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چکیده
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Studying the structure of the proteins using angular representations has attracted much attention recently, because of the ability of efficient modeling and taking into consideration the continuous conformational space of protein structures. Despite the presence of different statistical methods for modeling the protein backbone structure, there is a substantial need for sophisticated statistical tools to evaluate the goodness of fit of such models. This paper develops a method for joint estimation of multiple bivariate density functions for a collection of populations of protein backbone angles using their intrinsic manifold. The proposed method takes into account the circular nature of the angular data by using spherical spline. We showed that the joint density estimation of protein angles using the spherical spline is statistically more efficient than similar existing methods that does not fully consider the non-euclidean structure of the data. The proposed method has two important application in structure-based protein classification and quality assessment of protein structure prediction servers. This has been illustrated by simulations and real data examples.
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