Addressing Current Problems In Macromolecular Refinement . Rob Grothe, Washington University in St. Louis, Dept. of Electrical Engineering, Electronic Systems & Signals Research Lab.

The goal of this research is to develop new algorithms for macromolecular refinement by focusing on the shortcomings of current methods: 1) descriptions of crystal structure which do not capture its intrinsic conformational variability, 2) metrics which do not properly combine the effects of thermal fluctuations in the crystal and uncertainty in the intensity measurements, 3) limited radius of convergence, and 4) implementation on sequential machines.

We represent the crystal as a superposition of ideal crystals made up of unit cells containing identical static conformations. The number of elements in the superposition grows and shrinks, guided by the interplay between better fit of the data and the increased description complexity required to achieve it.

The validity of a structural description is its probability conditioned by the observed data. The probablility is derived from models of the physics of the crystal and the diffraction measurement and also description complexity.

Optimization techniques used in refinement are frustrated by the numerous local minima induced by local interatomic interactions in the crystal and phase ambiguity inherent in the diffraction data. Diffraction data, however, has a multi-scale property which can be used in refinement algorithms--as it has been in phasing methods--to extend radius of convergence. Structural descriptions are searched by a hybrid diffusion process whose drift is governed by coarse features of the structure, accepting or rejecting these states by applying the Metropolis criterion to the remaining terms, which convey fine details. Unlike simulated annealing, the underlying distribution is not distorted; the state trajectory can be used to compute estimates of statistics of the distribution (e.g. mean and variance of atom positions). The statistical approach avoids overfitting an underdetermined structural description to the data. Rather, we compute the average over all sample structural descriptions; these occur with frequency asymptotically in proportion with their estimated probabilities.

Finally, the computational bottlenecks--estimates of the van der Waals interactions and the diffraction intensities associated with a hypothetical structure and how these change with movements of atoms--are distributed among the 16384 processors of the Maspar MP-2 to reduce CPU time per iteration.