Mathematical Analysis of a Series of 4-Acetylamino-2-(3,5-dimethylpyrazol-1-yl)-6-pyridylpyrimidines: A Simple Way to Relate Quantum Similarity to Local Chemical Reactivity Using the Gaussian Orbitals Localized Theory
Molecular Quantum Similarity (MQS) descriptors and Density Functional Theory (DFT) based reactivity descriptors were studied for a series of 4-Acetylamino-2-(3,5-dimethylpyrazol-1-yl)-6-pyridylpyrimidines compounds used for Parkinson’s disease (PD) treatment. The quantification of the steric and electronic effects was shown through scales of quantitative convergence; such scales allow us to establish a methodology to quantify the similarity from the local chemical reactivity (Fukui Functions) point of view. This procedure provides new considerations in the local reactivity of the Adenosine receptor antagonists in a disease of difficult control as PD. In addition, we present new considerations to the localized bonding theory and show a new methodology for quantum similarity on the Fukui Functions. Considering that the Fukui functions under a condensation scheme may have ambiguities in the (DFT) context. 1. Introduction Parkinson’s disease (PD) is also known as idiopathic Parkinsonism or paralysis agitans [1]. PD is a chronic and degenerative disorder of the brain parts controlling the motor system. It occurs when nerve cells in the substantia nigra of the midbrain (a brain area that controls movement) die or suffer some deterioration [2]. PD is a chronic neurodegenerative disorder, which eventually leads to a progressive disability, for reasons still unknown [2–7]. PD is the second neurodegenerative disorder by their frequency, ranking behind only Alzheimer’s disease [2]. PD is not only a motor system disorder. It has a wider spectrum of affectedness such as emotional wellbeing, affecting sleep, cognition, visuospatial deficits, and sensation and perception [3–5]. For all these reasons there are also other aspects of PD to be considered such as social and economic cost, for instance, within families and work places of the PD affected patients. In this study is presented a method to quantify the steric and electronic factors in a set of 4-Acetylamino-2-(3,5-dimethylpyrazol-1-yl)-6-pyridylpyrimidines as adenosine receptor antagonists, reported by Zhang et al. [8] using the Molecular Quantum Similarity (MQS) [9–15]. Recently Bultinck and Carbó-Dorca have reported an analysis based on quantum similarity [16, 17], to define a link between quantum similarity and chemical reactivity. Taking into account this background, in this study we suggest a methodology for quantifying the steric and electronic effects of a series of adenosine receptor antagonists [8]. Additionally, a series of global and local reactivity descriptors such as chemical potential ( ),
References
[1]
J. Jankovic, “Parkinson’s disease: clinical features and diagnosis,” Journal of Neurology, Neurosurgery & Psychiatry, vol. 79, pp. 368–376, 2008.
[2]
C. A. Davie, “A review of Parkinson's disease,” British Medical Bulletin, vol. 86, no. 1, pp. 109–127, 2008.
[3]
M. Barnett-Cowan, R. T. Dyde, S. H. Fox, E. Moro, W. D. Hutchison, and L. R. Harris, “Multisensory determinants of orientation perception in Parkinson's disease,” Neuroscience, vol. 167, no. 4, pp. 1138–1150, 2010.
[4]
D. Garcia-Borreguero, O. Larrosa, and M. Bravo, “Parkinson's disease and sleep,” Sleep Medicine Reviews, vol. 7, no. 2, pp. 115–129, 2003.
[5]
M. Vaugoyeau, S. Viel, C. Assaiante, B. Amblard, and J. P. Azulay, “Impaired vertical postural control and proprioceptive integration deficits in Parkinson's disease,” Neuroscience, vol. 146, no. 2, pp. 852–863, 2007.
[6]
D. Aarsland, E. Londos, and C. Ballard, “Parkinson's disease dementia and dementia with Lewy bodies: different aspects of one entity,” International Psychogeriatrics, vol. 21, no. 2, pp. 216–219, 2009.
[7]
L. M. de Lau and M. M. Breteler, “Epidemiology of Parkinson's disease,” The Lancet Neurology, vol. 5, no. 6, pp. 525–535, 2006.
