Biomedical subjects

D A Langs

Publications and source records attributed to D A Langs.

At least 19 recordsLinked to original sources

PubMed2001

Map self-validation: improved criteria to resolve the SIR or SAS phase ambiguity.

A procedure was recently described that used the correlation coefficient (CC) agreement between the observed /F(h)/ and their associated unbiased 'omit map' extrapolated values /X(h)/ from an initial trial map as the basis for resolving the SIR or SAS phase ambiguity. It is noted here that a significant improvement in selectivity can be obtained if this agreement is expressed in terms of the complex-valued F(h) and X(h). A new scheme is outlined to exploit the weighted average of the two SIR or SAS phase choices. This procedure requires six FFTs per phase compared with three for the older method that randomly selected either of the two permitted phase choices from the Argand diagram as starting values. Trial calculations are encouraging for applications as low as 4 A resolution.

Computational Biology↗

PubMed2001

Improvement of SAS triple invariant estimates for macromolecular direct-methods phasing.

Single-wavelength anomalous dispersion (SAS) data can in principle be phased by direct methods since a priori estimates of the three-phase structure invariants can be computed from these data. The mean phase error of the most reliable triple estimates for a small protein, however, is typically no better than 60 degrees, and does not bode well for applications to larger structures. A procedure is described that can substantially lower the error in these estimates and introduce a larger number of useful triple invariants into the phasing process. The mean phase error of the most reliable triples for a 2.5 A resolution data set from a Pt derivative of a 115-residue protein was reduced from 55 to 25 degrees by this method. It was also possible to identify a significant number of the poorest triple estimates, those with mean phase errors approaching 90 degrees, such that they could be reliably down-weighted or excluded from the phasing process.

Crystallography, X-Ray↗

PubMed2001

Map self-validation: a useful discriminator of phase correctness at low resolution.

A new map-validation procedure is based on the correlation-coefficient agreement between the observed structure-factor magnitudes and their extrapolated values from suitably modified electron-density maps from which they have been each in turn systematically excluded. The correlation coefficient tends to a maximum as the phase errors in a map are reduced. This principle was used to resolve the single-wavelength anomalous scattering (SAS) and single-derivative isomorphous replacement (SIR) phase ambiguity for a number of error-free trial structures. Applications employing real data sets tend to be more difficult owing to data incompleteness and errors affecting the construction of the Argand diagram.

Crystallography↗

PubMed2000

Bulk-solvent correction in direct-methods phasing.

It is shown that for crystals of large proteins at low diffraction resolution, with N approximately 10 000 independent non-H protein atoms and d(min) approximately 8 A, a simple bulk-solvent correction yields the Sayre equation in its classical form, F(h) = q summation operator(k)F(k)F(h - k). In the low-resolution protein case, the proportionality factor becomes q = 1/[( - rho(S))V], where V is the unit-cell volume, rho(S) is the assumed constant electron density in the solvent regions of the crystal and is the average electron density in the protein regions. The classical form of the tangent formula follows from the bulk-solvent-corrected Sayre equation and its validity at low resolution is verified in empirical calculations.

Adenosylhomocysteinase↗

PubMed2000

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.

Crystallization↗

PubMed1999

Progress on the direct-methods solution of macromolecular structures using single-wavelength anomalous-dispersion (SAS) data.

In the past few years, a number of strategies have been outlined to resolve the SAS phase ambiguity given that unique estimates omega (h, k) of the triple invariants are available. A new least-squares method is described that can in principle resolve the phase ambiguity to determine macromolecular phases provided that omega (h, k) estimates are unbiased. Limitations of the method in practical applications are discussed. An example is given where the correct solution can be identified by use of the SAS tangent formula in the instance that traditional SAS phasing methods have lead to an incorrect heavy-atom substructure.

Anti-Bacterial Agents↗

PubMed1999

On 'globbicity' of low-resolution protein structures.

Using Harker's [Harker (1953). Acta Cryst. 6, 731-736] idea of spherically averaged polyatomic groups or 'globs' as the units of structure suitable for analyzing low-resolution diffraction data from protein crystals, 'globbic' scattering factors have been calculated for main-chain peptide units and amino-acid side-chain groups to 3 A resolution via Debye's [Debye (1915). Ann. Phys. (Leipzig), 46, 809-823] scattering formula. It is shown that the scattering factors are insensitive to intra-globbic conformational variation and can be approximated fairly well by a single-Gaussian formula, i.e. fg(s) = Zg exp(-1.7Zgs2), where s = (sin theta)/lambda and Zg is the total electron count for the atoms of the glob. Phase errors due to the globbic approximation and their effect on electron-density maps at 3.5 A resolution have been assessed via calculations for the crambin structure; this analysis indicates that the globbic scattering factors will be useful in efforts to develop procedures for direct-methods phasing of diffraction data to approximately 3.5 A resolution from protein crystals.

