FIGURE 4. Conceptual and real (MD) energy landscapes traversed along a molecular reaction coordinate under force.

a, Oriented at an angle to the molecular coordinate x, external force f adds a mechanical potential, -(f cos ) x, that tilts the landscape and lowers barriers. The inner barrier emerges to dominate kinetics when the outer barrier falls to a level k _BT below it under force. For sharp barriers, the local energy contours, called transition states, are highly curved and change little in shape or location under force. Even though the unbinding pathway may be tortuous and the orientation fluctuates wildly, the energy weighted locations of sharp barriers can project as constant distances x = x_ts cos along the direction of force. b, Instantaneous interaction energy between biotin and avidin computed along a half-nanosecond extraction from the binding pocket in the simulations of Israilev et al.¹⁰ (kindly provided to us by K.Schulten and co-workers, University of Illinois). Bordered by regions of rapid intense fluctuations, locations of rarified statistics reveal transition states expected in a thermally averaged free energy landscape⁷. Arrows mark barrier locations derived from the strength spectrum for biotin–avidin in Fig. 3b.