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Temperature-dependent thermodynamic contributions to the relative tautomeric stabilities of nucleic acid bases
Volume 204, number 5,6
CHEMICAL PHYSICS LETTERS
26 March 1993
Temperature-dependent thermodynamic contributions to the relative tautomeric stabilities of nucleic acid bases J6zef S. Kwiatkowski l and Jerry LeszczyMi Department of Chemistry Jackson State University, Jackson, MS 39217, USA Received 7 July 1992; in final form 18 December 1992
Temperature-dependent components of the enthalpy and entropy contributions to the AG Gibbs free tautomerixation energies of DNA bases and their derivatives are computed within the rigid rotor-harmonic oscillator-ideal gas approximation using the data (rotational constants, harmonic frequencies) from the SCF/3-2 1G calculations. For the tautomers existing in comparable concentrations, these contributions were found to be important parts of the AG energies, and they should be calculated for the proper comparison of the calculated and experimental tautomeric stabilities of the bases.
1. Introduction Recent studies of vibrational IR spectra of nucleic acid bases and their derivatives isolated in an inert matrix environment have provided accurate experimental data concerning the relative stabilities of several tautomeric forms of isolated bases (e.g., refs. [ 1,2 ] ). Such data are particularly important for testing the reliability of the tautomeric stability predictions from ab initio quantum-mechanical calculations, which refer mainly to isolated molecules, i.e. molecules that are not interacting with other species of the environment. However, the comparison of the theoretically predicted stabilities with the experimental data is often not made carefully enough, because one compares two different quantities, namely a relative internal energy at 0 K and a free tautomerization energy at the defined temperature T, i.e. the microscopic and macroscopic quantities. We shall briefly discuss this point here. For the case of tautomerism a-b the relationship between the equilibrium constant K at some temperature T, and the calculated difference in the zeropoint internal energy, L!&,(O) is given by K=
(d/d)
exp[
-A&,(0)/W
.
’ Permanent address: Instytut Fizyki, Uniwersytet M. Kopernika, 87- 100 Torun, Poland.
430
Each partition function qp can be written as the product of partition functions for the translational, rotational and vibrational degrees of freedom. However, since the masses and symmetry numbers of the a and b tautomers are the same, the ratios of the translational and rotational partition functions are equal to 1. Thus the pre-exponential factor can be approximated by the ratio of the vibrational partition functions, ( qb/qa)“ib. Each nonlinear tautomer has 3n- 6 normal modes of vibration, so the vibrational partition function is the product of 3n - 6 terms [l-exp(-hcv;,/kT)]/[l-exp(-hcVib/kT)] which can be expressed as [ 1 -exp( - 1.4388 Via/ T)]/ [ 1-exp( - 1.4388 v,JT) ] where vi, the wavenumber for the ith normal mode, is given in cm-‘. In order to predict the pre-exponential factor one should arrange the normal vibrational modes in order of decreasing wavenumber for each tautomer, and then calculate the above ratios. Analysis of the contributions of the ith vibrational frequencies to the total vibrational partition function allows for better understanding of the process of tautomerization. Generally, only lower frequency modes give contributions to the partition functions and these contributions decrease with the increase of the temperature T. One obtains experimental information about the stability of the tautomeric forms of a molecule (say a or b) from measurement of a tautomeric constant
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Volume204,number$6
CHEMICALPHYSICS LETTERS
&( T) for these forms (e.g. comparing the ratio of integrated intensities of the absorption bands in IR spectra of tautomers). As a consequence, the Gibbs free energy of tautomerization, AGJ T), at the defined temperature T can be estimated. On the other hand, a crude quantum-mechanical prediction of tautomeric stability involves usually only the computation of the relative internal energy A&,(O) at 0 K, which is approximated by a sum of the relative electronic energy (in the case of ab initio calculations that are computed at the SCF level and corrected by adding electron correlation energies) and the relative zerepoint vibrational energy (ZPE). The reader is referred to ref. [ 3 ] for the scope and limitation of the quantum-mechanical approach in prediction of several components of the relative internal tautomeric energies. Note that while the ZPEs can be calculated now with high accuracy, in spite of the progress in computational chemistry, the precise calculations of the electronic energies and particularly of the electron correlation contributions to the relative internal energies of tautomers are still difficult (e.g., ref. [ 43 ). The consequence of such a crude estimate of tautomeric stability is that when one compares the calculated A,!&, (0)values with the experimental AGGb( T) data, the assumption is made that temperature-dependent contributions to the relative free energies are negligible. We shall examine here this assumption by computing these contributions for several important tautomers of the nucleic acid bases and their derivatives.
