Probabilistic approach to determining unbiased random-coil carbon-13 chemical shift values from the protein chemical shift database.

We describe a probabilistic model for deriving, from the database of assigned chemical shifts, a set of random coil chemical shift values that are "unbiased" insofar as contributions from detectable secondary structure have been minimized (RCCSu). We have used this approach to derive a set of RCCSu values for 13Calpha and 13Cbeta for 17 of the 20 standard amino acid residue types by taking advantage of the known opposite conformational dependence of these parameters. We present a second probabilistic approach that utilizes the maximum entropy principle to analyze the database of 13Calpha and 13Cbeta chemical shifts considered separately; this approach yielded a second set of random coil chemical shifts (RCCSmax-ent). Both new approaches analyze the chemical shift database without reference to known structure. Prior approaches have used either the chemical shifts of small peptides assumed to model the random coil state (RCCSpeptide) or statistical analysis of chemical shifts associated with structure not in helical or strand conformation (RCCSstruct-stat). We show that the RCCSmax-ent values are strikingly similar to published RCCSpeptide and RCCSstruct-stat values. By contrast, the RCCSu values differ significantly from both published types of random coil chemical shift values. The differences (RCCSpeptide - RCCSu) for individual residue types show a correlation with known intrinsic conformational propensities. These results suggest that random coil chemical shift values from both prior approaches are biased by conformational preferences. RCCSu values appear to be consistent with the current concept of the "random coil" as the state in which the geometry of the polypeptide ensemble samples the allowed region of (phi, psi)-space in the absence of any dominant stabilizing interactions and thus represent an improved basis for the detection of secondary structure. Coupled with the growing database of chemical shifts, this probabilistic approach makes it possible to refine relationships among chemical shifts, their conformational propensities, and their dependence on pH, temperature, or neighboring residue type.