Molecular electric moments and electric field gradients from X-ray diffraction data: model studies

Spackman, Mark A.; Byrom, P. G.

doi:10.1107/s0108768196008294

Cited by 29 publications

(28 citation statements)

References 38 publications

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“…An important longer-range aim of our studies is to determine experimental electrostatic parameters for biological macromolecules and to calibrate the theoretically derived electrostatic parameters used in biomolecular modeling calculations (31). Net atomic charges can, for instance, be derived experimentally from x-ray diffraction data via pseudoatom modeling (3,27,31). In analyses of small-molecule structures, spherical-atom charges refitted after multipolar refinements have been shown to yield molecular electric moments that agree well with independently measured experimental values (3,27).…”

mentioning

confidence: 81%

“…Net atomic charges can, for instance, be derived experimentally from x-ray diffraction data via pseudoatom modeling (3,27,31). In analyses of small-molecule structures, spherical-atom charges refitted after multipolar refinements have been shown to yield molecular electric moments that agree well with independently measured experimental values (3,27). The refitted charges of the crambin peptide atoms after refinement II were: C a ϩ0.06, C ϩ0.32, O Ϫ0.18, N Ϫ0.44, H a ϩ0.08, and H N ϩ0.16 electrons.…”

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confidence: 99%

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Accurate protein crystallography at ultra-high resolution: Valence electron distribution in crambin

Jelsch

Teeter

Lamzin

et al. 2000

Proc. Natl. Acad. Sci. U.S.A.

213

171

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The charge density distribution of a protein has been refined experimentally. Diffraction data for a crambin crystal were measured to ultra-high resolution (0.54 Å) at low temperature by using shortwavelength synchrotron radiation. The crystal structure was refined with a model for charged, nonspherical, multipolar atoms to accurately describe the molecular electron density distribution. The refined parameters agree within 25% with our transferable electron density library derived from accurate single crystal diffraction analyses of several amino acids and small peptides. The resulting electron density maps of redistributed valence electrons (deformation maps) compare quantitatively well with a high-level quantum mechanical calculation performed on a monopeptide. This study provides validation for experimentally derived parameters and a window into charge density analysis of biological macromolecules.T he electronic charge density distribution of a molecule carries information (1) that determines its intermolecular interactions. For example, the charge distribution of an enzyme complements that of the substrate it recognizes and binds. The electrostatic potential and electric moments derivable from the charge density (1-3) provide maps that can guide the design of molecules for specified interactions. Furthermore, powerful insights into the nature and strength of hydrogen bonding and ionic interactions result from analysis of the electron density gradient and Laplacian (4-6). Extension of such analyses to proteins would permit a unique understanding of the driving forces between biomolecules as well as the subtleties of enzymatic reactions (7).Experimental electron density distributions are obtained by analysis of single-crystal x-ray diffraction data measured to ultra-high resolution, typically to a diffraction resolution limit d min Ϸ 0.5 Å (1,8,9). The crystallographic studies usually map and analyze the deformation density, which is the difference between the actual electron density of the molecule and the density calculated for the promolecule, a molecular superposition of spherical, neutral, i.e., free, atoms. The deformation density thus reveals the redistribution of valence electron density caused by chemical bonding and intermolecular interactions and also is used to calibrate theoretical electron density calculations (10). However, a difficulty in crystallography is the separation of the anisotropic atomic mean-square displacements from the static molecular electron distribution (11). Proper experimental deconvolution requires very accurate diffraction data to ultrahigh resolution. Thus, charge density studies have so far been limited to small-unit-cell crystals, and proteins still await study.We have shown (12, 13) that effective thermal displacement deconvolution and meaningful deformation density distributions can be achieved for larger structures at lower resolution by transferring average experimental electron density parameters. We have built a database of such parameters derived from ultra-high ...

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mentioning

confidence: 81%

mentioning

confidence: 99%

Accurate protein crystallography at ultra-high resolution: Valence electron distribution in crambin

Jelsch

Teeter

Lamzin

et al. 2000

Proc. Natl. Acad. Sci. U.S.A.

