Connecting thermal and mechanical protein (un)folding landscapes

Molecular dynamics simulations supplement single-molecule pulling experiments by providing the possibility of examining the full free energy landscape using many coordinates. Here, we use an all-atom structure-based model to study the force and temperature dependence of the unfolding of the protein filamin by applying force at both termini. The unfolding time-force relation $\tau $(F) indicates that the unfolding behavior can be characterized into three regimes: barrier-limited low- and intermediate-force regimes, and a barrierless high-force regime. Slope changes of $\tau $(F) separate the three regimes. We show that the behavior of $\tau $(F) can be understood from a two-dimensional free energy landscape projected onto the extension X and the fraction of native contacts Q. In the low-force regime, the unfolding rate is roughly force-independent due to the small (even negative) separation in X between the native ensemble and transition state ensemble (TSE). In the intermediate-force regime, force sufficiently separates the TSE from the native ensemble such that $\tau $(F) roughly follows an exponential relation. The TSE becomes increasingly structured with force. The high-force regime is characterized by barrierless unfolding, approaching a time limit of around 10 $\mu $s.