∆E – the relative electronic energy of the tautomerized complex; ∆∆ETS – the activation barrier of tautomerisation in terms of electronic energy; ΔΔE=ΔΔETS-ΔE – the reverse barrier of tautomerisation in terms of electronic energy; ν – the frequency of the vibrational mode of the tautomerized complex

Table 7. Energetic characteristics of DNA bases tautomerisation in studied base pairs obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of theory in vacuum#

In this study, we made an attempt to answer some actual questions related to physicochemical nature of spontaneous point mutations in DNA induced by prototropic

It was shown that the lifetime of mutagenic tautomers of all four canonical DNA bases exceeds by many orders not only the time required for replication machinery to enzymatically incorporate one incoming nucleotide into structure of DNA double helix (~4·10-4 s), and even a typical time of DNA replication in cell (~103 s). The high stability of mutagenic tautomers of DNA bases is mainly determined by the absence of intramolecular

This finding substantially supports the tautomeric hypothesis of the origin of spontaneous point mutations, for instance replication errors, removing all doubts on instability of mutagenic tautomers of isolated DNA bases, which are sometimes expressed by biologists. Notwithstanding a tremendous heuristic and methodological role of the classical Löwdin's mechanism of the origin of spontaneous point mutations during DNA replication, it was demonstrated that this mechanism probably has substantial limitations. From the physicochemical point of view, the advantage of Löwdin's mechanism lies in the fact that the tautomerisation of base pairs does not disturb standard Watson-Crick base-pairing geometry. Its main disadvantage is the instability of Ade\*·Thy\* base pair and metastability of Gua\*・Cyt\* base pair. The lifetime of tautomerized (Löwdin's) Ade\*Thy\* and Gua\*Cyt\* base pairs is less by orders than a characteristic time required for replication machinery to separate any Watson-Crick base pair (~10-9 s). Figuratively speaking, the Löwdin's base pairs "slip away" from replication apparatus: they transform to canonical base pairs and then dissociate without losing their canonical coding properties, as they haven't enough time to dissociate to mutagenic tautomers. These facts put the possibility of such mispairs involving mutagenic tautomers formation under a doubt, not to mention their complicated

∆∆ETS, kcal/mol ∆∆E ν,

cm-1 kcal/mol cm-1

∆E, kcal/mol

which becomes imaginary in the transition state of tautomerisation

H-bonds in their canonical and mutagenic forms.

dissociation into mutagenic tautomers.

Tautomerisation reaction

**6. Conclusions** 

tautomerism of its bases.

In this context, a topic of current importance is the search of novel physico-chemical mechanisms of tautomerisation of DNA bases in Watson-Crick base pairs: the pioneering, but encouraging steps have been already made in this direction (Brovarets', 2010; Cerón-Carrasco et al., 2009a, 2009b, 2011; Cerón-Carrasco & Jacquemin, 2011; Kryachko & Sabin, 2003).

It was found that a specific interaction of a single water molecule with the site of mutagenic tautomerisation in each of four canonical DNA bases could transform to into mutagenic tautomeric form in a definite time notably less than ~4·10-4 s. The most vulnerable point of this model of origin of replication error in DNA is a complete lack of experimental and especially theoretical support for a probability of the penetration of water molecules at a replication fork per one Watson-Crick base pair. Most likely such a probability is very low, since a compact, essentially hydrophobic organization of replisome (Marians, 2008; Pomerantz & O'Donnell, 2007) is supposed to minimize this probability.

In this work it was found that among all purine-pyrimidine base pairs with Watson-Crick geometry involving one base in mutagenic tautomeric form - AdeCyt\*, Gua\*Thy, Ade\*Cyt and GuaThy\*, GuaThy\* mispair is dynamically unstable and Ade\*Cyt mispair has very small lifetime (<<10-9 s) and therefore plays an intermediate role in DNA replication cycle, "sliding down" to the AdeCyt\* mispair. This fact substantially alters the Löwdin's scheme (Löwdin, 1963, 1965, 1966) of replication point errors fixation arising due to the prototropic tautomerism of DNA bases, which treats all four base pairs AdeCyt\*, Ade\*Cyt, Gua\*Thy and GuaThy\* as stable structures.

In our opinion, the results reported here not only provide more evidence in support of Watson and Crick classical tautomeric hypothesis of point mutations, but also fill it with concrete physico-chemical content.

By combining the data from the literature with our findings, we concluded that the tautomeric mechanism of the origin of mutations in DNA should satisfy the following thermodynamic and kinetic criteria:


Finishing our conclusions, we hope that this theoretical study gives valuable and thorough information on the chemically intriguing and biologically relevant questions of the DNA bases tautomerism. Our results presented here are believed to provide a new insight into the molecular nature of spontaneous point mutations in DNA and also be a promising and perspective tool for experimentalists working in the field of DNA mutagenesis.

Elementary Molecular Mechanisms of the Spontaneous Point

7657 (Print), 1993-6842 (Electronic).

7657 (Print), 1993-6842 (Electronic).

(Electronic).

1025-6415.

6842 (Electronic).

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 85

Brauer, N.B., Smolarek, S., Zhang, X., Buma, W.J. & Drabbels M. (2011). Electronic

Brovarets', O.O. & Hovorun, D.M. (2010b). Intramolecular tautomerisation and the

Brovarets', O.O., Bulavin, L.A. & Hovorun, D.M. (2010c). Can the proteins tautomerize the

Brovarets', O.O. & Hovorun, D.M. (2010d). By how many characters is the genetic

Brovarets', O.O., Zhurakivsky, R.O. & Hovorun, D.M. (2010e). Is there adequate ionization

Brovarets', O.O. & Hovorun, D.M. (2010f). Stability of mutagenic tautomers of uracil and its

Brovarets', O.O. PhD Thesis: Physico-chemical nature of the spontaneous and induced by

Brovarets', O.O. & Hovorun, D.M. (2011a). Intramolecular tautomerization and the

Brovarets', O.O. & Hovorun, D.M. (2011b). IR vibrational spectra of H-bonded complexes of

Brovarets', O.O., Yurenko, Y.P., Dubey, I.Ya. & Hovorun, D.M. (2012). Can DNA-binding

No. 1, (January-February 2010), pp. 5-17, ISSN: 1023-2427*.*

No. 6, (June 2010), pp. 175-179, ISSN: 1025-6415.

the mutagens transitions and transversions, Kyiv, 2010.

230, ISSN: 0233–7657 (Print), 1993-6842 (Electronic).

ISSN: 0030-400X (Print), 1562-6911 (Electronic).

*Struct. Dynam.,* ISSN: 0739-1102, (in press).

Vol. 2, No. 13, (June 2011), pp. 1563–1566, ISSN: 1948-7185 (Electronic). Brovarets', O.O. & Hovorun, D.M. (2010a). How stable are the mutagenic tautomers of DNA

1996), pp. 11042-11050, ISSN: 0021-9606 (Print), 1089-7690 (Electronic). Boys, S.F. & Bernardi, F. (1970). The calculation of small molecular interactions by the

analysis of the aniline inversion motion. *J. Chem. Phys.*, Vol. 105, No. 24, (December

differences of separate total energies. Some procedures with reduced errors. *Mol. Phys*., Vol. 19, No. 4, (1970), pp. 553-566, ISSN: 0026-8976 (Print), 1362-3028

spectroscopy of aniline ions embedded in helium nanodroplets. *J. Phys. Chem. Lett.*,

bases? *Biopolym. Cell,* Vol. 26, No.1, (January-February 2010), pp. 72-76, ISSN: 0233–

conformational variability of some classical mutagens - DNA purine bases derivatives: quantum chemical study. *Physics of the Alive (Fizyka zhyvoho)*, Vol. 18,

DNA base pairs: the physical answer to the biologically important question. *Reports of the National Academy of Sciences of Ukraine,* No. 2, (February 2010), pp. 76-82, ISSN:

information written in DNA? *Reports of the National Academy of Sciences of Ukraine,* 

mechanism of the spontaneous transitions? Quantum-chemical investigation. *Biopolym. Cell*, Vol. 26, No. 5, (September-October 2010), pp. 398-405, ISSN: 0233–

halogen derivatives: the results of quantum-mechanical investigation. *Biopolym. Cell,* Vol. 26, No. 4, (July-August 2010), pp. 295-298, ISSN: 0233–7657 (Print), 1993-

conformational variability of some classical mutagens – cytosine derivatives: quantum chemical study. *Biopolym. Cell*, Vol. 27, No. 3, (May-June 2011), pp. 221–

adenine, 2-aminopurine and 2-aminopurine+ with cytosine and thymine: quantumchemical study. *Opt. Spectrosc.,* Vol. 111, No. 5, (November 2011), pp. 750–757,

proteins of replisome tautomerize nucleotide bases? *Ab initio* model study. *J. Biol.* 

## **7. Acknowledgments**

This work was partly supported by the State Fund for Fundamental Research of Ukraine within the Ukrainian-Russian (0111U006629) and Ukrainian-Slovenian (0111U007526) research bilateral projects. Authors thank Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine and Ukrainian-American Laboratory of Computational Chemistry (President, Prof. Dr. Jerzy Leszczynski) for providing calculation resources and software allocation.

## **8. References**


This work was partly supported by the State Fund for Fundamental Research of Ukraine within the Ukrainian-Russian (0111U006629) and Ukrainian-Slovenian (0111U007526) research bilateral projects. Authors thank Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine and Ukrainian-American Laboratory of Computational Chemistry (President, Prof. Dr. Jerzy Leszczynski) for providing calculation

Aamouche, A., Ghomi, M., Grajcar, L., Baron, M.H., Romain, F., Baumruk, V., Stepanek, J.,

Alonso, J.L., Peña, I., López, J.C. & Vaquero, V. (2009). Rotational spectral signatures of four

Atkins, P.W. (January 1998). *Physical Chemistry* (6th edition), Oxford University Press, ISBN-

Basu, S., Majumdar, R., Das, G.K. & Bhattacharyya, D. (2005). Energy barrier and rates of

Bazsó, G., Tarczay, G., Fogarasi, G. & Szalay, P.G. (2011). Tautomers of cytosine and their

Beard, W.A. & Wilson, S.H. (1998). Structural insights into DNA polymerase β fidelity: hold

Beard, W.A. & Wilson, S.H. (2003). Structural insights into the origins of DNA polymerase

Bebenek, K., Pedersen, L.C. & Kunkel, T.A. (2011). Replication infidelity *via* a mismatch with

Bludský, O., Šponer, J., Leszczynski, J., Špirko, V. & Hobza, P. (1996). Amino groups in

2011), pp. 1862-1867, ISSN: 0027-8424 (Print), 1091-6490 (Electronic). Becke, A.D. (1993). Density-functional thermochemistry. III. The role of exact exchange*. J.* 

Coulombeau, C., Jobic, H. & Berthier, G. (1997). Neutron inelastic scattering, optical spectroscopies and scaled quantum mechanical force fields for analyzing the vibrational dynamics of pyrimidine nucleic acid bases: 3. Cytosine. *J. Phys. Chem. A,*  Vol. 101, No. 51, (December 1997), pp. 10063-10074, ISSN: 1089-5639 (Print), 1520-

tautomers of guanine. *Angew. Chem. Int. Ed*., Vol. 48, No. 33, (August 2009), pp.

tautomeric transitions in DNA bases: *ab initio* quantum chemical study. *Indian J. Biochem. Biophys*., Vol. 42, No. 6, (December 2005), pp. 378-385, ISSN: 0301-1208

excited electronic states: a matrix isolation spectroscopic and quantum chemical study. *Phys. Chem. Chem. Phys.*, Vol. 13, No. 15, (April 2011), pp. 6799-6807, ISSN:

tight if you want it right. *Chem. Biol*., Vol. 5, No. 1, (January 1998), pp. R7-R13,

fidelity. *Structure*, Vol. 11, No. 5, (May 2003), pp. 489–496, ISSN: 0969-2126 (Print),

Watson-Crick geometry. *Proc. Natl. Acad. Sci. U.S.A*., Vol. 108, No. 5, (February

*Chem. Phys.,* Vol. 98, No. 7, (April 1993), pp. 5648-5652, ISSN: 0021-9606 (Print),

nucleic acid bases, aniline, aminopyridines, and aminotriazine are nonplanar: results of correlated *ab initio* quantum chemical calculations and anharmonic

**7. Acknowledgments** 

**8. References** 

resources and software allocation.

5215 (Electronic).

AIMAll (Version 10.07.01), Keith, T.A., 2010 (aim.tkgristmill.com).

10: 0198501013, ISBN-13: 978-0198501015, Oxford, UK.

6141–6143, ISSN: 1521-3773 (Electronic).

1463-9076 (Print), 1463-9084 (Electronic).

ISSN: 1074-5521 (Print), 1879-1301 (Electronic).

(Print), 0975-0959 (Electronic).

1878-4186 (Electronic).

1089-7690 (Electronic).

analysis of the aniline inversion motion. *J. Chem. Phys.*, Vol. 105, No. 24, (December 1996), pp. 11042-11050, ISSN: 0021-9606 (Print), 1089-7690 (Electronic).


Elementary Molecular Mechanisms of the Spontaneous Point

1997), pp. 39-48, ISSN: 0009-2614 (Print).

ISSN: 0009-2665 (Print), 1520-6890 (Electronic).

(September 2005), pp. 285-293, ISSN: 0009-2614 (Print).

1227–1230, ISSN: 0036-8075 (Print), 1095-9203 (Electronic).

8424 (Print), 1091-6490 (Electronic).

(Electronic).

(Electronic).

5126 (Electronic).

0036-021X.

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 87

Choi, M.Y., Dong, F. & Miller, R.E. (2005). Multiple tautomers of cytosine identified and

No. 1827, (February 2005), pp. 393–413, ISSN: 1471-2962 (Electronic). Choi, M.Y. & Miller, R.E. (2006). Four tautomers of isolated guanine from infrared laser

2006), pp. 7320–7328, ISSN: 0002-7863 (Print), 1520-5126 (Electronic). Choi, M.Y., Dong, F., Han, S.W. & Miller, R.E. (2008). Nonplanarity of adenine: vibrational

108, No. 40, (October 2004), pp. 8237–8243, ISSN: 1089-5639 (Print), 1520-5215

characterized by infrared laser spectroscopy in helium nanodroplets: probing structure using vibrational transition moment angles. *Phil. Trans. R. Soc. A*, Vol. 363,

spectroscopy in helium nanodroplets. *J. Am. Chem. Soc*., Vol. 128, No. 22, (June

transition moment angle studies in helium nanodroplets. *J. Phys. Chem. A,* Vol. 112, No. 31, (August 2008), pp. 7185–7190, ISSN: 1089-5639 (Print), 1520-5215

thymine, and adenine in the gas phase*. Chem. Phys. Lett*., Vol. 269, No. 1-2, (April

dynamics in nucleic acids. *Chem. Rev.*, Vol. 104, No. 4, (April 2004), pp. 1977-2020,

a mutagenic tautomer of uracil. A density functional theory study. *J. Am. Chem. Soc*., Vol. 127, No. 7, (February 2005), pp. 2238-2248, ISSN: 0002-7863 (Print), 1520-

DNA rare base pairs: the molecular mechanism of the spontaneous substitution mutations conditioned by tautomerism of bases*. Chem. Phys. Lett.,* Vol. 412, No. 4-6,

structural anomalies. *RUSS CHEM REV*, Vol. 58, No. 8, (1989), pp. 758-777, ISSN:

biomolecules: a structural tool*. Science*, Vol. 298, No. 5596, (November 2002), pp.

M., Slupphaug, G. & Krokan, H.E. (2004). Alkylation damage in DNA and RNA repair mechanisms and medical significance. *DNA Repair*, Vol. 3, No. 11, (November 2004), pp. 1389–1407, ISSN: 1568-7864 (Print), 1568-7856 (Electronic). Drake, J.W. (1991). A constant rate of spontaneous mutation in DNA-based microbes. *Proc.* 

*Natl. Acad. Sci. U.S.A.,* Vol. 88, No. 16, (August 1991), pp. 7160–7164, ISSN: 0027-

Colarusso, P., Zhang, K., Guo, B. & Bernath, P.F. (1997). The infrared spectra of uracil,

Crespo-Hernández, C.E., Cohen, B., Hare, P.M. & Kohler, B. (2004). Ultrafast excited-state

Crick, F.H. (1966). Codon-anticodon pairing: the wobble hypothesis. *J. Mol. Biol.,* Vol. 19, No. 2, (August 1966), pp. 548–555, ISSN: 0022-2836 (Print), 1089-8638 (Electronic). Da̧bkowska, I., Gutowski, M. & Rak, J. (2005). Interaction with glycine increases stability of

Danilov, V.I., Anisimov, V.M., Kurita, N. & Hovorun, D. (2005). MP2 and DFT studies of the

Dolinnaya, N.G. & Gromova, E.S. (1983). Complementation interactions of oligonucleotides. *RUSS CHEM REV*, Vol. 52, No. 1, (1983), pp. 79-95, ISSN: 0036-021X. Dolinnaya, N.G. & Gryaznova, O.I. (1989). Complexes of oligo(poly)nucleotides with

Dong, F. & Miller, R.E. (2002). Vibrational transition moment angles in isolated

Drabløs, F., Feyzi, E., Aas, P.A., Vaagbø, C.B., Kavli, B., Bratlie, M.S., Peña-Diaz, J., Otterlei,


Brown, T., Kennard, O., Kneale, G. & Rabinovich, D. (1985). High-resolution structure of a

Brown, R.D., Godfrey, P.D., McNaughton, D. & Pierlot, A.P. (1989a). A study of the major

Brown, R.D., Godfrey, P.D., McNaughton, D. & Pierlot, A.P. (1989b). Tautomers of cytosine

Burda, J.V., Šponer, J. & Leszczynski, J. (2000). The interactions of square platinum(II)

Canuel, C., Mons, M., Piuzzi, F., Tardivel, B., Dimicoli, I. & Elhanine, M. (2005). Excited

2005), pp. 074316-074321, ISSN: 0021-9606 (Print), 1089-7690 (Electronic). Cerón-Carrasco, J.P., Requena, A., Michaux, C., Perpète, E.A. & Jacquemin, D. (2009a).

Cerón-Carrasco, J.P., Requena, A., Zúñiga, J., Michaux, C., Perpète, E. A. & Jacquemin, D.

Cerón-Carrasco, J.P., Zúñiga, J., Requena, A., Perpète, E. A., Michaux, C. & Jacquemin, D.

Cerón-Carrasco, J.P. & Jacquemin, D. (2011b). Influence of Mg2+ on the guanine-cytosine

Chatake, T., Hikima, T., Ono, A., Ueno, Y., Matsuda, A. & Takenaka, A. (1999).

Chen, H. & Li, S. (2006). Theoretical study on the excitation energies of six tautomers of

Chin, W., Mons, M., Piuzzi, F., Tardivel, B., Dimicoli, I., Gorb, L. & Leszczynski, J. (2004).

1985), pp.604-606, ISSN: 0028-0836 (Print), 1476-4687 (Electronic).

156, No. 1, (March 1989), pp. 61-63, ISSN: 0009-2614 (Print).

2308–2310, ISSN: 0002-7863 (Print), 1520-5126 (Electronic).

188, ISSN: 0949-8257 (Print), 1432-1327 (Electronic).

ISSN: 1463-9076 (Print), 1463-9084 (Electronic).

(Print), 1520-5215 (Electronic).

(Print), 1439-7641 (Electronic).

0022-2836 (Print), 1089-8638 (Electronic).

(Electronic).

(Electronic).

DNA helix containing mismatched base pairs. *Nature,* Vol. 315, No. 6020, (June

gas-phase tautomer of adenine by microwave spectroscopy. *Chem. Phys. Lett.,* Vol.

by microwave spectroscopy. *J. Am. Chem. Soc.*, Vol. 111, No. 6, (March 1989), pp.

complexes with guanine and adenine: a quantum-chemical *ab initio* study of metalated tautomeric forms. *J. Biol. Inorg. Chem.*, Vol. 5, No. 2, (April 2000), pp. 178-

states dynamics of DNA and RNA bases: characterization of a stepwise deactivation pathway in the gas phase*. J. Chem. Phys*., Vol. 122, No. 7, (February

Effects of hydration on the proton transfer mechanism in the adenine-thymine base pair. *J. Phys. Chem. A*, Vol. 113, No. 127, (June 2009), pp. 7892-7898, ISSN: 1089-5639

(2009b). Intermolecular proton transfer in microhydrated guanine-cytosine base pair: a new mechanism for spontaneous mutation in DNA. *J. Phys. Chem. A*, Vol. 113, No. 39, (September 2009), pp. 10549-10556, ISSN: 1089-5639 (Print), 1520-5215

(2011a). Combined effect of stacking and solvation on the spontaneous mutation in DNA. *Phys. Chem. Chem. Phys*., Vol. 13, No. 32, (August 2011), pp. 14584-14589,

tautomeric equilibrium: simulations of the induced intermolecular proton transfer. *Chem. Phys. Chem*., Vol. 12, No. 14, (October 2011), pp. 2615-2623, ISSN: 1439-4235

Crystallographic studies on damaged DNAs. II. N-6-methoxyadenine can present two alternate faces for Watson–Crick base-pairing, leading to pyrimidine transition mutagenesis*. J. Mol. Biol*., Vol. 294, No. 5, (December 1999), pp. 1223-1230, ISSN:

guanine: evidence for the assignment of the rare tautomers. *J. Phys. Chem. A*, Vol. 110, No. 45, (November 2006), pp. 12360–12362, ISSN: 1089-5639 (Print), 1520-5215

Gas phase rotamers of the nucleobase 9-methylguanine enol and its monohydrate: optical spectroscopy and quantum mechanical calculations. *J. Phys. Chem. A*, Vol. 108, No. 40, (October 2004), pp. 8237–8243, ISSN: 1089-5639 (Print), 1520-5215 (Electronic).


Elementary Molecular Mechanisms of the Spontaneous Point

ISSN: 0301-0104 (Print).

Washington, D.C.,USA.

(Electronic).

