Quantum Molecular Similarity. 3. QTMS Descriptors

Building on the ideas of a previous paper [part 1, J. Phys. Chem. A 1999, 103, 2883] we present a new molecular similarity method based on the topology of the electron density. This method is directly applicable to QSARs and is called quantum topological molecular similarity (QTMS). It has been tested for five sets of carboxylic systems including para- and meta-benzoic acid, para-phenylacetic acid, 4-X-bicyclo[2.2.2]octane-1-carboxylic acids, and polysubstituted benzoic acids. In combination with the partial least squares (PLS) procedure QTMS is able to produce excellent and statistically valid regressions. It is shown that QTMS avoids certain challenges of traditional Carbó-like similarity indices. Finally, QTMS is able to suggest a molecular fragment that contains the active center or the part of the molecule that is responsible for the QSAR.

[1]  C. Gardner Swain,et al.  Field and resonance components of substituent effects , 1968 .

[2]  Robert W. Taft,et al.  EVALUATION OF RESONANCE EFFECTS ON REACTIVITY BY APPLICATION OF THE LINEAR INDUCTIVE AND ENERGY RELATIONSHIP. VI. CONCERNING THE EFFECTS OF POLARIZATION AND CONJUGATION ON THE MESOMERIC ORDER , 1959 .

[3]  Gerhard Klebe,et al.  Superposition of molecules: Electron density fitting by application of fourier transforms , 1997, J. Comput. Chem..

[4]  A. Leach.  Molecular Modelling: Principles and Applications , 1996 .

[5]  Paul L. A. Popelier,et al.  Quantum molecular similarity. Part 2: The relation between properties in BCP space and bond length , 1999 .

[6]  Emili Besalú,et al.  A general survey of molecular quantum similarity , 1998 .

[7]  T. Ziegler.  Approximate Density Functional Theory as a Practical Tool in Molecular Energetics and Dynamics , 1991 .

[8]  Ramon Carbó-Dorca,et al.  Molecular basis of quantitative structure-properties relationships (QSPR): A quantum similarity approach , 1999, J. Comput. Aided Mol. Des..

[9]  S. Wold,et al.  The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses , 1984 .

[10]  Ramon Carbó-Dorca,et al.  Quantum similarity approach to LFER: substituent and solvent effects on the acidities of carboxylic acids , 1999 .

[11]  Paul L. A. Popelier,et al.  QUANTUM MOLECULAR SIMILARITY: USE OF ATOMS IN MOLECULES DERIVED QUANTITIES AS QSAR VARIABLES , 2000 .

[12]  A. J. Duke,et al.  Quantum topology of molecular charge distributions. 1 , 1979 .

[13]  Edward E. Hodgkin,et al.  A semi-empirical method for calculating molecular similarity , 1986 .

[14]  Svante Wold,et al.  Hierarchical multiblock PLS and PC models for easier model interpretation and as an alternative to variable selection , 1996 .

[15]  W. Graham Richards,et al.  Quantitative measures of similarity between pharmacologically active compounds , 1986 .

[16]  David Robert,et al.  Use of electron-electron repulsion energy as a molecular descriptor in QSAR and QSPR studies , 2000, J. Comput. Aided Mol. Des..

[17]  Rodolfo O. Esquivel,et al.  Molecular similarity based on information entropies and distances , 1998 .

[18]  Chengteh Lee,et al.  An approach to molecular similarity using density functional theory , 1994 .

[19]  David L. Cooper,et al.  Momentum-space electron densities and quantum molecular similarity , 1995 .

[20]  Ramon Carbó-Dorca,et al.  Toward a global maximization of the molecular similarity function: Superposition of two molecules , 1997, J. Comput. Chem..

[21]  K. Sen,et al.  Molecular Similarity I , 1995 .

[22]  Æleen Frisch,et al.  Exploring chemistry with electronic structure methods , 1996 .

[23]  Otto Exner,et al.  The role of meta and para Benzene derivatives in the evaluation of substituent effects : a multivariate data analysis , 1992 .

[24]  Anders Berglund,et al.  A serial extension of multiblock PLS , 1999 .

