Optimized free energies from bidirectional single-molecule force   spectroscopy
  An optimized method for estimating path-ensemble averages using data from processes driven in opposite directions is presented. Based on this estimator, bidirectional expressions for reconstructing free energies and potentials of mean force from single-molecule force spectroscopy - valid for biasing potentials of arbitrary stiffness - are developed. Numerical simulations on a model potential indicate that these methods perform better than unidirectional strategies. 
David D. L. Minh and Artur B. Adib