New Dynamical Window onto the Landscape for Forced Protein Unfolding

The unfolding of a protein by the application of an external force pulling two atoms of the protein can be detected by atomic force and optical tweezers technologies as have been broadly demonstrated in the past decade. Variation of the applied force results in a modulation of the free-energy barrier to unfolding and thus, the rate of the process, which is often assumed to have single exponential kinetics. It has been recently shown that it is experimentally feasible, through the use of force clamps, to estimate the distribution of unfolding times for a population of proteins initially in the native state. In this Letter we show how the analysis of such distributions under a range of forces can provide unique information about the underlying free-energy surface such as the height of the free-energy barrier, the preexponential factor and the force dependence of the unfolding kinetics without resorting to ad hoc kinetic models.

Figure 1

Cumulative probability of unfolding times at two different forces and 300 K. (a) A double exponential is required to fit the curve at $F=250\mathrm{pN}$. (b) At a lower force ($F=200\mathrm{pN}$) the free-energy barrier is larger and the distribution of unfolding times is closer to single exponential.

Figure 2

(a) Average unfolding time $⟨t⟩$ and fitting parameters from the double-exponential fit of the time distribution ${\tau }_1$ and ${\tau }_2$ (${\tau }_1+{\tau }_2\simeq ⟨t⟩$). (b) Amplitude $A_2$ of the leading term of the expansion in Eq. (2); $A_2$ tends to 0 (i.e., $P(t)$ can be approximated with a single exponential) for $F\le 200\mathrm{pN}$. (c) Fit of $A_1/A_2$ to Eq. (3). (d) Activated time ${\tau }_1$ fitted using Bell’s relation (black line), DHS with $\nu =1/2$ (red line) and $\nu =2/3$ (blue line); data points for $F>300\mathrm{pN}$ have been disregarded in the fits.