(Print).

911, ISSN: 1477-9226.

(Electronic).

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 89

Fogarasi, G. (2002). Relative stabilities of three low-energy tautomers of cytosine: a coupled

Fogarasi, G. (2008). Water-mediated tautomerization of cytosine to the rare imino form: an

Fonseca Guerra, C., Bickelhaupt, F.M., Saha, S. & Wang, F. (2006). Adenine tautomers:

Friedberg, E.C., Walker, G.C., Siede, W., Wood, R.D., Schultz, R.A. & Ellenberger, T. (May

Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.;

Fujii, M., Tamura, T., Mikami, N. & Ito, M. (1986). Electronic spectra of uracil in a supersonic

Furmanchuk, A., Isayev, O., Gorb, L., Shishkin, O.V., Hovorun, D.M. & Leszczynski, J.

García-Terán, J.P., Castillo, O., Luque, A., García-Couceiro, U., Beobide, G. & Román, P.

Goodman, M.F. (1997). Hydrogen bonding revisited: geometric selection as a principal

Govorun, D.N., Danchuk, V.D., Mishchuk, Ya.R., Kondratyuk, I.V., Radomsky, N.F. &

jet. *Chem. Phys. Lett*., Vol. 126, No. 6, (May 1986), pp. 583–587, ISSN: 0009-2614

(2011). Novel view on the mechanism of water-assisted proton transfer in the DNA bases: bulk water hydration. *Phys. Chem. Chem. Phys.,* Vol. 13, No. 10, (2011), pp.

(2006). Supramolecular architectures assembled by the interaction of purine nucleobases with metal-oxalato frameworks. Non-covalent stabilization of the 7Hadenine tautomer in the solid-state. *Dalton Trans.*, No. 7, (February 2006), pp. 902-

determinant of DNA replication fidelity. *Proc. Natl. Acad. Sci. U.S.A.*, Vol. 94, No. 20, (September 1997), pp. 10493-10495, ISSN: 0027-8424 (Print), 1091-6490

Zheltovsky, N.V. (1992). AM1 calculation of the nucleic acid bases structure and

pp. 1381–1390, ISSN: 1089-5639 (Print), 1520-5215 (Electronic).

Pople, J.A. *Gaussian 03, Revision C.02*, Gaussian, Inc.: 2003.

4311–4317, ISSN: 1463-9076 (Print), 1463-9084 (Electronic).

cluster electron correlation study. *J. Phys. Chem. A*, Vol. 106, No. 7, (February 2002),

*ab initio* dynamics study. *Chem. Phys.*, Vol. 349, No. 1-3, (June 2008), pp. 204–209,

relative stabilities, ionization energies, and mismatch with cytosine. *J. Phys. Chem. A*, Vol. 110, No. 11, (March 2006), pp. 4012-4020, ISSN: 1089-5639 (Print), 1520-5215

2006). *DNA Repair and Mutagenesis* (2nd edition), ASM Press, ISBN: 1-55581-319-4,

Montgomery, J.A., Jr.; Vreven, T.; Kudin, K.N.; Burant, J.C.; Millam, J.M.; Iyengar, S.S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G.A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J.E.; Hratchian, H.P.; Cross, J.B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R.E.; Yazyev, O.; Austin, A.J.; Cammi, R.; Pomelli, C.; Ochterski, J.W.; Ayala, P.Y.; Morokuma, K.; Voth, G.A.; Salvador, P.; Dannenberg, J.J.; Zakrzewski, V.G.; Dapprich, S.; Daniels, A.D.; Strain, M.C.; Farkas, O.; Malick, D.K.; Rabuck, A.D.; Raghavachari, K.; Foresman, J.B.; Ortiz, J.V.; Cui, Q.; Baboul, A.G.; Clifford, S.; Cioslowski, J.; Stefanov, B.B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R.L.; Fox, D.J.; Keith, T.; Al-Laham, M.A.; Peng, C.Y.; Nanayakkara, A.; Challacombe, M.; Gill, P.M.W.; Johnson, B.; Chen, W.; Wong, M.W.; Gonzalez, C.;


Dreyfus, M., Bensaude, O., Dodin, G. & Dubois, J.E. (1976). Tautomerism in cytosine and 3-

Echols, H. & Goodman, M.F. (1991). Fidelity mechanisms in DNA replication*. Annu. Rev.* 

Ehrlich, M., Norris, K.F., Wang, R.Y., Kuo, K.C. & Gehrke, C.W. (1986). DNA cytosine

Elshakre, M. (2005). *Ab initio* study of guanine tautomers in the S0 and D0 states. *Int. J.* 

Falk, M., Poole, A.G. & Goymour, C.G. (1970). Infrared study of the state of water in the

Fan, J.C., Shang, Z.C., Liang, J., Liu, X.H. & Jin, H. (2010). Systematic theoretical

Fersht, A.R. & Knill-Jones, J.W. (1983). Fidelity of replication of bacteriophage X174 DNA *in* 

Feyer, V., Plekan, O., Richter, R., Coreno, M., Vall-llosera, G., Prince, K.C., Trofimov, A.B.,

Feyer, V., Plekan, O., Richter, R., Coreno, M., de Simone, M., Prince, K.C., Trofimov, A.B.,

Florian, J., Hrouda, V. & Hobza, P. (1994). Proton transfer in the adenine-thymine base pair.

Florian, J., Leszczynski, J. & Scheiner, S. (1995). *Ab initio* study of the structure of guanine-

No. 3, (1995), pp. 469–480, ISSN: 0026-8976 (Print), 1362-3028 (Electronic). Florian, J. & Leszczynski, J. (1996). Spontaneous DNA mutations induced by proton transfer

Fogarasi, G. & Szalay, P.G. (2002). The interaction between cytosine tautomers and water: an

3, (April 2002), pp. 383–390, ISSN: 0009-2614 (Print).

*Biochem.*, Vol. 60, (July 1991), pp. 477-511, ISSN: 0066-4154.

pp. 387–393, ISSN: 0144-8463 (Print), 1573-4935 (Electronic).

ISSN: 0008-4042 (Print), 1480-3291 (Electronic).

2836 (Print), 1089-8638 (Electronic).

5639 (Print), 1520-5215 (Electronic).

(Print), 1520-5215 (Electronic).

(Print), 1520-5126 (Electronic).

(Electronic).

(Electronic).

(Print).

methylcytosine. A thermodynamic and kinetic study. *J. Am. Chem. Soc*., Vol. 98, No. 20, (September 1976), pp. 6338-6349, ISSN: 0002-7863 (Print), 1520-5126 (Electronic).

methylation and heat-induced deamination. *Biosci. Rep*., Vol. 6, No. 4, (April 1986),

*Quantum Chem*., Vol. 104, No. 1, (2005), pp. 1-15, ISSN: 0020-7608 (Print), 1097-461X

hydration shell of DNA*. Can. J. Chem.,* Vol. 48, No. 10, (May 1970), pp. 1536-1542,

investigations on the tautomers of thymine in gas phase and solution. *J. Mol. Struct.: THEOCHEM,* Vol. 939, No. 1-3, (January 2010), pp. 106-111, ISSN: 0166-1280

*vitro* and *in vivo. J. Mol. Biol.,* Vol. 165, No. 4, (April 1983), pp. 633-654, ISSN: 0022-

Zaytseva, I.L., Moskovskaya T.E., Gromov, E.V. & Schirmer, J. (2009). Tautomerism in cytosine and uracil: an experimental and theoretical core level spectroscopic study. *J. Phys. Chem. A*, Vol. 113, No. 19, (May 2009), pp. 5736–5742, ISSN: 1089-

Zaytseva, I.L. & Schirmer, J. (2010). Tautomerism in cytosine and uracil: a theoretical and experimental X-ray absorption and resonant auger study. *J. Phys. Chem. A*, Vol. 114, No. 37, (September 2010), pp. 10270–10276, ISSN: 1089-5639

*J. Am. Chem. Soc*., Vol. 116, No. 4, (February 1994), pp. 1457-1460, ISSN: 0002-7863

cytosine base pair conformers in gas phase and polar solvents. *Mol. Phys.,* Vol. 84,

in the guaninecytosine base pairs: an energetic perspective. *J. Am. Chem. Soc.*, Vol. 118, No. 12, (March 1996), pp. 3010–3017, ISSN: 0002-7863 (Print), 1520-5126

MP2 and coupled cluster electron correlation study*. Chem. Phys. Lett.*, Vol. 356, No.


Elementary Molecular Mechanisms of the Spontaneous Point

(Electronic).

ISSN: 1025-6415.

1097-461X.

(Electronic).

1544, ISSN: 0368-1769.

(Electronic).

0006-2960 (Print), 1520-4995 (Electronic).

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 91

Harris, V.H., Smith, C.L., Jonathan Cummins, W., Hamilton, A.L., Adams, H., Dickman, M.,

(March 2003), pp. 1389-1401, ISSN: 0022-2836 (Print), 1089-8638 (Electronic). Hauswirth, W. & Daniels, M. (1971). Fluorescence of thymine in aqueous solution at 300° K.

Hobza, P. & Šponer, J. (1999). Structure, energetics, and dynamics of the nucleic acid base

1999), pp. 3247-3276, ISSN: 0009-2665 (Print), 1520-6890 (Electronic). Hovorun, D.M., Danchuk, V.D., Mishchuk, Ya.R., Kondratyuk, І.V. & Zheltovsky, M.V.

Hornby, D.P. & Williams, D.M. (2003). The effect of tautomeric constant on the specificity of nucleotide incorporation during DNA replication: support for the rare tautomer hypothesis of substitution mutagenesis. *J. Mol. Biol.,* Vol. 326, No. 5,

*Photochem. Photobiol*., Vol. 13, No. 2, (February 1971), pp. 157-163, ISSN: 1751-1097

pairs: nonempirical *ab initio* calculations. *Chem. Rev.,* Vol. 99, No. 11, (November

(1995a). About the non-planarity and dipole non-stability of the canonical nucleotide bases methylated at the glycosidic nitrogen atom. *Reports of the National Academy of Sciences of Ukraine,* No. 6, (June 1995), pp. 117-119, ISSN: 1025-6415. Hovorun, D.M., Kondratyuk, І.V., Mishchuk, Ya.R. & Zheltovsky, M.V. (1995b). Non-

equivalence of the amine hydrogen atoms in the canonical nucelotide bases. *Reports of the National Academy of Sciences of Ukraine,* No. 8, (August 1995), pp. 130-132,

amino group in the canonical nucleotide bases. *Reports of the National Academy of* 

to the structural nonrigidity of the molecule: a post-Hartree-Fock *ab initio* study of 2-aminoimidazole. *Int. J. Quant. Chem*., Vol. 75, No. 3, (1999), pp. 245-253, ISSN:

cytosine base pair in DNA and its implications for mismatch repair. *Nature,* Vol. 320, No. 6062, (April 1986), pp. 552-555, ISSN: 0028-0836 (Print), 1476-4687

checkpoints. *Biochemistry*, Vol. 43, No. 45, (November 2004), pp. 14317–14324, ISSN:

state of DNA and RNA bases. *J. Am. Chem. Soc*., Vol. 124, No., 44, (November 2002),

methyluracil and 5-bromo-1-methyluracil. *J. Chem. Soc*., No. 0, (1962), pp. 1540–

and Z DNA; the GA base pair in B-DNA. *J. Biomol. Struct. Dyn.,* Vol. 3, No. 2,

facilitated by water: computational study of microsolvation. *J. Phys. Chem. A,* Vol. 111, No. 32, (August 2007), pp. 8007–8012, ISSN: 1089-5639 (Print), 1520-5215

Hovorun, D.M. & Kondratyuk, І.V. (1996). Anіsotropy of the rotational mobility of the

Hunter, W.N., Brown, T., Anand, N.N. & Kennard, O. (1986). Structure of an adenine-

Joyce, C.M. & Benkovic, S.J. (2004). DNA polymerase fidelity: kinetics, structure, and

Kang, H., Lee, K.T., Jung, B., Ko, Y.J. & Kim, S.K. (2002). Intrinsic lifetimes of the excited

Katritzky, A.R. & Waring, A.J. (1962). 299. Tautomeric azines. Part I. The tautomerism of 1-

Kennard, O. (1985). Structural studies of DNA fragments: the G·T wobble base pair in A, B

(October 1985), pp. 205−226, ISSN: 0739-1102 (Print), 1538-0254 (Electronic). Kim, H.-S., Ahn, D.-S., Chung, S.-Y., Kim, S.K. & Lee, S. (2007). Tautomerization of adenine

pp. 12958-12959, ISSN: 0002-7863 (Print), 1520-5126 (Electronic).

*Sciences of Ukraine*, No. 10, (October 1996), pp. 152-155, ISSN: 1025-6415. Hovorun, D.M., Gorb, L. & Leszczynski, J. (1999). From the nonplanarity of the amino group

vibrational spectra. *J. Mol*. *Struct.*, Vol. 267, (March 1992), pp. 99-103, ISSN: 0022- 2860.


Gonzalez, C. & Schlegel, H.B. (1989). An improved algorithm for reaction path following. *J.* 

Gorb, L. & Leszczynski, J. (1998a). Intramolecular proton transfer in monohydrated

Gorb, L. & Leszczynski, J. (1998b). Intramolecular proton transfer in mono- and dihydrated

Gorb, L., Podolyan, Y., Leszczynski, J., Siebrand, W., Fernandez-Ramos, A. & Smedarchina,

Gorb, L., Podolyan, Y., Dziekonski, P., Sokalski, W.A. & Leszczynsky, J. (2004). Double-

Gorb, L., Kaczmarek, A., Gorb, A., Sadlej, A.J. & Leszczynski, J. (2005). Thermodynamics

Gribov, L.A. & Mushtakova, S.P. (1999). *Quantum Chemistry: Textbook (Kvantovaya Khimiya: Uchebnik)*, Gardariki, ISBN: 5-8297-0017-4, Moscow, Russian Federation, pp 317-319. Gu, J. & Leszczynski, J. (1999). A DFT study of the water-assisted intramolecular proton

1999), pp. 2744-2750, ISSN: 1089-5639 (Print), 1520-5215 (Electronic). Guckian, K.M., Krugh, T.R. & Kool, E.T. (2000). Solution structure of a nonpolar, non-

(July 2000), pp. 6841-6847, ISSN: 0002-7863 (Print), 1520-5126 (Electronic). Gutowski, M., Van Lenthe, J.H., Verbeek, J., Van Duijneveldt, F.B. & Chalasinski, G. (1986).

Hanus, M., Kabeláč, M., Rejnek, J., Ryjáček, F. & Hobza, P. (2004). Correlated *ab initio* study

10119-10129, ISSN: 0002-7863 (Print), 1520-5126 (Electronic).

Vol. 70, No. 4-5, (1998), pp. 855-862, ISSN: 1097-461X.

2860.

1089-7690 (Electronic).

(Print), 1520-5207 (Electronic).

(Electronic).

(Electronic).

(Electronic).

vibrational spectra. *J. Mol*. *Struct.*, Vol. 267, (March 1992), pp. 99-103, ISSN: 0022-

*Chem. Phys*., Vol. 90, No. 4, (February 1989), pp. 2154-2161, ISSN: 0021-9606 (Print),

tautomers of cytosine: an *ab initio* post-Hartree–Fock study*. Int. J. Quant. Chem.*,

tautomers of guanine: an *ab initio* post Hartree-Fock study. *J. Am. Chem. Soc.,* Vol. 120, No. 20, (May 1998), pp. 5024-5032, ISSN: 0002-7863 (Print), 1520-5126

Z. (2001). A quantum-dynamics study of the prototropic tautomerism of guanine and its contribution to spontaneous point mutations in *Escherichia coli*. *Biopolymers,*  Vol. 61, No. 1, (2001/2002), p. 77-83, ISSN: 0006-3525 (Print), 1097-0282 (Electronic).

proton transfer in adenine-thymine and guanine-cytosine base pairs. A post-Hartree-Fock *ab initio* study. *J. Am. Chem. Soc.*, Vol. 126, No. 32, (August 2004), pp.

and kinetics of intramolecular proton transfer in guanine. Post Hartree-Fock study. *J. Phys. Chem. B,* Vol. 109, No. 28, (July 2005), pp. 13770–13776, ISSN: 1520-6106

transfer in the tautomers of adenine. *J. Phys. Chem. A.,* Vol. 103, No. 15, (March

hydrogen-bonded base pair surrogate in DNA. *J. Am. Chem. Soc.,* Vol. 122, No. 29,

The basis set superposition error in correlated electronic structure calculations*. Chem. Phys. Lett*., Vol. 124, No. 4, (1986), pp. 370-375, ISSN: 0009-2614 (Print). Hanus, M., Ryjáček, F., Kabeláč, M., Kubař, T., Bogdan, T.V., Trygubenko, S.A. & Hobza, P.

(2003). Correlated *ab initio* study of nucleic acid bases and their tautomers in the gas phase, in a microhydrated environment and in aqueous solution. Guanine: surprising stabilization of rare tautomers in aqueous solution. *J. Am. Chem. Soc*., Vol. 125, No. 25, (June 2003), pp. 7678-7688, ISSN: 0002-7863 (Print), 1520-5126

of nucleic acid bases and their tautomers in the gas phase, in a microhydrated environment, and in aqueous solution. Part 3. Adenine. *J. Phys. Chem. B*, Vol. 108, No. 6, (February 2004), pp. 2087-2097, ISSN: 1520-6106 (Print), 1520-5207


Elementary Molecular Mechanisms of the Spontaneous Point

0009-2614 (Print).

(Electronic).

1463-9084 (Electronic).

0022-3263 (Print), 1520-6904 (Electronic).

8368 (Print), 1469-896X (Electronic).

(Electronic).

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 93

Kwiatkowski, J.S. & Leszczynski, J. (1992). An *ab initio* quantum-mechanical study of

Kydd, R.A. & Krueger, P.J. (1977). The far-infrared vapour phase spectra of aniline-ND2 and

Kydd, R.A. & Krueger, P.J. (1978). The far-infrared vapor phase spectra of some

Labet, V., Grand, A., Morell, C., Cadet, J. & Eriksson, L.A. (2008). Proton catalyzed

Langan, P., Forsyth, V.T., Mahendrasingam, A., Pigram, W.J., Mason, S.A. & Fuller, W.

Larsen, N.W., Hansen, E.L. & Nicolaisen, F.M. (1976). Far infrared investigation of aniline and

Lee, C., Yang, W. & Parr, R.G. (1988). Development of the Colle-Salvetti correlation-energy

Li, Y. & Waksman, G. (2001). Crystal structures of a ddATP-, ddTTP-, ddCTP-, and ddGTP-

Lin, J., Yu, C., Peng, S., Akiyama, I., Li, K., Lee, L.K. & LeBreton, P.R. (1980). Ultraviolet

Lippert, B., Schoellhorn, H. & Thewalt, U. (1986). Metal-stabilized rare tautomers of

No. 2*,* (January 1988), pp. 785-789, ISSN: 0163-1829 (Print).

pp. 4627-4631, ISSN: 0002-7863 (Print), 1520-5126 (Electronic).

No. 1-2, (August 1992), pp. 35-44, ISSN: 0166-1280 (Print).

ISSN: 0021-9606 (Print), 1089-7690 (Electronic).

tautomerism of purine, adenine and guanine*. J. Mol. Struct.: THEOCHEM,* Vol. 208,

aniline-NHD. *Chem. Phys. Lett*., Vol. 49, No. 3, (August 1977), pp. 539-543, ISSN:

halosubstituted anilines. *J. Chem. Phys.,* Vol. 69, No. 2, (July 1978), pp. 827-832,

hydrolytic deamination of cytosine: a computational study. *Theor. Chem. Acc.,* Vol. 120, No. 4-6, (July 2008), pp. 429–435, ISSN: 1432-881X (Print), 1432-2234

(1992). A high angle neutron fiber diffraction study of the hydration of the A conformation of the DNA double helix. *J. Biomol. Struct. Dyn*., Vol. 10, No. 3, (December 1992), pp. 489-503, ISSN: 0739-1102 (Print), 1538-0254 (Electronic). Lapinski, L., Nowak, M.J., Reva, I., Rostkowska, H. & Fausto, R. (2010). NIR-laser-induced

selective rotamerization of hydroxy conformers of cytosine. *Phys. Chem. Chem. Phys.,* Vol. 12, No. 33, (September 2010), pp. 9615–9618, ISSN: 1463-9076 (Print),

4-fluoroaniline in the vapour phase. Inversion and torsion of the amino group. *Chem. Phys. Lett.,* Vol. 43, No. 3, (November 1976), pp. 584-586, ISSN: 0009-2614 (Print). Laxer, A., Major, D.T., Gottlieb, H.E. & Fischer, B. (2001). (15N5)-labeled adenine derivatives:

synthesis and studies of tautomerism by 15N NMR spectroscopy and theoretical calculations. *J. Org. Chem*., Vol. 66, No. 16, (August 2001), pp. 5463-5481, ISSN:

formula into a functional of the electron density. *Phys. Rev. Condens. Matter,* Vol. 37,

trapped ternary complex of Klentaq1: insights into nucleotide incorporation and selectivity. *Protein Science,* Vol. 10*,* No. 6, (June 2001), pp. 1225–1233, ISSN: 0961-

photoelectron studies of the ground-state electronic structure and gas-phase tautomerism of purine and adenine*. J. Am. Chem. Soc*., Vol. 102, No. 14, (July 1980),

nucleobases. 1. Iminooxo form of cytosine: formation through metal migration and estimation of the geometry of the free tautomer. *J. Am. Chem. Soc.,* Vol. 108, No. 21, (October 1986), pp. 6616–6621, ISSN: 0002-7863 (Print), 1520-5126 (Electronic). Lippert, B. & Gupta, D. (2009). Promotion of rare nucleobase tautomers by metal binding.

