The recently developed approach to analyze the rotamer dynamics from NMR data (D?akula, ?., Westler, W.M., Edison, A.S., Markley, J.L., J. Am. Chem. Soc. 1992, 114, 6195-6199), called ContinUous ProbabIlity Distribution of rotamers (CUPID), has been expanded to allow computation of the rotational potential from the Fourier coefficients of the angular probability distribution. This leads naturally to a general solution to the nonnegativity problem, which appears when the Fourier series for the probability distribution is severely truncated. In addition, equations are derived for translating uncertainties in experimental NMR input data into errors in calculated continuous probability distributions of rotamers. The dependence of errors on various features of distrubitons has been studied systematically from simulated probability distributions. The results show that, typically, the confidence intervals are +/- 30x for dihedral angles and +/- 0.2? for rotamer populations. In the case of ?1 rotamers of amino acids, the analysis is most sensitive to the uncertainties in C?-H? couplings. The simplifying assumption of identical widths for all probability peaks has been justified by showing that it does not lead to large errors in other CUPID parameters. Experimental data for CUPID analysis are collected on turkey ovomucoid third domain (OMTKY3) because its structure is well known and CUPID-based refinement can be performed easily. Rotationally averaged nuclear Overhauser effect (NOE) and scalar coupling data collected for several residues of this protein have been used in CUPID analysis which resulted in rotamers that were almost identical to those from the x-ray structure. Further experimental efforts will be directed towards measurements of spin-diffusion-free NOEs and heteronuclear scalar couplings in OMTKY3.
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