THEORY AND APPLICATION OF THE MAXIMUM-LIKELIHOOD PRINCIPLE TO NMR PARAMETER-ESTIMATION OF MULTIDIMENSIONAL NMR DATA

A general theory has been developed for the application of the maximum likelihood (ML) principle to the estimation of NMR parameters (freque ncy and amplitudes) from multidimensional time-domain NMR data. A comp uter program (ChiFit) has been written that carries out ML parameter e stimation in the D-1 indirectly detected dimensions of a D-dimensional NMR data set. The performance of this algorithm has been tested with experimental three-dimensional (HNCO) and four-dimensional (HN(CO)CAHA ) data from a small protein labeled with C-13 and N-15. These data set s, with different levels of digital resolution, were processed using C hiFit for ML analysis and employing conventional Fourier transform met hods with prior extrapolation of the time-domain dimensions by linear prediction. Comparison of the results indicates that the ML approach p rovides superior frequency resolution compared to conventional methods , particularly under conditions of limited digital resolution in the t ime-domain input data, as is characteristic of D-dimensional NMR data of biomolecules. Close correspondence is demonstrated between the resu lts of analyzing multidimensional time-domain NMR data by Fourier tran sformation, Bayesian probability theory [Chylla, R.A. and Markley, J.L . (1993) J. Biomol. NMR, 3, 515-533], and the ML principle.