*Dalton Trans*., No. 24, (2009), pp. 4619–4634, ISSN: 1477-9226 (Print), 1477-9234


Kim, N.J., Jeong, G., Kim, Y.S., Sung, J., Kim, S.K. & Park, Y.D. (2000). Resonant two-photon

Komarov, V.M. & Polozov, R.V. (1990). Nonplanar structure of aminosubstituted

Komarov, V.M., Polozov, R.V. & Konoplev, G.G. (1992). Non-planar structure of nitrous

Kondratyuk, I.V., Samijlenko, S.P., Kolomiets, I.M. & Hovorun, D.M. (2000). Prototropic

Kool, E.T., Morales, J.C. & Guckian, K.M. (2000). Mimicking the structure and function of

Kool, E.T. (2002). Active site tightness and substrate fit in DNA replication. *Annu. Rev.* 

Kornberg, A. & Baker, T.A. (January 1992). *DNA Replication*, W. H. Freeman, ISBN-10:

Kosenkov, D., Kholod, Y., Gorb, L., Shishkin, O., Hovorun, D.M., Mons, M. & Leszczynski, J.

Kosma, K., Schroter, C., Samoylova, E., Hertel, I.V. & Schultz, T. (2009). Excited-state

Kow, Y.W. (2002). Repair of deaminated bases in DNA. *Free Radic. Biol. Med*., Vol. 33, No. 7, (October 2002), pp. 886–893, ISSN: 0891-5849 (Print), 1873-4596 (Electronic). Kryachko, E.S. & Sabin, J.R. (2003). Quantum chemical study of the hydrogen-bonded

Kubinec, M.G., & Wemmer, D.E. (1992). NMR evidence for DNA bound water in solution. *J.* 

Kunz, C., Saito, Y. & Schär, P. (2009). DNA repair in mammalian cells: mismatched repair:

Kwiatkowski, J.S. & Pullman, B. (1975). Tautomerism and electronic structure of biological

Vol. 18, pp. 199-335, Academic Press, ISBN: 0-12-020618-8, New York, USA.

2009), pp. 16939-16943, ISSN: 0002-7863 (Print), 1520-5126 (Electronic). Kostko, O., Bravaya, K., Krylov, A. & Ahmed, M. (2010). Ionization of cytosine monomer

39, No. 6, (March 2000), pp. 990-1009, ISSN: 1521-3773 (Electronic).

Vol. 523, No. 1-3, (May 2000), pp. 109-118, ISSN: 0022-2860.

*Biochem.*, Vol. 71, (July 2002), pp. 191–219, ISSN: 0066-4154.

0716720035, ISBN-13: 978-0716720034, New York, USA.

ISSN: 1520-6106 (Print), 1520-5207 (Electronic).

9076 (Print), 1463-9084 (Electronic).

(2003), pp. 695-710, ISSN: 1097-461X.

1038, ISSN: 1420-682X (Print), 1420-9071 (Electronic).

(Print), 1520-5126 (Electronic).

(Print), 1089-7690 (Electronic).

(Print), 1555-6654 (Electronic).

(April 1992), pp. 281-294, ISSN: 0022-5193.

ionization and laser induced fluorescence spectroscopy of jet-cooled adenine. *J. Chem. Phys*., Vol. 113, No. 22, (December 2000), pp. 10051-10055, ISSN: 0021-9606

nitrogenous bases. *Biofizika,* Vol. 35, No. 2, (1990), pp. 367-368, ISSN: 0006-3509

bases and non-coplanarity of Watson-Crick pairs. *J. Theor. Biol.*, Vol. 155, No. 3,

molecular-zwitterionic tautomerism of xanthine and hypoxanthine. *J. Mol. Struct.*,

DNA: insights into DNA stability and replication. *Angew. Chem. Int. Ed. Engl.*, Vol.

(2009). *Ab initio* kinetic simulation of gas-phase experiments: tautomerization of cytosine and guanine. *J. Phys. Chem. B,* Vol. 113, No. 17, (April 2009), pp. 6140-6150,

dynamics of cytosine tautomers. *J. Am. Chem. Soc*., Vol. 131, No. 46, (November

and dimer studied by VUV photoionization and electronic structure calculations. *Phys. Chem. Chem. Phys*., Vol. 12, No. 12, (March 2010), pp. 2860–2872, ISSN: 1463-

patterns in A•T base pair of DNA: origins of tautomeric mispairs, base flipping, and Watson-Crick → Hoogsteen conversion. *Int. J. Quant. Chem*., Vol. 91, No. 6,

*Am. Chem. Soc*., Vol. 114, No. 22, (October 1992), pp. 8739-8740, ISSN: 0002-7863

variations on a theme. *Cell. Mol. Life Sci.*, Vol. 66, No. 6, (March 2009), pp. 1021-

pyrimidines, In: *Advances in Heterocyclic Chemistry,* Katritzky, A.R., Boulton, A.J.,


Elementary Molecular Mechanisms of the Spontaneous Point

pp. 919–934, ISSN: 1097-4547 (Electronic).

(July-August 2011), pp. 16-28, ISSN: 0201-8470.

ISSN: 1089-5639 (Print), 1520-5215 (Electronic).

(Print), 1993-6842 (Electronic).

7863 (Print), 1520-5126 (Electronic).

1089-7690 (Electronic).

(Electronic).

(Electronic).

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 95

Mons, M., Dimicoli, I., Piuzzi, F., Tardivel, B. & Elhanine, M. (2002). Tautomerism of the

Mons, M., Piuzzi, F., Dimicoli, I., Gorb, L. & Leszczynski, J. (2006). Near-UV resonant two-

Morales, J.C. & Kool, E.T. (2000). Varied molecular interactions at the active sites of several

Morsy, M.A., Al-Somali, A.M. & Suwaiyan, A. (1999). Fluorescence of thymine tautomers at

Nikolaienko, T.Yu., Bulavin, L.A. & Hovorun, D.M. (2011a). Conformational capacity of 5'-

Nikolaienko, T.Yu., Bulavin, L.A. & Hovorun, D.M. (2011b). The 5`-deoxyadenylic acid

Nikolaienko, T.Yu., Bulavin, L.A. & Hovorun, D.M. (2011c). Structural flexibility of

Nir, E., Kleinermanns, K., Grace, L. & de Vries, M.S. (2001a). On the photochemistry of

Nir, E., Janzen, Ch., Imhof, P., Kleinermanns, K. & de Vries, M.S. (2001b). Guanine

Nir, E., Muller, M., Grace, L.I. & de Vries, M.S. (2002a). REMPI spectroscopy of cytosine.

Nir, E., Plützer, Chr., Kleinermanns, K. & de Vries, M. (2002b). Properties of isolated DNA

5088–5094, ISSN: 1089-5639 (Print), 1520-5215 (Electronic).

10921–10924, ISSN: 1089-5639 (Print), 1520-5215 (Electronic).

DNA base guanine and its methylated derivatives as studied by gas-phase Infrared and Ultraviolet Spectroscopy. *J. Phys. Chem. A*, Vol. 106, No. 20, (May 2002), pp.

photon ionization spectroscopy of gas phase guanine: evidence for the observation of three rare tautomers. *J. Phys. Chem. A*, Vol. 110, No. 38, (September 2006), pp.

DNA polymerases: nonpolar nucleoside isosteres as probes. *J. Am. Chem. Soc.,* Vol. 122, No. 6, (February 2000), pp. 1001-1007, ISSN: 0002-7863 (Print), 1520-5126

room temperature in aqueous solutions. *J. Phys. Chem. B*, Vol. 103, No. 50, (December 1999), pp. 11205–11210, ISSN: 1520-6106 (Print), 1520-5207 (Electronic). Nakabeppu, Y., Tsuchimoto, D., Yamaguchi, H. & Sakumi, K. (2007). Oxidative damage in

nucleic acids and Parkinson's disease. *J. Neurosci. Res*., Vol. 85, No. 5, (April 2007),

deoxyguanylic acid molecule investigated by quantum-mechanical methods. *Biopolym. Cell*, Vol. 27, No. 4, (July-August 2011), pp. 291-299, ISSN: 0233–7657

molecule conformational capacity: quantum-mechanical investigation using density functional theory (DFT). *Ukr. Biochem. J.* (*Ukr. Biokhim. Zh*.), Vol. 83, No. 4,

canonical 2`-deoxyribonucleotides in DNA-like conformers*. Ukr. Biochem. J.* (*Ukr. Biokhim. Zh*.), Vol. 83, No. 5, (September-October 2011), pp. 22-32, ISSN: 0201-8470. Nir, E., Grace, L., Brauer, B. & de Vries, M.S. (1999). REMPI spectroscopy of jet-cooled

guanine. *J. Am. Chem. Soc*., Vol. 121, No. 20, (May 1999), pp. 4896–4897, ISSN: 0002-

purine nucleobases*. J. Phys. Chem. A*, Vol. 105, No. 21, (May 2001), pp. 5106-5110,

tautomerism revealed by UV-UV and IR-UV hole burning spectroscopy. *J. Chem. Phys*., Vol. 115, No. 10, (September 2001), pp. 4604-4611, ISSN: 0021-9606 (Print),

*Chem. Phys. Lett*., Vol. 355, No. 1-2, (March 2002), pp. 59–64, ISSN: 0009-2614 (Print).

bases, base pairs and nucleosides examined by laser spectroscopy. *Eur. Phys. J. D*, Vol. 20, No. 3, (September 2002), pp. 317–329, ISSN: 1434-6060 (Print), 1434-6079


Lister, D.G., Tyler, J.K., Hog, J.H. & Larsen, N.W. (1974). The microwave spectrum, structure

Loeb, L.A. (2001). A mutator phenotype in cancer. *Cancer Res.,* Vol. 61, No. 8, (April 2001),

López, J.C., Peña, M.I., Sanz, M.E. & Alonso, J.L. (2007). Probing thymine with laser ablation

López, J.C., Alonso, J.L., Peña, I. & Vaquero, V. (2010). Hydrogen bonding and structure of

42, (2010), pp. 14128–14134, ISSN: 1463-9076 (Print), 1463-9084 (Electronic). Löwdin, P.-O. (1963). Proton tunneling in DNA and its biological implications. *Rev. Mod.* 

Löwdin, P.-O. (1965). Isotope effect in tunneling and its influence on mutation rates. *Mutat.* 

Löwdin, P.-O. (1966). Quantum genetics and the aperiodic solid: some aspects on the

Lührs, D.C., Viallon, J. & Fischer, I. (2001). Excited state spectroscopy and dynamics of

Marians, K.J. (2008). Understanding how the replisome works. *Nat. Struct. Mol. Biol.,* Vol. 15,

Mejía-Mazariegos, L. & Hernández-Trujillo, J. (2009). Electron density analysis of tautomeric

Michalkova, A., Kosenkov, D., Gorb, L. & Leszczynski, J. (2008). Thermodynamics and

Min, A., Lee, S.J., Choi, M.Y. & Miller, R.E. (2009). Electric field dependence experiments

Mishra, S.K., Shukla, M.K. & Mishra, P.C. (2000). Electronic spectra of adenine and 2-

(2001), pp. 1827-1831, ISSN: 1463-9076 (Print), 1463-9084 (Electronic). Marian, C.M. (2007). The guanine tautomer puzzle: quantum chemical investigation of

1553, ISSN: 1089-5639 (Print), 1520-5215 (Electronic).

ISSN: 1520-6106 (Print), 1520-5207 (Electronic).

*Res.,* Vol. 2, No. 3, (June 1965), pp. 18-221, ISSN: 0027-5107 (Print).

pp. 3230–3239, ISSN: 0008-5472 (Print), 1538-7445 (Electronic).

253-264, ISSN: 0022-2860.

1539-0756 (Electronic).

USA, London, UK.

29, ISSN: 0009-2614 (Print).

3044, ISSN: 0253-2964.

(Electronic).

and dipole moment of aniline. *J. Mol. Struct*., Vol. 23, No. 2, (November 1974), pp.

molecular beam Fourier transform microwave spectroscopy. *J. Chem. Phys.*, Vol. 126, No. 19, (May 2007), pp. 191103-191106, ISSN: 0021-9606 (Print), 1089-7690

uracil–water and thymine–water complexes. *Phys. Chem. Chem. Phys.,* Vol. 12, No.

*Phys.*, Vol. 35, No. 3, (July-September 1963), pp. 724–732, ISSN: 0034-6861 (Print),

biological problems of heredity, mutations, aging, and tumors in view of the quantum theory of the DNA molecule, In: *Advances in Quantum Chemistry,* Löwdin, P.-O., Vol. 2, pp. 213-360, Academic Press, ISBN: 978-0-12-386477-2, New York,

isolated adenine and 9-methyladenine. *Phys. Chem. Chem. Phys.,* Vol. 3, No. 10,

ground and excited states. *J. Phys. Chem. A*, Vol. 111, No. 8, (March 2007), pp. 1545–

No*.* 2, (February 2008), pp. 125-127, ISSN: 1545-9993 (Print), 1545-9985 (Electronic).

mechanisms of adenine, thymine and guanine and the pairs of thymine with adenine or guanine. *Chem. Phys. Lett.*, Vol. 482, No. 1-3, (November 2009), pp. 24–

kinetics of intramolecular water assisted proton transfer in Na+-1-methylcytosine water complexes. *J. Phys. Chem. B,* Vol. 112, No. 29, (July 2008), pp. 8624–8633,

and *ab initio* calculations of three cytosine tautomers in superfluid helium nanodroplets. *Bull. Korean Chem. Soc.,* Vol. 30, No. 12, (December 2009), pp. 3039–

aminopurine: an *ab initio* study of energy level diagrams of different tautomers in gas phase and aqueous solution*. Spectrochim. Acta A: Mol. Biomol. Spectrosc*., Vol. 56, No. 7, (June 2000), pp. 1355-1384, ISSN: 1386-1425 (Print), 1873-3557 (Electronic).


Elementary Molecular Mechanisms of the Spontaneous Point

(Electronic).

(Electronic).

(Electronic).

3654 (Print).

1520-5215 (Electronic).

(Print), 1608-3245 (Electronic).

164, ISSN: 0966-842X (Print), 1878-4380 (Electronic).

116, No. 3-4, (May 1984), pp. 387–396, ISSN: 0022-2860.

(December 1991), pp. 285–289, ISSN: 0020-1693 (Print).

ISSN: 0021-2148 (Print), 1869-5868 (Electronic).

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 97

Peng, C. & Schlegel, H.B. (1993). Combining synchronous transit and quasi-Newton

Peng, C., Ayala, P.Y., Schlegel, H.B. & Frisch, M.J. (1996). Using redundant internal

Plekan, O., Feyer, V., Richter, R., Coreno, M., Vall-llosera, G., Prince, K.C., Trofimov, A.B.,

Plützer, Chr., Nir, E., de Vries, M.S. & Kleinermanns, K. (2001). IR–UV double-resonance

Poltev, V.I., Shulyupina, N.V. & Bruskov, V.I. (1998). Fidelity of nucleic acid biosynthesis.

Pomerantz, R.T. & O'Donnell, M. (2007). Replisome mechanics: insights into a twin DNA

Privé, G.G., Heinemann, U., Chandrasegaran, S., Kan, L.-S., Kopka, M.L. & Dickerson, R. E.

Quack, M. & Stockburger, M. (1972). Resonance fluorescence of aniline vapour. *J. Mol. Spectrosc*., Vol. 43, No. 1, (July 1972), pp. 87-116, ISSN: 0022-2852 (Print). Radchenko, E.D., Sheina, G.G., Smorygo, N.A. & Blagoi, Yu.P. (1984). Experimental and

Renn, O., Lippert, B. & Albinati, A. (1991). Metal-stabilized rare tautomers of nucleobases 3.

Robinson, H., Gao, Y.G., Bauer, C., Roberts, C., Switzer, C. & Wang, A.H.J. (1998). 2'-

Sabio, M., Topiol, S. & Lumma, W.C. (1990). An investigation of tautomerism in adenine and

(2001), pp. 5466-5469, ISSN: 1463-9076 (Print), 1463-9084 (Electronic). Plützer, Chr. & Kleinermanns, K. (2002). Tautomers and electronic states of jet-cooled

methods to find transition states. *Isr. J. Chem*., Vol. 33, No. 4, (1993), pp. 449-454,

coordinates to optimize equilibrium geometries and transition states*. J. Comput. Chem*., Vol. 17, No. 1, (January 1996), pp. 49-56, ISSN: 0192-8651 (Print), 1096-987X

Zaytseva, I.L., Moskovskaya, T.E., Gromov, E.V. & Schirmer, J. (2009). An experimental and theoretical core-level study of tautomerism in guanine. *J. Phys. Chem. A*, Vol. 113, No. 33, (August 2009), pp. 9376-9385, ISSN: 1089-5639 (Print),

spectroscopy of the nucleobase adenine. *Phys. Chem. Chem. Phys*., Vol. 3, No. 24,

adenine investigated by double resonance spectroscopy*. Phys. Chem. Chem. Phys*., Vol. 4, No. 20, (2002), pp. 4877-4882, ISSN: 1463-9076 (Print), 1463-9084 (Electronic).

Comparison of computer modeling results with experimental data. *Molecular Biology (Molekuliarnaia biologiia),* Vol. 32, No. 2, (1998), pp. 233-240, ISSN: 0026-8933

polymerase machine. *Trends in Microbiology*, Vol. 15, No. 4, (April 2007), pp. 156–

(1987). Helix geometry, hydration, and G·A mismatch in a B-DNA decamer. *Science*, Vol. 238, No. 4826, (October 1987), pp. 498-504, ISSN: 0036-8075 (Print), 1095-9203

theoretical studies of molecular structure features of cytosine. *J. Mol. Struct.*, Vol.

(1-methylthyminato-*N3*) (1-methylthymine-*N3*)-*cis*-diammineplatinum(II) hemihexachloroplatinate(IV) dihydrate. *Inorganica Chim. Acta*, Vol. 190, No. 2,

Deoxyisoguanosine adopts more than one tautomer to form base pairs with thymidine observed by high-resolution crystal structure analysis. *Biochemistry*, Vol. 37, No. 31, (August 1998), pp. 10897-10905, ISSN: 0006-2960 (Print), 1520-4995

guanine. *J. Phys. Chem*., Vol. 94, No. 4, (February 1990), pp. 1366-1372, ISSN: 0022-


Norinder, U. (1987). A theoretical reinvestigation of the nucleic bases adenine, guanine,

Nowak, M.J., Lapinski, L. & Fulara, J. (1989a). Matrix isolation studies of cytosine: the

Nowak, M.J., Lapinski, L., Kwiatkowski, J.S. & Leszczynski, J. (1991). Infrared matrix

Nowak, M.J., Rostkowska, H., Lapinski, L., Kwiatkowski, J.S. & Leszczynski, J. (1994a).

*Chem*., Vol. 98, No. 11, (March 1994), pp. 2813-2816, ISSN: 0022-3654 (Print). Nowak, M.J., Rostkowska, H., Lapinski, L., Kwiatkowski, J.S. & Leszczynski, J. (1994b).

Padermshoke, A., Katsumoto, Y., Masaki, R. & Aida, M. (2008). Thermally induced double

Patel, D.J., Kozlowski, S.A., Marky, L.A., Rice, J.A., Broka, C., Dallas, J., Itakura, K. &

Patel, D.J., Pardi, A. & Itakura, K. (1982b). DNA conformation, dynamics, and interactions in

Patel, D.J., Kozlowski, S.A., Ikuta, S. & Itakura, K. (1984a). Deoxyadenosine-deoxycytidine

1984), pp. 3218–3226, ISSN: 0006-2960 (Print), 1520-4995 (Electronic). Patel, D.J., Kozlowski, S.A., Ikuta, S. & Itakura, K. (1984b). Dynamics of DNA duplexes

1982), pp. 437-444, ISSN: 0006-2960 (Print), 1520-4995 (Electronic).

*Spectrosc.*, Vol. 50, No. 6, (June 1994), pp. 1081-1094, ISSN: 1386-1425. Nowak, M.J., Lapinski, L., Kwiatkowski, J.S. & Leszczynski, J. (1996). Molecular structure

(February 1996), pp. 3527-3534, ISSN: 0022-3654 (Print).

*Spectrosc.*, Vol. 45, No. 2, ( February 1989), pp. 229-242, ISSN: 1386-1425. Nowak, M.J., Lapinski, L. & Kwiatkowski, J.S. (1989b). An infrared matrix isolation study of

(May 1987), pp. 259-269, ISSN: 0166-1280 (Print).

1989), pp. 14-18, ISSN: 0009-2614 (Print).

8539.

2614 (Print).

(Print), 1095-9203 (Electronic).

ISSN: 0014-9446 (Print).

cytosine, thymine and uracil using AM1*. J. Mol. Struct.: THEOCHEM,* Vol. 151,

separation of the infrared spectra of cytosine tautomers. *Spectrochim. Acta A: Mol.* 

tautomerism in purine and adenine*. Chem. Phys. Lett*., Vol. 157, No. 1-2, (April

isolation and *ab initio* quantum mechanical studies of purine and adenine*. Spectrochim. Acta A: Mol. Spectrosc.,* Vol. 47, No. 1, (1991), pp. 87-103, ISSN: 0584-

Tautomerism N(9)H↔N(7)H of purine, adenine, and 2-chloroadenine: combined experimental IR matrix isolation and *ab initio* quantum mechanical studies*. J. Phys.* 

Experimental matrix isolation and theoretical *ab initio* HF/6-31G(d, p) studies of infrared spectra of purine, adenine and 2-chloroadenine*. Spectrochim. Acta A: Mol.* 

and infrared spectra of adenine. Experimental matrix isolation and density functional theory study of adenine 15N isotopomers. *J. Phys. Chem*., Vol. 100, No. 9,

proton transfer in GG and wobble GT base pairs: a possible origin of the mutagenic guanine. *Chem. Phys. Lett*., Vol. 457, No. 1-3, (May 2008), pp. 232–236, ISSN: 0009-

Breslauer, K.J. (1982a). Structure, dynamics, and energetics of deoxyguanosinethymidine wobble base pair formation in the self-complementary d(CGTGAATTCGCG) duplex in solution. *Biochemistry,* Vol. 21, No. 3, (February

solution. *Science,* Vol. 216, No. 4546, (May 1982), pp. 581-590, ISSN: 0036-8075

pairing in the d(C-G-C-G-A-A-T-T-C-A-C-G) duplex: conformation and dynamics at and adjacent to the dA.dC mismatch site. *Biochemistry,* Vol. 23, No. 14, (July

containing internal G·T, G·A, A·C, and T·C pairs: hydrogen exchange at and adjacent to mismatch sites. *Fed. Proc*., Vol. 43, No. 11, (August 1984), pp. 2663-2670,


Elementary Molecular Mechanisms of the Spontaneous Point

1988), pp. 101-110, ISSN: 0040-5744 (Print).

