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2007, 111, 5040-5042 Published on Web 04/13/2007
Tunable Delocalization of Unpaired Electrons of Nitroxide Radicals for Sickle-Cell Disease Drug Improvements Yun Hang Hu* and Eli Ruckenstein Department of Chemical and Biological Engineering, State UniVersity of New York at Buffalo, Buffalo, New York 14260 ReceiVed: February 22, 2007; In Final Form: April 2, 2007
Hydroxyurea is a drug recently approved to treat sickle cell diseases. Hydroxyurea benefits the patients by increasing the level of fetal hemoglobin via a nitroxide radical pathway. Here, we report an unpaired-electrondelocalization approach to tune the stability of nitroxide radicals. In this approach, the substitution by an unsaturated alkyl group containing conjugated CdC double bonds for the hydrogen on the nitrogen atom attached to the hydroxyl of hydroxyurea can significantly increase its ability to generate nitroxide radical. Furthermore, the increase can be remarkably enhanced by increasing the number of conjugated CdC double bonds. For a hydroxyurea derivative that contains two conjugated CdC double bonds, the reaction rate to generate its radical is 118 times faster than that of hydroxyurea, and for a hydroxyurea derivative containing 20 conjugated CdC double bonds, the reaction rate to form its radical is 238 times faster than that of hydroxyurea. For this reason, hydroxyurea derivatives with conjugated CdC double bonds may constitute new potential drugs for the treatment of sickle-cell diseases.
1. Introduction The use of hydroxyurea as an effective drug for sickle-cell disease, which is a genetic disease that most commonly affects African-Americans,1,2 represents the first specific therapy for this class of genetic diseases.3-5 The principal therapeutic effect of hydroxyurea in sickle-cell patients is believed to be an increase in the fraction of fetal hemoglobin3 via a nitroxide radical pathway.6 Therefore, the increase in the rate of generation of nitroxide radicals constitutes an effective approach to improve the efficiency of hydroxyurea.7-9 Recently, King and co-workers demonstrated experimentally that some derivatives of hydroxyurea can more rapidly generate nitroxide radicals than hydroxyurea.8 Furthermore, Rohrman and Mazziotti showed that the effectiveness of different hydroxyurea derivatives to generate nitroxide radicals depends on the relative stability of the nitroxide radical with respect to the molecule, quantified by the energy gap between the two.10 Therefore, the tuning of the stability of the nitroxide radicals constitutes an effective method to increase the efficiency of the hydroxyurea-based drugs. In this letter, we report a delocalization approach to tune the stability of the nitroxide radicals, which can significantly increase the reaction rate of hydroxyurea derivatives to their radicals. 2. Strategy to Tune Stability of Radicals One of the important characteristics of a radical is that it contains at least one unpaired electron, which is responsible for its instability.11,12 The generation of radicals depends on their stability relative to their original molecules. Our strategy is to * Corresponding author. Phone: 716-6452911, ext 2266. Fax: 7166453822. E-mail:
[email protected].
10.1021/jp071488u CCC: $37.00
increase the stability of a radical by delocalizing its unpaired electron(s) into a larger π orbital system. This delocalization can be achieved by substituting a linear carbon chain consisting of conjugated CdC double bonds for an atom connected to the functional group that contains the unpaired electron(s). More importantly, the delocalization can be tuned by the number of conjugated CdC double bonds. The stabilization energy of the unpaired electron depends on the size of the π orbital system in which it is delocalized. The larger the number of atoms involved in the π orbital system, the more stable the unpaired electron becomes. To examine the feasibility of this approach, density functional theory quantum chemistry calculations were carried out. 3. Calculation Details The density functional theory (DFT) is widely used because it accounts for the effect of electron correlation at an affordable computational cost.13 B3LYP, which is a combination of HF with a DFT based on Becke’s three-parameter exchange coupled with the Lee-Yang-Parr (LYP) correlation potential,13a is one of the most popular hybrid density functional theory methods. Furthermore, it was observed that the B3LYP and the highlevel coupled-cluster (CCSD) methods provide comparable results regarding the energy gap between hydroxyurea and its radical.10 For this reason, the hydroxyurea derivatives and their nitroxide radicals were examined by us with the B3LYP method using the 6-31G(d) basis set for both the geometry optimization and the energy evaluations. All calculations have been carried out using the Gaussian 03 program.14 4. Results and Discussion For comparison, we fully optimized the geometrical structure of hydroxyurea using the B3LYP/6-31G(d) method. The most © 2007 American Chemical Society
Letters
J. Phys. Chem. B, Vol. 111, No. 19, 2007 5041
TABLE 1: Unstable Energy and Relative Rate Constant of Nitroxide Radicals of Hydroxyurea Derivatives
molecule hydroxyurea H2N-CO-NH(OH) hydroxyurea derivatives 1. with saturated alkyl group H2N-CO-N(OH)-CH3 H2N-CO-N(OH)-CH2-CH3 H2N-CO-N(OH)-CH2-(CH2)2-CH3 H2N-CO-N(OH)-CH2-(CH2)6-CH3 2. with conjugated double bonds H2N-CO-N(OH)-CHdCH2 H2N-CO-N(OH)-CHdCHsCHdCH2 H2N-CO-N(OH)-(CHdCH)2-CHdCH2 H2N-CO-N(OH)-(CHdCH)4-CHdCH2 H2N-CO-N(OH)-(CHdCH)9-CHdCH2
unstable energya (kJ/mol)
R2/R1b
304.56
1
292.54 291.39 290.65 290.39
57 63 67 68
288.92 280.05 275.25 269.93 264.10
75 118 142 168 196
a Radical unstable energy calculated with eq 1 from the energies obtained through B3LYP/6-31G(d) calculations. b Calculated with eq 3.