Crystallography, X-Ray↗

PubMed1999

Gramicidin D conformation, dynamics and membrane ion transport.

The linear pentadecapeptide antibiotic, gramicidin D, a heterogeneous mixture of six components, is a naturally occurring product of Bacillus brevis known to form ion channels in synthetic and natural membranes. The conformation of gramicidin A in the solid state, in organic solvents, and in planar lipid bilayers and the relationship between the composition and the conformation of gramicidin and its selective transport of ions across membranes has been the subject of intense investigation for over 50 years. The x-ray crystal structure and nmr solution spectroscopy agree fully with one another and reveal that entirely different conformations of gramicidin are present in uncomplexed and ion complexed forms. Precise refinements of the three-dimensional structures of naturally occurring gramicidin D in crystals obtained from methanol, ethanol, and n-propanol demonstrate the unexpected presence of stable left-handed antiparallel double-helical heterodimers that vary with the crystallization solvent. The side chains of Trp residues in the three structures exhibit sequence-specific patterns of conformational preference. Tyr substitution for Trp at position 11 appears to favor beta ribbon formation and stabilization of the antiparallel double helix. This conformation acts as a template for gramicidin folding and nucleation of the different crystal forms. The fact that a minor component in a heterogeneous mixture influences aggregation and crystal nucleation has potential applications to other systems in which anomalous behavior is exhibited by aggregation of apparently homogeneous materials, such as the enigmatic behavior of prion proteins. The crystallographically determined structures of cesium, potassium, rubidium, and hydronium ion complexes of gramicidin A are in excellent agreement with the nmr structure determination of the cesium ion gramicidin complex in a methanol chloroform mixture (50 : 50). The right-handed antiparallel double stranded double helical structures (DSDHR) also exhibit geometric features compatible with the solid-state 15N and 2H nmr data recorded for gramicidin in planar lipid bilayers and attributed to the active form of gramicidin A. The DSDHR crystal structures reveal an ion channel with a single partially solvated cation distributed over three ion binding sites. The channel lumen is relatively smooth and electrostatically negative as required for cation passage, while the exterior is electrostatically neutral, a requirement for membrane insertion. The "coordination" of the Cs+ ion is achieved by interaction with the pi orbitals of the carbonyls which do not point toward the ions. The K+ binding sites, which are similar in position to Cs+ binding sites, are shifted off center slightly toward the wall of the channel.

Amino Acid Sequence↗

PubMed1998

The conducting form of gramicidin A is a right-handed double-stranded double helix.

The linear pentadecapeptide antibiotic, gramicidin D, is a naturally occurring product of Bacillus brevis known to form ion channels in synthetic and natural membranes. The x-ray crystal structures of the right-handed double-stranded double-helical dimers (DSDH) reported here agree with 15N-NMR and CD data on the functional gramicidin D channel in lipid bilayers. These structures demonstrate single-file ion transfer through the channels. The results also indicate that previous crystal structure reports of a left-handed double-stranded double-helical dimer in complex with Cs+ and K+ salts may be in error and that our evidence points to the DSDH as the major conformer responsible for ion transport in membranes.

Amino Acid Sequence↗

PubMed1998

Reinvestigation of the use of Patterson maps to extrapolate data to higher resolution.

Many years ago, Karle & Hauptman proposed that the Patterson function could be used for data extrapolation beyond the observed range of the actual measured data. Few people have subsequently attempted to exploit this interesting idea, which might suggest possible limitations of this method, even in structural applications of modest complexity. This appears not to be the case, however, but the original ideas for implementing the extrapolation can be significantly improved. New calculation protocols indicate that Patterson maps may be used to extend observed data sets from 1.0 to approximately 0.5 A resolution with reasonably good precision. Correlation coefficients between the extrapolated F(hkl)'s and their structure-computed expected values typically range between 0.40 and 0.70 across the unobserved range, even for structures containing as many as 600 non-H light atoms in the asymmetric unit. The method is equally good at extrapolating F values for small zones of data that may not have been recorded within the observed resolution range of the diffraction experiment. Furthermore, triplet phase invariants that incorporate one or two extrapolated terms are nearly as reliable as those formed using only the observed data.

Crystallography, X-Ray↗

PubMed1998

Heterodimer formation and crystal nucleation of gramicidin D.

