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Abstract

The determination of macromolecular structures from experimental data is an ill-posed inverse problem. Nevertheless, conventional techniques to structure determination attempt an inversion of the data by minimization of a target function. This approach leads to problems if the data are sparse, noisy, heterogeneous, or difficult to describe theoretically. We propose here to view biomolecular structure determination as an inference rather than an inversion problem. Probability theory then offers a consistent formalism to solve any structure determination problem: We use Bayesamp;amp;amp;lsquo; theorem to derive a probability distribution for the atomic coordinates and all additional unknowns. This distribution represents the complete information contained in the data and can be analyzed numerically by Markov chain Monte Carlo sampling techniques. We apply our method to data obtained from a nuclear magnetic resonance experiment and discuss the estimation of theory parameters.