0006-2960 (Print), 1520-4995 (Electronic).

2001), pp. 43-53, ISSN: 0166-1280 (Print).

ISSN: 0022-3654 (Print).

pp. 73-85, ISSN: 0201-8470.

ISSN: 0009-2614 (Print).

6106 (Print), 1520-5207 (Electronic).

0022-2860.

201- 218, ISSN: 0027-5107 (Print), 1873-135X (Electronic).

(Electronic).

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 99

Sloane, D.L., Goodman, M.F. & Echols, H. (1988). The fidelity of base selection by the

Sobolewski, A.L. & Adamowicz, L. (1995). Theoretical investigations of proton transfer

Sordo, J.A., Chin, S. & Sordo, T.L. (1988). On the counterpoise correction for the basis set

Sordo, J.A. (2001). On the use of the Boys–Bernardi function counterpoise procedure to

Sowers, L.C., Shaw, B.R., Veigl, M.L. & Sedwick, W.D. (1987). DNA base modification:

Šponer, J. & Hobza, P. (1994). Nonplanar geometries of DNA bases. *Ab initio* second-order

Šponer, J., Leszczynski, J. & Hobza, P. (2001). Hydrogen bonding, stacking and cation

Stepanian, S.G., Sheina, G.G., Radchenko, E.D. & Blagoi, Yu.P. (1985). Theoretical and

Stepanyugin, A.V., Kolomiets', I.M., Potyahaylo, A.L., Samijlenko, S.P. & Hovorun, D.M.

Sukhanov, O.S., Shishkin, O.V., Gorb, L., Podolyan, Y. & Leszczynski, J. (2003). Molecular

Suwaiyan, A., Morsy, M.A. & Odah, K.A. (1995). Room temperature fluorescence of 5-

*Biokhim. Zh*.), Vol. 74, No. 3, (May 2002), pp. 73-81, ISSN: 0201-8470. Stepanyugin, A.V., Potyahaylo, A.L., Kolomiets, I.M., Samijlenko, S.P. & Hovorun, D.M.

Vol. 537, No. 1-3, (March 2001), pp. 245-251, ISSN: 0166-1280 (Print). Sowers, L.C., Fazakerley, G.V., Kim, H., Dalton, L. & Goodman, M.F. (1986). Variation of

polymerase subunit of DNA polymerase III holoenzyme. *Nucleic Acids Res*., Vol. 16, No. 14A, (July 1988), pp. 6465-6475, ISSN: 0305-1048 (Print), 1362-4962 (Electronic).

reactions in a hydrogen bonded complex of cytosine with water. *J. Chem. Phys.*, Vol. 102, No. 14, (April 1995), pp. 5708-5718, ISSN: 0021-9606 (Print), 1089-7690

superposition error in large systems. *Theor. Chim. Acta*., Vol. 74, No. 2, (August

correct barrier heights for basis set superposition error*. J. Mol. Struct.: THEOCHEM,*

nonexchangable proton resonance chemical shifts as a probe of aberrant base pair formation in DNA. *Biochemistry,* Vol. 25, No. 14, (July 1986), pp. 3983–3988, ISSN:

ionized base pairs and mutagenesis. *Mutat. Res*., Vol. 177, No. 2, (April 1987), pp.

Moeller-Plesset study. *J. Phys. Chem.,* Vol. 98, No. 12, (March 1994), pp. 3161-3164,

binding of DNA bases. *J. Mol. Struct.: THEOCHEM,* Vol. 573, No. 1-3, (October

experimental studies of adenine, purine and pyrimidine isolated molecule structure. *J. Mol. Struct*., Vol. 131, No. 3-4, (November 1985), pp. 333-346, ISSN:

(2002a). UV spectra of adenine methyl and glycosyl derivatives and their transformation induced by amino acid carboxylic groups. *Ukr. Biochem. J.* (*Ukr.* 

(2002b). UV spectra of guanine methyl and glycosyl derivatives and their transformations induced by interactions with amino acids *via* carboxylic group in dimethylsulfoxide. *Ukr. Biochem. J.* (*Ukr. Biokhim. Zh*.), Vol. 74, No. 2, (March 2002),

structure and hydrogen bonding in polyhydrated complexes of adenine: a DFT study. *J. Phys. Chem. B*, Vol. 107, No. 12, (March 2003), pp. 2846-2852, ISSN: 1520-

chlorouracil tautomers*. Chem. Phys. Lett*., Vol. 237, No. 3-4, (May 1995), pp. 349–355,


Saha, S., Wang, F. & Brunger, M.J. (2006). Intramolecular proton transfer in adenine imino

Salter, L.M. & Chaban, G.M. (2002). Theoretical study of gas phase tautomerization reactions

Samijlenko, S.P., Bogdan, T.V., Trygubenko, S.A., Potyahaylo, A.L. & Hovorun, D.M. (2000).

Samijlenko, S.P., Potyahaylo, A.L., Stepanyugin, A.V., Kolomiets, I.M. & Hovorun, D.M.

Samijlenko, S.P., Krechkivs'ka, O.M., Kosach, D.A. & Hovorun, D.M. (2004). Transition to

Samijlenko, S.P., Yurenko, Y.P., Stepanyugin, A.V. & Hovorun, D.M. (2010). Tautomeric

Schneider, B., Cohen, D.M., Schleifer, L., Srinivasan, A.R., Olson, W.K. & Berman, H.M.

Schneider, B. & Berman, H.M. (1995). Hydration of the DNA bases is local. *Biophys. J.,* Vol.

Schoellhorn, H., Thewalt, U. & Lippert, B. (1989). Metal-stabilized rare tautomers of

Sheina, G.G., Stepanian, S.G., Radchenko, E.D. & Blagoi, Yu.P. (1987). IR spectra of guanine

Sinclair, W.E. & Pratt, D.W. (1996). Structure and vibrational dynamics of aniline and

pp. 2291-2303, ISSN: 0006-3495 (Print), 1542-0086 (Electronic).

ISSN: 0892-7022 (Print), 1029-0435 (Electronic).

(November-December 2000), pp. 92-95, ISSN: 0201-8470.

(Electronic).

0201-8470.

(Electronic).

2004), pp. 97-104, ISSN: 0022-2860.

0006-3525 (Print), 1097-0282 (Electronic).

ISSN: 0002-7863 (Print), 1520-5126 (Electronic).

pp. 275-292, ISSN: 0022-2860.

1089-7690 (Electronic).

tautomers. *Molecular Simulation*, Vol. 32, No. 15, (December 2006), pp. 1261–1270,

for the ground and first excited electronic states of adenine. *J. Phys. Chem. A*, Vol. 106, No. 16, (April 2002), pp. 4251-4256, ISSN: 1089-5639 (Print), 1520-5215

Deprotonated carboxylic group of amino acids transforms adenine into its rare prototropic tautomers. *Ukr. Biochem. J.* (*Ukr. Biokhim. Zh*.), Vol. 72, No. 6,

(2001). Recognition modes of hypoxanthine, xanthine and their derivatives by amino acid carboxylic group: UV spectroscopic and quantum chemical data. *Ukr. Biochem. J.* (*Ukr. Biokhim. Zh*.), Vol. 73, No. 6, (November 2001), pp. 61-72, ISSN:

high tautomeric states can be induced in adenine by interactions with carboxylate and sodium ions: DFT calculation data. *J. Mol. Struct.*, Vol. 708, No. 1-3, (December

equilibrium of uracil and thymine in model protein - nucleic acid contacts. Spectroscopic and quantum chemical approach. *J. Phys. Chem. B,* Vol. 114, No. 3, (January 2010), pp. 1454-1461, ISSN: 1520-6106 (Print), 1520-5207 (Electronic). Schneider, B., Cohen, D. & Berman, H.M. (1992). Hydration of DNA bases: analysis of

crystallographic data. *Biopolymers,* Vol. 32, No. 7, (July 1992), pp. 725-750, ISSN:

(1993). A systematic method for studying the spatial distribution of water molecules around nucleic acid bases. *Biophys. J.,* Vol. 65, No. 6, (December 1993),

69, No. 6, (December 1995), pp. 2661-2669, ISSN: 0006-3495 (Print), 1542-0086

nucleobases. 2. 2-Oxo-4-hydroxo form of uracil: crystal structures and solution behavior of two platinum(II) complexes containing iminol tautomers of 1 methyluracil. *J. Am. Chem. Soc.,* Vol. 111, No. 18, (August 1989), pp. 7213–7221,

and hypoxanthine isolated molecules. *J. Mol. Struct.*, Vol. 158, No. 3, (May 1987),

aniline-Ar from high resolution electronic spectroscopy in the gas phase. *J. Chem. Phys*., Vol. 105, No. 18, (November 1996), pp. 7942-7956, ISSN: 0021-9606 (Print),


Elementary Molecular Mechanisms of the Spontaneous Point

0028-0836 (Print), 1476-4687 (Electronic).

(Print).

(Electronic).

Mutations in DNA: A Novel Quantum-Chemical Insight into the Classical Understanding 101

Wang, S. & Schaefer III, H.F. (2006). The small planarization barriers for the amino group in

Wang, W., Hellinga, H.W., Beese, L.S. (2011). Structural evidence for the rare tautomer

Wang, Y., Saebo, S. & Pittman, C.U. Jr. (1993). The structure of aniline by *ab initio* studies. *J.* 

Watson, J.D. & Crick, F.H.C. (1953a). The structure of DNA. *Cold Spring Harbor Symp. Quant. Biol.,* Vol. 18, 1953, pp. 123-131. ISSN: 0091-7451 (Print), 1943-4456 (Electronic). Watson, J.D. & Crick, F.H.C. (1953b). Molecular structure of nucleic acids: a structure for

Wigner, E. (1932). Über das Überschreiten von Potentialschwellen bei chemischen Reaktionen. *Z. Phys. Chem.,* Vol. B19, (1932), pp. 203−216, ISSN: 0044-3336. Wiorkiewicz-Kuczera, J. & Karplus*,* M. (1990). *Ab initio* study of the vibrational spectra of

(June 1990), pp. 5324-5340, ISSN: 0002-7863 (Print), 1520-5126 (Electronic). Yang, Z. & Rodgers, M.T. (2004). Theoretical studies of the unimolecular and bimolecular

Yu, H., Eritja, R., Bloom, L.B. & Goodman, M.F. (1993). Ionization of bromouracil and

Yurenko, Y.P., Zhurakivsky, R.O., Ghomi, M., Samijlenko, S.P. & Hovorun, D.M. (2007a).

2007), pp. 6263-6271, ISSN: 1520-6106 (Print), 1520-5207 (Electronic). Yurenko, Y.P., Zhurakivsky, R.O., Ghomi, M., Samijlenko, S.P. & Hovorun, D.M. (2007b).

2749–2757, ISSN: 1463-9076 (Print), 1463-9084 (Electronic).

(October 2007), pp. 140-146, ISSN: 0009-2614 (Print).

1250, ISSN: 1520-6106 (Print), 1520-5207 (Electronic).

044310, ISSN: 0021-9606 (Print), 1089-7690 (Electronic).

the nucleic acid bases. *J. Chem. Phys.*, Vol. 124, No. 4, (January 2006), pp. 044303-

hypothesis of spontaneous mutagenesis. *Proc. Natl. Acad. Sci. U.S.A.*, Vol. 108, No. 43, (October 2011), pp. 17644-17648, ISSN: 0027-8424 (Print), 1091-6490 (Electronic).

*Mol. Struct.: THEOCHEM*, Vol. 281, No. 2-3, (April 1993), pp. 91-98, ISSN: 0166-1280

deoxyribose nucleic acid. *Nature,* Vol. 171, No. 4356, (April 1953), pp. 737-738, ISSN:

N9-H and N7-H adenine and 9-methyladenine. *J. Am. Chem. Soc*., Vol. 112, No. 13,

tautomerization of cytosine. *Phys. Chem. Chem. Phys.*, Vol. 6, No. 10, (2004), pp.

fluorouracil stimulates base mispairing frequencies with guanine. *J. Biol. Chem.,*  Vol. 268, No. 21, (July 1993), pp. 15935–15943, ISSN: 0021-9258 (Print), 1083-351X

Comprehensive conformational analysis of the nucleoside analogue 2'-β-deoxy-6 azacytidine by DFT and MP2 calculations*. J. Phys. Chem. B,* Vol. 111, No. 22, (June

How many conformers determine the thymidine low-temperature matrix infrared spectrum? DFT and MP2 quantum chemical study*. J. Phys. Chem. B,* Vol. 111, No. 32, (August 2007), pp. 9655-9663, ISSN: 1520-6106 (Print), 1520-5207 (Electronic). Yurenko, Y.P., Zhurakivsky, R.O., Samijlenko, S.P., Ghomi, M. & Hovorun, D.M. (2007c)*.* 

The whole of intramolecular H-bonding in the isolated DNA nucleoside thymidine. AIM electron density topological study. *Chem. Phys. Lett.,* Vol. 447, No. 1-3,

*initio* comprehensive conformational analysis of 2'-deoxyuridine, the biologically significant DNA minor nucleoside, and reconstruction of its low-temperature matrix infrared spectrum. *J. Phys. Chem. B,* Vol. 112, No. 4, (January 2008), pp. 1240-

bonds CH…O in biologically significant conformers of canonical 2΄ deoxyribonucleosides: *ab initio* topological analysis of the electron density. *Physics* 

Yurenko, Y.P., Zhurakivsky, R.O., Ghomi, M., Samijlenko, S.P. & Hovorun, D.M. (2008). *Ab* 

Yurenko, Y.P., Zhurakivsky, R.O. & Hovorun, D.M. 37. (2009). Intramolecular hydrogen


Sygula, A. & Buda, A. (1983). MNDO study of the tautomers of nucleic bases: Part II.

Szczepaniak, K. & Szczesniak, M. (1987). Matrix isolation infrared studies of nucleic acid

Szczesniak, M., Szczepaniak, K., Kwiatkowski, J.S., KuBulat, K. & Person, W.B. (1988)*.* 

Trygubenko, S.A., Bogdan, T.V., Rueda, M., Orozco, M., Luque, F.J., Šponer, J., Slavíček, P. &

Tsuchiya, Y., Tamura, T., Fujii, M. & Ito, M. (1988). Keto-enol tautomer of uracil and

Tunis, M.J.B., & Hearst, J.E. (1968). On the hydration of DNA. II. Base composition

Villani, G. (2005). Theoretical investigation of hydrogen transfer mechanism in the adenine–

Villani, G. (2006). Theoretical investigation of hydrogen transfer mechanism in the guanine–

Villani, G. (2010). Theoretical investigation of hydrogen atom transfer in the cytosine-

Vrkic, A.K., Taverner, T., James, P.F. & O'Hair, R.A.J. (2004). Gas phase ion chemistry of

2, (2004), pp. 197-208, ISSN: 1477-9226 (Print), 1477-9234 (Electronic). Wang, J.H. (1955). The hydration of desoxyribonucleic acid. *J. Am. Chem. Soc*., Vol. 77, No. 2, (January 1955), pp. 258-260, ISSN: 0002-7863 (Print), 1520-5126 (Electronic).

1968), pp. 1345-1353, ISSN: 0006-3525 (Print), 1097-0282 (Electronic). Ullrich, S., Schultz, T., Zgierski, M. Z. & Stolow, A. (2004). Electronic relaxation dynamics in

pp. 267-277, ISSN: 0166-1280 (Print).

0836 (Print), 1476-4687 (Electronic).

4203, ISSN: 1463-9076 (Print), 1463-9084 (Electronic).

ISSN: 1520-6106 (Print), 1520-5207 (Electronic).

2860.

(Print).

1463-9084 (Electronic).

0301-0104 (Print).

0301-0104 (Print).

Adenine and guanine*. J. Mol. Struct.: THEOCHEM,* Vol. 92, No., 3-4, (April 1983),

constituents: Part 4. Guanine and 9-methylguanine monomers and their keto-enol tautomerism. *J. Mol. Struct.*, Vol. 156, No. 1-2, (January 1987), pp. 29-42, ISSN: 0022-

Matrix isolation infrared studies of nucleic acid constituents. 5. Experimental matrix-isolation and theoretical *ab initio* SCF molecular orbital studies of the infrared spectra of cytosine monomers. *J. Am. Chem. Soc.,* Vol. 110, No. 25, (December 1988), pp. 8319–8330, ISSN: 0002-7863 (Print), 1520-5126 (Electronic). Topal, M.D. & Fresco, J.R. (1976). Complementary base pairing and the origin of substitution

mutations. *Nature,* Vol. 263, No. 5575, (September 1976), pp. 285-289, ISSN: 0028-

Hobza, P. (2002). Correlated *ab initio* study of nucleic acid bases and their tautomers in the gas phase, in a microhydrated environment and in aqueous solution. Part 1. Cytosine. *Phys. Chem. Chem. Phys.*, Vol. 4, No. 17, (2002), pp. 4192–

thymine. *J. Phys. Chem*., Vol. 92, No. 7, (April 1988), pp. 1760–1765, ISSN: 0022-3654

dependence of the net hydration of DNA. *Biopolymers,* Vol. 6, No. 9, (September

DNA and RNA bases studied by time-resolved photoelectron spectroscopy*. Phys. Chem. Chem. Phys*., Vol. 6, No. 10, (2004), pp. 2796-2801, ISSN: 1463-9076 (Print),

thymine base pair. *Chem. Phys.,* Vol. 316, No. 1-3, (September 2005), pp. 1–8, ISSN:

cytosine base pair. *Chem. Phys.*, Vol. 324, No. 2-3, (May 2006), pp. 438–446, ISSN:

guanine base pair and its coupling with electronic rearrangement. Concerted *vs* stepwise mechanism. *J. Phys. Chem. B*, Vol. 114, No. 29, (July 2010), pp. 9653–9662,

biomolecules, part 38. Gas phase ion chemistry of charged silver (I) adenine ions *via* multistage mass spectrometry experiments and DFT calculations. *Dalton Trans.,* No.


**5** 

*Brazil* 

**Quantum Chemistry and Chemometrics** 

*2Departamento de Física, Instituto de Biociências, Letras e Ciências Exatas,* 

Molecular structure plays a special role in science. Knowledge of the atomic arrangement is essential in order to be able to elucidate chemical properties and processes. The first advances in determining molecular structure occurred in nineteenth century. Around 1812, Jean-Baptiste Biot, a French physicist, discovered optical activity by observing polarized light shifting when crossing a quartz crystal. He observed that the light was displaced to the right in some cases and to the left in others. The conclusion was that rotation of polarized light by quartz is an inherent property of the crystal. Interested in the phenomenon, Biot noticed in further studies that similar effects were found when polarized light passed through certain liquids such as natural oils (lemon extract and laurel), alcoholic solutions of camphor, some sugars and tartaric acid. (Drayer, 1993; Cintas, 2007; Gal, 2011) Biot's observations were very important in

In 1948, Louis Pasteur discovered molecular chirality when studying a mixture of tartaric acid crystals.(Gal, 2007) He patiently performed the manual separation of tartarate enantiomer crystals (Cintas, 2007) and observed that each solution made with them was able to displace polarized light in one direction. He concluded that compounds with nonsuperimposable molecular asymmetry have identical chemical properties despite the inverse behavior related to polarized light. Pasteur argued that the optical activity of organic solutions is related to molecular geometry. This insight was far ahead of the organic structural theory of the time.(Drayer, 1993) Although Pasteur was the first to show a relationship between optical activity and molecular symmetry, he was not able to say exactly how a molecule could be right- or left-handed. The main advances in this idea occurred in 1874 when a theory of organic structure in three dimensions was independently and simultaneously developed by Jacobus Henricus van't Hoff in Holland, and Joseph

In 1865, August Kekulé proposed his theory of the benzene molecular structure and proposed that the carbon atom has valence 4.(Brush, 1999) His principal idea was that the carbon atom is

**1. Introduction** 

**1.1 Conformational analysis: Early history and Importance** 

laying foundation for the concept of optical activity.

Achille Le Bel in France. (Drayer, 1993; Cintas, 2007)

**Applied to Conformational Analysis** 

Aline Thaís Bruni1 and Vitor Barbanti Pereira Leite2

*Ciências e Letras de Ribeirão Preto, Universidade de São Paulo* 

*1Departamento de Química, Faculdade de Filosofia,* 

*Universidade Estadual Paulista, São José do Rio Preto* 

*of the Alive (Fizyka zhyvoho),* Vol. 17, No. 1, (January-February 2009), pp. 44-53, ISSN: 1023-2427*.*


## **Quantum Chemistry and Chemometrics Applied to Conformational Analysis**

Aline Thaís Bruni1 and Vitor Barbanti Pereira Leite2 *1Departamento de Química, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo 2Departamento de Física, Instituto de Biociências, Letras e Ciências Exatas, Universidade Estadual Paulista, São José do Rio Preto Brazil* 

## **1. Introduction**

102 Quantum Chemistry – Molecules for Innovations

Zamora, F., Kunsman, M., Sabat, M. & Lippert, B. (1997). Metal-stabilized rare tautomers of

Zhao, Z.-M., Zhang, Q.R., Gao, C.Y. & Zhuo, Y.Z. (2006). Motion of the hydrogen bond

*Lett. A,* Vol. 359, No. 1, (November 2006), pp. 10–13, ISSN: 0375-9601 (Print). Zhou, J., Kostko, O., Nicolas, C., Tang, X., Belau, L., de Vries, M.S. & Ahmed, M. (2009).

