A Bayesian statistics approach to multiscale coarse graining.

Coarse-grained (CG) modeling provides a promising way to investigate many important physical and biological phenomena over large spatial and temporal scales. The multiscale coarse-graining (MS-CG) method has been proven to be a thermodynamically consistent way to systematically derive a CG model from atomistic force information, as shown in a variety of systems, ranging from simple liquids to proteins embedded in lipid bilayers. In the present work, Bayes' theorem, an advanced statistical tool widely used in signal processing and pattern recognition, is adopted to further improve the MS-CG force field obtained from the CG modeling. This approach can regularize the linear equation resulting from the underlying force-matching methodology, therefore substantially improving the quality of the MS-CG force field, especially for the regions with limited sampling. Moreover, this Bayesian approach can naturally provide an error estimation for each force field parameter, from which one can know the extent the results can be trusted. The robustness and accuracy of the Bayesian MS-CG algorithm is demonstrated for three different systems, including simple liquid methanol, polyalanine peptide solvated in explicit water, and a much more complicated peptide assembly with 32 NNQQNY hexapeptides.