Fold Catastrophes and the Dependence of Free-Energy Barriers to Conformational Transitions on Applied Force

Abstract

Applied mechanical force (f) can activate conformational change in molecules by reducing the height of a free-energy barrier (DeltaG(b)). In this paper, molecular dynamics simulations are carried out with umbrella sampling and self-consistent histogram methods to determine free-energy profiles for a coarse-grained model of a protein under an applied force. Applied force is shown to cause fold catastrophes, where free-energy minima are destabilized until they disappear. It is well-known that a fold catastrophe at force f = B implies the scaling DeltaG(b) approximately |B - f|(3/2) in the limit of DeltaG(b) --> 0, but it is not clear whether this scaling is accurate for physically relevant barrier heights. The simulation results show that the fold catastrophe scaling is in fact accurate in the physically relevant regime and that the two-parameter function DeltaG(b) = A(B - f)(3/2) is superior to the two-parameter linear function for parametrizing changes in free-energy barriers with applied force.

Kinetic Ductility and Force-Spike Resistance of Proteins from Single-Molecule Force Spectroscopy

“…A need to account for the ductile regime has emerged also from earlier theoretical and molecular simulation studies of protein unfolding. Stretching forces required to destabilize some folded states were thermodynamically larger than previously expected (32), and both all-atom and coarse-grained simulations showed a nonlinear dependence of the activation barrier on force, indicative of kinetically ductile behavior (33)(34)(35).…”

Noise-activated dissociation of soft elastic contacts

“…The findings of the later studies [38][39][40][41] agree with Garg [36] in that the applied force ( f ) modifies the energy barrier as ~ (1-f/f c ) 1.5 , where f c is the critical force of detachment. Recently, such a scaling has been verified in molecular dynamics simulations as well [42,43]. The finding of Lacks et al [42] is particularly interesting in that they showed that it is not only the energy barrier, but also the free energy barrier that follows the scaling of ~(1-f/f c ) 1.5 .…”

“…Recently, such a scaling has been verified in molecular dynamics simulations as well [42,43]. The finding of Lacks et al [42] is particularly interesting in that they showed that it is not only the energy barrier, but also the free energy barrier that follows the scaling of ~(1-f/f c ) 1.5 . In the light of these previous studies, we write the overall frequency of rupture of a soft sphere from a solid substrate (assuming a linear friction) as follows:…”

Perspective: Mechanochemistry of biological and synthetic molecules

“…Near the critical force, it can be shown that the barrier vanishes as |F − F c | 3/2 , this behavior being universal and independent of detailed molecular properties. [45][46][47][48] More specifically (see Appendix B), the transition rate can be approximated by…”

“…Although, strictly speaking, these results hold only in the vicinity of the critical force F c , simulations suggest that the catastrophe theory predictions often remain accurate even far away from the catastrophe point. 45,48,49,87 Combined with the easier accessibility of the high force regime, these arguments suggest that most experimental studies happen to be on the Hammond part of the reaction path, which is well described by the one-dimensional cubic parabola model. This may further explain the wide success of the cubic parabola model in interpreting singlemolecule data.…”