AN INTENSITY-BASED LIKELIHOOD FUNCTION FOR STRUCTURE REFINEMENT. Navraj S. Pannu and Randy J. Read, Department of Mathematical Sciences and Medical Microbiology & Immunology, University of Alberta, Edmonton, Alberta T6G 2H7, Canada

In order to improve the quality of a model, structural refinement attempts to optimize the agreement between the observed and the calculated diffraction measurements. The process of structural refinement is commonly based on a least-squares analysis. Since the probability distribution of the observed structure factor amplitude given the calculated structure factor amplitude is not a Gaussian centered at k|Fc|, where k is a scale factor, least-squares is not theoretically justified. Accordingly, least-squares refinement does not make optimal use of the discrepancies between observed and calculated diffraction measurements. Therefore, in order to improve the process of structural refinement, a more general maximum likelihood analysis is considered.

A maximum likelihood target function has been derived and implemented in XPLOR. This function takes into account errors both in the model and in the measurements. Furthermore, this function is intensity-based allowing the use of negative intensities derived from the values observed in the diffraction experiment.

Preliminary tests show that the intensity-based likelihood function can achieve more than twice the improvement in average phase error compared to a conventional least-squares refinement. As a result, the electron density maps are clearer and suffer less from model bias.

Research supported by AHFMR, MRC, NSERC and HHMI.