Zhurakivsky, R.O. & Hovorun, D.M. (2006). Conformational properties of cytidine: the DFT

Zhurakivsky, R.O. & Hovorun, D.M. (2007a). Complete conformational analysis of

Zhurakivsky, R.O. & Hovorun, D.M. (2007b). The comprehensive conformational analysis of

Zierkiewicz, W., Komorowski, L., Michalska, D., Cerny, J. & Hobza, P. (2008). The amino

Van Zundert, G.C.P., Jaeqx, S., Berden, G., Bakker, J.M., Kleinermanns, K., Oomens, J. & Rijs,

1023-2427*.*

5215 (Electronic).

ISSN: 1025-6415.

1669 (Print), 1520-510X (Electronic).

3, (May-June 2006), pp. 33-46, ISSN: 1023-2427.

1520-6106 (Print), 1520-5207 (Electronic).

1439-4235 (Print), 1439-7641 (Electronic).

*of the Alive (Fizyka zhyvoho),* Vol. 17, No. 1, (January-February 2009), pp. 44-53, ISSN:

nucleobases. 6-Imino tautomer of adenine in a mixed-nucleobase complex of mercury(II). *Inorg. Chem*., Vol. 36, No. 8, (April 1997), pp. 1583–1587, ISSN: 0020-

proton in cytosine and the transition between its normal and imino states. *Phys.* 

Experimental observation of guanine tautomers with VUV photoionization. *J. Phys. Chem. A*, Vol. 113, No. 17, (April 2009), pp. 4829–4832, ISSN: 1089-5639 (Print), 1520-

quantum mechamical investigation. *Physics of the Alive (Fizyka zhyvoho)*, Vol. 14, No.

deoxyadenosine by density functional theory. *Biopolym. Cell,* Vol. 23, No. 1, (January-February 2007), pp. 45-53, ISSN: 0233–7657 (Print), 1993-6842 (Electronic).

2′-deoxyguanosine molecule by the quantum-chemical density functional method. *Reports of the National Academy of Sciences of Ukraine,* No. 4, (April 2007), pp. 187-195,

group in adenine: MP2 and CCSD(T) complete basis set limit calculations of the planarization barrier and DFT/B3LYP study of the anharmonic frequencies of adenine. *J. Phys. Chem. B*, Vol. 112, No. 51, (December 2008), pp. 16734-16740, ISSN:

A.M. (2011). IR spectroscopy of isolated neutral and protonated adenine and 9 methyladenine. *ChemPhysChem*., Vol. 12, No. 10, (July 2011), pp. 1921-1927, ISSN:

## **1.1 Conformational analysis: Early history and Importance**

Molecular structure plays a special role in science. Knowledge of the atomic arrangement is essential in order to be able to elucidate chemical properties and processes. The first advances in determining molecular structure occurred in nineteenth century. Around 1812, Jean-Baptiste Biot, a French physicist, discovered optical activity by observing polarized light shifting when crossing a quartz crystal. He observed that the light was displaced to the right in some cases and to the left in others. The conclusion was that rotation of polarized light by quartz is an inherent property of the crystal. Interested in the phenomenon, Biot noticed in further studies that similar effects were found when polarized light passed through certain liquids such as natural oils (lemon extract and laurel), alcoholic solutions of camphor, some sugars and tartaric acid. (Drayer, 1993; Cintas, 2007; Gal, 2011) Biot's observations were very important in laying foundation for the concept of optical activity.

In 1948, Louis Pasteur discovered molecular chirality when studying a mixture of tartaric acid crystals.(Gal, 2007) He patiently performed the manual separation of tartarate enantiomer crystals (Cintas, 2007) and observed that each solution made with them was able to displace polarized light in one direction. He concluded that compounds with nonsuperimposable molecular asymmetry have identical chemical properties despite the inverse behavior related to polarized light. Pasteur argued that the optical activity of organic solutions is related to molecular geometry. This insight was far ahead of the organic structural theory of the time.(Drayer, 1993) Although Pasteur was the first to show a relationship between optical activity and molecular symmetry, he was not able to say exactly how a molecule could be right- or left-handed. The main advances in this idea occurred in 1874 when a theory of organic structure in three dimensions was independently and simultaneously developed by Jacobus Henricus van't Hoff in Holland, and Joseph Achille Le Bel in France. (Drayer, 1993; Cintas, 2007)

In 1865, August Kekulé proposed his theory of the benzene molecular structure and proposed that the carbon atom has valence 4.(Brush, 1999) His principal idea was that the carbon atom is

Quantum Chemistry and Chemometrics Applied to Conformational Analysis 105

molecular systems, making it possible to produce three-dimensional representations that provide insights into their behavior. As computer tools have enjoyed a spectacular increase in last decades, theoretical methods are invariably associated with computer modeling. This has become a powerful tool for evaluating molecular structure, from which special chemical

For the theoretical and computational determination of molecular properties it is necessary to previously determine the minimum energy structure of the system being studied. A central issue is to probe the equilibrium configuration of the molecular system. The way that energy varies with the coordinates is usually referred to as the potential energy surface. At the atomic level, the interaction energy between atoms is essentially ruled by quantum mechanics, which provides the basic elements and methods used in molecular modeling. However, the potential energy surface can be addressed with different degrees of approximation, *i.e.*, *ab initio*, effective potentials or even more coarse-grained potentials. Irrespective of the details with which the system is considered, one usually faces the problem of a highly dimensional system with the occurrence of multiple minima. Low energy minima play an important role in determining molecular properties, and the determination of these minima conformational states is a non-trivial task, usually referred to

If four or more atoms are connected in chain by single bonds we can suppose that there is considerable flexibility in the molecule. The existence of hindered rotation about a single bond is one of the fundamental concepts in conformational analysis.(Mo & Gao, 2007) The understanding of the connections between the atoms is related to the internal coordinate parameters, *i.e.*, bond length, bond angle and dihedral angle, and is essential in designing

For instance, let us consider a molecule composed of four different atoms which are singlebond linked (Figure 1). The green arrows represent the bond stretch and the average value is the bond length; the red arrows correspond to the angle formed by three sequential atoms, *i.e.*, the angle bond; the curved blue arrow indicates the free rotation around the only single

bond able to perform changes in the molecule conformation, as shown in Figure 2:

information about molecular behavior can be inferred. (Pietropaolo et al., 2011)

as energy minimization method for exploring the energy surface.

Fig. 1. Model for a generic molecule with four different atoms.

**2. Statement of the problem** 

molecular models.

tetravalent and can form valence bonds with other carbon atoms yielding to chains. These carbon chains can sometimes have closed arrangements, forming rings. (Drayer, 1993)

Van't Hoff and Le Bel proposed that the four valences of the carbon atom were not planar, but directed into three-dimensional space. Van't Hoff specifically proposed that the spatial arrangement was tetrahedral. Later, he used the tetrahedron as a graphic representation of the valence arrangement around the carbon atom and also used this model to explain the physical property of optical activity.(Ramberg & Somsen, 2001) A compound containing a four different substituted carbon – described by Van't Hoff as asymmetric carbon - would be capable of existing in two distinctly different nonsuperimposable forms. Finally, he stated that the asymmetric carbon atom was the cause of molecular asymmetry and optical activity.(Drayer, 1993)

Le Bel, in turn, also published his stereochemical ideas in 1874, but with a different approach to the problem from that presented by Van't Hoff. His hypothesis was not based on the tetrahedral model for the carbon atom and the fixed valences between the atoms. His investigation was into the asymmetry as a whole, without evaluating the individual atoms. The full system was considered in his evaluation, and his interpretation could be inserted into the field that is currently understood as molecular asymmetry. He mentions the tetrahedral carbon atom only in special cases, and not as a general principle. Many molecules confirm Le Bel's concepts of molecular asymmetry. Allenes, spiranes, and biphenyls are some examples of asymmetric molecules that do not contain any asymmetric carbons.

Van't Hoff's and Le Bel's different approaches can be explained by the origin of their formation. Van't Hoff, based on Kekulé tetrahedron models, suggested the concept of the asymmetric carbon atom. On the other hand, Le Bel based his investigations on Pasteur's considerations of the connections between optical rotation and molecular structure.(Drayer, 1993)

The historical development of conformational search does not end here and has many other important aspects and particularities. Our goal was just to give a basic outline of the initial concepts and how they influence current conformational understanding. Despite the historical progress in conformational studies, the advances in structure determination has been relatively recent and have been made possible by the development of analytical instruments and computational tools. Early structural studies were applied only to small molecules or substructures that could be expressed in terms of a few settings.(Allen et al., 2010)

Currently, a great evolution is occurring in mechanisms for determining and understanding molecular structures. The relationship between geometry and energy is experimentally measurable and gives an idea of the balance between energy factors involved in each structure. (Pietropaolo et al., 2011) Reactivity and other properties are directly linked to the conformational arrangement of molecules.(Hunger & Huttner, 1999) Every chemical property must be understood according to its molecular structure and atomic connections. (Pietropaolo et al., 2011) Indeed, knowledge of structural arrangement is important since it underlies studies in chemical reactions and other molecular behaviors. There are experimental techniques for the structural determination, such as X-ray, magnetic resonance, infrared, mass spectroscopy and others.

In this chapter we will discuss theoretical methods for molecular conformational determination. The field that concerns ways to mimic the behavior of molecules and molecular systems is molecular modeling. It seeks a simplified or idealized description of molecular systems, making it possible to produce three-dimensional representations that provide insights into their behavior. As computer tools have enjoyed a spectacular increase in last decades, theoretical methods are invariably associated with computer modeling. This has become a powerful tool for evaluating molecular structure, from which special chemical information about molecular behavior can be inferred. (Pietropaolo et al., 2011)

## **2. Statement of the problem**

104 Quantum Chemistry – Molecules for Innovations

tetravalent and can form valence bonds with other carbon atoms yielding to chains. These

Van't Hoff and Le Bel proposed that the four valences of the carbon atom were not planar, but directed into three-dimensional space. Van't Hoff specifically proposed that the spatial arrangement was tetrahedral. Later, he used the tetrahedron as a graphic representation of the valence arrangement around the carbon atom and also used this model to explain the physical property of optical activity.(Ramberg & Somsen, 2001) A compound containing a four different substituted carbon – described by Van't Hoff as asymmetric carbon - would be capable of existing in two distinctly different nonsuperimposable forms. Finally, he stated that the asymmetric carbon atom was the cause of molecular asymmetry and optical

Le Bel, in turn, also published his stereochemical ideas in 1874, but with a different approach to the problem from that presented by Van't Hoff. His hypothesis was not based on the tetrahedral model for the carbon atom and the fixed valences between the atoms. His investigation was into the asymmetry as a whole, without evaluating the individual atoms. The full system was considered in his evaluation, and his interpretation could be inserted into the field that is currently understood as molecular asymmetry. He mentions the tetrahedral carbon atom only in special cases, and not as a general principle. Many molecules confirm Le Bel's concepts of molecular asymmetry. Allenes, spiranes, and biphenyls are some examples of

Van't Hoff's and Le Bel's different approaches can be explained by the origin of their formation. Van't Hoff, based on Kekulé tetrahedron models, suggested the concept of the asymmetric carbon atom. On the other hand, Le Bel based his investigations on Pasteur's considerations of

The historical development of conformational search does not end here and has many other important aspects and particularities. Our goal was just to give a basic outline of the initial concepts and how they influence current conformational understanding. Despite the historical progress in conformational studies, the advances in structure determination has been relatively recent and have been made possible by the development of analytical instruments and computational tools. Early structural studies were applied only to small molecules or

Currently, a great evolution is occurring in mechanisms for determining and understanding molecular structures. The relationship between geometry and energy is experimentally measurable and gives an idea of the balance between energy factors involved in each structure. (Pietropaolo et al., 2011) Reactivity and other properties are directly linked to the conformational arrangement of molecules.(Hunger & Huttner, 1999) Every chemical property must be understood according to its molecular structure and atomic connections. (Pietropaolo et al., 2011) Indeed, knowledge of structural arrangement is important since it underlies studies in chemical reactions and other molecular behaviors. There are experimental techniques for the structural determination, such as X-ray, magnetic

In this chapter we will discuss theoretical methods for molecular conformational determination. The field that concerns ways to mimic the behavior of molecules and molecular systems is molecular modeling. It seeks a simplified or idealized description of

asymmetric molecules that do not contain any asymmetric carbons.

the connections between optical rotation and molecular structure.(Drayer, 1993)

substructures that could be expressed in terms of a few settings.(Allen et al., 2010)

resonance, infrared, mass spectroscopy and others.

carbon chains can sometimes have closed arrangements, forming rings. (Drayer, 1993)

activity.(Drayer, 1993)

For the theoretical and computational determination of molecular properties it is necessary to previously determine the minimum energy structure of the system being studied. A central issue is to probe the equilibrium configuration of the molecular system. The way that energy varies with the coordinates is usually referred to as the potential energy surface. At the atomic level, the interaction energy between atoms is essentially ruled by quantum mechanics, which provides the basic elements and methods used in molecular modeling. However, the potential energy surface can be addressed with different degrees of approximation, *i.e.*, *ab initio*, effective potentials or even more coarse-grained potentials. Irrespective of the details with which the system is considered, one usually faces the problem of a highly dimensional system with the occurrence of multiple minima. Low energy minima play an important role in determining molecular properties, and the determination of these minima conformational states is a non-trivial task, usually referred to as energy minimization method for exploring the energy surface.

If four or more atoms are connected in chain by single bonds we can suppose that there is considerable flexibility in the molecule. The existence of hindered rotation about a single bond is one of the fundamental concepts in conformational analysis.(Mo & Gao, 2007) The understanding of the connections between the atoms is related to the internal coordinate parameters, *i.e.*, bond length, bond angle and dihedral angle, and is essential in designing molecular models.

Fig. 1. Model for a generic molecule with four different atoms.

For instance, let us consider a molecule composed of four different atoms which are singlebond linked (Figure 1). The green arrows represent the bond stretch and the average value is the bond length; the red arrows correspond to the angle formed by three sequential atoms, *i.e.*, the angle bond; the curved blue arrow indicates the free rotation around the only single bond able to perform changes in the molecule conformation, as shown in Figure 2:

Quantum Chemistry and Chemometrics Applied to Conformational Analysis 107

The main questions on molecular modeling are concerned with a good way of finding the global minimum energy structure. Important information is also concerned with the behavior of the conformational space. It is not only necessary to know which is the global minimum, but also the whole shape of the potential energy surface (PES). The main characteristic of this conformational phase space is that it is exponentially large, and a computationally hard problem. (Fraenkel, 1993) One problem that illustrates this difficulty is the protein folding, in which one searches for the global energy minimum structure associated with its functional conformation. If a method can be used to describe the relevant potential energy surface of a given molecule, it can also accurately elucidate its behavior

Many techniques have been presented, and it is not the goal of this work to make a deep study on them. A good discussion of practical methods is given by Leach.(Leach, 2001) We intend to give a brief idea of the most popular techniques used for investigating the molecular structure computationally. For conformational sampling, one can imagine a hierarchy of methods with different computational costs.(Seabra et al., 2009) However, there is no sovereign truth about what is the best method for performing a conformational analysis. Each situation must be evaluated. The best method is one that has the best fit to the problem studied; in practical terms it will provide the answer as quickly as possible, using

The literature reports many methods for trying to solve multiconformational problems, and most of them are based on stochastic approaches. Put simply, stochastic methods work with random variables, such as initial conformations for the search or the steps probing the configuration phase space. The simple criterion for establishing a minimum energy conformation is that the first derivatives of the energy *E* with respect to each variable (*xi*) is

> 0 *i E x*

and

The algorithms that search for minimum energy states can be classified into two groups: those which use derivatives of the energy with respect to the coordinates, and those which do not. The most used derivative minimization methods are the steepest descent, line search in one dimension and conjugate gradient methods.(Leach, 2001) These algorithms are very useful for conducting local (restricted) searches of minima, or downhill searches to the nearest minimum, since they are not able to overcome energy barriers. They are often used

In the remainder of this section we discuss examples of stochastic methods. Havel, Kuntz and Crippen described distance geometry algorithms in conformational analysis.(Havel et al., 1983b) Given the impossibility of examining all possible conformations, they introduced a method which is capable of finding global optima without considering all possible solutions by means of combinatorial optimization. The method is known as *brunch and bound* and involves logical tests that allow whole classes of solutions to be eliminated without

2 <sup>2</sup> 0. *i E x* 

against many interest situations.

the least amount of computer resources.

zero and the second derivatives are all positive:

in combination with other stochastic methods.

**3. Stochastic methods of conformational analysis** 

Fig. 2. 90° rotation around the single bond.

In other words, different conformations are obtained when a dihedral angle is rotated. A dihedral angle is that composed by the planes formed by the sequence of three atoms (Figure 3):

Fig. 3. Dihedral angle representation for the molecule ABCD.

In other words, different conformations are obtained when a dihedral angle is rotated. A dihedral angle is that composed by the planes formed by the sequence of three atoms (Figure 3):

Fig. 2. 90° rotation around the single bond.

Fig. 3. Dihedral angle representation for the molecule ABCD.

The main questions on molecular modeling are concerned with a good way of finding the global minimum energy structure. Important information is also concerned with the behavior of the conformational space. It is not only necessary to know which is the global minimum, but also the whole shape of the potential energy surface (PES). The main characteristic of this conformational phase space is that it is exponentially large, and a computationally hard problem. (Fraenkel, 1993) One problem that illustrates this difficulty is the protein folding, in which one searches for the global energy minimum structure associated with its functional conformation. If a method can be used to describe the relevant potential energy surface of a given molecule, it can also accurately elucidate its behavior against many interest situations.

Many techniques have been presented, and it is not the goal of this work to make a deep study on them. A good discussion of practical methods is given by Leach.(Leach, 2001) We intend to give a brief idea of the most popular techniques used for investigating the molecular structure computationally. For conformational sampling, one can imagine a hierarchy of methods with different computational costs.(Seabra et al., 2009) However, there is no sovereign truth about what is the best method for performing a conformational analysis. Each situation must be evaluated. The best method is one that has the best fit to the problem studied; in practical terms it will provide the answer as quickly as possible, using the least amount of computer resources.

#### **3. Stochastic methods of conformational analysis**

The literature reports many methods for trying to solve multiconformational problems, and most of them are based on stochastic approaches. Put simply, stochastic methods work with random variables, such as initial conformations for the search or the steps probing the configuration phase space. The simple criterion for establishing a minimum energy conformation is that the first derivatives of the energy *E* with respect to each variable (*xi*) is zero and the second derivatives are all positive:

$$\frac{\partial E}{\partial \mathbf{x}\_i} = 0 \quad \text{and} \quad \frac{\partial^2 E}{\partial \mathbf{x}\_i^2} > 0.$$

The algorithms that search for minimum energy states can be classified into two groups: those which use derivatives of the energy with respect to the coordinates, and those which do not. The most used derivative minimization methods are the steepest descent, line search in one dimension and conjugate gradient methods.(Leach, 2001) These algorithms are very useful for conducting local (restricted) searches of minima, or downhill searches to the nearest minimum, since they are not able to overcome energy barriers. They are often used in combination with other stochastic methods.

In the remainder of this section we discuss examples of stochastic methods. Havel, Kuntz and Crippen described distance geometry algorithms in conformational analysis.(Havel et al., 1983b) Given the impossibility of examining all possible conformations, they introduced a method which is capable of finding global optima without considering all possible solutions by means of combinatorial optimization. The method is known as *brunch and bound* and involves logical tests that allow whole classes of solutions to be eliminated without

Quantum Chemistry and Chemometrics Applied to Conformational Analysis 109

near minima and connecting transition structures.(Jorgensen & TiradoRives, 1996; Grouleff & Jensen, 2011) However, large differences are found in sampling and configuring space available to the system. For MC, a new configuration is generated by selecting a random molecule or part of it, rotating it, translating it, and performing an internal structural variation. These changes do not necessarily need to follow a realistic physical trajectory. The acceptance of the new configuration is, however, determined by the Metropolis sampling algorithm. The sampling criterion is set in a way that enhances the likelihood of probing low energy conformations. Application over enough configurations yields properly Boltzmann-weighted averages for structure and thermodynamic properties. For MD, given a set of initial conditions (position and velocities of all atoms), new configurations are generated by application of Newton's equations of motion, so that the new atomic positions and velocities of all atoms are determined simultaneously over a small time step. In both cases, the force field controls the total energy (MC) and forces (MD), which determines the evolution of the systems. (Jorgensen

Examples of problems related to large systems are the interaction between drug and the receptor, and protein behavior and folding. Molecular docking procedures are capable of predicting the three-dimensional structure of macromolecular complexes and their binding affinity. The information required is simple and corresponds to the structures of the receptor and ligand and the presumable interfacing region between them. Besides the simplicity of these docking procedures, they have low computational costs. However, molecular plasticity and solvation effects are not, or are only approximately, taken into account in these approaches. Free energy simulations may be then used to investigate the molecular

It is important to realize that sometimes the probing of PES addresses singular questions, which involve association of several methods, also called hybrid methods. A particular wellknown tailored one is the quantum mechanics/molecular dynamics approach, also known as QM/MM approach. This is a molecular simulation method that combines the strength of both QM (high accuracy in specific regions) and MD fast calculations (in not so crucial regions), in such a way that it efficiently allows the study of chemical processes in solution

When stochastic methods are used to find minimum energy conformations, asymptotic states in restricted regions of the phase space are probed. This means that there is no end

As seen before, stochastic techniques use different heuristics to randomly cover the conformational space. These algorithms apply a perturbation to the initial conformer and minimum energy conformation is associated with the lowest energy state that is found through out this procedure. They provide a sampling of energy minima structures and the

Beyond the stochastic methods there are procedures that do not work with random choice to cover conformational space. These classes of methods are described as deterministic and are capable of searching the conformational map in a systematic way, providing a direct

association process and to predict binding affinity. (Biarnés et al., 2011)

point in the search, and the convergence cannot be assured.

**4. Systematic search in conformational analysis** 

shape of the PES is obtained in an indirect way.

