannose complex. The experimental data are taken from Thomas et al. (13,27).

Figure 7

Same as Fig. 5, but for the FimH/mannose complex with the ramp-rate r = 2500 pN s⁻¹. The experimental data are taken from Yakovenko et al. (51).

Figure 8

Force dependence of the ratio of the relaxation rates v_l(f)/v_a(f) from Eq. 14, obtained using the model parameters for the FimH/mannose complex and k⁰₂₁ = 5 s⁻¹.