Force-dependent switch in protein unfolding pathways and transition state movements

Although known that single domain proteins fold and unfold by parallel pathways, demonstration of this expectation has been difficult to establish in experiments. Unfolding rate, $k_\mathrm{u}(f)$, as a function of force $f$, obtained in single molecule pulling experiments on src SH3 domain, exhibits upward curvature on a $\log k_\mathrm{u}(f)$ plot. Similar observations were reported for other proteins for the unfolding rate $k_\mathrm{u}([C])$. These findings imply unfolding in these single domain proteins involves a switch in the pathway as $f$ or $[C]$ is increased from a low to a high value. We provide a unified theory demonstrating that if $\log k_\mathrm{u}$ as a function of a perturbation ($f$ or $[C]$) exhibits upward curvature then the underlying energy landscape must be strongly multidimensional. Using molecular simulations we provide a structural basis for the switch in the pathways and dramatic shifts in the transition state ensemble (TSE) in src SH3 domain as $f$ is increased. We show that a single point mutation shifts the upward curvature in $\log k_\mathrm{u}(f)$ to a lower force, thus establishing the malleability of the underlying folding landscape. Our theory, applicable to any perturbation that affects the free energy of the protein linearly, readily explains movement in the TSE in a $\beta$-sandwich (I27) protein and single chain monellin as the denaturant concentration is varied. We predict that in the force range accessible in laser optical tweezer experiments there should be a switch in the unfolding pathways in I27 or its mutants.