stable structure, which is nonplanar, was obtained (see Supporting Information), consistent with the results of Remko et al.15 We also performed geometrical optimization for its corresponding nitroxide radical. Furthermore, we calculated the unstable energy (Eus) of a radical relative to its molecule using the following expression:
Eus ) Eradical + EH - Emolecule
(1)
where Emolecule, Eradical, and EH are the energies of the molecule, radical, and H atom, respectively. The unstable energy of the radical generated from the most stable hydroxyurea is 304.56 kJ/mol. First, B3LYP/6-31G(d) calculations were carried out for hydroxyurea derivatives generated by using saturated alkyl groups as substituents for the hydrogen on the nitrogen atom attached to the hydroxyl of hydroxyurea. From Table 1, one
can see that the unstable energies of the radicals are 292.54, 291.39, 290.65, and 290.39 kJ/mol for the derivatives containing -CH3, -CH2CH3, -CH2-(CH2)2-CH3, and -CH2-(CH2)6CH3 as substituents, respectively. Although the substitution of the methyl (CH3) group for the hydrogen decreases the unstable energy of the radical of hydroxyurea by 12 kJ/mol, the unstable energy is little decreased by increasing the number of carbons in the chain of saturated alkyl substituents. In contrast, when unsaturated polyene groups with conjugated CdC bonds were used as substituents for the hydrogen on nitrogen atom attached to the hydroxyl of the hydroxyurea, the unstable energies of the radicals of the resulted derivatives were significantly affected by the number of conjugated CdC double bonds. Table 1 shows that the unstable energy of hydroxyurea decreased from 304.56 to 288.92, 280.05, 275.25, 269.93, and 264.10 kJ/mol by using -CHdCH2, -CHdCH-CHdCH2, -(CHdCH)2-CHdCH2, -(CHdCH)4-CHdCH2, and -(CHdCH)9-CHdCH2 as substituents for the hydrogen atom, respectively. This indicates that the unstable energy decreases remarkably with an increasing number of conjugated CdC double bonds, which confirms the prediction of the delocalization principle that we suggested. The delocalization of an unpaired electron (originally located at oxygen) in a radical with conjugated CdC double bonds can also be demonstrated on the basis of the bond length and Wiberg bond order analysis. Indeed, the unpaired electron of oxygen partially forms a π bond with nitrogen, leading to a partial OdN double bond, and the partial OdN double bond is connected to the substituent via a N-C single bond, forming a conjugated OdN-CHdCH-......-CHdCH-CHdCH2 system, in which the bond lengths of all single bonds decrease and those of all double bonds increase (Figure 1). In other words, a mutual overlap of all π orbitals occurs, leading to a larger π orbital system in which the original unpaired electron of oxygen is delocalized over all atoms. The following correlation between the unstable energy (Eus) and the number (n) of conjugated CdC double bonds was obtained:
Figure 1. The Wiberg bond orders and the bond lengths (in parentheses) of H2N-CO-N(OH)-(CHdCH)4-CHdCH2: (a) neutral molecule and (b) nitroxide radical.
