Abstract
The structural dynamics of a biopolymer is governed by a process of diffusion through its conformational energy landscape. In pulling experiments using optical tweezers, features of the energy landscape can be extracted from the probability distribution of the critical force at which the polymer unfolds. The analysis is often based on rate equations having Bell-Evans form, although it is understood that this modeling is inadequate and leads to unreliable landscape parameters in many common situations. Dudko and co-workers [Phys. Rev. Lett. 96, 108101 (2006)] have emphasized this critique and proposed an alternative form that includes an additional shape parameter (and that reduces to Bell-Evans as a special case). Their fitting function, however, is pathological in the tail end of the pulling force distribution, which presents problems of its own. We propose a modified closed-form expression for the distribution of critical forces that correctly incorporates the next-order correction in pulling force and is everywhere well behaved. Our claim is that this new expression provides superior parameter extraction and is valid even up to intermediate pulling rates. We present results based on simulated data that confirm its utility.
Highlights
The contribution of explicitly quantum processes notwithstanding [1], classical energy landscape theory [2,3,4,5] provides a useful framework for describing the evolution of biopolymers between various folded and unfolded configurations through a process of thermally driven escape from local confining potentials [6]
In pulling experiments using optical tweezers [33], the determination of landscape features has historically been carried out based on Bell-Evans phenomenological theory [34,35,36,37,38], which assumes that the rate constant k(F ) scales up exponentially with applied force from its unperturbed, intrinsic value k0 according to the Arrhenius law, kBE(F ) = k0e βFx‡
We find that our proposal outperforms the Bell-Evans and Dudko expressions, across many different choices of energy landscape and over a broad range of pulling rates
Summary
The contribution of explicitly quantum processes notwithstanding [1], classical energy landscape theory [2,3,4,5] provides a useful framework for describing the evolution of biopolymers between various folded and unfolded configurations through a process of thermally driven escape from local confining potentials [6]. Even in the moderate pulling regime, it incorrectly predicts the rupture force distribution It ignores self-consistency effects in the sense that it does not account for the fact that the distance x‡ and the energy barrier G‡ are themselves force dependent and both diminish with increasing F as the energy landscape is tilted. When the Bell-Evans rate, kBE(F ), is used as the basis for a fit to experimental data, the extracted parameters, G‡, x‡, and k0, may be incorrectly predicted. Fits of simulation data to the Bell-Evans cumulative probability distribution, insofar as they are able to produce good values of k0 and x‡ at all, only do so at the very slowest pulling rates. The cutoff itself introduces a significant element of uncertainty in the fit, since where best to put the cutoff cannot be determined if the landscape is not yet known
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