OVERCOMING NONISOMORPHISM BY PHASE PERMUTATION AND LIKELIHOOD SCORING- SOLUTION OF THE TRPRS CRYSTAL-STRUCTURE

Entropy maximization to maximum likelihood, constrained jointly by the best available experimental phases and by a sufficiently good envelop e, can bring about substantial model-independent map improvement, even at medium (3.1 angstrom) resolution [Xiang, Carter, Bricogne & Gilmor e (1993). Acta Cryst. D49, 193-212]. In the crystal structure determin ation of the Bacillus stearothermophilus tryptophanyl-tRNA synthetase (TrpRS), however, the following had to be dealt with simultaneously: ( 1) a serious lack of isomorphism in the heavy-atom derivatives, result ing in large starting-phase errors; and (2) an initially poorly known molecular envelope. Because the constraints - both phases and envelope - were insufficiently well determined at the outset, maximum-entropy solvent flattening as previously applied was unsuccessful. Rather than improving the maps, it led to a deterioration of their quality, accom panied by a dramatic decrease of die log-likelihood gain as phases wer e extended from about 5 angstrom resolution to the 2.9 angstrom limit of the diffraction data. This deadlock was broken by the identificatio n of strong reflections, which were initially unphased and which were inaccessible by maximum-entropy extrapolation from the phased ones, an d by permutation of the phases of these reflections so as to sample th e space of possible electron-density and envelope modifications they r epresented. Permutation was carried out by successive full and incompl ete factorial designs [Carter & Carter (1979). J. Biol. Chem. 254, 122 19-12223] for 28 strong reflections selected in decreasing order of th eir 'renormalized' structure-factor amplitudes. The permuted reflectio ns included one reflection for which the probability distribution from multiple isomorphous replacement with anomalous scattering (MIRAS) in dicated an incorrect phase with a high figure of merit and which conse quently had a large renormalized structure factor. A similar permutati on was carried out for six different binary choices related to the cal culation and description of the molecular envelope. Permutation experi ments were scored using the log-likelihood gain and contrasts for each main effect were analyzed by multiple-regression least squares. Stude nt t tests provided significant and reliable indications for a large m ajority of the permuted reflections and for all six hypotheses related to the molecular envelope. The resulting phase improvement made it po ssible to assign positions (hitherto unobtainable) for nine of the ten selenium atoms in an isomorphous difference Fourier map for selenomet hionine-substituted TrpRS crystals and hence to solve the structure. P hase-permutation methods continued to be useful in producing improved maps from all the available isomorphous-replacement phase information and therefore played a critical role in solving the structure. This pr ocess rescued phases for the tetragonal TrpRS structure (now solved) f rom an otherwise crippling lack of isomorphism. It represents the firs t application of a fully fledged Bayesian phase-determination process [Bricogne (1988). Acta Cryst. A44, 517-5451 to the solution of an unkn own structure and demonstrates the feasibility of using these methods with low-to-medium-resolution data.