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J Karle

Publications and source records attributed to J Karle.

At least 37 records · Page 2Linked to original sources
PubMed1982

Special phase invariant formulas of higher order: Expected values.

Formulas for the cosines of the higher-order phase invariants that arise in crystal structure analysis are derived as expected values from determinantal joint probability distributions. The values of the cosines of the invariants are expressed in terms of averages over simple functions of known structure factor magnitudes. The formulas are termed "special" to distinguish them from formulas that have more general averages. The latter will be presented in a future publication. The best opportunity for obtaining useful information from these formulas is provided by embedded seminvariants formed from the invariants by use of relationships among the phases that arise from the space group symmetries.

Journal Article↗
PubMed1982

General phase-invariant formulas of higher order: Expected values.

Formulas for the cosines of the higher order phase invariants that arise in crystal structure analysis are derived as expected values from determinantal joint probability distributions. The values of the cosines of the invariants are expressed in terms of averages over simple functions of known structure factor magnitudes. The formulas are termed "general" to distinguish them from formulas that have more restricted averages and are termed "special." As with the special formulas, the best opportunity for obtaining useful information from these formulas is provided by embedded seminvariants formed from the invariants by use of relationships among the phases that arise from the space group symmetries.

Journal Article↗
PubMed1981

Anomalous dispersion of sulfur in quinidine sulfate, (C(20)H(25)N(2)O(2))(2)SO(4).2H(2)O: Implications for structure analysis.

A Patterson-type map computed with Bijvoet differences squared as coefficients, (F(h) - F(-h))(2), as recommended by Rossmann, readily yielded the position of the S atom. The experiment was performed with Cu Kalpha radiation which is far from the absorption edge for sulfur. The coordinates of the remainder of the 54C, N, and O atoms were derived by means of partial structure development by use of the tangent formula. The latter was used only to effect phase extension, not phase refinement. A main purpose of this experiment was to reaffirm, as first shown in the investigation of the protein crambin by Hendrickson and Teeter, that, in the presence of a large number of lighter atoms, sulfur atoms can be located by use of anomalous dispersion at wave-lengths far from the absorption edge. The space group is P2(1) with a = 26.718(8) A, b = 6.987(3) A, c = 10.857(6) A, and beta = 99.51(4) degrees and contains two quinidyl ions, one sulfate ion, and two water molecules per asymmetric unit. The conformations of the two independent quinidyl ions differ mainly in the torsional angle of the bond between the vinyl side chain and the quinuclidine moiety. The R factor is 4.9% for all 2869 data.

Journal Article↗
PubMed1981

Conformation of cyclo(Gly-L-Pro-L-Pro-Gly-L-Pro-L-Pro)(2)Mg complex crystallized from CH(3)CN solution.

The cyclic hexapeptides (Gly-L-Pro-L-Pro-Gly-L-Pro-L-Pro) in the (peptide-Mg-peptide)(2+) complex have nearly identical asymmetric conformations. Each has two cis Pro-Pro linkages and lacks any intraring hydrogen bonds. The Mg(2+) ion forms six ligands in a regular octahedral array with the carbonyl oxygen atoms of the two Gly residues and one Pro residue of each peptide. The "sandwich" complex has an approximate 2-fold rotation axis through the Mg(2+) relating the two peptide moieties. Cyclo(Gly-Pro-Pro-Gly-Pro-Pro)(2)Mg(ClO(4))(2). 4C(2)H(3)CN crystallizes in space group P3(1) with a = b = 15.744(4) A, c = 24.002(6) A, gamma = 120 degrees , and Z = 3. A highlight of the structure determination is the ready location of the Mg self-vector in a Harker section and the development of the entire structure by use of the tangent formula starting with the known position of the Mg atom.

Journal Article↗
PubMed1980

Determination of molecular formula and stereoconfiguration of unique steroids by X-ray diffraction analysis.

X-Ray diffraction analyses can determine chemical composition, molecular formula and stereoconfiguration and can provide geometric parameters with uncertainties for bond distances of the order of 0.01 A and for bond angles of the order of 1 degrees. These analyses are especially useful when the substance analyzed is present only in very small quantities and is of uncertain composition or molecular formula. Only one suitable crystal is required for the analysis to proceed. There are many instances in which such circumstances have prevailed in the diffraction analysis of steroids. Among the examples given here is a new type of natural plant hormone with profound growth-stimulating capabilities when applied in nanogram quantities per plant. The structure determination of this substance has greatly facilitated attempts to synthesize it and thereby to derive sufficient quantities for widespread testing.