2. Results and discussion To overcome the crude assumptions mentioned above, the relative Gibbs free energy of the two tautomers a and b at temperature T can be expressed as
[51
where AK+( 0) is the relative internal energy A&+(O) at 0 K, the second term with the relative heat capacity AC, is a temperature-dependent com-
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ponent of the tautomerization enthalpy A&b(T), and the last term is the entropy contribution ti to &,,b( T) #‘. Table 1 collects calculated temperature-dependent components of relative free energies and the sum of these components, 6G,,b( T) zAG,,~( r) - AG,,b(O), for several tautomeric pairs of the nucleic acid bases. The model applied in the calculations uses the rigid rotor-harmonic oscillator-ideal gas approximation [ 5 1. Rotational constants and vibrational wavenumbers of the tautomers (computed within the harmonic approximation) were taken from our SCF/32 1G calculations for the bases #‘. The data presented in table 1 were calculated by numerical integration of the AC, term over the considered temperature range assuming a pressure of one atmosphere and three different temperatures of 298.15 (room temperature), 400 and 500 K, respectively. The last two temperatures were chosen because the concentration ratios of tautomers measured from matrix-isolation IR studies correspond to tautomeric equilibria in the gas phase at temperature of the furnace (usually in a range of 400-500 K) from which a sample is sublimed just before it is trapped in the matrix. We did not attempt to carry out the calculations for higher temperature because the nucleic acid bases decompose at T larger than 550-600 K. The use of theoretical data in this study deserves some comments. The rotational constants (A, B,C) calculated from the optimized SCF/3-21G geometries of the bases are higher than the corresponding experimental constants [ 13 1. However, since the rotational contribution appears only in the entropy (as a term involving In (ABC)),the use of the same scaling factors for both tautomers to multiply their rotational constants would not change the relative entropy values. Also the harmonic vibrational ” Thestandardexpressions forheatcapacityandentropyforan ideal gaa in the canonical ensemble were taken from ref. [ 51.The same expressions are ked in the GAUSSIAN programs, which in a standardoptioncalculatethe thermochemical propertiesonly at T= 298.15 K using the computed vibrational frequencies and rotational constants. We have written a short program to evaluate the thermochemical properties at any temperature using as an input data the vibrational wavenumbers (unscaled, scaled, experimental) and rotational constants. s* For cytosine see refs. [ 6,7], for Pmethylguanine ref. [ 81, for puke and adenine ref. [9], for uracil ref. [IO], for isocytosine ref. [ 1I ] and for isoguanine ref. [ 121.
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CHEMICAL PHYSICS LETTERS
26 March 1993
Table 1 Relative thermodynamic contributions to tautomeric stabilities of the nucleic acid bases and their derivatives. All quantities in kJ/mol Pair ‘)
JoTAC,(T) dT
-TM(T)
AC(T)-AC(O)
1. Purn(9)H-PurN(7)H
-0.05(-0.05) -0.08( -0.09) -O.ll(-0.11) -0.69( -0.70) -0.94( -0.93) - 1.13(-1.10) +0.21(+0.27) to.4q to.49) tO.65(+0.67) -0.06( -0.10) -0.24( -0.31) -0.47( -0.54) +0.22(+0.19) +0.14(+0.09) to.oz( -0.04) to.o7( +0.04) -0.02( -0.06) -0.14( -0.20) to.oI(to.o3) +0.10(+0.11) +0.15(+0.14)
+o.os( to.09) +0.15(+0.16) +0.22( to.23) +1.26(+1.35) +1.99( +2.08) t 2.70( +2.78) +0.02( -0.06) -O-26( -0.35) -0.55 (-0.63) -0.04(+0.01) +0.15(+0.24) +0.44(to.57) -0.58(-0.64) -0.69( -0.75) -0.72(-0.79) -0.42( -0.40) -0.46( -0.42) -0.44(-0.38) to.28(+0.25) +0.27( +0.24) to.28(+0.27)
8. iCyt-iCyt*
-0.24(-0.19)
+0.65( +0.63)
9. iGuaN(9)H-iGua*N(9)H
-0.15(-0.08) O.OO(+0.08) to.30($0.29) +0.34(+0.31) +0.34(+0.29)
+0.78(+0.72) +0.81(+0.73) -0.71(-0.72) -l.oO(-1.00) -1.24(-1.23)
t 0.03( to.04) to.o7( to.07) +0.11(+0.12) +0.57( t0.65) +1.05(+1.15) +1.57(+1.68) +0.23( +0.21) to.zo( to.14) +o.lo( to.04) -O.lO( -0.09) -0.09( -0.07) -0.03( t 0.03) -0.36( -0.45) -0.55( -0.66) -0.71( -0.75) -0.35( -0.36) -0.48( -0.48) -0.58( -0.58) +0.29( to.28) +0.37( to.35) +0.43( to.41) f0.42( +0.44) +0.63( t0.64) +0.81( tO.81) -0.41( -0.43) -0.66( -0.69) -0.90( -0.94)
2. AdeN(9)H_AdeN(7)H
3. AdeN(9)H-Ade*N(9)H
4. ura-ura*
5.9MeGua-9MeGua*(c)
6. Cyt-Cyt(h)
7. cyt-cyt*