& TiradoRives, 1996)

and in proteins.

examining them one by one. The method converts a set of distance ranges (or "bounds") into a set of Cartesian coordinates that are consistent with those bounds. (Spellmeyer et al., 1997) The efficiency of a *branch and bound* algorithm depends on how effective these tests are compared to the time required to perform them. (Havel et al., 1983a; Havel et al., 1983b) In another study, Havel *et al* presented the basic theorems of distance geometry in Euclidean space. They proposed new algorithms and described refinements to the existing ones. All these algorithms were similar because they utilize geometric principles in order to interpret structural relationships. (Havel et al., 1983b)

According to Leach and Smellie,(Leach & Smellie, 1992) distance geometry is a method for searching conformational space in which a structure is initially formulated in terms of interatomic distances. Any molecular system can be described as the set of minimum and maximum interatomic distances between all pairs of atoms in the molecule. The complete conformational space of the molecule is contained within this space. In distance geometry, a matrix is defined as the set of minimum and maximum distances, and then used to create a series of conformers that are consistent with those distances.(Spellmeyer et al., 1997)

Another tool for performing conformational searches is the genetic algorithm, a stochastic method first introduced by Holland in 1975. Genetic algorithm (GA) is a method applied to solve problems using a natural evolution process simulation. It is a stochastic method developed in analogy to Darwin's theory of evolution in order to perform the optimization.(Brodmeier & Pretsch, 1994; Lucasius, 1993; Nair & Goodman, 1998)

Genetic algorithm is commonly used for studying a large-scale space of possible solutions. The goal is to identify the best solutions within that space without the need to evaluate all possibilities.(Yanmaz et al., 2011) The GA is the optimization of a large number of possible solutions using a randomly generated population. When applied to conformational analysis, the population of interest consists of different conformations. The biological evolution of this population is simulated. A population of trial solutions is iteratively manipulated by a series of genetic operators to satisfy an objective function. The adjustment is calculated, and a new population is generated according to operators, such as selective reproduction, recombination and mutation. The process is repeated until the minimum energy structures are obtained.(Lucasius & Kateman, 1994; Beckers et al., 1996; Beckers et al., 1997)

Artificial Neural Networks (ANN) are another example of stochastic methods used in conformational analysis. This method is based on concepts of the behavior of the human brain. Although artificial neural networks are primitive compared to their biological counterparts, they exhibit some interesting properties which make them useful as multivariate tools in various fields of research. During the last decade, ANN have been successfully applied in non-linear modeling, classification, signal processing and process control.(Derks & Buydens, 1996) The properties of a molecule are intimately linked to the conformations that it adopts and so an understanding of the conformational space is important in rationalizing and predicting its behavior.(Jordan et al., 1995)

Among the most popular stochastic methods for covering the conformational space are Monte Carlo (MC) and Molecular Dynamics (MD). They are similar in the sense that both procedures include the same representation of molecules and use classical force fields for the potential energy terms, under periodic boundary conditions. The main purpose of these methods is to sample the phase space and to use the force fields ability to represent the conformational space

examining them one by one. The method converts a set of distance ranges (or "bounds") into a set of Cartesian coordinates that are consistent with those bounds. (Spellmeyer et al., 1997) The efficiency of a *branch and bound* algorithm depends on how effective these tests are compared to the time required to perform them. (Havel et al., 1983a; Havel et al., 1983b) In another study, Havel *et al* presented the basic theorems of distance geometry in Euclidean space. They proposed new algorithms and described refinements to the existing ones. All these algorithms were similar because they utilize geometric principles in order to interpret

According to Leach and Smellie,(Leach & Smellie, 1992) distance geometry is a method for searching conformational space in which a structure is initially formulated in terms of interatomic distances. Any molecular system can be described as the set of minimum and maximum interatomic distances between all pairs of atoms in the molecule. The complete conformational space of the molecule is contained within this space. In distance geometry, a matrix is defined as the set of minimum and maximum distances, and then used to create a

Another tool for performing conformational searches is the genetic algorithm, a stochastic method first introduced by Holland in 1975. Genetic algorithm (GA) is a method applied to solve problems using a natural evolution process simulation. It is a stochastic method developed in analogy to Darwin's theory of evolution in order to perform the

Genetic algorithm is commonly used for studying a large-scale space of possible solutions. The goal is to identify the best solutions within that space without the need to evaluate all possibilities.(Yanmaz et al., 2011) The GA is the optimization of a large number of possible solutions using a randomly generated population. When applied to conformational analysis, the population of interest consists of different conformations. The biological evolution of this population is simulated. A population of trial solutions is iteratively manipulated by a series of genetic operators to satisfy an objective function. The adjustment is calculated, and a new population is generated according to operators, such as selective reproduction, recombination and mutation. The process is repeated until the minimum energy structures

Artificial Neural Networks (ANN) are another example of stochastic methods used in conformational analysis. This method is based on concepts of the behavior of the human brain. Although artificial neural networks are primitive compared to their biological counterparts, they exhibit some interesting properties which make them useful as multivariate tools in various fields of research. During the last decade, ANN have been successfully applied in non-linear modeling, classification, signal processing and process control.(Derks & Buydens, 1996) The properties of a molecule are intimately linked to the conformations that it adopts and so an understanding of the conformational space is

Among the most popular stochastic methods for covering the conformational space are Monte Carlo (MC) and Molecular Dynamics (MD). They are similar in the sense that both procedures include the same representation of molecules and use classical force fields for the potential energy terms, under periodic boundary conditions. The main purpose of these methods is to sample the phase space and to use the force fields ability to represent the conformational space

series of conformers that are consistent with those distances.(Spellmeyer et al., 1997)

optimization.(Brodmeier & Pretsch, 1994; Lucasius, 1993; Nair & Goodman, 1998)

are obtained.(Lucasius & Kateman, 1994; Beckers et al., 1996; Beckers et al., 1997)

important in rationalizing and predicting its behavior.(Jordan et al., 1995)

structural relationships. (Havel et al., 1983b)

near minima and connecting transition structures.(Jorgensen & TiradoRives, 1996; Grouleff & Jensen, 2011) However, large differences are found in sampling and configuring space available to the system. For MC, a new configuration is generated by selecting a random molecule or part of it, rotating it, translating it, and performing an internal structural variation. These changes do not necessarily need to follow a realistic physical trajectory. The acceptance of the new configuration is, however, determined by the Metropolis sampling algorithm. The sampling criterion is set in a way that enhances the likelihood of probing low energy conformations. Application over enough configurations yields properly Boltzmann-weighted averages for structure and thermodynamic properties. For MD, given a set of initial conditions (position and velocities of all atoms), new configurations are generated by application of Newton's equations of motion, so that the new atomic positions and velocities of all atoms are determined simultaneously over a small time step. In both cases, the force field controls the total energy (MC) and forces (MD), which determines the evolution of the systems. (Jorgensen & TiradoRives, 1996)

Examples of problems related to large systems are the interaction between drug and the receptor, and protein behavior and folding. Molecular docking procedures are capable of predicting the three-dimensional structure of macromolecular complexes and their binding affinity. The information required is simple and corresponds to the structures of the receptor and ligand and the presumable interfacing region between them. Besides the simplicity of these docking procedures, they have low computational costs. However, molecular plasticity and solvation effects are not, or are only approximately, taken into account in these approaches. Free energy simulations may be then used to investigate the molecular association process and to predict binding affinity. (Biarnés et al., 2011)

It is important to realize that sometimes the probing of PES addresses singular questions, which involve association of several methods, also called hybrid methods. A particular wellknown tailored one is the quantum mechanics/molecular dynamics approach, also known as QM/MM approach. This is a molecular simulation method that combines the strength of both QM (high accuracy in specific regions) and MD fast calculations (in not so crucial regions), in such a way that it efficiently allows the study of chemical processes in solution and in proteins.

When stochastic methods are used to find minimum energy conformations, asymptotic states in restricted regions of the phase space are probed. This means that there is no end point in the search, and the convergence cannot be assured.

## **4. Systematic search in conformational analysis**

As seen before, stochastic techniques use different heuristics to randomly cover the conformational space. These algorithms apply a perturbation to the initial conformer and minimum energy conformation is associated with the lowest energy state that is found through out this procedure. They provide a sampling of energy minima structures and the shape of the PES is obtained in an indirect way.

Beyond the stochastic methods there are procedures that do not work with random choice to cover conformational space. These classes of methods are described as deterministic and are capable of searching the conformational map in a systematic way, providing a direct

Quantum Chemistry and Chemometrics Applied to Conformational Analysis 111

Fig. 4. A general structure with many single bonds.

Fig. 5. Branches generated by the dihedral angles A, B, C and D.

knowledge of PES shape. These searches divide conformational space into quantized units and apply algorithms to search this discrete space or define a set of heuristic rules that are used to drive the search.(Smellie et al., 2003)

Systematic methods are those that explore all conformational space at some fixed degree of resolution. To perform the systematic search, a molecule must be numerically described by its atoms' internal coordinates. The internal coordinates are bond length, angle bond and dihedral (torsion) angle. For a given initial structure the systematic conformational search is conducted by regular variation in dihedral angles (Figure 2).

Although a systematic search can obtain the morphology of a molecule's energetic behavior directly, this method is not feasible for evaluating complex systems. (Beusen et al., 1996) Systematic search is most usefully applied for molecules with few degrees of freedom.(Li Manni et al., 2009)

According to literature (Beusen et al., 1996), to cover the PES corresponding to the conformational space, different molecular structures must be systematically generated by rotating the torsion angles around the single bonds between 0° and 360°. The number of conformations is given by:

$$\text{Number of configurations} = \text{s}^{\text{N}} \tag{1}$$

where N is the number of free rotation angles, and s is the number of defining steps according to the angle increment:

$$\text{ls} = \frac{360^{\circ}}{\text{\(\theta\_{\text{l}}\)}} \tag{2}$$

with θi being the dihedral increment of angle i.

An examination of equation (1) reveals that the number of conformations generated will exponentially increase in proportion to the number of bonds with free rotation in the molecule under study. A problem arises if the number of steps is large, *i.e.*, when a very refined surface is required by small angle increments. This problematic behavior of the systematic study of PES, described as combinatorial explosion, is the major restriction involved in this kind of search. Figures 4 and 5 illustrate how combinatorial explosion works. In Figure 4, we have a representation of the system growth where many single bonds can be rotated.

The combinatorial explosion problem is represented by Figure 5. The number of branches to be considered is shown by the ramification achieved according the number of angles (A, B, C, D…) and will depend on the dihedral increment chosen. Due to the problem involved in combinatorial explosion, systematic search becomes nonviable for studying large molecules, since the number of degrees of freedom increases. A useful strategy for reducing the dimensionality of the conformational space is to perform systematic conformational searches on small portions of the molecule (either as isolated fragments or *in situ*). Using these optimal parts, one builds the conformation of the whole molecule with only limited additional searching of the relative conformations of the fragments. Approaches that incorporate this principle are known as ''build-up'' methods. (Beusen et al., 1996; Izgorodina et al., 2007) There are some strategies for overcoming the combinatorial explosion. We will focus our discussion on procedures that involve chemometrical approaches.

Fig. 4. A general structure with many single bonds.

knowledge of PES shape. These searches divide conformational space into quantized units and apply algorithms to search this discrete space or define a set of heuristic rules that are

Systematic methods are those that explore all conformational space at some fixed degree of resolution. To perform the systematic search, a molecule must be numerically described by its atoms' internal coordinates. The internal coordinates are bond length, angle bond and dihedral (torsion) angle. For a given initial structure the systematic conformational search is

Although a systematic search can obtain the morphology of a molecule's energetic behavior directly, this method is not feasible for evaluating complex systems. (Beusen et al., 1996) Systematic search is most usefully applied for molecules with few degrees of freedom.(Li

According to literature (Beusen et al., 1996), to cover the PES corresponding to the conformational space, different molecular structures must be systematically generated by rotating the torsion angles around the single bonds between 0° and 360°. The number of

where N is the number of free rotation angles, and s is the number of defining steps

360° θ�

An examination of equation (1) reveals that the number of conformations generated will exponentially increase in proportion to the number of bonds with free rotation in the molecule under study. A problem arises if the number of steps is large, *i.e.*, when a very refined surface is required by small angle increments. This problematic behavior of the systematic study of PES, described as combinatorial explosion, is the major restriction involved in this kind of search. Figures 4 and 5 illustrate how combinatorial explosion works. In Figure 4, we have a

The combinatorial explosion problem is represented by Figure 5. The number of branches to be considered is shown by the ramification achieved according the number of angles (A, B, C, D…) and will depend on the dihedral increment chosen. Due to the problem involved in combinatorial explosion, systematic search becomes nonviable for studying large molecules, since the number of degrees of freedom increases. A useful strategy for reducing the dimensionality of the conformational space is to perform systematic conformational searches on small portions of the molecule (either as isolated fragments or *in situ*). Using these optimal parts, one builds the conformation of the whole molecule with only limited additional searching of the relative conformations of the fragments. Approaches that incorporate this principle are known as ''build-up'' methods. (Beusen et al., 1996; Izgorodina et al., 2007) There are some strategies for overcoming the combinatorial explosion. We will

s =

representation of the system growth where many single bonds can be rotated.

focus our discussion on procedures that involve chemometrical approaches.

Number of conformations = s� (1)

(2)

used to drive the search.(Smellie et al., 2003)

Manni et al., 2009)

conformations is given by:

according to the angle increment:

with θi being the dihedral increment of angle i.

conducted by regular variation in dihedral angles (Figure 2).

Fig. 5. Branches generated by the dihedral angles A, B, C and D.

Quantum Chemistry and Chemometrics Applied to Conformational Analysis 113

described by previous principal components. A variety of algorithms can be used to calculate the principal components. The most commonly employed approach is singular

Fig. 6. PCA procedure: (a) original data set; (b) PCA on original data set and (c) Variables

A matrix of arbitrary size can be decomposed into the product of three matrices in such a

where **U** and **V** are square orthogonal matrices. The matrix **U** (whose columns are the eigenvectors of **XX**<sup>t</sup> ) contains the coordinates of samples along the PC axes. The **V** matrix (which contains the eigenvectors of the correlation matrix **X**t**X**) contains the information about how the original variables were used to make the new axes[ci,j coefficients in eq. (3)]. The **S**  matrix is a diagonal matrix that contains the eigenvalues of the correlation matrix (standard deviations) or singular values of each of the new PCs. The diagonalization of symmetric matrices (such as **XX**<sup>t</sup> and **X**t**X**) and SVD are fundamental problems in linear algebra (Golub & Loan, 1996), for which computationally efficient software has been developed and can be used

(4) ୲܄܁܃ ൌ ܆

value decomposition SVD. (Golub & Loan, 1996)

according to the new PC coordinates.(Beebe, 1998)

on a routine basis (Hanselma et al., 1997) for very large-size matrices.

way that:

#### **5. Chemometrics and structure determination**

A conformational search, independently of the method chosen, usually involves large amounts of data. Sometimes, data achieved from a given methodology must be explored by an additional technique. According to Geladi (2003) *"data exploration means taking a look at the data to find interesting phenomena, often without prior expectations. As a result, outliers, clustering of objects and gradients between clusters may be detected."*(Geladi, 2003)

Chemometrics has been used extensively in recent years for exploring chemical problems by means of computer tools and statistical observations. The literature presents many definitions for chemometrics. For our purposes, this field of knowledge is better defined as a combination of two definitions found in the literature:


The above definitions indicate that chemometrics offers a broad approach to chemical measurement sciences. It is not restricted to the actual experimental analysis but also considers what happens before and after it. (Massart et al., 2004) It is the goal of chemometrics to extract the information from the data. (Ramos et al., 1986) Chemometrical approaches have been applied to conformational analysis for handling special difficulties of large amounts of data generated both by stochastic and by systematic searches.

Among the various chemometrical techniques, Principal Component Analysis (PCA) is the most commonly used for conformational problems. In many ways, it forms the basis for multivariate data analysis**.** PCA is a multivariate method of analysis whose main concern is to reduce the dimensions needed to portray accurately the characteristics of a large dimensional data matrix.(Beebe, 1998; Wold et al., 1987) This mathematical procedure consists of eliminating a large number of correlated variables without changing the characteristics of the original data-set that contribute most to its variance.

For an easy graphical representation, consider a two-dimensional set of variables as shown in Figure 6 (a).

PCA can be performed on the original variables as shown in Figure 6 (b) and new axes, called Principal Components, arise to account for the maximum variation. A subsequent rotation (Figure 6(c)) is made on these new PC axes in order to rewrite the original variables in terms of this new axes-system. Each PC is constructed as a linear combination of variables:

$$\mathbf{P\_l} = \sum\_{\mathbf{j=1}}^{\nu} \mathbf{C\_{l,j} x\_{\mathbf{j}}} \tag{3}$$

where Pi is the ith principal component and ci,j is the coefficient of the variable xi,j. (Leach, 2001) There are ν such variables. The first principal component PC1 is chosen in order to maximize the data variance of the axis. The second and subsequent ones are chosen to be orthogonal to each other and account for the maximum variance in the data not yet

A conformational search, independently of the method chosen, usually involves large amounts of data. Sometimes, data achieved from a given methodology must be explored by an additional technique. According to Geladi (2003) *"data exploration means taking a look at the data to find interesting phenomena, often without prior expectations. As a result, outliers, clustering* 

Chemometrics has been used extensively in recent years for exploring chemical problems by means of computer tools and statistical observations. The literature presents many definitions for chemometrics. For our purposes, this field of knowledge is better defined as a

a. According to Wold (1995), chemometrics can be understood as a way "*to get chemically relevant information out of measured chemical data, how to represent and display this* 

b. For Beeb (1998), chemometrics corresponds to *"the entire process whereby data (e.g., numbers in a table) are transformed into information used for decision making."* (Beebe, 1998) The above definitions indicate that chemometrics offers a broad approach to chemical measurement sciences. It is not restricted to the actual experimental analysis but also considers what happens before and after it. (Massart et al., 2004) It is the goal of chemometrics to extract the information from the data. (Ramos et al., 1986) Chemometrical approaches have been applied to conformational analysis for handling special difficulties of

Among the various chemometrical techniques, Principal Component Analysis (PCA) is the most commonly used for conformational problems. In many ways, it forms the basis for multivariate data analysis**.** PCA is a multivariate method of analysis whose main concern is to reduce the dimensions needed to portray accurately the characteristics of a large dimensional data matrix.(Beebe, 1998; Wold et al., 1987) This mathematical procedure consists of eliminating a large number of correlated variables without changing the

For an easy graphical representation, consider a two-dimensional set of variables as shown

PCA can be performed on the original variables as shown in Figure 6 (b) and new axes, called Principal Components, arise to account for the maximum variation. A subsequent rotation (Figure 6(c)) is made on these new PC axes in order to rewrite the original variables in terms of this new axes-system. Each PC is constructed as a linear combination of

> P� ������x� �

(3)

���

where Pi is the ith principal component and ci,j is the coefficient of the variable xi,j. (Leach, 2001) There are ν such variables. The first principal component PC1 is chosen in order to maximize the data variance of the axis. The second and subsequent ones are chosen to be orthogonal to each other and account for the maximum variance in the data not yet

**5. Chemometrics and structure determination** 

combination of two definitions found in the literature:

*of objects and gradients between clusters may be detected."*(Geladi, 2003)

*information, and how to get such information into data*";(Wold, 1995)

large amounts of data generated both by stochastic and by systematic searches.

characteristics of the original data-set that contribute most to its variance.

in Figure 6 (a).

variables:

described by previous principal components. A variety of algorithms can be used to calculate the principal components. The most commonly employed approach is singular value decomposition SVD. (Golub & Loan, 1996)

Fig. 6. PCA procedure: (a) original data set; (b) PCA on original data set and (c) Variables according to the new PC coordinates.(Beebe, 1998)

A matrix of arbitrary size can be decomposed into the product of three matrices in such a way that:

$$\mathbf{X} = \mathbf{U}\mathbf{S}\mathbf{V}\_{\mathbf{t}} \tag{4}$$

where **U** and **V** are square orthogonal matrices. The matrix **U** (whose columns are the eigenvectors of **XX**<sup>t</sup> ) contains the coordinates of samples along the PC axes. The **V** matrix (which contains the eigenvectors of the correlation matrix **X**t**X**) contains the information about how the original variables were used to make the new axes[ci,j coefficients in eq. (3)]. The **S**  matrix is a diagonal matrix that contains the eigenvalues of the correlation matrix (standard deviations) or singular values of each of the new PCs. The diagonalization of symmetric matrices (such as **XX**<sup>t</sup> and **X**t**X**) and SVD are fundamental problems in linear algebra (Golub & Loan, 1996), for which computationally efficient software has been developed and can be used on a routine basis (Hanselma et al., 1997) for very large-size matrices.