The linear pentadecapeptide antibiotic gramicidin D is a heterogeneous mixture of six components. Precise refinements of three-dimensional structures of naturally occurring gramicidin D in crystals obtained from methanol, ethanol, and n-propanol demonstrate the unexpected presence of stable left-handed antiparallel double-helical heterodimers that vary with the crystallization solvent. The side chains of Trp residues in the three structures exhibit sequence-specific patterns of conformational preference. Tyr substitution for Trp at position 11 appears to favor beta ribbon formation and stabilization of the antiparallel double helix that acts as a template for gramicidin folding and nucleation of different crystal forms. The fact that a minor component in a heterogeneous mixture influences aggregation and crystal nucleation has potential applications to other systems in which anomalous behavior is exhibited by aggregation of apparently homogeneous materials, such as the enigmatic behavior of prion proteins.

Anti-Bacterial Agents↗

PubMed1997

On integrating the techniques of direct methods with anomalous dispersion. IV. A simplified perturbation treatment for SAS phasing.

Results from probabilistic theory for the single-wavelength anomalous-scattering (SAS) Friedel pair, two-phase structure invariants, psi H = phi H + phi-H, are used to show that the SAS three-phase structure invariants, psi HK = phi H + phi K + phi-H-K, tend to positive values that are easily estimated. Appropriate averages of the estimates provide SAS perturbation corrections in the form of positive origin shifts for the probability distribution of psi HK values and for the tangent formula. The theoretical probabilistic results are verified by empirical statistical analyses of model-calculated phases and experimentally measured structure-factor magnitudes for a small-molecule and a protein crystal structure.

Chemistry, Physical↗

PubMed1997

The X-ray structure of the monoclinic crystal form of [D-Hyi2, L-Hyi4] meso-valinomycin.

The conformation and intermolecular association of [D-Hyi2, L-Hyi4] meso-valinomycin [cyclo[-D-Val-D-Hyi-L-Val-L-Hyi-(D-Val-L-Hyi-L-Val-D-+ ++Hyi)2-], C60H102N6O18] in a crystal form obtained from ethanol solution has been determined by x-ray crystallography. Two depsipeptides and one ethanol molecule per asymmetric unit crystallize in space group P2(1) (Z = 4); a = 14.579, b = 39.795, c = 13.928 A, beta = 116.90, Rl = 0.0757. The molecular conformation is very similar to that observed in the trigonal P3(2) crystal form obtained from acetone solution [V. Z. Pletnev et al. (1991) Biopolymers, Vol. 31, pp. 409-415]. Both independent molecules in the crystal adopt a similar distorted bracelet structure with a sterically inaccessible, partially formed, ion-binding center that is stabilized by six 4-->1 type H bonds. The observed conformation accounts for the inability of the molecule to complex ions. Close examination of the three crystallographically independent molecules reveals that differences in the backbone conformation associated with solvent interaction are significantly larger than those associated with hydrophobic van der Waals interactions of crystal packing.

Crystallization↗

PubMed1997

The crystal and molecular structure of a valinomycin analogue cyclo[(D-Val-L-Lac-L-Ala-D-Hyi)2(D-Val-L-Lac-L-Val-D-Hyi)]. H2O(C50H82N6 O18.H2O).

The crystal and molecular structure of the valinomycin analogue, cyclo[(D-Val-L-Lac-L-Ala-D-Hyi)2(D-Val-L-Lac-L-Val-D-Hyi)] has been solved by x-ray direct methods using the "Shake and Bake" procedure. The crystals, grown from a mixture of octane/CH2Cl2, belong to space group P2(1) (Z = 4) with cell parameters a = 10.29, b = 32.08, c = 18.73 A, beta = 97.05 degrees, and contain two molecules per asymmetric unit. After anisotropic refinement the standard reliability factor was Rl = 0.058. The conformations of both independent molecules is similar to that observed for isoleucinomycin, cyclo[-(D-Ile-L-Lac-L-Ile-D-Hyi)3] [V. Z. Pletnev et al. (1980) Biopolymers, Vol. 19, pp. 1517-1534]. The structure has an asymmetric conformation stabilized by six intramolecular H bonds, five bonds being of the 4-->1 type and one bond being of the 5-->1 type. One water molecule is caged in the internal cavity of each cyclodepsipeptide. This conformation could represent an intermediate state between free and complexed forms of valinomycin.

Crystallography, X-Ray↗

PubMed1996

Molecular structure and mechanisms of action of cyclic and linear ion transport antibiotics.