5042 J. Phys. Chem. B, Vol. 111, No. 19, 2007
Eus ) 287.97 - 10.801 ln(n)
Letters
(2)
where the units of Eus are kJ/mol. Using this equation, one can easily predict the unstable energy for any hydroxyurea derivative containing an unsaturated polyene group consisting of conjugated CdC double bonds. For example, when the number of conjugated CdC double bonds in the substitution group is 20, the unstable energy of the resulted derivative is 255.61 kJ/mol. To obtain a quantitative relationship between the reaction rate constant to form a nitroxide radical and the radical unstable energy, we calculated the unstable energies at the B3LYP/ 6-31G(d) level for other hydroxyurea derivatives (see the Supporting Information), for which experimental rate constants of their reactions with oxyhemoglobin to form radicals are available in the literature.8 Therefore, one can correlate the ratio of the rate constant (R2) of a hydroxyurea derivative to that (R1) of hydroxyurea, with the difference between the unstable energies of the derivative and of the hydroxyurea leading to the following expression:
R2 ) 4.8814(Eus1 - Eus2) - 1.2718 R1
(3)
where Eus1 and Eus2 are the unstable energies of the radicals of hydroxyurea and derivative, respectively. The correlation figure (Figure 5 in the Supporting Information) shows that only one experimental rate constant has a large deviation from the correlation line. From this equation, one can see that the reaction rate of a hydroxyurea derivative with oxyhemoglobin to form its nitroxide radical is very sensitive to the stability of the radical relative to the molecule. For a derivative with two conjugated CdC bonds, the unstable energy of its nitroxide radical is 24.51 kJ/mol lower than that of the radical of hydroxyurea. According to eq 3, the ratio of its rate constant to that of hydroxyurea is 118. Furthermore, when a derivative contains 20 conjugated CdC double bonds, its unstable energy of its nitroxide radical is 255.61 kJ/mol, which is 48.95 kJ/mol lower than that of the radical of hydroxyurea. Therefore, the ratio of its rate constant to that of the hydroxyurea is 238. Although one cannot expect these estimations of the rate constants to be very accurate, they can at least qualitatively indicate that the hydroxyurea derivatives with conjugated CdC double bonds can much more easily generate nitroxide radicals than hydroxyurea. However, it should be noted that the increase in the length of a conjugated chain can cause steric constraints, which may affect the formation and dissociation of nitroxide radicals. In summary, the substitution by an unsaturated alkyl group with conjugated CdC double bonds for the hydrogen on nitrogen atom attached to the hydroxyl of hydroxyurea can significantly increase its ability to generate nitroxide radicals. Furthermore, the increase can be remarkably enhanced by
increasing the number of conjugated CdC double bonds. For this reason, hydroxyurea derivatives with conjugated CdC double bonds constitute new potential drugs for the treatment of sickle-cell diseases. In addition, the delocalization of unpaired electrons in a changeable π orbital system may also provide an effective approach to tune the stabilities of other radicals. Supporting Information Available: (1) Structures of hydroxyurea, hydroxyurea derivatives, and their corresponding nitroxide radicals; (2) energetic data from DFT calculations; and (3) other relationships between energies and number of conjugated CdC bonds. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Luzzatto, L.; Goodfellow, P. Nature 1989, 337, 17. (2) Eaton, W. A.; Hofrichter, J. Science 1995, 268, 1142. (3) Charache, S.; Terrin, M. L.; Moore, R. D.; Dover, G. J.; Barton, F. B.; Eckert, S. V.; McMahon, R. P.; Bonds, D. R. N. Engl. J. Med. 1995, 332, 1317. (4) Platt, O. S.; Orkin, S. H.; Dover, G.; Beardsley, G. P.; Miller, B.; Nathan, D. G. J. Clin. InVest. 1984, 74, 652. (5) Bunn, H.F.; Forget, B.G. Hemoglobin; Molecular, Genetic, and Clinical Aspects; Saunders: Philadephia, 1986. (6) Cokic, V. P.; Smith, R. D.; Beleslin-Cokic, B. B.; Njoroge, J. M.; Miller, J. L.; Gladwin, M. T.; Schechter, A. N. J. Clin. InVest. 2003, 111, 231. (7) Rupon, J. W.; Domingo, S. R.; Smith, S. V.; Gummadi, B. K.; Shields, H.; Ballas, S. K.; King, S. B.; Kim-Shapiro, D. B. Biophys. Chem. 2000, 84, 1. (8) Huang, J.; Zou, Z.; Kim-Shapiro, D. B.; Ballas, S. K.; King, S. B. J. Med. Chem. 2003, 46, 3748. (9) Huang, J.; Kim-Shapiro, D. B.; King, S. B. J. Med. Chem. 2004, 47, 3495. (10) Rohrman, B.; Mazziotti, D. A. J. Phys. Chem. B 2005, 109, 13392. (11) Zipse, H. Radicals in Synthesis I: Methods and Mechanisms. To.in Curr. Chem. 2006, 263, 163. (12) Mohr, M.; Zipse, H. Phys. Chem. Chem. Phys. 2001, 3, 1246. (13) (a). Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B: Condens. Matter Mater. Phys. 1988, 37, 785. (b). Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2005, 109, 5656. (c) Faglioni, F.; Goddard, W. A. J. Chem. Phys. 2005, 122, 14704. (d). Buhl, M.; Thiel, W. Inorg. Chem. 2004, 43, 6377. (e). Hu, Y. H. J. Am. Chem. Soc. 2003, 125, 4388. (f). Hu, Y. H.; Ruckenstein, E. J. Am. Chem. Soc. 2005, 127, 11277. (g). Hu, Y. H.; Ruckenstein, E. Chem. Phys. Lett. 2004, 399, 503. (14) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; 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.; Bakken, V.; 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.; Pople, J. A. Gaussian 03, revision C.02, Gaussian, Inc.: Wallingford, CT, 2004. (15) Remko, M.; Lyne, P. D.; Richards, G. Phys. Chem. Chem. Phys. 1999, 1, 5353.
