Single-molecule unfolding force distributions reveal a funnel-shaped energy landscape

Abstract

The protein folding process is described as diffusion on a high-dimensional energy landscape. Experimental data showing details of the underlying energy surface are essential to understanding folding. So far in single-molecule mechanical unfolding experiments a simplified model assuming a force-independent transition state has been used to extract such information. Here we show that this so-called Bell model, although fitting well to force velocity data, fails to reproduce full unfolding force distributions. We show that by applying Kramers' diffusion model, we were able to reconstruct a detailed funnel-like curvature of the underlying energy landscape and establish full agreement with the data. We demonstrate that obtaining spatially resolved details of the unfolding energy landscape from mechanical single-molecule protein unfolding experiments requires models that go beyond the Bell model.

FIGURE 1

A comparison between the commonly used Bell view and Kramers' view for analysis of protein unfolding data. (A) The pulling velocity data of the native-state unfolding of ddFLN4 show a logarithmic behavior within the experimental error. The inset shows a schematic illustration of the experimental setup. (B) Schematic reconstruction of the energy landscape in the Bell view along the NC-terminal vector. (C) Normalized unfolding probability force distributions (histogram with statistical error) at four different pulling velocities in comparison with the theoretical distributions using the Bell model (lines). (D) Pulling velocity data modeled using Kramers' theory. (E) The reconstructed energy landscape shows detailed curvature along the unfolding/folding pathway. (F) The characteristic behavior of the experimental unfolding force distributions with increasing pulling velocity is reproduced well using the Kramers' model.