a) For each pair the contributions are calculated at 298.15,400 and 500 K, respectively. Contributions calculated with the scaled wavenumbers are presented in the parentheses (one scaling factor 0.9 was used except 9-methylguanine tautomers for which we used the scaling factors 0.9 for in plane modes, 0.9 18 for OH stretch and 0.8 1 for out-of-plane mode; for details see ref. [ 8 ] ). The first tautomer is a reference form. Three-letter abbreviations for the nucleic acid bases are used according to recommendation of the International Union of Pure and Applied Chemistry and of the International Union of Biochemistry. The other abbreviations: i, iso form; h, hydroxy form; N(9)H and N( 7)H, tautomeric forms of purines with the hydrogen atom at nitrogens N(9) and N(7) of the imidazole ring, respectively; the asterisk marks “rare” forms (imino form of adenine or cytosine; hydroxy form of uracil, guanines or isocytosine); C, cis conformer of hydroxy form (the cis position of hydrogen of the OH group relative to N( 1) atom of a ring).
from the SCF/3-2 1G calculations are higher (about 10%) than the experimental fundamental wavenumbers, and in this case a common procedure is a scaling down of the calculated wavenumbers by a single factor of 0.9 [ 141. In this study, we have used both the unscaled and scaled rotational constants and vibrational wavenumbers. Before discussing the data presented in table 1 some remarks concerning tautomeric stabilities of the isolated bases seem to be necessary. The tautomeric pairs in table 1 can be classified into three types: (i) The pairs l-4 for which only one tautomer is exclusively observed [ 1,2,9,15]. In this case it is impos-
wavenumbers
432
sible to obtain the &a values from the direct measurement. (ii) The guanine and cytosine tautomeric pairs 5, 6 for which both tautomeric forms do exist in similar concentrations [ 1,2,6-&l 61 (J&x0.41.O). (iii) The pairs 7-9 with one dominating form and small (but measured experimentally) concentration of the second tautomer [ 1,2,6,7,11,12,17 ] (&,x 1O-l- 10m2). It should be mentioned that the A&,(O) values predicted by recent ab initio calculations [2,4,6,&l 1,12,17-191 correlate well with these experimental findings giving the AEhb(0) values of order 20-50, O-l and 4-9 kJ/mol for the (i), (ii) and (iii) pair types, respectively.
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As we can see (table 1) the calculated enthalpy and contributions to the AG free energy are generally small. In some cases they are of opposite signs yielding the total SG values to be smaller than 1 W/ mol (except the AdeN(9)H_AdeN(7)H pair). The application of the scaled harmonic frequencies in the reported calculations changes the SG values by no more than 0.1 kI/mol, while the scaling effect of the rotational constants is negligible (the 6Gchanges are smaller than 10m3kJ/mol, so they are not presented in table 1). In addition, the effect of the theory level applied in the vibrational IR spectra predictions on the calculated thermodynamical contributions has been studied. Both the enthalpy and entropy contributions depend on the basis set quality and on the electron correlations, however the computed changes of SG values are of the order of a tenth of kl/mol. The detailed discussion will be presented elsewhere. For the tautomeric pairs l-4 characterized by the relatively large internal energy Al&,,(O) values, the SG( T) contributions in the range of the considered temperatures (up to 500 K) are small fractions ( c 5 x 1O-‘) of the AGJ T) values, and generally they may be omitted when the predicted AE,,b(O) values are compared with the experimental AC,,(T) data. That is not however the case for the oxo-hydroxy pairs of cytosine and 9-methylguanine (the 5, 6 pairs), because the SG values are of the same order as the relative internal energies. For the third group of the considered species (the 7-9 pairs), the computed SG contributions are of less importance, although they might not be negligible. In conclusion, in both cases when the experimental data indicate that the concentration ratio of the two considered tautomers is in a range of 0- 1Om2or the predicted A,&(O) energies are between 0 and f 10 kJ/mol, we recommend the additional computation of the SG values x3.This is particularly important when the accurate ab initio calculations are carried out to estimate relative internal energies for tautomers. The formulae for both temperature-de-
entropy
x3 It is nota generalrulethatgG( T) contributions are important for the tautomers existing in comparable amounts. For instance, pair (that system has been treated in many papers as a model for the oxohydroxy tautomeric equilibria of the DNA bases), the SG(T) value is negligible [ 20,2 11, although the experimental WE (0) value is in the order of 2-3 kJ/mo1[21]. in the case of the 2( lH)-pyridinone/2-hydroxypyridine
26 March 1993
pendent enthalpy and entropy contributions are simple, and the calculation of these contributions does not require sophisticated computer resources.
