A “black-box” re-weighting analysis can correct flawed simulation data, after the fact

There is a great need for improved statistical sampling in a range of physical, chemical and biological systems. Even simulations based on correct algorithms suffer from statistical error, which can be substantial or even dominant when slow processes are involved. Further, in key biomolecular applications, such as the determination of protein structures from NMR data, non-Boltzmann-distributed ensembles are generated. We therefore have developed the “black-box” strategy for re-weighting a set of configurations generated by arbitrary means to produce an ensemble distributed according to any target distribution. In contrast to previous algorithmic efforts, the blackbox approach exploits the configuration-space density observed in a simulation, rather than assuming a desired distribution has been generated. Successful implementations of the strategy, which reduce both statistical error and bias, are developed for a one-dimensional system, and a 50-atom peptide, for which the correct 250-to-1 population ratio is recovered from a heavily biased ensemble.