Ionophores are antibiotics that induce ion transport across natural and artificial membranes. The specific function of a given ionophore depends upon its selectivity and the kinetics of ion capture, transport, and release. Systematic studies of complexed and uncomplexed forms of linear and cyclic ionophores provide insight into molecular mechanisms of ion capture and release and the basis for ion selectivity. The cyclic dodecadepsipeptide valinomycin, cyclo[(-L-Val-D-Hyi-D-Val-L-Lac)3-], transports potassium ions across cellular membrane bilayers selectively. The x-ray crystallographic and nmr spectroscopic data concerning the structures of Na+, K+, and Ba+2 complexes are consistent and provide a rationale for the K+ selectivity of valinomycin. Three significantly different conformations of valinomycin are observed in anhydrous crystals, in hydrated crystals grown from dimethylsulfoxide, and in crystals grown from dioxane. Each of these conformations suggests a different mechanism of ion capture. One of the observed conformations has an elliptical structure stabilized by four 4<--1 intramolecular hydrogen bonds and two 5<--1 hydrogen bonds. Ion capture could be readily achieved by disruption of the 5<--1 hydrogen bonds to permit coordination to a potassium ion entering the cavity. The conformation found in crystals obtained from dimethyl sulfoxide is an open flower shape having three petals and three 4<--1 hydrogen bonds. Complexation could proceed by a closing up of the three petals of the flower around the desolvating ion. In the third form, water molecules reside in the central cavity of a bracelet structure having six 4<--1 hydrogen bonds. Two of these bracelets stack over one another with their valine-rich faces surrounding a dioxane molecule. The stacked molecules form a channel approximately 20 A in length, suggesting that under certain circumstances valinomycin might function as a channel. A series of analogues of valinomycin differing in ring composition and size have been synthesized and their transport properties tested. Peptide substitution and chiral variation in the dodecadepsipeptide can result in stabilization or modification of the different conformers. While contraction of the ring size results in loss of ion transport properties, expansion of the ring size permits complexation of larger ions and small positively charged molecules. Gramicidin A is a pentadecapeptide that functions as a transmembrane channel for transporting monovalent cations. Crystal structures of the cesium chloride complex and two uncomplexed forms of gramicidin A have been reported. In all three structures the gramicidin A molecule is a left-handed, antiparallel, double-stranded helical dimer. In the cesium complex the beta 7.2-helix has 6.4 residues per turn with an internal cavity large enough to accommodate cesium ions. In the uncomplexed structures the channel is 31 A long and has 5.6 amino acids per turn. Because the helix is too tightly wound to permit ion transport, ion transport would require breaking and reforming of hydrogen bonds.

Amino Acid Sequence↗

PubMed1995

Use of globic scattering factors for protein structures at low resolution.

At 3 to 4 A resolution, the electron density of a protein may be modeled by a continuous chain of 'globs' representing the amide region of the peptide backbone and the side-chain residues. Group scattering factors are derived from a trans planar C alpha C = ONC alpha backbone segment and most favored side-chain conformer for 18 different amino acids. Trial calculations indicate that the phase error and crystallographic residual comparing the atomic and 'globic' models rapidly decrease from high to low resolution. At 3 A resolution, the phase error is approximately 80 degrees. These results indicate that the electron density of a protein composed of N amino acid residues may be adequately modeled by 2N globs at low resolution.

Amino Acids↗

PubMed1995

TDSIR phasing: direct use of phase-invariant distributions in macromolecular crystallography.

A new strategy for employing three phase triples invariant estimates from Hauptman's single isomorphous replacement (SIR) and anomalous dispersion (SAS) joint probability distribution formulae is outlined which produces a single unique phase-invariant solution in the case where the positions of the heavy-atom scatterers is known. A similar but non-identical result is obtained for the phase invariants of a structure for which a molecular-replacement solution has been obtained. It is important to note that the values of the individual native/derivative phases can be determined directly from the probability distribution formulae without having to utilize the phase-invariant estimates in an active way. Elimination of the multisolution aspect of utilizing phase-invariant estimates should have important repercussions with regard to phasing macromolecular sets of derivatized data. Trial calculations based on experimentally measured 2.5 A data for three derivatives of cytochrome c550 are encouraging. The average of the three SIR maps resolves a number of structural ambiguities seen in the published multiple isomorphous replacement (MIR) map obtained from eight derivatives.

Crystallography, X-Ray↗

PubMed1995

Efficient methods for the linearization and solution of phase-invariant equations.

This paper describes a linear least-squares procedure, whereby, through quadrupole relationships, the 2 pi integers that linearize sets of unique phase-invariant estimates can be determined. It is subsequently shown that the phase solutions for these linear equations can be obtained, even for basis sets of thousands of phases, without having to either build or invert the full least-squares matrix. The final r.m.s. phase errors achieved by this method can typically be less that 5 or 10 degrees.

Algorithms↗