[8]
X. Zhang, J. E. Tellew, Z. Luo et al., “Lead optimization of 4-acetylamino-2-(3,5-dimethylpyrazol-1-yl)-6- pyridylpyrimidines as A2A adenosine receptor antagonists for the treatment of Parkinson's disease,” Journal of Medicinal Chemistry, vol. 51, no. 22, pp. 7099–7110, 2008.
[9]
R. Carbó-Dorca and L. Mercado, “Commentaries on quantum similarity (1): density gradient quantum similarity,” Journal of Computational Chemistry, vol. 31, pp. 2195–2212, 2010.
[10]
R. Carbó-Dorca, E. Besalú, and L. Mercado, “Communications on quantum similarity, part 3: a geometric-quantum similarity molecular superposition algorithm,” Journal of Computational Chemistry, vol. 32, pp. 582–599, 2011.
[11]
R. Carbó-Dorca and X. Gironés, “Foundation of quantum similarity measures and their relationship to QSPR: density function structure, approximations, and application examples,” International Journal of Quantum Chemistry, vol. 101, no. 8, p. 20, 2005.
[12]
R. Carbó-Dorca and X. Gironés, “Foundation of quantum similarity measures and their relationship to QSPR: density function structure, approximations, and application examples,” International Journal of Quantum Chemistry, vol. 101, no. 1, pp. 8–20, 2005.
[13]
L. Amatand and R. Carbó-Dorca, “Use of promolecular ASA density functions as a general algorithm to obtain starting MO in SCF calculations,” International Journal of Quantum Chemistry, vol. 87, pp. 59–67, 2002.
[14]
R. Carbó-Dorca and E. Besalú, “Communications on quantum similarity (2): a geometric discussion on holographic electron density theorem and confined quantum similarity measures,” Journal of Computational Chemistry, vol. 31, pp. 2452–2462, 2010.
[15]
R. Carbó-Dorca, M. Arnau, and L. Leyda, “How similar is a molecule to another? An electron density measure of similarity between two molecular structures,” International Journal of Quantum Chemistry, vol. 17, pp. 1185–1189, 1980.
[16]
P. Bultinck and R. J. Carbó-Dorca, “Molecular quantum similarity using conceptual DFT descriptors,” Journal of Chemical Sciences, vol. 117, pp. 425–435, 2005.
[17]
R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules, Oxford University Press, New York, NY, USA, 1989.
[18]
R. Vivas-Reyes, F. de Proft, P. Geerlings et al., “A DFT and HF quantum chemical study of the tin nanocluster [(RSn)12O14(OH)6]2+ and its interactions with anions and neutral nucleophiles: confrontation with experimental data,” New Journal of Chemistry, vol. 26, no. 9, pp. 1108–1117, 2002.
[19]
R. Mejia-Urueta, F. Nu？ez-Zarur, and R. Vivas-Reyes, “Density functional study on electronic structures and reactivity in carbazol-oxadiazole dyads used in organic light emitting diodes,” International Journal of Quantum Chemistry, vol. 112, pp. 2808–2815, 2012.
[20]
F. de Proft, R. Vivas-Reyes, M. Biesemans, R. Willem, J. M. L. Martin, and P. Geerlings, “Density functional study of the complexation reaction of Sn(CH3)3X (X = F, Cl, Br and I) with Halide Anions,” European Journal of Inorganic Chemistry, no. 20, pp. 3803–3810, 2003.
[21]
A. Morales-Bayuelo and R. J. Vivas-Reyes, “Topological model to quantify the global reactivity indexes as local in Diels-Alder reactions, using density function theory (DFT) and local quantum similarity (LQS),” Journal of Mathematical Chemistry, vol. 51, pp. 125–143, 2013.
[22]
A. Morales-Bayuelo and A. J. Vivas-Reyes, “Theoretical model for the polarization molecular and Hückel treatment of PhosphoCyclopentadiene in an external electric field: Hirschfeld study,” Journal of Mathematical Chemistry, vol. 51, pp. 1835–1852, 2013.