Quantum Chemistry and Chemometrics Applied to Conformational Analysis 115

2. **Dihedral Pair Rotation:** The PDA-SA conformational search begins and the combination of the existing pairs of angles is taking account. Sometimes it is only possible to choose a dihedral increment with a less refined value. A rough PES is obtained in this case. The matrix to be analyzed consists of energy values from potential surfaces for angle combinations, and they are grouped according to Figure 7 for N angles. Appendix A shows the energy values for omprazole basic structure. The idea is to perform a cyclical permutation on the data, and this matrix form ensures that no information about the total PES is lost. The energy values obtained for each angle rotation as a function of the others allow the conformational space to be completely mapped. The major advantage is that the shape of these small portions can be visually

3. **PCA application on data matrix:** After the energy matrix statement, PCA is performed on the data. The regions with minimum energy points on the grid search can be easily selected. The number of selected regions will depend on the nature of the studied system. 4. **Refinement with a short dihedral increment:** The regions initially obtained in step 3 can be refined with a small angle increment. It is important to emphasize that this step is not obligatory, since a small dihedral increment can be used in step 3, depending on the studied system. However, previous experience in this methodology (Bruni et al., 2002; Bruni & Ferreira, 2008) shows that this is the easiest procedure, *i.e.*, firstly make rotations with a large dihedral increment and subsequently refine the minimum energy

5. **Optimization of the final structure:** the procedure described above provides angle values for the conformational search with a good level of accuracy. When these values are combined, we obtain all the possible minimum structures. Those structures constrained by the angle values obtained by PCA analysis are submitted to final optimization and the

In the study that introduced this method, the approach was successfully tested in the analysis of omeprazole and its derivatives, in which the results were in agreement with the

In a second study, the technique was used to find minimum energy conformations of omeprazole derivative molecules in a QSAR study. (Bruni & Ferreira, 2002) It was shown that conformational analysis is crucial when establishing SAR/QSAR models using theoretically calculated descriptors, and they are strongly dependent on the details of molecular structure. Though all minima conformation have similar energetic values, some calculated properties are very sensitive to the structural variation, which is understandable since electronic properties are intrinsically dependent on molecular conformation.(Bruni &

Omeprazole's racemization barrier and decomposition reaction was also studied. Quantum chemistry coupled to PDA-SA chemometric method was used to find all omeprazole minimum energy structures. To obtain the racemization barriers it was essential that the starting structure was in a global energy minimum. In that work, for all the studied structures, there was no change in the values of the racemization barriers, which confirmed the identification of the most stable structures for omeprazole.(Bruni & Ferreira, 2008)

observed, since we have a 3-D fitting. (see Figures 9 and 10)

regions selected by PCA with small dihedral increments.

experimental ones.(Bruni et al., 2002)

Ferreira, 2002)

resulting structures are considered to be those of minimum energy.

In chemistry, PCA was introduced by Malinowski around 1960 under the name Principal Factor Analysis, and further developed after 1970.(Malinowski, 2003) Principal Component Analysis can be used for crystallographic structure data; in its general form, conformational analysis is applied to multivariate numerical problems. (Allen et al., 2010) Many studies report on the use of PCA for handling Molecular Dynamics data. Among them, we highlight the application that uses PCA for mapping potential energy surfaces, by the quantitative visualization of a macromolecular energy funnel. (Becker, 1998) Other examples where PCA can be applied in molecular structure determination can also be found in recent studies. (Das et al., 2011; Araujo-Andrade et al., 2010; Kiralj et al. 2007; Oblinsky et al., 2009; Silva et al., 2011)

#### **6. Pairs of dihedral angles-systematic analysis**

There is a variety of theoretical methods that are capable of locating minimum energy structures in the potential energy surface. The problem of stochastic methods is that there is no natural end point for the conformational search. In some cases, only a small subset of conformational space is explored and the convergence of the system is not guaranteed. Only Systematic Conformational Analysis maps the conformational space completely. We stress the principal difficulty inherent in this method is the combinatorial explosion. In a previous study (Bruni et al., 2002), a new methodology was introduced for controlling the combinatorial explosion through a systematic reduction in the size of the system by means of chemometrics.

This method consists of a small systematic conformational analysis, in which the conformational space is studied by rotation of the important free rotation in pairs, described as Pairs of Dihedral Angles-Systematic Analysis – PDA-SA. The main objective is to reduce the dimension of the investigated system. The idea is to address the conformational space in small portions, evaluating PES in combinations of angles in pairs. If the problem of combinatorial explosion is controlled, the conformational space can be sufficiently refined in the regions of minimum energy, taking care to minimize the information lost. The energy surfaces are obtained for each pair of angles and the number of conformations is given by Equation 5:

$$\text{Number of configurations} = \text{s}^2 \frac{\text{N(N-1)}}{2} \tag{5}$$

where s and N have the same meaning as in Equation 1. The number of conformations, in this case, is given by the combinatory arrangement of the N dihedrals in pairs.

The main observation of the comparison between equations (1) and (5) is that the number of conformations as given by Eq. (1) increases exponentially with the number of bonds with free rotation, while from Eq. (5), the number of studied conformations increases quadratically with *N*. As the number of free rotation angles increases, the difference in the number of conformers generated by these two equations becomes more evident.

The computational procedure for PDA-SA can be organized in five basic steps:

1. **Molecular Building:** The interest molecule must be defined in terms of its internal coordinates: bond length, angle bond and dihedral angles. There are many softwares able to define this molecular initial structure. A quantum chemistry optimization is required at this step in order to adjust internal parameters. The best method must be chosen according to the system under study.

In chemistry, PCA was introduced by Malinowski around 1960 under the name Principal Factor Analysis, and further developed after 1970.(Malinowski, 2003) Principal Component Analysis can be used for crystallographic structure data; in its general form, conformational analysis is applied to multivariate numerical problems. (Allen et al., 2010) Many studies report on the use of PCA for handling Molecular Dynamics data. Among them, we highlight the application that uses PCA for mapping potential energy surfaces, by the quantitative visualization of a macromolecular energy funnel. (Becker, 1998) Other examples where PCA can be applied in molecular structure determination can also be found in recent studies. (Das et al., 2011; Araujo-

There is a variety of theoretical methods that are capable of locating minimum energy structures in the potential energy surface. The problem of stochastic methods is that there is no natural end point for the conformational search. In some cases, only a small subset of conformational space is explored and the convergence of the system is not guaranteed. Only Systematic Conformational Analysis maps the conformational space completely. We stress the principal difficulty inherent in this method is the combinatorial explosion. In a previous study (Bruni et al., 2002), a new methodology was introduced for controlling the combinatorial explosion through a systematic reduction in the size of the system by means

This method consists of a small systematic conformational analysis, in which the conformational space is studied by rotation of the important free rotation in pairs, described as Pairs of Dihedral Angles-Systematic Analysis – PDA-SA. The main objective is to reduce the dimension of the investigated system. The idea is to address the conformational space in small portions, evaluating PES in combinations of angles in pairs. If the problem of combinatorial explosion is controlled, the conformational space can be sufficiently refined in the regions of minimum energy, taking care to minimize the information lost. The energy surfaces are obtained for each pair of angles and the number of conformations is given by Equation 5:

<sup>2</sup> N(N-1) Number of conformations = s

where s and N have the same meaning as in Equation 1. The number of conformations, in

The main observation of the comparison between equations (1) and (5) is that the number of conformations as given by Eq. (1) increases exponentially with the number of bonds with free rotation, while from Eq. (5), the number of studied conformations increases quadratically with *N*. As the number of free rotation angles increases, the difference in the

1. **Molecular Building:** The interest molecule must be defined in terms of its internal coordinates: bond length, angle bond and dihedral angles. There are many softwares able to define this molecular initial structure. A quantum chemistry optimization is required at this step in order to adjust internal parameters. The best method must be

this case, is given by the combinatory arrangement of the N dihedrals in pairs.

number of conformers generated by these two equations becomes more evident. The computational procedure for PDA-SA can be organized in five basic steps:

chosen according to the system under study.

2 (5)

Andrade et al., 2010; Kiralj et al. 2007; Oblinsky et al., 2009; Silva et al., 2011)

**6. Pairs of dihedral angles-systematic analysis** 

of chemometrics.


In the study that introduced this method, the approach was successfully tested in the analysis of omeprazole and its derivatives, in which the results were in agreement with the experimental ones.(Bruni et al., 2002)

In a second study, the technique was used to find minimum energy conformations of omeprazole derivative molecules in a QSAR study. (Bruni & Ferreira, 2002) It was shown that conformational analysis is crucial when establishing SAR/QSAR models using theoretically calculated descriptors, and they are strongly dependent on the details of molecular structure. Though all minima conformation have similar energetic values, some calculated properties are very sensitive to the structural variation, which is understandable since electronic properties are intrinsically dependent on molecular conformation.(Bruni & Ferreira, 2002)

Omeprazole's racemization barrier and decomposition reaction was also studied. Quantum chemistry coupled to PDA-SA chemometric method was used to find all omeprazole minimum energy structures. To obtain the racemization barriers it was essential that the starting structure was in a global energy minimum. In that work, for all the studied structures, there was no change in the values of the racemization barriers, which confirmed the identification of the most stable structures for omeprazole.(Bruni & Ferreira, 2008)

Quantum Chemistry and Chemometrics Applied to Conformational Analysis 117

Three PES were obtained for a 30° dihedral increment and are showed in Figures 9 and 10. Figure 9 shows the original energy values and Figure 10 shows the same surfaces, but with a 0,12 hartrees cut off for better visualization. PCA was performed on autoscaled original data and the results are shown in Figure 11. 64% of the whole information is cumulated in first and second Factors (or Principal Components-PCs). The convergence of the points for one region is observed. Figure 12 shows the PCA results for the leveled data in 0,12 hartrees.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

> Ângulos 1 e 3

> > Ângulo 3

Ângulo 2

Energia

Ângulo 1

Fig. 9. Orignal PES obtained from PDA-SA method for structure from Fig. 8.

Ângulos 1 e 2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

Energia

Fig. 8. Basic structure for omeprazole and derivatives.

0.1 0.2 0.3 0.4 0.5 0.6

> Ângulos 2 e 3

Energia

Factor 1 and Factor 2 now cumulate 73% of the entire information.


Fig. 7. Matrix scheme for N angles: the discrete energy values for each rotation angle must be evaluated. *Eij* are the energy matrices with elements *Eijkm*, in which *k* and *m* are the angle increment indices for the angles *i* and *j*, respectively.

This approach is straightforward and in principle would have no size limits for its application. However, it presents limitation due to some initial condition dependence. Given a system with *N* degrees of freedom, for each pair of angles there are *N-2* parameters that can interfere in the method. For example, in Figure 4 the potential energy surface for first and last dihedral angle combinations depends on the dihedral angles conformation between them. When the dihedral angles are too far from each other along the chain of atoms, the method may not become feasible. In this case the method may need to be repeated with different initial conditions to improve the sampling of the configurational phase space, and moreover we cannot be sure that we have reached the global minimum. When the correlations between the pairs of angles do not depend strongly on these initial conditions the method is very useful. Such system corresponds to small molecules, not so flexible, in which there are few large potential basins, such as omeprazol and its derivatives.(Bruni et al., 2002; Bruni & Ferreira, 2002; Bruni & Ferreira, 2008)

The limit of validity for this method is under investigation. We are applying this method to study the IAN peptide, which is a tetrapeptide isobutyryl-(ala)3-NH-methyl. (Nascimento et al., 2009) This is the smallest polypeptide that can have secondary-like structure (an helix) (Becker & Karplus, 1997) and it has 11 free rotation bonds. For a flexible system, such as this, the initial condition dependence in the calculation of the minimum energy conformations is expected to increase with the size of the system. Since the system is more flexible and expected to be more rugged, we partially overcome this problem by using small angle increments steps, in order to probe all local minima of the system and compare them.

## **7. Numerical results**

#### **7.1 Study of basic structure for omeprazole and derivatives**

Initially, the basic structure of omeprazole and derivatives was evaluated. This structure has three bonds with free rotation. To validate the proposed methodology, two different approaches were performed. In the first approach, pairs of angles were taken account ((1,2), (1,3) e (2,3) in Fig. 8) and the number of conformations is given according to Equation 5. The resulting matrix analyzed was composed by the energy values from the potential energy surface for each angle combination (see matrix example in Figure 7). A matrix with discrete energy values for the basic structures with 30° angle increment in Equation 2 is showed in Appendix A.

Fig. 8. Basic structure for omeprazole and derivatives.

Fig. 7. Matrix scheme for N angles: the discrete energy values for each rotation angle must be evaluated. *Eij* are the energy matrices with elements *Eijkm*, in which *k* and *m* are the angle

This approach is straightforward and in principle would have no size limits for its application. However, it presents limitation due to some initial condition dependence. Given a system with *N* degrees of freedom, for each pair of angles there are *N-2* parameters that can interfere in the method. For example, in Figure 4 the potential energy surface for first and last dihedral angle combinations depends on the dihedral angles conformation between them. When the dihedral angles are too far from each other along the chain of atoms, the method may not become feasible. In this case the method may need to be repeated with different initial conditions to improve the sampling of the configurational phase space, and moreover we cannot be sure that we have reached the global minimum. When the correlations between the pairs of angles do not depend strongly on these initial conditions the method is very useful. Such system corresponds to small molecules, not so flexible, in which there are few large potential basins, such as omeprazol and its

The limit of validity for this method is under investigation. We are applying this method to study the IAN peptide, which is a tetrapeptide isobutyryl-(ala)3-NH-methyl. (Nascimento et al., 2009) This is the smallest polypeptide that can have secondary-like structure (an helix) (Becker & Karplus, 1997) and it has 11 free rotation bonds. For a flexible system, such as this, the initial condition dependence in the calculation of the minimum energy conformations is expected to increase with the size of the system. Since the system is more flexible and expected to be more rugged, we partially overcome this problem by using small angle increments steps, in order to probe all local minima of the system and compare them.

Initially, the basic structure of omeprazole and derivatives was evaluated. This structure has three bonds with free rotation. To validate the proposed methodology, two different approaches were performed. In the first approach, pairs of angles were taken account ((1,2), (1,3) e (2,3) in Fig. 8) and the number of conformations is given according to Equation 5. The resulting matrix analyzed was composed by the energy values from the potential energy surface for each angle combination (see matrix example in Figure 7). A matrix with discrete energy values for the basic structures with 30° angle increment in Equation 2 is showed in

derivatives.(Bruni et al., 2002; Bruni & Ferreira, 2002; Bruni & Ferreira, 2008)

**7.1 Study of basic structure for omeprazole and derivatives** 

increment indices for the angles *i* and *j*, respectively.

**7. Numerical results** 

Appendix A.

Three PES were obtained for a 30° dihedral increment and are showed in Figures 9 and 10. Figure 9 shows the original energy values and Figure 10 shows the same surfaces, but with a 0,12 hartrees cut off for better visualization. PCA was performed on autoscaled original data and the results are shown in Figure 11. 64% of the whole information is cumulated in first and second Factors (or Principal Components-PCs). The convergence of the points for one region is observed. Figure 12 shows the PCA results for the leveled data in 0,12 hartrees. Factor 1 and Factor 2 now cumulate 73% of the entire information.

Fig. 9. Orignal PES obtained from PDA-SA method for structure from Fig. 8.

Quantum Chemistry and Chemometrics Applied to Conformational Analysis 119

Angle 1 Angle 2 Angle 3

Fig. 11. PCA for data from original PES (Fig.9).

(third column) resulting in the fourth column.

Fig. 12. Principal Component Analysis forPES from Fig. 10, with a 0,12 cutoff.

Factor 1 accounts to the minimum region in each case and Factor 2 accounts for the energy range for the different combinations. Table 1 shows the selected minimum energy for each angle. The first column shows that two different regions were chosen for Angle 1 and only one region for Angles 2 and 3. Second column shows the rotation over the initial angle value

Fig. 10. PES obtained from PDA-SA method for structure from Fig. 8, with a 0,12 hartress cutoff.

Ângulos 2 e 3

Ângulo 1

Ângulos 1 e 3

Ângulos 1 e 2

 0.1172 -- 0.1200 0.1145 -- 0.1172 0.1117 -- 0.1145 0.1090 -- 0.1117 0.1062 -- 0.1090 0.1035 -- 0.1062 0.1007 -- 0.1035 0.0980 -- 0.1007

 0.1172 -- 0.1200 0.1145 -- 0.1172 0.1117 -- 0.1145 0.1090 -- 0.1117 0.1062 -- 0.1090 0.1035 -- 0.1062 0.1007 -- 0.1035 0.0980 -- 0.1007

 0.1172 -- 0.1200 0.1145 -- 0.1172 0.1117 -- 0.1145 0.1090 -- 0.1117 0.1062 -- 0.1090 0.1035 -- 0.1062 0.1007 -- 0.1035 0.0980 -- 0.1007

Ângulos 2 e 3

Ângulo 2

Ângulo 2

 Fig. 10. PES obtained from PDA-SA method for structure from Fig. 8, with a 0,12 hartress

Ângulo 3

Ângulo 3

cutoff.

0.10

0.11

Energia

0.12

0.10

0.10

0.11

Energia

0.12

Ângulo 1

Ângulos 1 e 3

Ângulos 1 e 2

0.11

Energia

0.12

Fig. 11. PCA for data from original PES (Fig.9).

Fig. 12. Principal Component Analysis forPES from Fig. 10, with a 0,12 cutoff.

Factor 1 accounts to the minimum region in each case and Factor 2 accounts for the energy range for the different combinations. Table 1 shows the selected minimum energy for each angle. The first column shows that two different regions were chosen for Angle 1 and only one region for Angles 2 and 3. Second column shows the rotation over the initial angle value (third column) resulting in the fourth column.

Quantum Chemistry and Chemometrics Applied to Conformational Analysis 121

Angle Rotation Initial Value Value obtained by PCA

Conformation Angle Obtained value Hf (PM3)/kcal mol-1 Ee(6-31G\*\*)/hartree

A 2 107.10 54.96 -1134.33

B 2 175.70 54.71 -1134.35

1 (a) 45 48,48 - 108,48 93,48 1 (b) 45 228,48 - 288,48 273,48 2 45 209,79 - 269,79 254,79 3 35 259,09 - 319,09 294,09

Table 2. Regions obtained through PCA

1 92.29

 3 298.32 1 266.45

3 296.45

**7.2 IAN preliminary studies** 

Table 3. Minimum conformation characteristics (basic structure)

Fig. 14. Optimized superposed conformations for structure from Fig. 8.

In the second approach, the conformational analysis was made according to Equation 1 and took into account all possible conformations. PCA was performed on data matrix and minimum energy regions were selected. The next step a lower dihedral increment of 5° was used to refine those selected regions. PCA was performed again, and the same structures and energy, shown in Table 3, were obtained. This indicates that the two approaches are equivalent. The details of this complete systematic search can be found in (Bruni et al., 2002).

IAN (isobutyryl-Ala3-NH-methyl) tetrapeptide has also been studied to validate PDA-SA methodology. IAN has 11 consecutives dihedrals and its main characteristic is to be the shorter peptide able to make a complete helix turn. Figure 15 shows the IAN 2D structure


Table 1. Regions separated by PCA

Once minima energy regions were defined, a small angle increment (5°) was used on them. Results for PCA are in Figure 13. In all cases a parabolic behavior was observed. When data variation decreases, curves are more easily observed and the minimum point is detectable. The amount of information accounted for both first and second PC´s (Factors) is around 90%. Table 2 shows the final values for each angle. When these values are combined, two different geometries were obtained with similar energy values (Table 3). These conformations are shown in Figure 14.

Fig. 13. PCA results for 5° angle increment refinement.


Table 2. Regions obtained through PCA

Angle Rotation Initial Value Value obtained by PCA 1 (a) 0 - 60 48,48 48,48 - 108,48 1 (b) 180 - 240 48,48 228,48 - 288,48 2 0 - 60 209,79 209,79 - 269,79 3 330 - 30 289,09 259,09 - 319,09

Once minima energy regions were defined, a small angle increment (5°) was used on them. Results for PCA are in Figure 13. In all cases a parabolic behavior was observed. When data variation decreases, curves are more easily observed and the minimum point is detectable. The amount of information accounted for both first and second PC´s (Factors) is around 90%. Table 2 shows the final values for each angle. When these values are combined, two different geometries were obtained with similar energy values (Table 3). These

Angle 1(a)

Angle 3 Angle 2

Angle 1(b)

Fig. 13. PCA results for 5° angle increment refinement.

Table 1. Regions separated by PCA

conformations are shown in Figure 14.


Table 3. Minimum conformation characteristics (basic structure)

Fig. 14. Optimized superposed conformations for structure from Fig. 8.

In the second approach, the conformational analysis was made according to Equation 1 and took into account all possible conformations. PCA was performed on data matrix and minimum energy regions were selected. The next step a lower dihedral increment of 5° was used to refine those selected regions. PCA was performed again, and the same structures and energy, shown in Table 3, were obtained. This indicates that the two approaches are equivalent. The details of this complete systematic search can be found in (Bruni et al., 2002).

#### **7.2 IAN preliminary studies**

IAN (isobutyryl-Ala3-NH-methyl) tetrapeptide has also been studied to validate PDA-SA methodology. IAN has 11 consecutives dihedrals and its main characteristic is to be the shorter peptide able to make a complete helix turn. Figure 15 shows the IAN 2D structure

Quantum Chemistry and Chemometrics Applied to Conformational Analysis 123

Angle 1 Angle 2 Angle 3 Angle 4 Angle 5 Angle 6 Angle 7 Angle 8 Angle 9 Angle 10 Angle 11

Table 5 shows the obtained energy values for the final structures and they indicate that some correspond to identical conformations. Three different groups were identified. Figure 17 shows the group that corresponds to structures 1, 5, 6, 9 and 10 superposed (blue ones in Table 5). Structure 9 shows a slightly different value on 0 but it does not change the energy value. These five structures have two stabilizing hydrogen bonds which are indicated by the

Number Energy <sup>0</sup> <sup>0</sup> <sup>0</sup> <sup>1</sup> <sup>1</sup> <sup>1</sup> <sup>2</sup> <sup>2</sup> <sup>2</sup> <sup>3</sup> <sup>3</sup> 1 - 181.498 70.50 176.87 85.57 66.93 -177.14 -85.01 67.39 179.60 -112.24 -46.78 177.92 2 - 180.70 -61.83 -172.66 -78.26 25.05 157.24 -90.68 -29.19 177.15 -110.70 -45.10 178.62 3 - 179.661 79.45 -168.99 -64.80 -44.71 171.76 -84.61 44.32 179.26 143.99 -59.33 178.07 4 -179.276 72.93 -174.15 -104.24 -32.54 -179.9 -82.66 70.38 -179.69 -115.57 -51.50 179.42 5 -181.498 70.49 -176.89 -85.56 66.89 -177.17 -84.96 67.52 179.62 -112.34 -46.80 177.93 6 -181.498 70.49 -176.88 -85.57 66.93 -177.15 -85.01 67.40 179.61 -112.26 -46.78 177.92 7 -179.276 72.93 -174.15 -104.24 -32.52 -179.9 -82.65 70.39 -179.69 -115.58 -51.50 179.44 8 -179.276 72.94 -174.14 -104.27 -32.45 -179.89 -82.66 70.40 -179.67 -115.55 -51.48 179.36 9 -182.385 -62.43 -177.31 -84.72 67.46 -177.22 -84.95 67.38 179.58 -112.28 -46.85 177.94 10 -181.498 70.49 -176.89 -85.56 66.93 -177.15 -85.00 67.43 179.62 -112.32 -46.82 177.91 Table 5. Energy (kcal mol-1) and dihedrals values (degrees) for each obtained IAN structure.

red circle and the resulting conformations for them resemble a beta-sheet.

