New method for deciphering free energy landscape of three-state proteins

We have developed a new simulation method to estimate the distance between the native state and the first transition state, and the distance between the intermediate state and the second transition state of a protein which mechanically unfolds via intermediates. Assuming that the end-to-end extension $\Delta R$ is a good reaction coordinate to describe the free energy landscape of proteins subjected to an external force, we define the midpoint extension $\Delta R^$ between two transition states from either constant-force or constant loading rate pulling simulations. In the former case, $\Delta R^$ is defined as a middle point between two plateaus in the time-dependent curve of $\Delta R$, while, in the latter one, it is a middle point between two peaks in the force-extension curve. Having determined $\Delta R^*$, one can compute times needed to cross two transition state barriers starting from the native state. With the help of the Bell and microscopic kinetic theory, force dependencies of these unfolding times can be used to locate the intermediate state and to extract unfolding barriers. We have applied our method to the titin domain I27 and the fourth domain of {\em Dictyostelium discoideum} filamin (DDFLN4), and obtained reasonable agreement with experiments, using the C$_{\alpha}$-Go model.

💡 Research Summary

The authors present a novel computational framework for quantitatively mapping the free‑energy landscape of proteins that unfold mechanically through an intermediate state, i.e., a three‑state (N → TS1 → I → TS2 → U) process. The central hypothesis is that the end‑to‑end extension ΔR, measured under an external pulling force, serves as an adequate reaction coordinate. Two pulling protocols are considered: constant‑force (CF) and constant loading‑rate (CLR) simulations. In CF simulations the time series ΔR(t) exhibits two distinct plateaus corresponding to the native‑to‑first‑transition and intermediate‑to‑second‑transition regimes; the midpoint between these plateaus is defined as ΔR*. In CLR simulations the force‑extension curve shows two peaks, each representing a transition barrier; the midpoint between the peaks is likewise taken as ΔR*. This ΔR* provides a geometric reference for the distances from the native state to the first transition state (Δx‡1) and from the intermediate to the second transition state (Δx‡2).

Using the Bell model together with microscopic Kramers theory, the mean first‑passage times τ1(F) and τ2(F) for crossing each barrier under a given force F are expressed as τ(F)=τ0 exp