Acknowledgement This work was supported in part by the State Committee for Scientific Research (Poland) within the grant KBN-4.007891 .Ol and in part by a contract (DAAL03-89-0038) from the Army High Performance Computing Research Center (USA).
References [ 11W.B. Person, K. Szczepaniak, M. Szczesniak, J.S. Kwiatkowski, L. Hemandez and R. Czerminski, J. Mol. Struct. 194 ( 1989) 239; Yu.P. Blagoi, E.D. Radchenko, S.G. Stepanian and G.G. Sheina, in: Laser scattering spectroscopy of biological objects, eds. J. Stepanek, P. Anzenbacher and B. Scdlacek (Elsevier, Amsterdam, 1987) p. 161; D. Shugar and A. Psoda, in: Landolt-B&nstein, New Series, Biophysics. Part 1. Nucleic acids, VII/ 1D (Springer, Berlin, 1990) p. 308. [2] J.S. Kwiatkowski and W.B. Person, in: Theoretical biochemistry and molecular biophysics, Vol. 1. DNA, eds. D.L. Bcveridge and R. Lavery (Adenine Press, Guilderland, 1990) p. 153. [3] J.S. Kwiatkowski, T.J. Zielinski and R. Rein, Advan. Quantum Chem. 18 ( 1986) 85. [4] L. Adamowicz, Chem. Phys. Letters 153 (1988) 147; 161 (1989) 73; A. LeS, L. Adamowicz and R.J. Bartlett, J. Phys. Chem. 93 (1989) 4001. [ 51D. McQuarrie, Statistical mechanics (Harper and Row, New York, 1976). [6] J.S. Kwiatkowski, W.B. Person, M. Szczesniak and K. Szczepaniak, Acta Biochim. Polon. 34 (1987) 165. [7] M. Szczesniak, K. Szczepaniak, J.S. Kwiatkowski, K. KuBulat and W.B. Person, J. Am. Chem. Sot. 110 (1988) 8319. [8] K. Szczepaniak, M. Szczesniak, W. Szajda, J. LeszczytU and W.B. Person, Can. J. Chem. 69 (199 1) 1705. [9] M.J. Nowak, L. Lapinski, J.S. Kwiatkowski and J. Leszczydski, Spectrochim. Acta 47A ( 1991) 87. [lo] J. Leszczydski, J. Phys. Chem. 96 (1992) 1649. [ 1I ] M. Szczesniak, W.B. Person, J.S. Kwiatkowski and I. Lcszczydski, in preparation. [ 12]M. Szczesniak, K. Szczepaniak, W.B. Person, J.S. Kwiatkowski and J. Leszczydski, in preparation. [ 131R.D. Brown, P.D. Godfrey, D. McNaughton and A.P. Pierlot, J. Am. Chem. Sot. 111 (1989) 2308.
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[ 141 B.A. Hess Jr., L.L. Schaad, P. Carsky and R. Zahradnik, Chem. Rev. 86 (1986) 709. [ 151R.D. Brown, P.D. Godfrey, P. McNaughton and A.P. Pierlot, Chem. Phys. Letters 156 (1989) 61; M.J. Nowak, L. Lapinski and J.S. Kwiatkowski, Chem. Phys. Letters 157 (1989) 14. [ 161 M.J. Nowak, L. Lapinski and J. Fulara, Spectrochim. Acta 45A (1989) 229. [ 171 M. Szczesniak, J. LeszczyUi and W.B. Person, J. Am. Chem. Sot. 114 (1992) 2731.
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[ 18 ] J.S. Kwiatkowski and J. Lcszczynski, J. Mol. Struct. THEOCHEM 208 ( 1990) 35; J. Leszczydski, Chem. Phys. Letters 174 (1990) 347. [ 19 ] M. Sabio, S. Topiol and W.C. Lumma Jr. I. Phys. Chem. 94 (1991) 1366. [20] C. Krebs, H.-J. Hofmann, H.-J. Kohler and C. Weiss, Chem. Phys. Letters 69 (1980) 537. [21] M.J. Nowak, L. Lapinski, J. Fulara, A. LcS and L. Adamowicz, J. Phys. Chem. 96 (1992) 1562.
