Experimental umbrella sampling of a rotary nanomachine

The free-energy landscape of a molecular system, which describes its free energy as a function of a few collective coordinates, governs its dynamics and function, but is challenging to determine experimentally. In molecular simulations, enhanced-sampling methods such as umbrella sampling use bias potentials to access regions of this landscape that are rarely visited by equilibrium fluctuations. Here, we transfer this concept to a single-molecule experiment: we combine electric-field biasing, in situ calibration of the bias potentials, and statistical reweighting to reconstruct the angular free-energy landscapes of rotary DNA nanomachines. The method resolves barriers exceeding 10 kBT and detects changes in local landscape shape caused by small modifications of the stator design. A systematic analysis of bias calibration, sampling, and finite-exposure averaging establishes the conditions required for accurate reconstruction. Experimental umbrella sampling thus relates nanoscale structure to the underlying free-energy landscape and supports the physics-informed design of artificial molecular machinery.