Fig. 16. PCA results for IAN peptide.

(Becker, 1998). Red arrows indicate the ψ, Φ e ω dihedrals. The dihedral angles ψ, ω and Φ are related to the rotations of single bonds between atoms in the main chain C (i)-C, OC-NH and N-C(i+1), respectively, where C (i) is the ith alpha carbon of the polypeptide chain. Angles ψ and Φ are connected to two arrays of functional protein chain: alpha-helix or beta-sheet.

Fig. 15. 2D IAN peptide structure.

Ten random different starting conformations were studied. Table 4 shows the angles and energy values corresponding to these initial conformations. The red values indicate dihedrals that were changed in comparison to initial conformation number 1. The starting conformation 2 is close to an alpha-helix. Energy values correspond to single point AM1 semi-empirical calculation, in kcal mol-1.


Table 4. Energy(kcal mol-1) and dihedrals values (degrees) for each starting IAN structure.

IAN was analyzed using the PDA-SA procedure. The eleven dihedral angles provide 55 different conformations according to all possible combinations. Conformational analysis was performed with a 20° increment. PCA was carried out and Figure 16 shows that all points converge to specific regions of the phase space. Each selected region for each angle was refined with a 5° angle increment. PCA was performed again and the final structures characteristics are shown in Table 5.

Fig. 16. PCA results for IAN peptide.

(Becker, 1998). Red arrows indicate the ψ, Φ e ω dihedrals. The dihedral angles ψ, ω and Φ are related to the rotations of single bonds between atoms in the main chain C (i)-C, OC-NH and N-C(i+1), respectively, where C (i) is the ith alpha carbon of the polypeptide chain. Angles ψ and Φ are connected to two arrays of functional protein chain: alpha-helix or beta-sheet.

Ten random different starting conformations were studied. Table 4 shows the angles and energy values corresponding to these initial conformations. The red values indicate dihedrals that were changed in comparison to initial conformation number 1. The starting conformation 2 is close to an alpha-helix. Energy values correspond to single point AM1

Number Energy <sup>0</sup> <sup>0</sup> <sup>0</sup> <sup>1</sup> <sup>1</sup> <sup>1</sup> <sup>2</sup> <sup>2</sup> <sup>2</sup> <sup>3</sup> <sup>3</sup> 1 -179.66 79.45 -169.01 -64.73 -44.75 171.78 -84.62 44.47 179.30 -144.22 -59.37 178.07 2 -122.24 **-60.55 179.00** -64.73 **-64.75 -180.00 -64.62 -65.55 180.00 -64.22** -59.37 178.07 3 -156.02 79.45 **170.99** -64.73 **-34.75** 171.78 -84.62 **74.47** 179.30 **-124.22** -59.37 178.07 4 195.46 79.45 -169.01 **-14.73** -44.75 171.78 **-134.62** 44.47 179.30 -144.22 **-39.37** 178.07 5 -80.48 **49.45** -169.01 -64.73 -44.75 **151.78** -84.62 44.47 179.30 -144.22 **-39.37** 178.07 6 -169.24 79.45 **-149.01** -64.73 -44.75 171.78 -84.62 44.47 **159.30** -144.22 **-79.37** 178.07 7 -149.11 **59.45** -169.01 **-84.73** -44.75 **-168.22** -84.62 **74.47** 179.30 -144.22 -59.37 178.07 8 -147.67 79.45 -169.01 -64.73 **-24.75** 171.78 **-104.62** 44.47 **-160.70** -144.22 **-39.37** 178.07 9 -29.05 **109.45** -169.01 -64.73 -44.75 171.78 -84.62 **24.47** 179.30 **-174.22** -59.37 178.07 10 -167.76 79.45 -169.01 **-44.73** -44.75 **-178.22** -84.62 44.47 179.30 -144.22 -59.37 178.07

Table 4. Energy(kcal mol-1) and dihedrals values (degrees) for each starting IAN structure.

IAN was analyzed using the PDA-SA procedure. The eleven dihedral angles provide 55 different conformations according to all possible combinations. Conformational analysis was performed with a 20° increment. PCA was carried out and Figure 16 shows that all points converge to specific regions of the phase space. Each selected region for each angle was refined with a 5° angle increment. PCA was performed again and the final structures

Fig. 15. 2D IAN peptide structure.

semi-empirical calculation, in kcal mol-1.

characteristics are shown in Table 5.

Table 5 shows the obtained energy values for the final structures and they indicate that some correspond to identical conformations. Three different groups were identified. Figure 17 shows the group that corresponds to structures 1, 5, 6, 9 and 10 superposed (blue ones in Table 5). Structure 9 shows a slightly different value on 0 but it does not change the energy value. These five structures have two stabilizing hydrogen bonds which are indicated by the red circle and the resulting conformations for them resemble a beta-sheet.


Table 5. Energy (kcal mol-1) and dihedrals values (degrees) for each obtained IAN structure.

Quantum Chemistry and Chemometrics Applied to Conformational Analysis 125

Fig. 19. Superposed final conformations for structures 2 and 3 (black ones in Table 5).

investigated. A gradual increase in the size of the chain is also been explored.

**8. Conclusion** 

methods provides the optimum solution.

**9. Acknowledgment** 

practical use in the study of more complex molecules.

Desempenho em São Paulo (CENAPAD-SP), Brazil.

Results presented for IAN peptide are partial and were only performed for one minimum region for each starting structure. Other minimum energy regions of this system are being

The arrangement of atoms in a molecule or its structure determination has intrigued scientists through history. However only with recent experimental and computational advances the discussions on this theme became more effective and elucidative. The nature of PES is intrinsically multidimensional, usually has a very complex landscape. The global minima search, like the one encountered in the protein folding problem, is a NP-hard problem. This means that this task belongs to a large set of computational problems, assumed to be very hard ("conditionally intractable") (Fraenkel, 1993). The search for its relevant minima in molecular modeling has motivated the development of methods with very specific applications, as discussed in this chapter. For each particular problem one finds a variety of methods that allows feasible solutions, and most likely a combination of

In this chapter, we discussed some aspects of conformational search that controls the combinatorial explosion. In particular, Principal Component Analysis was associated with a systematic search method to find structures with low energy in PES. The methodology can be useful to handle small- and medium-size molecules. The maximum size which the method can efficiently handle is being investigated (Nascimento et al., 2009). Due to the PCA dimension reduction, the method's efficiency is highly increased, allowing it to be of

We thank Prof. Márcia M.C. Ferreira (Unicamp) for the helpful discussions. We were supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. Computational resources were provided by Centro Nacional de Processamento e Alto

Fig. 17. Superposed final conformations for 1, 5, 6, 9 and 10 structures (blue ones in Table 5).

The second group is composed by final conformations 4, 7 and 8 (green ones in Table 5). The superposed conformations can be observed in Figure 18. These conformations are more open and have only one hydrogen-bond (red circle in Fig.18). The last group, the black ones in Table 5, are superposed in Figure 19. The resulting structures show an alpha-helix like behavior, with two stabilizing hydrogen bond (red circles, Fig. 19).

Fig. 19. Superposed final conformations for structures 2 and 3 (black ones in Table 5).

Results presented for IAN peptide are partial and were only performed for one minimum region for each starting structure. Other minimum energy regions of this system are being investigated. A gradual increase in the size of the chain is also been explored.

## **8. Conclusion**

124 Quantum Chemistry – Molecules for Innovations

Fig. 17. Superposed final conformations for 1, 5, 6, 9 and 10 structures (blue ones in

Fig. 18. Superposed final conformations for 4,7and 8 structures (green ones in Table 5).

behavior, with two stabilizing hydrogen bond (red circles, Fig. 19).

The second group is composed by final conformations 4, 7 and 8 (green ones in Table 5). The superposed conformations can be observed in Figure 18. These conformations are more open and have only one hydrogen-bond (red circle in Fig.18). The last group, the black ones in Table 5, are superposed in Figure 19. The resulting structures show an alpha-helix like

Table 5).

The arrangement of atoms in a molecule or its structure determination has intrigued scientists through history. However only with recent experimental and computational advances the discussions on this theme became more effective and elucidative. The nature of PES is intrinsically multidimensional, usually has a very complex landscape. The global minima search, like the one encountered in the protein folding problem, is a NP-hard problem. This means that this task belongs to a large set of computational problems, assumed to be very hard ("conditionally intractable") (Fraenkel, 1993). The search for its relevant minima in molecular modeling has motivated the development of methods with very specific applications, as discussed in this chapter. For each particular problem one finds a variety of methods that allows feasible solutions, and most likely a combination of methods provides the optimum solution.

In this chapter, we discussed some aspects of conformational search that controls the combinatorial explosion. In particular, Principal Component Analysis was associated with a systematic search method to find structures with low energy in PES. The methodology can be useful to handle small- and medium-size molecules. The maximum size which the method can efficiently handle is being investigated (Nascimento et al., 2009). Due to the PCA dimension reduction, the method's efficiency is highly increased, allowing it to be of practical use in the study of more complex molecules.

#### **9. Acknowledgment**

We thank Prof. Márcia M.C. Ferreira (Unicamp) for the helpful discussions. We were supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. Computational resources were provided by Centro Nacional de Processamento e Alto Desempenho em São Paulo (CENAPAD-SP), Brazil.

Quantum Chemistry and Chemometrics Applied to Conformational Analysis 127

Allen, F. H., Galek, P. T. a, & Wood, P. a. (2010). Energy matters! *Crystallography Reviews*,

Araujo-Andrade, C., Lopes, S., Fausto, R., & Gómez-Zavaglia, A. (2010). Conformational

Becker, Oren M., & Karplus, M. (1997). The topology of multidimensional potential energy

Beckers, M. L. M., Derks, E. P. P. A., Melssen, W. J., & Buydens, L. M. C. (1996). Pergamon

Beckers, M. L., Buydens, L. M., Pikkemaat, J. a, & Altona, C. (1997). Application of a genetic

Beebe, K. R. (1998). *Chemometrics: A Practical Guide* (p. 360). Wiley-Blackwell. Retrieved from http://www.amazon.co.uk/Chemometrics-Practical-Wiley-Interscience-

Automation/dp/0471124516/ref=sr\_1\_1?ie=UTF8&qid=1320084260&sr=8-1 Beusen, D. D., Shands, E. F. B., Karasek, S. F., Marshall, G. R., & Dammkoehler, R. A. (1996).

Biarnés, X., Bongarzone, S., Vargiu, A. V., Carloni, P., & Ruggerone, P. (2011). Molecular

Bruni, A. T., Leite, V. B. P., & Ferreira, M. M. C. (2002). Conformational analysis: A new

Bruni, A. T., & Ferreira, M. M. C. (2008). Theoretical study of omeprazole behavior:

Bruni, A. T., & Ferreira, M. M. C. (2002). Omeprazole and analogue compounds: a QSAR

Brush, S. G. (1999). Dynamics of Theory Change in Chemistry : Part 1 . The Benzene Problem

*Chemistry*, *108*(6), 1097-1106. doi:10.1002/qua.21597

*Chemometrics*, *16*(8-10), 510-520. doi:10.1002/cem.737

Systematic search in conformational analysis. *Theochem-Journal of Molecular Structure*, *370*(2-3), 157-171. Po Box 211, 1000 Ae Amsterdam, Netherlands: Elsevier

motions in drug design: the coming age of the metadynamics method. *Journal of computer-aided molecular design*, *25*(5), 395-402. doi:10.1007/s10822-011-9415-3 Brodmeier, T., & Pretsch, E. (1994). Application of genetic algorithms in molecular

modeling. *Journal of Computational Chemistry*, *15*(6), 588-595.

approach by means of chemometrics. *Journal Of Computational Chemistry*, *23*(2), 222- 236. Commerce Place, 350 Main St, Malden 02148, MA USA: Wiley-Blackwell.

Racemization barrier and decomposition reaction. *International Journal of Quantum* 

study of activity againstHelicobacter pylori using theoretical descriptors. *Journal of* 

study of arbutin by quantum chemical calculations and multivariate analysis. *Journal of Molecular Structure*, *975*(1-3), 100-109. doi:10.1016/j.molstruc.2010.04.002 Becker, O M. (1998). Principal coordinate maps of molecular potential energy surfaces.

*Journal of Computational Chemistry*, *19*(11), 1255-1267. 605 Third Ave, New York, NY 10158-0012 Usa: John Wiley & Sons Inc. doi:10.1002/(SICI)1096-

surfaces: Theory and application to peptide structure and kinetics. *The Journal of* 

algorithm in the conformational analysis of methylene-acetal-linked thymine dimers in DNA: comparison with distance geometry calculations. *Journal of* 

*16*(3), 169-195. doi:10.1080/08893110903476919

987X(199808)19:11<1255::AID-JCC5>3.3.CO;2-H

*Chemical Physics*, *106*(4), 1495. doi:10.1063/1.473299

oo!n-8485(%~6-0. *Science*, *20*(4), 449-457.

*biomolecular NMR*, *9*(1), 25-34. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/9081542

**11. References** 

Laboratory-

Science Bv.

doi:10.1002/jcc.540150604

doi:10.1002/jcc.10004

1865 – 1945. *Science*, *30*(1), 21-79.

### **10. Apendix A**

Matrix with the discrete values for each rotation angle and its corresponding energy value for the first rotation for basic structure in Figure 8. Labels in bold were not used in PCA analysis, they are shown to help the matrix notation and visualization.


#### **11. References**

126 Quantum Chemistry – Molecules for Innovations

Matrix with the discrete values for each rotation angle and its corresponding energy value for the first rotation for basic structure in Figure 8. Labels in bold were not used in PCA

analysis, they are shown to help the matrix notation and visualization.

**10. Apendix A** 


Automation/dp/0471124516/ref=sr\_1\_1?ie=UTF8&qid=1320084260&sr=8-1


Quantum Chemistry and Chemometrics Applied to Conformational Analysis 129

Hunger, J., & Huttner, G. (1999). Optimization and analysis of force field parameters by

Izgorodina, E. I., Lin, C. Y., & Coote, M. L. (2007). Energy-directed tree search: an efficient

Jorgensen, W. L., & TiradoRives, J. (1996). Monte Carlo vs molecular dynamics for

Leach, A. (2001). *Molecular Modelling: Principles and Applications (2nd Edition)*. Prentice Hall.

Leach, A. R., & Smellie, A. S. (1992). A combined model-building and distance-geometry

Lucasius, C. (1993). Understanding and using genetic algorithms Part 1. Concepts,

Malinowski, E. R. (2003). *Factor Analysis in Chemistry*. *Technometrics* (Vol. 45, pp. 180-181).

Li Manni, G., Barone, G., Duca, D., & Murzin, D. Y. (2009). Systematic conformational search

Massart, D. L., Heyden, Y. V., & Brussel, V. U. (2004). What Can Chemometrics Do for

Mo, Y., & Gao, J. (2007). Theoretical analysis of the rotational barrier of ethane. *Accounts of* 

Nair, N., & Goodman, J. M. (1998). Genetic Algorithms in Conformational Analysis. *Journal of Chemical Information and Modeling*, *38*(2), 317-320. doi:10.1021/ci970433u Nascimento, R. R., Bruni, A. T. , & Leite, V. B. P. (2009). Estudo conformacional do peptídeo

http://www.athena.biblioteca.unesp.br/exlibris/bd/brp/33004153068P9/2009/na

*Information and Modeling*, *32*(4), 379-385. doi:10.1021/ci00008a019

*Organic Chemistry*, (June 2009), n/a-n/a. doi:10.1002/poc.1595

*chemical research*, *40*(2), 113-9. doi:10.1021/ar068073w

Elsevier Science Bv. doi:10.1016/0169-7439(94)85038-0

combination of genetic algorithms and neural networks. *Journal of Computational Chemistry*, *20*(4), 455-471. doi:10.1002/(SICI)1096-987X(199903)20:4<455::AID-

systematic algorithm for finding the lowest energy conformation of molecules. *Physical chemistry chemical physics : PCCP*, *9*(20), 2507-16. doi:10.1039/b700938k Jordan, S. N., Leach, A. R., & Bradshaw, J. (1995). The Application of Neural Networks in

Conformational Analysis. 1. Prediction of Minimum and Maximum Interatomic Distances. *Journal of Chemical Information and Modeling*, *35*(3), 640-650.

conformational sampling. *Journal of Physical Chemistry*, *100*(34), 14508-14513. 1155 16th St, Nw, Washington, Dc 20036: Amer Chemical Soc. doi:10.1021/jp960880x Kiralj, R., Ferreira, M. C., Donate, P. M., & Silva, R. (2007). Combined Computational , Database Mining , NMR , and Chemometric Approaches. *Analysis*, 6316-6333. Lucasius, C. B., & Kateman, G. (1994). Understanding and Using Genetic Algorithms.2.

Representation, Configuration and Hybridization. *Chemometrics and Intelligent Laboratory Systems*, *25*(2), 99-145. Po Box 211, 1000 Ae Amsterdam, Netherlands:

Retrieved from http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-

approach to automated conformational analysis and search. *Journal of Chemical* 

properties and context. *Chemometrics and Intelligent Laboratory Systems*, *19*(1), 1-33.

analysis of the SRR and RRR epimers of 7-hydroxymatairesinol. *Journal of Physical* 

IAN e seus fragmentos pelo método de análise sistemática reduzida. *07/10/09*.

http://www.ncbi.nlm.nih.gov/pubmed/6656266

JCC6>3.0.CO;2-1

doi:10.1021/ci00025a035

20&path=ASIN/0582382106

doi:10.1016/0169-7439(93)80079-W

Wiley. doi:10.1198/tech.2003.s145

Separation Science ? *Europe*, *17*(9).

Retrieved November 1, 2011, from

scimento\_rr\_me\_sjrp\_parcial.pdf


Cintas, P. (2007). Tracing the origins and evolution of chirality and handedness in chemical

Das, G., Gentile, F., Coluccio, M. L., Perri, a M., Nicastri, a, Mecarini, F., Cojoc, G., et al.

Derks, E. P. P. A., & Buydens, L. M. C. (1996). E. P. P. A DERKS,\* M. L. M. BECKER& W. J.

Drayer, D. (1993). The Early History of Stereochemistry: From the Discovery of Molecular

Fraenkel, a S. (1993). Complexity of protein folding. *Bulletin of mathematical biology*, *55*(6),

http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3042729&tool=pmce

Gal, J. (2007). Review Article Carl Friedrich Naumann and the Introduction of Enantio

Gal, J. (2011). Review Article Louis Pasteur , Language , and Molecular Chirality . I .

Geladi, P. (2003). Chemometrics in spectroscopy. Part 1. Classical chemometrics.

Golub, G. H., & Loan, C. F. van V. (1996). *Matrix Computations (Johns Hopkins Studies in* 

Grouleff, J., & Jensen, F. (2011). Searching Peptide Conformational Space. *Journal of Chemical* 

Hanselman, D., Littlefield, B., Inc., M., & Mathworks. (1997). *The Student Edition of Matlab* 

Havel, T. F., Kuntz, I. D., & Crippen, G. M. (1983). The combinatorial distance geometry

Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/6197591

problem. *Journal of theoretical biology*, *104*(3), 359-81. Retrieved from

Terminology : A Review and Analysis on the 150th Anniversary. *Chirality*, *98*(May

Background and Dissymmetry. *Clinical Laboratory*, *16*(March 2010), 1-16.

*Spectrochimica Acta Part B Atomic Spectroscopy*, *58*(5), 767-782. doi:10.1016/S0584-

*Mathematical Sciences)(3rd Edition)* (p. 728). The Johns Hopkins University Press. Retrieved from http://www.amazon.com/Computations-Hopkins-Studies-

*Version 5 User's Guide* (p. 429). Prentice Hall College Div. Retrieved from http://www.amazon.com/Student-Matlab-Version-Users-Guide/dp/0132725509 Havel, T. F., Crippen, G. M., Kuntz, I. D., & Blaney, J. M. (1983). The combinatorial distance

geometry method for the calculation of molecular conformation. II. Sample problems and computational statistics. *Journal of theoretical biology*, *104*(3), 383-400.

method for the calculation of molecular conformation. I. A new approach to an old

doi:10.1002/anie.200603714

1199-210. Retrieved from

ntrez&rendertype=abstract

2006), 89-98. doi:10.1002/chir

Mathematical-Sciences/dp/0801854148

*Theory and Computation*, 1783-1790.

doi:10.1002/chir

8547(03)00037-5

doi:10.1016/j.molstruc.2010.12.044

MELSSEN and L. M. C. BUYDENS, *20*(4), 439-448.

al+Carbon+Of+Van+?+T+Hoff+And+Le+Bel+\*#0

language. *Angewandte Chemie (International ed. in English)*, *46*(22), 4016-24.

(2011). Principal component analysis based methodology to distinguish protein SERS spectra. *Journal of Molecular Structure*, *993*(1-3), 500-505. Elsevier B.V.

Asymmetry and the First Resolution of a Racemate by Pasteur to the Asymmetrical Chiral Carbon of van't Hoff and Le Bel. *Clinical Pharmacology-New York-Marcel Dekker Incorporated-*, *18*(3), 1–1. Marcel Dekker Ag. Retrieved from http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:The+Early+His tory+of+Stereochemistry+:+From+the+Discovery+of+Molecular+Asymmetry+and +the+First+Resolution+of+A+Racemate+By+Pasteur+To+The+Asymmetrical+Chir

http://www.ncbi.nlm.nih.gov/pubmed/6656266


 http://www.athena.biblioteca.unesp.br/exlibris/bd/brp/33004153068P9/2009/na scimento\_rr\_me\_sjrp\_parcial.pdf

**Part 3** 

**Molecules to Nanodevices** 

