  In single molecule laser optical tweezer (LOT) pulling experiments a protein
or RNA is juxtaposed between DNA handles that are attached to beads in optical
traps. The LOT generates folding trajectories under force in terms of
time-dependent changes in the distance between the beads. How to construct the
full intrinsic folding landscape (without the handles and the beads) from the
measured time series is a major unsolved problem. By using rigorous theoretical
methods---which account for fluctuations of the DNA handles, rotation of the
optical beads, variations in applied tension due to finite trap stiffness, as
well as environmental noise and the limited bandwidth of the apparatus---we
provide a tractable method to derive intrinsic free energy profiles. We
validate the method by showing that the exactly calculable intrinsic free
energy profile for a Generalized Rouse Model, which mimics the two-state
behavior in nucleic acid hairpins, can be accurately extracted from simulated
time series in a LOT setup regardless of the stiffness of the handles. We next
apply the approach to trajectories from coarse grained LOT molecular
simulations of a coiled-coil protein based on the GCN4 leucine zipper, and
obtain a free energy landscape that is in quantitative agreement with
simulations performed without the beads and handles. Finally, we extract the
intrinsic free energy landscape from experimental LOT measurements for the
leucine zipper, which is independent of the trap parameters.