CHEMICAL PHYSICS LETTERS
26 March 1993
Temperature-dependent thermodynamic contributions to the relative tautomeric stabilities of nucleic acid bases J6zef S. Kwiatkowski l and Jerry LeszczyMi Department of Chemistry Jackson State University, Jackson, MS 39217, USA Received 7 July 1992; in final form 18 December 1992
Temperature-dependent components of the enthalpy and entropy contributions to the AG Gibbs free tautomerixation energies of DNA bases and their derivatives are computed within the rigid rotor-harmonic oscillator-ideal gas approximation using the data (rotational constants, harmonic frequencies) from the SCF/3-2 1G calculations. For the tautomers existing in comparable concentrations, these contributions were found to be important parts of the AG energies, and they should be calculated for the proper comparison of the calculated and experimental tautomeric stabilities of the bases.
1. Introduction Recent studies of vibrational IR spectra of nucleic acid bases and their derivatives isolated in an inert matrix environment have provided accurate experimental data concerning the relative stabilities of several tautomeric forms of isolated bases (e.g., refs. [ 1,2 ] ). Such data are particularly important for testing the reliability of the tautomeric stability predictions from ab initio quantum-mechanical calculations, which refer mainly to isolated molecules, i.e. molecules that are not interacting with other species of the environment. However, the comparison of the theoretically predicted stabilities with the experimental data is often not made carefully enough, because one compares two different quantities, namely a relative internal energy at 0 K and a free tautomerization energy at the defined temperature T, i.e. the microscopic and macroscopic quantities. We shall briefly discuss this point here. For the case of tautomerism a-b the relationship between the equilibrium constant K at some temperature T, and the calculated difference in the zeropoint internal energy, L!&,(O) is given by K=
(d/d)
exp[
-A&,(0)/W
.
’ Permanent address: Instytut Fizyki, Uniwersytet M. Kopernika, 87- 100 Torun, Poland.
430
Each partition function qp can be written as the product of partition functions for the translational, rotational and vibrational degrees of freedom. However, since the masses and symmetry numbers of the a and b tautomers are the same, the ratios of the translational and rotational partition functions are equal to 1. Thus the pre-exponential factor can be approximated by the ratio of the vibrational partition functions, ( qb/qa)“ib. Each nonlinear tautomer has 3n- 6 normal modes of vibration, so the vibrational partition function is the product of 3n - 6 terms [l-exp(-hcv;,/kT)]/[l-exp(-hcVib/kT)] which can be expressed as [ 1 -exp( - 1.4388 Via/ T)]/ [ 1-exp( - 1.4388 v,JT) ] where vi, the wavenumber for the ith normal mode, is given in cm-‘. In order to predict the pre-exponential factor one should arrange the normal vibrational modes in order of decreasing wavenumber for each tautomer, and then calculate the above ratios. Analysis of the contributions of the ith vibrational frequencies to the total vibrational partition function allows for better understanding of the process of tautomerization. Generally, only lower frequency modes give contributions to the partition functions and these contributions decrease with the increase of the temperature T. One obtains experimental information about the stability of the tautomeric forms of a molecule (say a or b) from measurement of a tautomeric constant
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&( T) for these forms (e.g. comparing the ratio of integrated intensities of the absorption bands in IR spectra of tautomers). As a consequence, the Gibbs free energy of tautomerization, AGJ T), at the defined temperature T can be estimated. On the other hand, a crude quantum-mechanical prediction of tautomeric stability involves usually only the computation of the relative internal energy A&,(O) at 0 K, which is approximated by a sum of the relative electronic energy (in the case of ab initio calculations that are computed at the SCF level and corrected by adding electron correlation energies) and the relative zerepoint vibrational energy (ZPE). The reader is referred to ref. [ 3 ] for the scope and limitation of the quantum-mechanical approach in prediction of several components of the relative internal tautomeric energies. Note that while the ZPEs can be calculated now with high accuracy, in spite of the progress in computational chemistry, the precise calculations of the electronic energies and particularly of the electron correlation contributions to the relative internal energies of tautomers are still difficult (e.g., ref. [ 43 ). The consequence of such a crude estimate of tautomeric stability is that when one compares the calculated A,!&, (0)values with the experimental AGGb( T) data, the assumption is made that temperature-dependent contributions to the relative free energies are negligible. We shall examine here this assumption by computing these contributions for several important tautomers of the nucleic acid bases and their derivatives.
