Catch bonding in the forced dissociation of a polymer endpoint

Applying a force to certain supramolecular bonds may initially stabilize them, manifested by a lower dissociation rate. We show that this behavior, known as catch bonding and by now broadly reported in numerous biophysics bonds, is generically expected when either or both the trapping potential and the force applied to the bond possess some degree of nonlinearity. We enumerate possible scenarios and for each identify the possibility and, if applicable, the criterion for catch bonding to occur. The effect is robustly predicted by Kramers theory and Mean First Passage Time theory and confirmed in direct molecular dynamics simulation. Among the catch scenarios, one plays out essentially any time the force on the bond originates in a polymeric object, implying that some degree of catch bond behavior is to be expected in many settings relevant to polymer network mechanics or optical tweezer experiments.

Figure 1

(a) Illustration of the bond; the bead (red) is trapped in a potential well while an external potential acts on it. (b) Scenarios for the energy landscapes with corresponding catch bond criteria.

Figure 2

(a) The average unbinding time $\langle \tau \left(x_0\right)\rangle$ obtained by Eq. (23) for a cross-link which released at $x_0$ at $t=0$. The sum of ${\kappa }_c$ and ${\kappa }_s$ is 2 (black line), 4 (blue line), and 6 (red line). (b) The first three terms of terms of the perturbed system for $\kappa =2$.

Figure 3

(a) Potentials $U_{\mathrm{ext}}(x,0)$ and (b) average unbinding times relative to their $\varepsilon =0$ values for a particle attached to a semiflexible fiber with ${\ell }_p={\ell }_c=20$ (black line), the first harmonic approximation to the WLC (dashed blue line), and the first anharmonic approximation (dotted red line).

Figure 4

(a) Normalized lifetime of particle attached to a bead-spring polymer obtained by MD simulation. (b) Mean square displacement of the end-bead showing subdiffusive motion.