A black-box re-weighting analysis can correct flawed simulation data

Abstract

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 "blackbox" strategy for reweighting 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 black-box 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.canonical sampling | free energy | non-Boltzmann | molecular simulation E nsemble averages over configurations are fundamental to the analysis of finite-temperature systems of physical, chemical, and biological interest, as well as to any statistically defined system. Yet it is well appreciated that estimates of such averages based on computer simulations can suffer from both systematic and statistical error (1, 2). We therefore ask: Given a set of previously generated configurations of uncertain quality, what is the best way to estimate ensemble averages? Our proposed answer, the "black-box reweighting" (BBRW) strategy described below, appears promising in its ability to overcome both types of error in some systems.Statistical error is a ubiquitous problem of underappreciated practical importance. Every algorithm known to the authors, including sophisticated methods (3-5), relies on repeated visits to a state (a subset of configuration space) to generate statistical reliability or precision in the population estimate for that state. If we define the simulation-and-system-specific correlation time t corr as the time required to visit all important states at least once, then statistical precision requires a long total simulation time, t sim t corr . Standard square-root-of-duration arguments (1, 2) suggest that a simulation retains a fractional imprecision of √ t corr /t sim (on a unit scale). Below, we show that BBRW dramatically cuts statistical error, avoiding the slow square-root behavior.Systematic bias is typical in some systems of great practical importance-such as full-sized proteins-where, to date, it is not clear that any atomically detailed simulation has come close to reaching t corr . Indeed, surprisingly lengthy simulations are required to obtain statistical ensembles for small peptides (6). Nevertheless, biased non-Boltzmann distributed sets of atomically detailed protein structures are regularly generated, e.g., for NMR structure determination (7) and i...

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