摘要:

A knowledge‐based approach to crystal structure determination is presented. The approach integrates direct‐methods and artificial‐intelligence strategies to rephrase the structure determination process as an exercise inscene analysis. A general joint probability distribution framework, which allows the incorporation of isomorphous replacement, anomalous scattering anda prioristructural information, forms the basis of the direct‐methods strategies. The accumulated knowledge on crystal and molecular structures is exploited through the use of artificial‐intelligence strategies, which include techniques of knowledge representation, search and machine

ISSN:1399-0047    

DOI:10.1107/S090744499200917X

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

A new direct‐methods procedure has been devised which consists of phase refinementviathe minimal function,R(ϕ), alternated with Fourier summation and real space filtering. All phases are initially assigned values by computing structure factors for a randomly positioned set of atoms. These phases are then refined by using a parameter shift method to minimizeR(ϕ). The refined phases are Fourier transformed, and a specified number of the largest peaks in the electron‐density function are found and used as a new trial structure. The probability of a trial structure converging to a solution appears to depend on structural complexity and a number of refinement parameters. This procedure shows potential for providing fully automatic routine solutions for structures in the 200–400 ato

ISSN:1399-0047    

DOI:10.1107/S090744499200876X

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

A complementary relationship between the entropy (S) and the variance (σ2) of an electron‐density map is derived by approximating the logarithmic term in the entropy expression by a series expansion around the average map density. The resulting expression isS≃ ln N−σ2, whereNis the number of grid points and σ is the r.m.s. deviation from the mean in a map normalized to unit mean. The algebraic expression is of interest because it is consistent with and allows numerical evaluation of the surprising argument that noisedecreasesthe entropy of a map. The argument is that a noise contribution by itself generates a certain variance that is independent of the atomic structure and that adds to the variance due to the structure. Increased variance corresponds to decreased entropy. This property of noise provides an intuitively reasonable justification for maximizing the entropy of an electron‐density map in the quest for more readily interpretable maps of macromolecules. The entropy–variance relationship also extends the range of applicability of the entropy concept to maps with a limited amount of negative density. The approximation which leads to the entropy–variance relationship is most applicable where it is most likely to be useful – in experimental maps of relatively low st

ISSN:1399-0047    

DOI:10.1107/S0907444992010084

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

The crystallographic phase problem is indeterminate in the absence of additional chemical information. A successfulab initioapproach to the macromolecular phase problem must employ sufficient chemical constraints to limit the solutions to a manageably small number. Here we show that commonly employed chemical constraints – positivity, atomicity and a solvent boundary – leave the phase problem greatly underdetermined for Fourier data sets of moderate (2.5–3.0 Å) resolution. Entropy maximization is also beset by multiple false solutions: electron‐density maps are readily generated which satisfy the same Fourier amplitude constraints but have higher entropies than the true solution. We conclude that a successfulab initioapproach must make use of high‐resolution Fourier data and/or stronger chemical constraints. One such constraint is the connectivity of the macromolecule. We describe a rapid algorithm for measuring the connectivity of a map, and show its utility in reducing the multiplicity of solutions to the p

ISSN:1399-0047    

DOI:10.1107/S0907444992008801

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

A practical generally applicable procedure for exponential modeling to maximum likelihood of macromolecular data sets constrained by a moderately large basis set of reliable phases and a molecular envelope is described, based on the computer programMICE[Bricogne&Gilmore (1990).Acta Cryst. A46, 284297]. Procedures were first tested with simulated data sets. Exact and randomly perturbed amplitudes and phases were generated, together with a known envelope for solvent‐free protein and for protein in an electron‐dense crystal mother liquor typical of many real protein crystals. These experiments established useful guidelines and values for various parameters. Tests with basis sets chosen from the largest amplitudes indicate that exponential models with considerable correct extrapolated phase and amplitude information can be constructed from as few as 16% of the total number of reflections, with mean phase errors of about 30°, at resolution limits of either 5 or 3 Å. When the shape of the solvent channels in macromolecular crystals is known, it offers an important additional source of information.MICEwas, therefore, adapted to average the density outside the molecular boundary defined by an input envelope. This flattening process imposes a uniform density distribution in solvent‐filled channels as an additional constraint on the exponential model and is analogous to the treatment of solvent in conventional solvent flattening. Experimental data for cytidine deaminase, a structure recently solved by making extensive use of conventional solvent flattening, provides an example of the performance of maximum‐entropy methods in a real situation and a compelling comparison of this method to standard procedures. Exponential models of the electron density constrained by the most reliable phases obtained by multiple isomorphous replacement with anomalous scattering (MIRAS) (figure of merit>0.7, representing 34% of the total number of reflections) and by the envelope give rise to centroid electron‐density maps which are quantitatively superior by numerous statistical criteria to conventionally solvent‐flattened density. Similarity of these maps to the 2Fobs−Fcalcmap 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 with the MIRAS map, contains substantial errors. It is proposed that errors of this sort may account for previously noted deficiencies of the solvent‐flattening method [Fenderson, Herriott&Adman (1990).J. Appl. Cryst.23, 115131] and for the occasional tendency of incorrect interpretations to be `locked in' by crystallographic refinement [Brändén&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 models, using the experimental amplitudes and the most reliable phases. It should, therefore, become a valuable and generally useful procedure in macromolecular cr

ISSN:1399-0047    

DOI:10.1107/S0907444992008540

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

The constraints of correct electron‐density distribution, solvent flatness, correct local shape of the electron density and equal molecules are combined in an integrated procedure for macromolecular phase refinement and extension. These constraints on electron densities are satisfied simultaneously by solving a system of non‐linear equations. The electron‐density solution is further filtered by a phase combination procedure. The non‐crystallographic symmetry operations are refined by a rotation and translation space search and a least‐squares minimization method, thereby reducing the chance of introducing systematic phase errors during averaging. The effect of each constraint on phase refinement and extension is examined. The constraints are found to work synergistically in phase improvement. Test results on 2Zn insulin are

ISSN:1399-0047    

DOI:10.1107/S0907444992007911

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY