Presentation on theme: "Quantum Chemical Descriptors in Computational Medicinal Chemistry for Chemoinformatics V. Subramanian Chemical Laboratory Central Leather Research Institute."— Presentation transcript:
Quantum Chemical Descriptors in Computational Medicinal Chemistry for Chemoinformatics V. Subramanian Chemical Laboratory Central Leather Research Institute Chennai 600 020 Feb 17- 2005, Pondicherry Central University
Schematics Introduction to Informatics Molecular Models QSAR Descriptors for QSAR Conceptual DFT DFT based Reactivity Descriptors Applications Summary
Information technology designed to generate and access genetic data and derive information from it Information technology used to design molecular libraries to interact with identified targets Informatics Bioinformatics Chemoinformatics
IT for managing chemical information and solving chemical problems Chemistry + information science + computer science Driven by drug discovery research Chemoinformatics
Chemoinformatics is the amalgamation of those chemical information resources to transform data into vital information and chemical information into knowledge for the intended purpose of making better decisions faster in the area of drug lead identification and organization
Chemoinformatics tasks Manage information about Chemical properties Chemical synthesis Biological effects
Combinatorial chemistry Synthesizing large numbers of related chemical compounds Can help design drug leads Information rich Physiology of the biological effect Starting material properties Synthesis protocols
Central Paradigm of Bioinformatics GeneticInformationMolecularStructureBiochemicalFunctionSymptoms(Phenotype)
Chemical + biological system desired response? Drug discovery
Related Aspects Bioinformatics and chemoinformatics are generic terms that encompass the design, creation, organization, management, retrieval, analysis, dissemination, visualization and use of chemical and biological information
Chemometrics strategies problem hypothesis goal experiment planning experiments dataData explorationCluster analysis classification regressionoptimization Qualitative modelQuantitative modelEmpirical model
Molecular Models Semi Empirical Ab initio/DFT Empirical/ Molecular Modeling Full Accounting of Electrons Neglect Core Electrons Approximate/ parameterize HF Integrals Neglect Electrons
Quantum Methods Wavefunction Density Function Hartree-Fock DFT MP2, CI
Brief summary of methods HF: Most simple MO method CI: Very accurate, very expensive method MP2:More accurate and marginally more expensive than HF DFT: Significantly more accurate while marginally more expensive than HF
Locality of the model Local Models: Specific chemical interactions Mechanism-based approaches Chemical class Relative potencies QSAR Large - scale activity discrimination Structure-alerting features Activity cluster analysis Global Prediction Models Rules Expert judgement Heuristics Distinguish mechanism classes Weight-of-evidence
QSAR The quantitative structure- activity relationship (QSAR) and the quantitative structure- property relationship (QSPR) are the important tools of the bio-chemo-informatics which can be built essentially based on the data generated from the molecular modeling and computational chemistry
QSAR Quantitative Structure Activity Relationship is a set of methods that tries to find a mathematical relationship between a set of descriptors of molecules and their activity. The descriptors can be experimentally or computationally derived. Using regression analysis, one can extract a mathematical relationship between chemical descriptors and activity.
QSAR Postulates the molecular structure is responsible for all the activities Similar compounds have similar biological and chemico- physical properties (Meyer 1899) Hansch postulate (1963) biological system + compound = f 1 (Lipolificity) + f 2 (Electronics) + f 3 (Steric) + f 4 (Molecular-prop) Congenericity postulate QSAR is applicable only to similar compounds
Descriptors in QSAR study Constitutional Descriptors Topological Descriptors Geometrical Descriptors Electrostatic Descriptors Quantum Chemical Descriptors MO Related Descriptors Thermodynamic Descriptors DFT based Reactivity Descriptors
Constitutional Descriptors Total number of atoms in the molecule Absolute and relative numbers of atoms of certain chemical identity (C, H, O, N, F, etc.) in the molecule Absolute and relative numbers of certain chemical groups and functionalities in the molecule Total number of bonds in the molecule Absolute and relative numbers of single, double, triple, aromatic or other bonds in the molecule Total number of rings, number of rings divided by the total number of atoms Total and relative number of 6 membered aromatic rings Molecular weight and average atomic weight
Topological Descriptors Wiener index Randi's molecular connectivity index Randi indices of different orders Balaban's J index Kier and Hall valence connectivity indices Kier shape indices Kier flexibility index Mean information content index Structural information content index Complementary information content index Bonding information content index Topological electronic indices
Geometrical Descriptors Molecular surface area Solvent-accessible molecular surface area Molecular volume Solvent-excluded molecular volume Gravitational indexes Principal moments of inertia of a molecule Shadow areas of a molecule Relative shadow areas of a molecule
Electrostatic Descriptors Gasteiger-Marsili empirical atomic partial charges Zefirov's empirical atomic partial charges Mulliken atomic partial charges Minimum (most negative) and maximum (most positive) atomic partial charges Polarity parameters Dipole moment Molecular polarizability Molecular hyperpolarizability Average ionization energy Minimum electrostatic potential at the molecular surface Maximum electrostatic potential at the molecular surface Local polarity of molecule Total variance of the surface electrostatic potential Electrostatic balance parameter
Quantum Chemical Descriptors Total energy of the molecule Total electronic energy of the molecule Standard heat of formation Electron-electron repulsion energy for a given atomic species Nuclear-electron attraction energy for a given atomic species Electron-electron repulsion between two given atoms Nuclear-electron attraction energy between two given atoms Nuclear repulsion energy between two given atoms Electronic exchange energy between two given atoms Resonance energy between given two atomic species Total electrostatic interaction energy between two given atomic species Total interaction energy between two given two atomic species Total molecular one-center electron-electron repulsion energy Total molecular one-center electron-nuclear attraction energy Total intramolecular electrostatic interaction energy Electron kinetic energy density Energy of protonation 21
Quantum Chemical Descriptors
MO Related Descriptors Highest Occupied Molecular Orbital (HOMO) energy Lowest Unoccupied Molecular Orbital (LUMO) energy Absolute hardness Activation hardness Fukui atomic nucleophilic reactivity index Fukui atomic electrophilic reactivity index Fukui atomic one-electron reactivity index Mulliken bond orders Free valence
Thermodynamic Descriptors Vibrational enthalpy of the molecule Translational enthalpy of the molecule Vibrational entropy of the molecule Rotational entropy of the molecule Translational entropy of the molecule Vibrational heat capacity of the molecule Normal coordinate eigen values (EVA)
Density Functional Theory (DFT) Instead of calculating a wavefunction, tries to calculate the exact density of the molecule Based on the Hohenberg-Kohn proof, which stipulates that a given density corresponds to a particular wavefunction and potential Calculate the exact density obtain the exact wavefunction from the exact density Do everything you’d normally do with a MO wavefunction
DFT Evolution Thomas-Fermi Theory (1926-28)- established the direct mapping between electron density and potential. Landau Theory of Fermi liquids(1956-58) - introduced the energy of the system as a functional of charge distribution. Hohenberg-Kohn-Shem Theory (1964-65) - proved one-to-one mapping of the density and potential. Derived the equations for single electron wave functions, which can be solved in a mode of self- consistent-field. Talman-Shadwick Theory (1976) and Its Krieger- Li-Iafrate approximation (1992) - exact expression for exchange potential.
DFT based Reactivity Descriptors Global Descriptors Chemical Potential Chemical Hardness Softness Electrophilicity Index Local Descriptors Condensed Fukui Function Philicity Group Philicity
Chemical Potential The Chemical Potential of DFT measures the escaping tendency of an electronic cloud. It is a constant, through all space, for the ground state of an atom, molecule or solid, and equals the slope of the Energy versus N curve at constant Potential v ( r ), It is the negative of Electronegativity,
Finite difference approximation to Chemical Potential gives, where HOMO Highest Occupied Molecular Orbital LUMO Lowest Unoccupied Molecular Orbital I and A are the Ionization Potential and Electron Affinity of themolecules respectively
Related Concept… (Sanderson’s Electronegativity Equalization Principle) “ When atoms of different chemical potential unite to form a molecule with its own characteristic chemical potential, to the extent that the atoms retain their identity; their chemical potential must equalize”
Chemical Hardness The theoretical definition of chemical hardness has been provided by the density functional theory as the second derivative of electronic energy with respect to the number of electrons N, for a constant external potential V(r)
Finite difference approximation to Chemical Hardness gives, For Insulator and Semiconductor, hardness is half of the band gap
Softness Related concept… (Hard Soft Acid Base (HSAB) Principle) “Hard Acids prefer Hard Bases, and Soft Acids prefer Soft Bases”
Electrophilicity Index Electrophilicity index is a measure of energy lowering due to maximal electron flow between donor and acceptor. Electrophilicity index ( ) is defined as,
Fukui Function Fukui function measures how sensitive a systems chemical potential is to an external perturbation at particular point. It is defined as, where is the electron density
Condensed Fukui Function In order to describe the reactivity of an atom in a molecule, it is necessary to condense the values of f(r) around each atomic site into a single value (f k ) that characterizes the atomic contribution in a molecule. For an atom k in a molecule, the f k values are defined as Nucleophilic attack Electrophilic attack Radical attack
Related concept… (Frontier-electron theory) “ Of two different sites with generally similar dispositions for reacting with a given reagent, the reagent prefers the one, which on the reagents approach is associated with the maximum response of the systems chemical potential”
Philicity Chattaraj et al. has provided a unified treatment of chemical reactivity and selectivity through a generalized philicity concept by using a resolution of identity. This local philicity index is given as
or its condensed- to- atom variants for the atomic site k in a molecule is defined as ( = +, -, 0) represents nucleophilic, electrophilic and radical attack respectively.
Group Philicity The condensed philicity summed over a group of relevant atoms is defined as the “group philicity”. It can be expressed as where n : number of atoms coordinated to the reactive atom, : local electrophilicity of the atom k, g : group philicity obtained by adding the local philicity of the nearby bonded atoms, ( = +, -, 0) represents nucleophilic, electrophilic and radical attack respectively
Polarizability The electric dipole polarizability is a measure of the linear response of the electron density in the presence of an infinitesimal electric field F and it represents a second order variation in energy The polarizability is calculated as the mean value as given in the following equation,
Charge Transfer The amount of charge transfer between any two systems (say, A and B) can be obtained by applying the formula,
Applications Bio-chemo-informatics related studies have been carried out by our group using Conceptual Density Functional Theory derived global and local quantum chemical descriptors on the following selected systems Polychlorinated biphenyls Benzidine Testosterone and Estrogen derivatives Alkanes (C 2 -C 8 )
Optimized Structures of PCBs 22′55′- TCBP 33`44`5- PCBP
Analysis of PCBs The geometry of 22′55′- TCBP and 33`44`5- PCBP were optimized by using Becke’s three parameter hybrid density functional, B3LYP/6-31G*, which includes both Hartree-Fock exchange and DFT exchange correlation functionals. Above calculations are carried out using the GAUSSIAN 98 package. The optimized geometries were characterized by harmonic vibrational frequencies which confirmed that the structure of 22′55′- TCBP is a minimum on the potential energy surface.
Table 1: Calculated Relative Energy, Chemical Hardness, Chemical Potential, Polarizability, and Electrophilicity Index of 2,2’,5,5’- TCBP
Figure 1: The variation of relative energy (kJ/mol), chemical hardness (eV) and scaled hardness (eV) with the torsional angle (degrees) for 33′44′5 - PCBP.
Analysis of PCBs To select proper electronic descriptor based on DFT, for the possible toxicity of the 22′55′- TCBP, the various reactivity and selectivity descriptors such as chemical hardness, chemical potential, polarizability, electrophilicity index and the local electrophilic power are calculated for all the rotated conformations (Table 1). It has been found that 22`55`- TCBP has very large rotational energy barrier at =0 and =180 with relative energy of 53.17 kJ/mol. Due to large rotational barrier, this molecule cannot adapt planar conformation and hence it is less toxic.
Analysis of PCBs In the case of 33`44`5- PCBP with very small rotational energy barrier of 7.36 kJ/mol at the planar orientation (Figure 1), is shown to have flexible planarity so that it changes its conformation while moving in biological systems, thereby interacting readily, exhibiting its toxic properties.
The electron accepting nature of PCB is evident from the charge transfer calculation.
Interaction of benzidine with B-DNA through (a) minor groove, (b) major groove and (c) intercalation a b c ArylaminesBinding Energy (kcal/mol) Minor GrooveMajor GrooveIntercalation Benzidine64.1529.8267.27 –naphthylamine 63.97195.6077.73
Table 2:Calculated Global Parameters for Benzidine
Analysis of Benzidine The relative energy of benzidine is calculated as a function of torsional angle, (rotation through the C (atom No.7)-C (atom No. 3) bond). To calculate the relative energy, the geometry at various values were optimized at B3LYP/6-31G* level.
Analysis of Benzidine It is possible to note from the rotational energy barrier (Table 2), which has a small variation (0 to 11.19 kJ/mol) that this molecule is highly flexible and it can adopt variety of conformations. This rotational freedom allows benzidine to freely interact with the cellular components in the realistic environment and hence their toxic nature.
The molecular electrostatic potential surfaces for various conformation of Benzidine. -30 0 30 60 90 120 150 180 210 MESP contours at 0.5 a. uMESP contours at -0.04 a. u
Charge Transfer( N) between Benzidine and constituents of Biomolecules
MESP for Benzidine The MESP surface of benzidine reveals the site of attack and also provides clues for the role of electrostatic interactions involved in the reactivity. Further the charge transfer between benzidine and nucleic acid bases/base pairs, AHH receptors has clearly revealed the electron donating nature of benzidine.
Structure of Testosterone and Estrogen OH O A B C D HO OH A B C D Testosterone Estrogen
Table 3: Electrophilicity index of testosterone derivatives with their observed and calculated biological activity in terms of relative binding affinity (RBA)
Table 4: Electrophilicity index of 16 -substituted estradiol derivatives with their observed and calculated biological activity
Relationship between various biological activity of Testosterone derivatives and Electrophilicity index
Relationship between RBA valuesof Estrogen derivatives and Electrophilicity index
QSAR analysis of testosterone and estrogen derivatives The biological activity of testosterone and estrogen derivatives has been analyzed by our group using electrophilicity index as a descriptor. In this context, the SAR based on electrophilicity has been shown to be promising.
QSAR analysis of testosterone and estrogen derivatives Since the electrophilicity index is a chemical reactivity descriptor and its definition has strong foundation from the density functional theory, it is appropriate to make use of this descriptor in the QSAR parlance and the usefulness of such application was evident from our investigation. Results emanated from that study (above Tables and Figures) showed that the electrophilicity can be used as a descriptor of biological activity and it is quite interesting that a single descriptor can provide such a beautiful correlation.
