ENTROPY MAXIMIZATION CONSTRAINED BY SOLVENT FLATNESS - A NEW METHOD FOR MACROMOLECULAR PHASE EXTENSION AND MAP IMPROVEMENT

A practical generally applicable procedure for exponential modeling to maximum likelihood of macromolecular data sets constrained by a moder ately large basis set of reliable phases and a molecular envelope is d escribed, based on the computer program MICE [Bricogne & Gilmore (1990 ). Acta Cryst. A46, 284-297]. Procedures were first tested with simula ted data sets. Exact and randomly perturbed amplitudes and phases were generated, together with a known envelope for solvent-free protein an d for protein in an electron-dense crystal mother liquor typical of ma ny real protein crystals. These experiments established useful guideli nes and values for various parameters. Tests with basis sets chosen fr om the largest amplitudes indicate that exponential models with consid erable correct extrapolated phase and amplitude information can be con structed from as few as 16% of the total number of reflections, with m ean phase errors of about 30-degrees, at resolution limits of either 5 or 3 angstrom. When the shape of the solvent channels in macromolecul ar crystals is known, it offers an important additional source of info rmation. MICE was, therefore, adapted to average the density outside t he molecular boundary defined by an input envelope. This flattening pr ocess imposes a uniform density distribution in solvent-filled channel s as an additional constraint on the exponential model and is analogou s to the treatment of solvent in conventional solvent flattening. Expe rimental data for cytidine deaminase, a structure recently solved by m aking extensive use of conventional solvent flattening, provides an ex ample of the performance of maximum-entropy methods in a real situatio n and a compelling comparison of this method to standard procedures. E xponential models of the electron density constrained by the most reli able phases obtained by multiple isomorphous replacement with anomalou s scattering (MIRAS) (figure of merit > 0.7, representing 34% of the t otal number of reflections) and by the envelope give rise to centroid electron-density maps which are quantitatively superior by numerous st atistical criteria to conventionally solvent-flattened density. Simila rity of these maps to the 2F(obs) - F(calc) map calculated with phases obtained after crystallographic refinement of the model implies that maximum-entropy extrapolation provides better phases for the remaining 66% of the reflections than the original centroid MIRAS distributions . Importantly, the solvent-flattened electron density, although it did permit interpretation of the map which was not readily accomplished w ith the MIRAS map, contains substantial errors. It is proposed that er rors of this sort may account for previously noted deficiencies of the solvent-flattening method [Fenderson, Herriott & Adman (1990). J. App l. Cryst. 23, 115-1311 and for the occasional tendency of incorrect in terpretations to be 'locked in' by crystallographic refinement [Brande n & Jones (1990). Nature (London), 343, 687-689, and references cited therein]. Solvent flattening with combined maximization of entropy and likelihood represents a phase-refinement path independent of atomic m odels, using the experimental amplitudes and the most reliable phases. It should, therefore, become a valuable and generally useful procedur e in macromolecular crystal structure determination.