THE CUPID METHOD FOR CALCULATING THE CONTINUOUS PROBABILITY-DISTRIBUTION OF ROTAMERS FROM NMR DATA

We present a new method, ContinUous Probability Distribution of rotamers (CUPID), for determining the distribution of rotamer probability rho(chi) about a dihedral angle-chi. This method utilizes measured vicinal homonuclear and heteronuclear spin-spin coupling constants (J) and nuclear Overhauser enhancements (NOEs) from NMR spectra and demands no prior assumption about the conformations or the degree of flexibility across the bond. To analyze the NMR measurements, it is necessary to know J(chi), the angular dependence of each coupling constant, and r(chi), the angular dependence of each interatomic distance giving rise to an NOE. With 2N or more measured coupling constants and/or NOEs and with known functions J(chi) and r(chi), one determines the probability distribution by solving for the coefficients of the Fourier expansion of rho(chi) to order N. As a further refinement to rho(chi), we make the assumption that the distribution functions are sums of Gaussians. The theory underlying CUPID is presented here; the accompanying article (Dzakula, Z; Edison, A. S.; Westler, W. M.; Markley, J. L. J. Am. Chem. Soc., following paper in this issue) demonstrates an application of CUPID to the analysis of simulated data for an alpha-helix in a protein.