The condensed philicity summed over a group of relevant atoms is defined as the “group philicity” where n is the number of atoms coordinated to the reactive atom is the local electrophilicity of the atom k, and is the group philicity obtained by adding the local philicity of the nearby bonded atoms, ( = +, -, 0) represents nucleophilic, electrophilic and radical attack respectively
f k + s k + Group Softnesss k + / s k - k + g + Mulliken Population Analysis HCHO0.3030.019 0.0630.5770.2980.983 CH 3 CHO0.2870.018 0.0400.5900.2220.493 CH 3 COCH 3 0.2460.016 0.0210.5570.1650.221 C 2 H 5 COC 2 H 5 0.2510.016 0.0190.5630.1570.186 C 6 H 5 CHO0.1560.013 0.0400.3660.1680.501 p-MeOC 6 H 4 CHO0.1410.012 0.0390.3450.1150.366 CH 2 =CHCHO0.1520.012 0.0380.3580.1860.615 CH 3 CH=CHCHO0.1550.012 0.0380.3670.1610.508 C 6 H 5 CH=CHCHO0.0960.009 0.0210.2480.1070.243 CH 3 COCl0.0330.002 0.0460.1640.0370.823 CH 3 COOCH 3 0.3030.017 0.0280.5460.1940.316 Hirshfeld Population Analysis HCHO0.3970.102 0.2580.1701.8564.673 CH 3 CHO0.3000.072 0.1850.1291.0272.654 CH 3 COCH 3 0.2110.049 0.1370.1090.5901.630 C 2 H 5 COC 2 H 5 0.1350.031 0.0890.0900.3551.010 C 6 H 5 CHO0.1420.043 0.1270.0800.7832.303 p-MeOC 6 H 4 CHO0.1420.042 0.1190.0700.6421.847 CH 2 =CHCHO0.2060.067 0.1580.1541.3003.075 CH 3 CH=CHCHO0.1740.055 0.1700.1110.9332.902 C 6 H 5 CH=CHCHO0.1080.039 0.1320.0830.7332.490 CH 3 COCl0.2330.047 0.1590.0760.9523.246 CH 3 COOCH 3 0.1290.023 0.0720.0790.2580.818 Calculated local molecular reactivity descriptors of the carbonyl carbon atoms of selected molecules
Reactivity trends using Philicity Group philicity values derived from both MPA and HPA schemes have provided the expected reactivity trends in all sets of molecules considered for evaluation. Hence philicity and group philicity can be used as better chemical reactivity descriptors when compared to all other local reactivity descriptors.
QSAR studies on Alkanes (C 2 -C 8 )
Table 6: Abbreviations of the selected alkanes and their isomers (C 2 -C 8 )
Table 7: Regression equations and statistical parameters of the six quantum chemical descriptors for the five macroscopic properties
Table 8: Experimental and calculated values of five selected macroscopic properties of C 2 -C 8 alkanes and their isomers using ionisation potential as a descriptor
QSAR/QSPR analysis on Alkanes (C 2 -C 8 ) The present study reveals that ionisation potential can be used as a descriptor to understand structure activity and structure property relationship. Within the framework of Hartree-Fock theory, the computed IP has excellent correlation with the macroscopic properties such as boiling point, heat of formation or enthalpy, entropy, heat capacity and heat of vaporisation. The correlation coefficient has been found to be high for the relationship between I and BP.
QSAR/QSPR analysis on Alkanes (C 2 -C 8 ) Hardness and softness indices exhibit similar correlation coefficient in the range of 0.80-0.95 for all the macroscopic properties, which confirms the fact that both the microscopic properties are interrelated. Maximum correlation coefficient for both the indices has been found to be 0.945 for heat of formation. This observation reinforces the existing fact that, hardness ( ) holds direct relationship with the stability of a molecule.
Summary The success of DFT based global and local quantum chemical descriptors in predicting the Chemo and Bio-activities of several systems selected by our group are highlighted in this work. The simple calculation procedure and the usefulness of all DFT based descriptors in the QSAR and QSPR parlance have also been probed in detail. In this study, the applications of global and local descriptors in the development of QSAR and QSPR have been presented for prediction of physical properties of series of alkanes, biological activity of testosterone and estrogen derivatives and toxicity of polychlorinated biphenyls, and benzidines.
Summary It has been shown that the global descriptors such as electrophilicity and ionization potential are capable of predicting the biological activity of the selected molecules Local descriptors such as philicity and group philicity are capable of identifying the activity of a particular site in the molecule and also in analyzing its toxicity as well as its behavior during an intermolecular reaction.
Acknowledgements T. Ramasami P. K. Chattaraj R. Parthasarathi J. Padmanabhan M. Elango DST and CSIR for funding