Correlation functions as a tool for protein modeling and structure analysis

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Abstract
Proteins present unique folding structures whose conformations are determined primarily by their amino acid sequences. At present, there is no algorithm that would correlate the sequences with the structures determined by X‐ray analysis or NMR. Comparative modeling of a new protein sequence based on the known structure of a functionally related protein promises to yield model structures that may provide relevant properties of the protein. To analyze the quality of a model structure, a set of correlation functions was derived from calculations on a subset of proteins from the structure database. Twenty‐three highly resolved protein structures with resolutions of at least 1.7 Å from various protein families were used as the primary database. The purpose of this initial work was to find highly sensitive functions (including statistical error limits for the parameters) that describe properties of “real” proteins. Each correlation described is characterized by the correlation coefficient, the parameters for linear or nonlinear regression (coefficients of the equation), standard deviation and variance, and the confidence limits describing the statistical probability for values to occur within these limits, e.g., the natural variability of the property under examination. In addition, a method was developed for creating reasonably misfolded proteins. The ability of a correlation function to discriminate between the native structure and the misfolded conformations is expressed by the reliability index, which indicates the sensitivity of a correlation function. The term correlation functions thus summarizes a variety of efforts to find a mathematical description for the properties of protein structures, for their correlation, and for their significance.