2. Results and discussion To overcome the crude assumptions mentioned above, the relative Gibbs free energy of the two tautomers a and b at temperature T can be expressed as
[51
where AK+( 0) is the relative internal energy A&+(O) at 0 K, the second term with the relative heat capacity AC, is a temperature-dependent com-
26 March1993
ponent of the tautomerization enthalpy A&b(T), and the last term is the entropy contribution ti to &,,b( T) #‘. Table 1 collects calculated temperature-dependent components of relative free energies and the sum of these components, 6G,,b( T) zAG,,~( r) - AG,,b(O), for several tautomeric pairs of the nucleic acid bases. The model applied in the calculations uses the rigid rotor-harmonic oscillator-ideal gas approximation [ 5 1. Rotational constants and vibrational wavenumbers of the tautomers (computed within the harmonic approximation) were taken from our SCF/32 1G calculations for the bases #‘. The data presented in table 1 were calculated by numerical integration of the AC, term over the considered temperature range assuming a pressure of one atmosphere and three different temperatures of 298.15 (room temperature), 400 and 500 K, respectively. The last two temperatures were chosen because the concentration ratios of tautomers measured from matrix-isolation IR studies correspond to tautomeric equilibria in the gas phase at temperature of the furnace (usually in a range of 400-500 K) from which a sample is sublimed just before it is trapped in the matrix. We did not attempt to carry out the calculations for higher temperature because the nucleic acid bases decompose at T larger than 550-600 K. The use of theoretical data in this study deserves some comments. The rotational constants (A, B,C) calculated from the optimized SCF/3-21G geometries of the bases are higher than the corresponding experimental constants [ 13 1. However, since the rotational contribution appears only in the entropy (as a term involving In (ABC)),the use of the same scaling factors for both tautomers to multiply their rotational constants would not change the relative entropy values. Also the harmonic vibrational ” Thestandardexpressions forheatcapacityandentropyforan ideal gaa in the canonical ensemble were taken from ref. [ 51.The same expressions are ked in the GAUSSIAN programs, which in a standardoptioncalculatethe thermochemical propertiesonly at T= 298.15 K using the computed vibrational frequencies and rotational constants. We have written a short program to evaluate the thermochemical properties at any temperature using as an input data the vibrational wavenumbers (unscaled, scaled, experimental) and rotational constants. s* For cytosine see refs. [ 6,7], for Pmethylguanine ref. [ 81, for puke and adenine ref. [9], for uracil ref. [IO], for isocytosine ref. [ 1I ] and for isoguanine ref. [ 121.
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Table 1 Relative thermodynamic contributions to tautomeric stabilities of the nucleic acid bases and their derivatives. All quantities in kJ/mol Pair ‘)
JoTAC,(T) dT
-TM(T)
AC(T)-AC(O)
1. Purn(9)H-PurN(7)H
-0.05(-0.05) -0.08( -0.09) -O.ll(-0.11) -0.69( -0.70) -0.94( -0.93) - 1.13(-1.10) +0.21(+0.27) to.4q to.49) tO.65(+0.67) -0.06( -0.10) -0.24( -0.31) -0.47( -0.54) +0.22(+0.19) +0.14(+0.09) to.oz( -0.04) to.o7( +0.04) -0.02( -0.06) -0.14( -0.20) to.oI(to.o3) +0.10(+0.11) +0.15(+0.14)
+o.os( to.09) +0.15(+0.16) +0.22( to.23) +1.26(+1.35) +1.99( +2.08) t 2.70( +2.78) +0.02( -0.06) -O-26( -0.35) -0.55 (-0.63) -0.04(+0.01) +0.15(+0.24) +0.44(to.57) -0.58(-0.64) -0.69( -0.75) -0.72(-0.79) -0.42( -0.40) -0.46( -0.42) -0.44(-0.38) to.28(+0.25) +0.27( +0.24) to.28(+0.27)
8. iCyt-iCyt*
-0.24(-0.19)
+0.65( +0.63)
9. iGuaN(9)H-iGua*N(9)H
-0.15(-0.08) O.OO(+0.08) to.30($0.29) +0.34(+0.31) +0.34(+0.29)
+0.78(+0.72) +0.81(+0.73) -0.71(-0.72) -l.oO(-1.00) -1.24(-1.23)
t 0.03( to.04) to.o7( to.07) +0.11(+0.12) +0.57( t0.65) +1.05(+1.15) +1.57(+1.68) +0.23( +0.21) to.zo( to.14) +o.lo( to.04) -O.lO( -0.09) -0.09( -0.07) -0.03( t 0.03) -0.36( -0.45) -0.55( -0.66) -0.71( -0.75) -0.35( -0.36) -0.48( -0.48) -0.58( -0.58) +0.29( to.28) +0.37( to.35) +0.43( to.41) f0.42( +0.44) +0.63( t0.64) +0.81( tO.81) -0.41( -0.43) -0.66( -0.69) -0.90( -0.94)
2. AdeN(9)H_AdeN(7)H
3. AdeN(9)H-Ade*N(9)H
4. ura-ura*
5.9MeGua-9MeGua*(c)
6. Cyt-Cyt(h)
7. cyt-cyt*
