Comparisons of three-dimensional structures of proteins using hierarchical models and regularization for between-protein variations

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A method for comparing protein structures was developed. We consider a collection of three-dimensional coordinates of multiple proteins in which each protein has multiple conformations. The method exploits this protein-conformation hierarchy, and is based on the mixed-effects models on between- and within-protein variability. The estimation procedure is that of the EM-algorithm, in which the individual deviations of proteins are estimated and restricted using maximum-a-posteriori estimatorsand L1-regularization. At each iteration of the algorithm, the superposition of conformations can be made using a usual singular-value-decomposition but for specializedcovariance matrices. The results of numerical tests indicate that the method can be effective for characterizing the structures of multiple proteins simultaneously.