In the 3-dimensional profile method, the compatibility of an amino acid sequence for a given protein structure is scored as the sum of the preferences of the residues for their environments in the 3D structure. In the original method (Bowie JU, Lüthy R, Eisenberg D, 1991, Science 253:164-170), residue environments were quantized into 18 discrete environmental classes. Here, amino acid residue preferences are expressed as a continuous function of environmental variables (residue area buried and fractional area buried by polar atoms). This continuous representation of residue preferences, expressed as a Fourier series, avoids the abrupt change of preference of residues in slightly different environments, as encountered in the original method with its 18 discrete environmental classes. When compared with the discrete 18-class representation of residue environments, this continuous 3D profile is found to be more sensitive in identifying sequences that fold into the profiled structure but share with it little sequence identity. The continuous 3D profile is also less sensitive to errors in environmental variables than is the discrete 3D profile. The continuous 3D profile can also be used to detect wrong folds or incorrectly modeled segments in an otherwise correct structure, as could the discrete 3D profile (Lüthy R, Bowie JU, Eisenberg D, 1992, Nature 356:83-85). Moreover, the progress of structure improvement during atomic refinement can also be monitored by examining the profile scores in a moving-window scan. Finally, by defining a functional form for profile scores, we open the way to profile atomic refinement in which an atomic structure adjusts to produce residue environments more compatible with the protein side chains.
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