a) For each pair the contributions are calculated at 298.15,400 and 500 K, respectively. Contributions calculated with the scaled wavenumbers are presented in the parentheses (one scaling factor 0.9 was used except 9-methylguanine tautomers for which we used the scaling factors 0.9 for in plane modes, 0.9 18 for OH stretch and 0.8 1 for out-of-plane mode; for details see ref. [ 8 ] ). The first tautomer is a reference form. Three-letter abbreviations for the nucleic acid bases are used according to recommendation of the International Union of Pure and Applied Chemistry and of the International Union of Biochemistry. The other abbreviations: i, iso form; h, hydroxy form; N(9)H and N( 7)H, tautomeric forms of purines with the hydrogen atom at nitrogens N(9) and N(7) of the imidazole ring, respectively; the asterisk marks “rare” forms (imino form of adenine or cytosine; hydroxy form of uracil, guanines or isocytosine); C, cis conformer of hydroxy form (the cis position of hydrogen of the OH group relative to N( 1) atom of a ring).
from the SCF/3-2 1G calculations are higher (about 10%) than the experimental fundamental wavenumbers, and in this case a common procedure is a scaling down of the calculated wavenumbers by a single factor of 0.9 [ 141. In this study, we have used both the unscaled and scaled rotational constants and vibrational wavenumbers. Before discussing the data presented in table 1 some remarks concerning tautomeric stabilities of the isolated bases seem to be necessary. The tautomeric pairs in table 1 can be classified into three types: (i) The pairs l-4 for which only one tautomer is exclusively observed [ 1,2,9,15]. In this case it is impos-
wavenumbers
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sible to obtain the &a values from the direct measurement. (ii) The guanine and cytosine tautomeric pairs 5, 6 for which both tautomeric forms do exist in similar concentrations [ 1,2,6-&l 61 (J&x0.41.O). (iii) The pairs 7-9 with one dominating form and small (but measured experimentally) concentration of the second tautomer [ 1,2,6,7,11,12,17 ] (&,x 1O-l- 10m2). It should be mentioned that the A&,(O) values predicted by recent ab initio calculations [2,4,6,&l 1,12,17-191 correlate well with these experimental findings giving the AEhb(0) values of order 20-50, O-l and 4-9 kJ/mol for the (i), (ii) and (iii) pair types, respectively.
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As we can see (table 1) the calculated enthalpy and contributions to the AG free energy are generally small. In some cases they are of opposite signs yielding the total SG values to be smaller than 1 W/ mol (except the AdeN(9)H_AdeN(7)H pair). The application of the scaled harmonic frequencies in the reported calculations changes the SG values by no more than 0.1 kI/mol, while the scaling effect of the rotational constants is negligible (the 6Gchanges are smaller than 10m3kJ/mol, so they are not presented in table 1). In addition, the effect of the theory level applied in the vibrational IR spectra predictions on the calculated thermodynamical contributions has been studied. Both the enthalpy and entropy contributions depend on the basis set quality and on the electron correlations, however the computed changes of SG values are of the order of a tenth of kl/mol. The detailed discussion will be presented elsewhere. For the tautomeric pairs l-4 characterized by the relatively large internal energy Al&,,(O) values, the SG( T) contributions in the range of the considered temperatures (up to 500 K) are small fractions ( c 5 x 1O-‘) of the AGJ T) values, and generally they may be omitted when the predicted AE,,b(O) values are compared with the experimental AC,,(T) data. That is not however the case for the oxo-hydroxy pairs of cytosine and 9-methylguanine (the 5, 6 pairs), because the SG values are of the same order as the relative internal energies. For the third group of the considered species (the 7-9 pairs), the computed SG contributions are of less importance, although they might not be negligible. In conclusion, in both cases when the experimental data indicate that the concentration ratio of the two considered tautomers is in a range of 0- 1Om2or the predicted A,&(O) energies are between 0 and f 10 kJ/mol, we recommend the additional computation of the SG values x3.This is particularly important when the accurate ab initio calculations are carried out to estimate relative internal energies for tautomers. The formulae for both temperature-de-
entropy
x3 It is nota generalrulethatgG( T) contributions are important for the tautomers existing in comparable amounts. For instance, pair (that system has been treated in many papers as a model for the oxohydroxy tautomeric equilibria of the DNA bases), the SG(T) value is negligible [ 20,2 11, although the experimental WE (0) value is in the order of 2-3 kJ/mo1[21]. in the case of the 2( lH)-pyridinone/2-hydroxypyridine
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pendent enthalpy and entropy contributions are simple, and the calculation of these contributions does not require sophisticated computer resources.
