Measuring the energy landscape roughness and the transition state location of biomolecules using single molecule mechanical unfolding experiments

Single molecule mechanical unfolding experiments are beginning to provide profiles of the complex energy landscape of biomolecules. In order to obtain reliable estimates of the energy landscape characteristics it is necessary to combine the experimental measurements ( the force - extension curves, the mechanical unfolding trajectories, force or loading rate dependent unfolding rates) with sound theoretical models and simulations. Here, we show how by using temperature as a variable in mechanical unfolding of biomolecules in laser optical tweezer or AFM experiments the roughness of the energy landscape can be measured without making any assumptions about the underlying reaction coordinate. The efficacy of the formalism is illustrated by reviewing experimental results that have directly measured roughness in a protein - protein complex. The roughness model can also be used to interpret experiments on forced unfolding of proteins in which temperature is varied. Estimates of other aspects of the energy landscape such as free energy barriers or the transition state ( TS) locations could depend on the precise model used to analyse the experimental data. We illustrate the inherent difficulties in obtaining the transition state location from loading rate or force dependent unfolding rates. Because the transition state moves as the force or the loading rate is varied it is in general difficult to invert the experimental data unless the curvature at the top of the one dimensional free energy profile is large, i. e. the barrier is sharp. The independence of the TS location of the force holds good only for brittle or hard biomolecules whereas the TS location changes considerably if the molecule is soft or plastic. We also comment on the usefulness of extension of the molecule as a surrogate reaction coordinate especially in the context of force- quench refolding of proteins and RNA.