Models, Molecular↗
PubMed1980

Triplet phase invariants: Formula for acentric case from fourth-order determinantal joint probability distributions.

A conditional probability distribution for triplet invariants is derived for noncentrosymmetric crystals from fourth-order determinantal joint probability distributions. The formula makes use of the entire data set in the computations for each invariant. Test calculations indicate that the formula can be used to help select invariants whose values are distributed close to zero and also to evaluate special invariants associated with seminvariant phases.

Journal Article↗
PubMed1979

Triplet phase invariants: Formula for centric case from fourth-order determinantal joint probability distributions.

A formula is derived for centrosymmetric crystals from fourth-order determinantal joint probability distributions that provides, for the triplet invariants, values of P(+)/P(-), the ratio of the probability that an invariant has a plus sign associated with it to the probability that it has a minus sign. The formula makes use of the entire data set in the computations for each invariant. Test calculations indicate that many hundreds of invariants can be selected by use of the formula with essential certainty that their value is equal to zero. Several invariants whose value is equal to pi can also be selected on occasion with very high reliability.

Journal Article↗
PubMed1978

Joint probability distribution of the invariants comprising determinantal inequalities: Heuristic derivation.

Joint probability distributions are derived that are expressed in terms of the determinants that form the determinantal inequalities associated with the non-negative Fourier series that represent crystal structures. The derivation involves heuristic considerations. It is therefore appropriate to test the distributions extensively by making comparisons with results obtained by other theoretical means and evaluations of the implications of the distributions. Those performed thus far on the low-order determinants (third and fourth orders) have provided satisfactory results. The determinantal probability distributions imply a general maximum determinant rule, contain a wealth of information, and provide numerous paths that may be followed for future development.

Journal Article↗
PubMed1976

Conformation of uncomplexed [Phe4, Val6] antamanide crystallized from nonpolar solvents.

[Phe4, Val6] antamanide, a synthetic, biologically active analog of the cyclic decapeptide antitoxin isolated from Amanita phalloides, has been crystallized from a mixture of n-hexane and methyl acetate, and its conformation has been established by the direct method of x-ray diffraction analysis, i.e., without the benefit of any heavy atom. The uncomplexed molecule contains a 2-fold rotation axis and cis peptide linkages between Pro2-Pro3 and Pro7-Pro8. Otherwise, its conformation differs extensively from that of the Na+[Phe4, Val6] antamanide-C2H5OH complex. The 30-membered ring is elongated and relatively planar as compared to the folded ring in the Na+ complex. The six NH groups are directed toward the anterior of the molecule. There is one pair of intra-molecular NH---O=C bonds of the 5 leads to 1 type containing a cis peptide unit. The other four NH groups participate in hydrogen bonds to three H2O sites in the interior of the molecule. The 10 hydrophobic side groups cover the bottom and surround the perimeter of the molecule with the phenyl groups in the four Phe residues folded against the molecule. The conformation found for [Phe4, Val6] antamanide crystallized from nonpolar solvents is different from any conformations proposed for antamanide in solution based on nuclear magnetic resonance data.

Crystallography↗
PubMed1973

Conformations of the li-antamanide complex and na-[phe, val]antamanide complex in the crystalline state.

Antamanide, a cyclic decapeptide isolated from the poisonous mushroom Amanita phalloides, preferably complexes with Na(+), but in less polar solvents, e.g., acetonitrile, also with Li(+) or K(+). The selectivity of complexation makes it an important model for the study of conformational requirements of ion binding. The conformations of the lithium antamanide complex and the Na-[Phe(4), Val(6)]antamanide complex have been established by x-ray diffraction analyses of single crystals. The two compounds are isostructural, but not isomorphous. The complexes are folded into a globular shape with an approximate 2-fold axis. Two of the peptide linkages are in the cis conformation, Pro(2)-Pro(3) and Pro(7)-Pro(8). There are only two intramolecular hydrogen bonds. Four C==O groups have their O atoms directed inward to form four Li-O or Na-O ligands. The fifth ligand to the metal ion is provided by a solvent molecule. The conformation found in the crystalline state is different from any of the conformations proposed for the sodium antamanide complex in solution on the basis of nuclear magnetic resonance data.

Journal Article↗