A maximum likelihood method for determining D-a(PQ) and R for sets of dipolar coupling data

The algorithms available today that use dipolar coupling data for macromole cular structure determination require the independent determination of two parameters, D-a(PQ) and R, Methods exist for obtaining these parameters whe n the set of dipolar couplings available is large and the orientations of t he interatomic vectors on which they report is isotropically distributed. T hese methods are less satisfactory when the set is small and anisotropic. D escribed here is a maximum likelihood method that extracts accurate values for D-a(PQ) and R from small, anisotropic data sets. Also demonstrated is a procedure for estimating the errors associated with the values of D-a(PQ) and R obtained and for incorporating these errors into refinement protocols . (C) 2001 Academic Press.