[25]  Robert Ponec,et al.  Similarity Models in the Theory of Pericyclic Reactions , 1995 .

[26]  Paul L. A. Popelier,et al.  Quantum molecular similarity. 1. BCP space , 1999 .

[27]  S Fortier,et al.  Molecular scene analysis: application of a topological approach to the automated interpretation of protein electron-density maps. , 1994, Acta crystallographica. Section D, Biological crystallography.

[28]  Emili Besalú,et al.  Quantum mechanical origin of QSAR: theory and applications , 2000 .

[29]  Ramon Carbó-Dorca,et al.  Quantum similarity measures under atomic shell approximation: First order density fitting using elementary Jacobi rotations , 1997 .

[30]  Ramon Carbo,et al.  How similar is a molecule to another? An electron density measure of similarity between two molecular structures , 1980 .

[31]  K. Sen,et al.  Molecular Similarity II , 1995 .

[32]  R Carbó-Dorca,et al.  Simple linear QSAR models based on quantum similarity measures. , 1999, Journal of medicinal chemistry.

[33]  Tom Ziegler,et al.  Approximate Density Functional Theory as a Practical Tool in Molecular Energetics and Dynamics , 1992 .

[34]  Frank H. Allen,et al.  Shape information from a critical point analysis of calculated electron density maps: Application to DNA-drug systems , 1994, J. Comput. Aided Mol. Des..

[35]  S H Unger,et al.  "Aromatic" substituent constants for structure-activity correlations. , 1973, Journal of medicinal chemistry.

[36]  David Robert,et al.  Quantum similarity QSAR: Study of inhibitors binding to thrombin, trypsin, and factor Xa, including a comparison with CoMFA and CoMSIA methods , 2000 .

[37]  S. Wold,et al.  Partial Least Squares Projections to Latent Structures (PLS) in Chemistry , 2002 .

[38]  David L. Cooper,et al.  Charge partitioning by zero‐flux surfaces: The acidities and basicities of simple aliphatic alcohols and amines , 1983 .

[39]  R. Bader.  Atoms in molecules : a quantum theory , 1990 .

[40]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[41]  Ranbir Singh,et al.  J. Mol. Struct. (Theochem) , 1996 .

[42]  Paul L. A. Popelier,et al.  Atomic properties of selected biomolecules. Part 1. The interpretation of atomic integration errors , 2000 .

[43]  Michael D. Miller,et al.  Molecular Superposition , 1998 .

[44]  Paul L. A. Popelier,et al.  Atoms in Molecules: An Introduction , 2000 .

[45]  Paul L. A. Popelier,et al.  A ROBUST ALGORITHM TO LOCATE AUTOMATICALLY ALL TYPES OF CRITICAL-POINTS IN THE CHARGE-DENSITY AND ITS LAPLACIAN , 1994 .

[46]  J. Macgregor,et al.  Analysis of multiblock and hierarchical PCA and PLS models , 1998 .

[47]  John D. Roberts,et al.  Electrical Effects of Substituent Groups in Saturated Systems. Reactivities of 4-Substituted Bicyclo [2.2.2]octane-1-carboxylic Acids , 1953 .

[48]  David J. Livingstone,et al.  Data analysis for chemists , 1995 .

[49]  David L. Cooper,et al.  A quantum molecular similarity approach to anti-HIV activity , 1998 .

[50]  W. Graham Richards,et al.  Alignment of molecules by the Monte Carlo optimization of molecular similarity indices , 1997 .

[51]  Edward E. Hodgkin,et al.  Molecular similarity based on electrostatic potential and electric field , 1987 .

[52]  H. H. Jaffé,et al.  A Reëxamination of the Hammett Equation. , 1953 .

[53]  W. Graham Richards,et al.  Molecular similarity in terms of valence electron density , 1986 .

[54]  Paul L. A. Popelier,et al.  Molecular similarity and complementarity based on the theory of atoms in molecules , 1995 .

[55]  S. Wold,et al.  PLS: Partial Least Squares Projections to Latent Structures , 1993 .

[56]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[57]  C. D. Johnson.  The Hammett Equation , 1973 .