Optimal reconstruction of the folding landscape using differential energy surface analysis

摘要

In experiments and in simulations, the free energy of a state of a system can be determined from the probabilitynthat the state is occupied. However, it is often necessary to impose a biasing potential on the system so that highnenergy states are sampled with sufficient frequency. The unbiased energy is typically obtained from the datanusing the weighted histogram analysis method (WHAM). Here we present differential energy surface analysisn(DESA), in which the gradient of the energy surface, dE/dx, is extracted from data taken with a series ofnharmonic biasing potentials. It is shown that DESA produces a maximum likelihood estimate of the foldingnlandscape gradient. DESA is demonstrated by analyzing data from a simulated system as well as data from ansingle-molecule unfolding experiment in which the end-to-end distance of a DNA hairpin ismeasured. It is shownnthat the energy surface obtained from DESA is indistinguishable from the energy surface obtained whenWHAMnis applied to the same data. Two criteria are defined which indicate whether the DESA results are self-consistent.nIt is found that these criteria can detect a situation where the energy is not a single-valued function of the measurednreaction coordinate. The criteria were found to be satisfied for the experimental data analyzed, confirming thatnend-to-end distance is a good reaction coordinate for the experimental system. The combination of DESA andnthe optical trap assay in which a structure is disrupted under harmonic constraint facilitates an extremely accuratenmeasurement of the folding energy surface.