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Abstract
In chemistry, the basic molecular structure information is represented in
terms of molecular graphs established from Xray diffraction experiments or
mechanistic calculations. From that information, a 3D molecular property
that is relevant to the study of molecular shape and interactions, i.e.,
the electron density (ED) distribution, can be calculated using quantum
chemistry approaches. We show how working at various resolution levels may
help in the identification of patterns useful to the comparison of different
molecular structures.
In the present work, three methods are used in order to obtain ED images at
various resolution levels. (a) In crystallography, the resolution of an ED
map is defined by the ratio sinQ/l (2Q is the angle between the diffracted
Xray and the primary beam of wavelength l). Theory allows to calculate a
promolecular ED map from known atomic coordinates as the Fourier transform
of a set of calculated structure factors selected according to the resolution
level [1]. (b) Another fast approach that is useful to obtain a promolecular
ED function consists in a summation over 1s atomic Gaussian functions fitted
over atomic RHFLCAO results [2]. Smoothed images are then obtained using
an analytical method derived from the multiple minima problem solving [3].
(c) The calculation of ED images at various resolution levels can be achieved
using wavelet analysis, a mathematical tool in smoothing/denoising
signals using convolution products between the original fonction and a
lowpass filter [4]. This approach is applied to charge distributions of
small molecules obtained from molecular RHFMOLCAO calculations.
The ED calculation stage is followed by the application of a topological
analysis approach [5] in order to determine a critical point representation
(local density maxima, saddle points) which is easily manipulated for structural
interpretation and analysis. Graphs of critical points (points where the
gradient of the density equals zero) are used as representations of molecular
ED distribution functions. Comparisons of graphs are carried out using a Monte
Carlo/Simulated Annealing program. Multiple alignment results are obtained
with programs which look for best matchings between critical points of a
reference molecule and critical points of the other compounds. The method is
applied to a selected set of benzodiazepinerelated molecules. It is observed
that, at low resolution, the graphs of critical points correspond to the
pharmacophore already presented in the litterature, and molecules with similar
affinities have a similar topology. Also, a hierarchical description of the
binding mode of molecules with respect to their receptor is suggested.
[1] XTAL 3.0 User's Manual, S. R. Hall and J. M. Stewart (Eds.),
Universities of Western Australia and Maryland (1990)
[2] L. Amat, R. CarboDorca, J. Comput. Chem. 19, 2023 (1997)
[3] J. Kostrowicki et al., J. Phys. Chem. 95, 4113 (1991)
[4] J.L. Stark et al., Image Processing and Data Analysis  The Multiscale
Approach, Cambridge, University Press, Cambridge, UK, 1997
[5] C. K. Johnson, Proc. Am. Crystallogr. Assoc. Meet., Asilomar CA (USA),
1977: abstract JQ6
terms of molecular graphs established from Xray diffraction experiments or
mechanistic calculations. From that information, a 3D molecular property
that is relevant to the study of molecular shape and interactions, i.e.,
the electron density (ED) distribution, can be calculated using quantum
chemistry approaches. We show how working at various resolution levels may
help in the identification of patterns useful to the comparison of different
molecular structures.
In the present work, three methods are used in order to obtain ED images at
various resolution levels. (a) In crystallography, the resolution of an ED
map is defined by the ratio sinQ/l (2Q is the angle between the diffracted
Xray and the primary beam of wavelength l). Theory allows to calculate a
promolecular ED map from known atomic coordinates as the Fourier transform
of a set of calculated structure factors selected according to the resolution
level [1]. (b) Another fast approach that is useful to obtain a promolecular
ED function consists in a summation over 1s atomic Gaussian functions fitted
over atomic RHFLCAO results [2]. Smoothed images are then obtained using
an analytical method derived from the multiple minima problem solving [3].
(c) The calculation of ED images at various resolution levels can be achieved
using wavelet analysis, a mathematical tool in smoothing/denoising
signals using convolution products between the original fonction and a
lowpass filter [4]. This approach is applied to charge distributions of
small molecules obtained from molecular RHFMOLCAO calculations.
The ED calculation stage is followed by the application of a topological
analysis approach [5] in order to determine a critical point representation
(local density maxima, saddle points) which is easily manipulated for structural
interpretation and analysis. Graphs of critical points (points where the
gradient of the density equals zero) are used as representations of molecular
ED distribution functions. Comparisons of graphs are carried out using a Monte
Carlo/Simulated Annealing program. Multiple alignment results are obtained
with programs which look for best matchings between critical points of a
reference molecule and critical points of the other compounds. The method is
applied to a selected set of benzodiazepinerelated molecules. It is observed
that, at low resolution, the graphs of critical points correspond to the
pharmacophore already presented in the litterature, and molecules with similar
affinities have a similar topology. Also, a hierarchical description of the
binding mode of molecules with respect to their receptor is suggested.
[1] XTAL 3.0 User's Manual, S. R. Hall and J. M. Stewart (Eds.),
Universities of Western Australia and Maryland (1990)
[2] L. Amat, R. CarboDorca, J. Comput. Chem. 19, 2023 (1997)
[3] J. Kostrowicki et al., J. Phys. Chem. 95, 4113 (1991)
[4] J.L. Stark et al., Image Processing and Data Analysis  The Multiscale
Approach, Cambridge, University Press, Cambridge, UK, 1997
[5] C. K. Johnson, Proc. Am. Crystallogr. Assoc. Meet., Asilomar CA (USA),
1977: abstract JQ6
Original language  English 

Publication status  Published  Jun 2000 
Event  Xth International Congress of Quantum Chemistry  Menton (France Duration: 5 Jun 2000 → … 
Conference
Conference  Xth International Congress of Quantum Chemistry 

City  Menton (France 
Period  5/06/00 → … 
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Projects
 1 Active

Multiresolution analysis of electron density maps
LEHERTE, L., Vercauteren, D. & Meurice, N.
1/09/95 → …
Project: Research
Activities
 1 Participation in conference

Xth International Congress of Quantum Chemistry (ICQC2000)
Laurence Leherte (Poster)
5 Jun 2000 → 10 Jun 2000Activity: Participating in or organising an event types › Participation in conference