Projects per year

### Abstract

In chemistry, the basic molecular structure information is represented in

terms of molecular graphs established from X-ray 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

X-ray 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 RHF-LCAO 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

low-pass filter [4]. This approach is applied to charge distributions of

small molecules obtained from molecular RHF-MO-LCAO 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 benzodiazepine-related 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. Carbo-Dorca, 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 X-ray 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

X-ray 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 RHF-LCAO 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

low-pass filter [4]. This approach is applied to charge distributions of

small molecules obtained from molecular RHF-MO-LCAO 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 benzodiazepine-related 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. Carbo-Dorca, 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 → … |

## Fingerprint Dive into the research topics of 'Multiresolution Analyses of Molecular Charge Distributions: From Small to Large Biomolecules'. Together they form a unique fingerprint.

## 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 2000

Activity: Participating in or organising an event types › Participation in conference

## Cite this

Leherte, L. (2000).

*Multiresolution Analyses of Molecular Charge Distributions: From Small to Large Biomolecules*. Poster session presented at Xth International Congress of Quantum Chemistry, Menton (France, .