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The most informative probability distribution functions (PDFs) describing the Ramachandran phi-psi dihedral angle pair, a fundamental descriptor of backbone conformation of protein molecules, are derived from high-resolution X-ray crystal structures using an information-theoretic approach. The Information Maximization Device (IMD) is established, based on fundamental information-theoretic concepts, and then applied specifically to derive highly resolved phi-psi maps for all 20 single amino acid and all 8000 triplet sequences at an optimal resolution determined by the volume of current data. The paper shows that utilizing the latent information contained in all viable high-resolution crystal structures found in the Protein Data Bank (PDB), totaling more than 77,000 chains, permits the derivation of a large number of optimized sequence-dependent PDFs. This work demonstrates the effectiveness of the IMD and the superiority of the resulting PDFs by extensive fold recognition experiments and rigorous comparisons with previously published triplet PDFs. Because it automatically optimizes PDFs, IMD results in improved performance of knowledge-based potentials, which rely on such PDFs. Furthermore, it provides an easy computational recipe for empirically deriving other kinds of sequence-dependent structural PDFs with greater detail and precision. The high-resolution phi-psi maps derived in this work are available for download.

Deriving High-Resolution Protein Backbone Structure Propensities from All Crystal Data Using the Information Maximization Device