[23]
A. Morales-Bayuelo and R. Vivas-Reyes, “Topological model on the inductive effect in alkyl halides using local quantum similarity and reactivity descriptors in the density functional theory,” Journal Quantum Chemistry, vol. 2014, Article ID 850163, 12 pages, 2014.
[24]
M. V. Putz, “Density functionals of chemical bonding,” International Journal of Molecular Sciences, vol. 9, no. 6, pp. 1050–1095, 2008.
[25]
M. V. Putz, “Markovian approach of the electron localization functions,” International Journal of Quantum Chemistry, vol. 105, pp. 1–10, 2005.
[26]
M. V. Putz, “Chemical action and chemical bonding,” Journal of Molecular Structure: THEOCHEM, vol. 900, no. 1–3, pp. 64–70, 2009.
[27]
E. Matito and M. V. Putz, “New link between conceptual density functional theory and electron delocalization,” Journal of Physical Chemistry A, vol. 115, no. 45, pp. 12459–12462, 2011.
[28]
G. Haskó, J. Linden, B. Cronstein, and P. Pacher, “Adenosine receptor signaling in the brain immune system,” Nature Reviews Drug Discovery, vol. 7, pp. 759–770, 2008.
[29]
A. Morales-Bayuelo, H. Ayazo, and R. Vivas-Reyes, “Three-dimensional quantitative structure-activity relationship CoMSIA/CoMFA and LeapFrog studies on novel series of bicyclo [4.1.0] heptanes derivatives as melanin-concentrating hormone receptor R1 antagonists,” European Journal of Medicinal Chemistry, vol. 45, no. 10, pp. 4509–4522, 2010.
[30]
M. Ahumedo, A. Díaz, and R. Vivas-Reyes, “Theoretical and structural analysis of the active site of the transcriptional regulators LasR and TraR, using molecular docking methodology for identifying potential analogues of acyl homoserine lactones (AHLs) with anti-quorum sensing activity,” European Journal of Medicinal Chemistry, vol. 45, pp. 608–615, 2010.
[31]
X. Gironés and R. Carbó-Dorca, “TGSA-Flex: extending the capabilities of the Topo-Geometrical superposition algorithm to handle flexible molecules,” Journal of Computational Chemistry, vol. 25, pp. 153–159, 2003.
[32]
L. Chen, “Substructure and maximal common substructure searching,” in Computational Medicinal Chemistry for Drug Discovery, P. Bultinck, H. de Winter, W. Langenaeker, and J. P. Tollenaere, Eds., p. 483, Marcel Dekker, New York, NY, USA, 2003.
[33]
M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., GAUSSIAN 09, Revision A.02, Gaussian, Wallingford, UK, 2009.
[34]
A. D. Becke, “Density-functional exchange-energy approximation with correct asymptotic behavior,” Physical Review A, vol. 38, p. 3098, 1988.
[35]
C. Lee, W. Yang, and R. G. Parr, “Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density,” Physical Review B, vol. 37, no. 2, pp. 785–789, 1988.
[36]
W. J. Hehre, L. Radom, P. V. R. Schleyer, and J. A. Pople, Ab Initio Molecular Orbital Theory, John Wiley & Sons, New York, NY, USA, 1986.
[37]
R. Bultinck, X. Girones, and R. Carbó-Dorca, “Molecular quantum similarity: theory and applications,” Reviews in Computational Chemistry, vol. 21, pp. 127–207, 2005.
[38]
E. E. Hodgkin and W. G. Richards, “Molecular Similarity,” Chemische Berichte, vol. 24, p. 1141, 1988.
[39]
F. L. Hirshfeld, “Bonded-atom fragments for describing molecular charge densities,” heoretica Chimica Acta, vol. 44, pp. 129–138, 1977.
[40]
F. de Proft, C. van Alsenoy, A. Peeters, W. Langenaeker, and P. Geerlings, “Atomic charges, dipole moments, and Fukui functions using the Hirshfeld partitioning of the electron density,” Journal of Computational Chemistry, vol. 23, no. 12, pp. 1198–1209, 2002.
