It has become a common practice of probing various aspects of biological polymers via force spectroscopy. Interestingly, a crossover in the unfolding kinetics of the ubiquitin protein has been observed in molecular simulations: The inverse of the unfolding time (i.e., the rate coefficient of transitioning from a collapsed state to an expanded state) is practically constant at low forces and essentially exponential at high forces [1]. This behavior has been noted in other proteins, suggesting in turn that the crossover may be a universal signature of force spectroscopy. In this work, we consequently examine such a possibility via molecular simulations of a biomimetic polymer: Although this homopolymer is solely based on a bead-spring model with a square-well potential, it is capable of universally capturing the protein-like unfolding of any heteropolymer [2]. Foremost, via the Wang-Landau procedure [3], we calculate at zero force the free energy as a function of an order parameter of interest [4]. We continue via perturbation theory, determining the free energy at nonzero force. We then proceed by examining the unfolding kinetics of the biomimetic polymer as a function of force. For this purpose, we invoke "Transition Path Sampling" with replica exchanges [5], and we especially focus on the evluation of the reaction coordinate [6]. Importantly, except that we vary the magnitude of the force, we also apply the force on different sets of monomeric sites. Overall, it appears that the reaction coordinate might have significant ramifications on the crossover observed for the rate coefficient.
[1] R. B. Best, E. Paci, G. Hummer, and O. K. Dudko. Pulling direction as a reaction coordinate for the mechanical unfolding of single molecules. Journal of Physical Chemistry B 112:5968-5976, 2008.
[2] M. P. Taylor, W. Paul, and K. Binder. All-or-none proteinlike folding transition of a flexible homopolymer chain. Physical Review E 79:050801, 2009.
[3] F. Wang and D. P. Landau. Efficient, multiple-range random walk algorithm to calculate the density of states. Physical Review Letters 86:2050-2053, 2001.
[4] C. Leitold and C. Dellago. Folding mechanism of a polymer chain with short-range attractions. The Journal of Chemical Physics 141:134901, 2014.
[5] T. S. van Erp. Reaction rate calculation by parallel path swapping. Physical Review Letters 98:268301, 2007.
[6] B. Peters and B. L. Trout. Obtaining reaction coordinates by likelihood maximization. The Journal of Chemical Physics 125:054108, 2006.
