Globbic approximation in low-resolution direct-methods phasing

Probabilistic direct-methods phasing theory, originally based on a uniform atomic distribution hypothesis, is shown to be adaptable to a non-uniform bulk-solvent-compensated globbic approximation for protein crystals at low resolution. The effective number n(g) of non-H protein atoms per polyatomic glob increases with decreasing resolution; low-resolution phases depend on the positions of only N(g) = N(a)/n(g) globs rather than N(a) atoms. Test calculations were performed with measured structure-factor data and the refined structural parameters from a protein crystal with approximately 10 000 non-H protein atoms per molecule and approximately 60% solvent volume. Low-resolution data sets with d(min) ranging from 15 to 5 A gave n(g) = ad(min) + b, with a = 1.0 A(-1) and b = -1.9 for the test case. Results of tangent-formula phase-estimation trials emphasize that completeness of the low-resolution data is critically important for probabilistic phasing.