[41]
M. Randic, “Design of molecules with desired properties,” in Concepts and Applications of Molecular Similarity, M. A. Johnson and G. M. Maggiora, Eds., pp. 77–145, Wiley-Interscience, New York, NY, USA, 1990.
[42]
G. Boon, C. van Alsenoy, F. de Proft, P. Bultinck, and P. Geerlings, “Molecular quantum similarity of enantiomers of amino acids: a case study,” Journal of Molecular Structure: THEOCHEM, vol. 727, no. 1–3, pp. 49–56, 2005.
[43]
P. G. Mezey, “Molecular physics: an international journal at the interface between chemistry and physics,” Molecular Physics, vol. 96, pp. 169–178, 1999.
[44]
L. Amat and R. Carbó-Dorca, “Quantum similarity measures under atomic shell approximation: first order density fitting using elementary Jacobi rotations,” Journal of Computational Chemistry, vol. 18, pp. 2023–2039, 1997.
[45]
R. G. Parr and W. T. Yang, “Density functional approach to the frontier-electron theory of chemical reactivity,” Journal of the American Chemical Society, vol. 106, pp. 4049–4050, 1984.
[46]
M. Putz, “Systematic formulations for electronegativity and hardness and their atomic scales within density functional softness theory,” International Journal of Quantum Chemistry, vol. 106, pp. 361–389, 2006.
[47]
P. Bultinck and R. Carbó-Dorca, “A mathematical discussion on density and shape functions, vector semispaces and related questions,” Journal of Mathematical Chemistry, vol. 36, pp. 191–200, 2004.
[48]
R. M. Dreizler, Gross EKU Density Functional Theory, Springer, Berlin, Germany, 1990.
[49]
R. F. Nalewajski and R. G. Parr, “Legendre transforms and Maxwell relations in density functional theory,” The Journal of Chemical Physics, vol. 77, no. 1, pp. 399–407, 1982.
[50]
M. Randic and C. L. Wilkins, “Graph theoretical approach to recognition of structural similarity in molecules,” Journal of Chemical Information and Modeling, vol. 19, pp. 31–37, 1979.
[51]
R. G. Parr and R. G. Pearson, “Absolute hardness: companion parameter to absolute electronegativity,” Journal of the American Chemical Society, vol. 105, no. 26, pp. 7512–7516, 1983.
[52]
M. Berkowitz and R. G. Parr, “Molecular hardness and softness, local hardness and softness, hardness and softness kernels, and relations among these quantities,” The Journal of Chemical Physics, vol. 88, no. 4, pp. 2554–2557, 1988.
[53]
R. G. Parr and L. J. Bartolotti, “Some remarks on the density functional theory of few-electron systems,” Journal of Physical Chemistry, vol. 87, no. 15, pp. 2810–2815, 1983.
[54]
A. C. Good and W. G. Richards, “Rapid evaluation of shape similarity using Gaussian functions,” Journal of Chemical Information and Modeling, vol. 33, pp. 112–116, 1993.
[55]
M. Putz, “Semiclassical electronegativity and chemical hardness,” Journal of Theoretical and Computational Chemistry, vol. 6, p. 33, 2007.
[56]
R. F. W. Bader, Atoms in Molecules. A Quantum Theory, Oxford Science Publications/Clarendon Press, London, UK, 1990.
[57]
P. Bultinck, S. Fias, C. van Alsenoy, P. W. Ayers, and R. Carbó-Dorca, “Critical thoughts on computing atom condensed Fukui functions,” Journal of Chemical Physics, vol. 127, no. 3, Article ID 034102, 2007.
[58]
K. Fukui, “Role of frontier orbitals in chemical reactions,” Science, vol. 217, pp. 747–754, 1982.
[59]
W. Yang, R. G. Parr, and R. Pucci, “Electron density, Kohn-Sham frontier orbitals, and Fukui functions,” The Journal of Chemical Physics, vol. 81, no. 6, pp. 2862–2863, 1984.