213

171

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“…From the superposition Jeffrey et al (1980) 176 (50%) Savariault & Lehmann (1980) 133 (33%) Swaminathan, Craven & McMullan (1984) 490 (39%) Boese et al (1994) 89 (12%) Nijveldt & Vos (1988) 535 (26%) Destro, Marsh & Bianchi (1988) of these molecules in the unit cell, two sets of structure factors were generated; one set ('dynamic') incorporates experimental thermal motion, while the other set ('static') does not. Full details of the method have been given in a previous paper (Spackman & Byrom, 1996) and will not be repeated here. These sets of structure factors have known magnitudes and phases and, therefore, enable us to determine how well a number of structure factor models retrieve both the phases and magnitudes of Ft(H ) and, just as importantly, the errors arising from approximating ~/9 t by ~0 m in a Fourier map of Ap.…”

Section: F(h) = If(h)i Exp (I~ot(h))mentioning

confidence: 99%

“…Molecular properties derived from the multipole refined electron density are also important (Spackman & Byrom, 1996) and in Table 2 we provide estimates of the trace of the molecular second moment tensor (r 2) and the octopole moment ~ (xyz) for HMT. Clearly eigenvalue filtering applied in a routine manner as carried out here can impose a constraint which leads to a significantly worse scale factor (by as much as 7 % in this case) and hence compromise estimates of the molecular properties which are derived from the rescaled electron distribution.…”

Section: The Special Case Of Hexamethylenetetraminementioning

confidence: 99%

Retrieval of Structure-Factor Phases in Non-centrosymmetric Space Groups. Model Studies Using Multipole Refinements

Spackman¹,

Byrom²

1997

Acta Crystallogr Sect B

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Structure factors with known magnitude and phase are constructed for seven different molecular crystals in non-centrosymmetric space groups and used to calibrate the retrieval of structure-factor phase information with several different scattering factor models. Monopole models are confirmed to be inadequate, yielding poor estimates of phases and underestimating the Fourier deformation electron density by as much as 50%. Multipole models are generally successful, with the conspicuous exception of hexamethylenetetramine (HMT). The results confirm the known difficulty of phasing structure-factor magnitudes for HMT, but reveal a broad spectrum of behaviour of phase retrieval in various non-centrosymmetric space groups, depending partly on the number of reflections with restricted phases. For several systems (urea, hydrogen peroxide, L-alanine and borazine) the results confirm that multipole refinements of scattering factor models against experimental data are capable of yielding highly accurate phases and hence reliable electron distributions. For the exceptional case of HMT a simple eigenvalue filtering technique enables retrieval of phases and electron densities with an accuracy comparable to the best of the other non-centrosymmetric systems studied.

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“…[6] It was concluded that, in general, quite reliable molecular dipole moments can be derived from multipolar modeling of diffraction data. A big advantage of estimating electrostatic moments from X-ray diffraction data is that both the size and the direction of the solid state molecular dipole moment is obtained.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of the Solid State Dipole Moment and Pyroelectric Coefficient of Phosphangulene by Multipolar Modeling of X-ray Structure Factors

et al. 2000

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The electron density distribution of the molecular pyroelectric material phosphangulene has been studied by multipolar modeling of X-ray diffraction data. The "in-crystal" molecular dipole moment has been evaluated to 4.7 D corresponding to a 42% dipole moment enhancement compared with the dipole moment measured in a chloroform solution. It is substantiated that the estimated standard deviation of the dipole moment is about 0.8 D. The standard uncertainty (s.u.) of the derived dipole moment has been derived by splitting the dataset into three independent data-sets. A novel method for obtaining pyroelectric coefficients has been introduced by combining the derived dipole moment with temperature-dependent measurements of the unit cell volume. The derived pyroelectric coefficient of 3.8(7) x 10-6 Cm 2K-1 is in very good agreement with the measured pyroelectric coefficient of p = 3 +/- 1 x 10-6 Cm-2 K-1. This method for obtaining the pyroelectric coefficient uses information from the X-ray diffraction experiment alone and can be applied to much smaller crystals than traditional methods.

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Molecular electric moments and electric field gradients from X-ray diffraction data: model studies

Cited by 29 publications

References 38 publications

Accurate protein crystallography at ultra-high resolution: Valence electron distribution in crambin

Accurate protein crystallography at ultra-high resolution: Valence electron distribution in crambin

Retrieval of Structure-Factor Phases in Non-centrosymmetric Space Groups. Model Studies Using Multipole Refinements

Evaluation of the Solid State Dipole Moment and Pyroelectric Coefficient of Phosphangulene by Multipolar Modeling of X-ray Structure Factors

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