Jerome Karle

Internal Motion and Molecular Structure Studies by Electron Diffraction

A procedure has been developed for the determination of molecular structure by electron diffraction which yields accurate intensity data and obviates the necessity for visual examination of the diffraction photographs. The theory for computing radial distribution curves has been extended to permit accurate curves to be obtained from scattering data covering only a restricted range of angle. From this method, it is possible to obtain not only equilibrium distances but also the probability distributions for the vibrational motion between pairs of atoms in a molecule. The procedure has been applied to CCl4 and CO2 and when comparisons may be made with spectroscopic results, satisfactory agreement is obtained.

Internal Motion and Molecular Structure Studies by Electron Diffraction. II. Interpretation and Method

The application of a recently developed objective procedure to the analysis of electron diffraction photographs from more complex molecules is discussed in terms of the further development of the details of some of the theoretical and experimental aspects of the procedure. The topics discussed are the physical significance of measured vibrational amplitudes, the method for drawing a background line, the calibration of photographic plates, and the computation of intensity curves by means of IBM machines.

Internal Motion and Molecular Structure Studies by Electron Diffraction. III. Structure of CH2CF2 and CF2CF2

The interatomic distances and vibrational amplitudes projected on the lines connecting pairs of atoms at equilibrium have been determined for CH2CF2 and CF2CF2 by an objective procedure for analyzing electron diffraction photographs. Distances involving hydrogen atoms have been evaluated and the procedure for resolving radial distribution peaks involving more than one distance is illustrated. The effects on the accuracy of the method of various characteristics such as sample spread and multiple scattering have been analyzed.

Crystalline Ordering in Silica and Germania Glasses

The diffraction patterns of both silica and germania glasses are consistent with a structure in which nearly all of the atoms belong to tridymite-like regions of up to about 20 angstroms or more that are bonded efficiently together in a manner analogous to that found in twinned crystals.

The transition state for formation of the peptide bond in the ribosome

Using quantum mechanics and exploiting known crystallographic coordinates of tRNA substrate located in the ribosome peptidyl transferase center around the 2-fold axis, we have investigated the mechanism for peptide-bond formation. The calculation is based on a choice of 50 atoms assumed to be important in the mechanism. We used density functional theory to optimize the geometry and energy of the transition state (TS) for peptide-bond formation. The TS is formed simultaneously with the rotatory motion enabling the translocation of the A-site tRNA 3′ end into the P site, and we estimated the magnitude of rotation angle between the A-site starting position and the place at which the TS occurs. The calculated TS activation energy, Ea, is 35.5 kcal (1 kcal = 4.18 kJ)/mol, and the increase in hydrogen bonding between the rotating A-site tRNA and ribosome nucleotides as the TS forms appears to stabilize it to a value qualitatively estimated to be ≈18 kcal/mol. The optimized geometry corresponds to a structure in which the peptide bond is being formed as other bonds are being broken, in such a manner as to release the P-site tRNA so that it may exit as a free molecule and be replaced by the translocating A-site tRNA. At TS formation the 2′ OH group of the P-site tRNA A76 forms a hydrogen bond with the oxygen atom of the carboxyl group of the amino acid attached to the A-site tRNA, which may be indicative of its catalytic role, consistent with recent biochemical experiments.

Crystal structure analysis of sea lamprey hemoglobin at 2 Å resolution

Abstract The crystal structure of the predominant hemoglobin component of blood from the sea lamprey, Petromyzon marinus, has been determined by X-ray diffraction analysis. Crystals for this analysis were grown from cyanide methemoglobin V as crystal type D2. These crystals are in space group P212121 and have unit cell dimensions of a = 44.57 A , b = 96.62 A and c = 31.34 A . Isomorphous heavyatom derivatives were prepared by soaking crystals in solutions of Hg(CN)2, K2Hg(CNS)4 and KAu(CN)2. Diffracted intensities to as far as 2 A spacings were measured on a diffractometer. Phases were found by means of the isomorphous replacements and anomalous scattering, with supplementary information provided by the tangent formula. An atomic model was fitted to the final electron density map in a Richards optical comparator. The lamprey hemoglobin molecule is generally similar in structure to other globins, but differs in many details. Each molecule is in contact with ten neighboring molecules in the crystal lattice. The nature of the binding of the heavy atoms to lamprey hemoglobin has been interpreted.

Electron Diffraction Investigation of Dimethyl Diselenide

The molecular structure of dimethyl diselenide has been determined by an electron diffraction investigation of the vapor. A computerized background correction routine, satisfying the positivity and area criteria, was employed to reduce the data and obtain a final molecular intensity curve. The values for a set of nine distances and amplitudes were obtained from a least‐squares fit to the final molecular intensity curve. The bonded distances are rg(C–H) = 1.131 ± 0.008 A, rg(C–Se) = 1.954 ± 0.005 A, and rg(Se–Se) = 2.326 ± 0.004 A. The corresponding amplitudes are l(C–H) = 0.079 ± 0.007 A, l(C–Se) = 0.054 ± 0.003 A, and l(Se–Se) = 0.056 ± 0.002 A. The ∠CSeSe = 98.9 ± 0.02° and the ∠HCSe = 108.4 ± 0.8°. The errors are estimated to be at the 99% confidence level. The methyl groups are unsymmetrically placed with respect to the CSeSe planes. They are rotated about the C–Se bonds such that one of the HCSe planes in each CH3Se moiety makes an angle of 36.1 ± 6° with the respective CSeSe plane. Dimethyl diseleni...

The Structure and Internal Motion of 1,2‐Dichloroethane

The structure and internal motion of 1,2‐dichloroethane were investigated by means of electron diffraction. Values were obtained for several distances involving hydrogen atoms. In addition, the average amplitude of vibration was found for many of the distances. The predominant isomer was in the trans‐form and the less abundant one was in the gauche‐positions at 109±5° from the trans‐equilibrium position. The amount of gauche‐isomer was found to be 27±5 percent at 22°C.

Some developments in anomalous dispersion for the structural investigation of macromolecular systems in biology

A discussion is given of the anomalous dispersion technique in structure analysis. This is accompanied by a general algebraic analysis with no approximations for any number and type of anomalous scatterer. The resulting relations are largely linear with appropriate selection of unknown quantities. The quantities of interest are expressed only in terms of functions of the nonanomalous parts of the atomic scattering factors and are separate for each type of anomalous scatterer. This theory, the advent of increased ease in performing multiple-wavelength experiments, and some recent progres made in applying a one-wavelength experiment to the solution of a protein structure suggest considerable potential for the future application of the anomalous dispersion technique to structural investigations of complex macromolecular systems in biology.

The Kernel Energy Method: Application to a tRNA

The Kernel Energy Method (KEM) may be used to calculate quantum mechanical molecular energy by the use of several model chemistries. Simplification is obtained by mathematically breaking a large molecule into smaller parts, called kernels. The full molecule is reassembled from calculations carried out on the kernels. KEM is as yet untested for RNA, and such a test is the purpose here. The basic kernel for RNA is a nucleotide that in general may differ from those of DNA. RNA is a single strand rather than the double helix of DNA. KEM energy has been calculated for a tRNA, whose crystal structure is known, and which contains 2,565 atoms. The energy is calculated to be E = –108,995.1668 (a.u.), in the Hartree–Fock approximation, using a limited basis. Interaction energies are found to be consistent with the hydrogen-bonding scheme previously found. In this paper, the range of biochemical molecules, susceptible of quantum studies by means of the KEM, have been broadened to include RNA.