Acknowledgement This work was supported in part by the State Committee for Scientific Research (Poland) within the grant KBN-4.007891 .Ol and in part by a contract (DAAL03-89-0038) from the Army High Performance Computing Research Center (USA).
References [ 11W.B. Person, K. Szczepaniak, M. Szczesniak, J.S. Kwiatkowski, L. Hemandez and R. Czerminski, J. Mol. Struct. 194 ( 1989) 239; Yu.P. Blagoi, E.D. Radchenko, S.G. Stepanian and G.G. Sheina, in: Laser scattering spectroscopy of biological objects, eds. J. Stepanek, P. Anzenbacher and B. Scdlacek (Elsevier, Amsterdam, 1987) p. 161; D. Shugar and A. Psoda, in: Landolt-B&nstein, New Series, Biophysics. Part 1. Nucleic acids, VII/ 1D (Springer, Berlin, 1990) p. 308. [2] J.S. Kwiatkowski and W.B. Person, in: Theoretical biochemistry and molecular biophysics, Vol. 1. DNA, eds. D.L. Bcveridge and R. Lavery (Adenine Press, Guilderland, 1990) p. 153. [3] J.S. Kwiatkowski, T.J. Zielinski and R. Rein, Advan. Quantum Chem. 18 ( 1986) 85. [4] L. Adamowicz, Chem. Phys. Letters 153 (1988) 147; 161 (1989) 73; A. LeS, L. Adamowicz and R.J. Bartlett, J. Phys. Chem. 93 (1989) 4001. [ 51D. McQuarrie, Statistical mechanics (Harper and Row, New York, 1976). [6] J.S. Kwiatkowski, W.B. Person, M. Szczesniak and K. Szczepaniak, Acta Biochim. Polon. 34 (1987) 165. [7] M. Szczesniak, K. Szczepaniak, J.S. Kwiatkowski, K. KuBulat and W.B. Person, J. Am. Chem. Sot. 110 (1988) 8319. [8] K. Szczepaniak, M. Szczesniak, W. Szajda, J. LeszczytU and W.B. Person, Can. J. Chem. 69 (199 1) 1705. [9] M.J. Nowak, L. Lapinski, J.S. Kwiatkowski and J. Leszczydski, Spectrochim. Acta 47A ( 1991) 87. [lo] J. Leszczydski, J. Phys. Chem. 96 (1992) 1649. [ 1I ] M. Szczesniak, W.B. Person, J.S. Kwiatkowski and I. Lcszczydski, in preparation. [ 12]M. Szczesniak, K. Szczepaniak, W.B. Person, J.S. Kwiatkowski and J. Leszczydski, in preparation. [ 131R.D. Brown, P.D. Godfrey, D. McNaughton and A.P. Pierlot, J. Am. Chem. Sot. 111 (1989) 2308.
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[ 141 B.A. Hess Jr., L.L. Schaad, P. Carsky and R. Zahradnik, Chem. Rev. 86 (1986) 709. [ 151R.D. Brown, P.D. Godfrey, P. McNaughton and A.P. Pierlot, Chem. Phys. Letters 156 (1989) 61; M.J. Nowak, L. Lapinski and J.S. Kwiatkowski, Chem. Phys. Letters 157 (1989) 14. [ 161 M.J. Nowak, L. Lapinski and J. Fulara, Spectrochim. Acta 45A (1989) 229. [ 171 M. Szczesniak, J. LeszczyUi and W.B. Person, J. Am. Chem. Sot. 114 (1992) 2731.
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[ 18 ] J.S. Kwiatkowski and J. Lcszczynski, J. Mol. Struct. THEOCHEM 208 ( 1990) 35; J. Leszczydski, Chem. Phys. Letters 174 (1990) 347. [ 19 ] M. Sabio, S. Topiol and W.C. Lumma Jr. I. Phys. Chem. 94 (1991) 1366. [20] C. Krebs, H.-J. Hofmann, H.-J. Kohler and C. Weiss, Chem. Phys. Letters 69 (1980) 537. [21] M.J. Nowak, L. Lapinski, J. Fulara, A. LcS and L. Adamowicz, J. Phys. Chem. 96 (1992) 1562.