P. R. STOESSER AND S. J. GILL
564
Calorimetric Study of Self-Association of 6-Methylpurine in Water1
by P. R. Stoesser and S. J. Gill Department of Chemistrg, Un~vws&of Colorado, Boulder, Colorado
(Received July $9, 1966)
A determination of the thermodynamics of self-association of 6-methylpurine in water has been made from heat of dilution measurements. Theoretical equations which relate the concentration dependence of the relative molal enthalpy are used to obtain one estimate of both the self-association constant, K , and the enthalpy of self-association, AH", from calorimetrjc data. The respective values are 8.6 f 1.1 m-l and -5.6 f 0.2 kcal/ mole. A second estimate of the enthalpy of self-association is made by a combination of heat of dilution data and osmotic coefficient data (Ts'o) to give a value of -6.3 f 0.1 kcal/mole. An average value of AHo = -6.0 f 0.4 kcal/mole is suggested from these values. With TS'O'Svalue of AGO = -1.1 kcal/mole a value of AS" = -16 & 1 eu is obtained at 25".
Introduction The work of Ts'o and colleague^^^^ has demonstrated that aqueous solutions of 6-methylpurine form complexes of various degrees of polymerization depending upon the total concentration. A stacked configuration is indicated from nuclear resonance data.3v4 The forces which govern the formation of such complexes are of considerable interest both from a theoretical v i e w p ~ i n tas ~ well , ~ as their likely presence in stabilizing polynucleotide structures6J and polynucleotide-nucleotide Determination of the vapor pressures as a function of temperature for a series of purine and pyrimidine compounds has provided a measure of the interaction forces in the crystal from the heats of ~ublimation.~ Several recent spectroscopic studies on adenylic acid oligomers10-12 in water have given estimates of the interaction enthalpy between purine rings of the order of -9 kcal mole-l. In all of these studies a variety of effects may be present so that it is difficult to sort out the importance of various types of interactions. The system of 6-methylpurine avoids some of these problems. It is uncharged. The equilibrium between various species can be considered to be characterized by a single equilibrium constant.2 The mode of complexation has been indicated to be that of stacking. It was felt that a direct calorimetric measurement of the enthalpy of association of the complex could provide relevant information on the particular inter394
The Journal o j Physical Chemistry
action forces of this complex. Furthermore with the availability of enthalpy data the entropy of formation could be calculated by use of the equilibrium constant,. In this way a complete thermodynamic description of the purine ring interaction for 6-methylpurine could be obtained.
Theory The enthalpy of self-association for a dissolved compound can be determined from an analysis of heats of dilution using either additional equilibrium informat,ion13or assuming particularly simple reaction param(1) (a) Presented in part by P. R. Stoesser in a Ph.D. thesis, University of Colorado, 1966; (b) presented at the 40th National Colloid Symposium, University of Wisconsin, June 16, 196G. (2) P.0. P.Ts'o and S. I. Chan, J . Am. Chem. SOC.,86,4176 (1964). ( 3 ) S.I. Chan, M. P. Schweiger, P. 0. P. Ts'o, and G. K. Helmkamp, ibid., 86,4182 (1964). (4) 0. Jardetzky, Biopolymers Symp., I , 501 (1964). (5) B.Pullman, J . Chem. Phys., 43, 5233 (1965). (6) D.M.Crothers and Bruno H. Zimin, J . Mol. Biol., 9, 1 (1964). (7) D. N. Holcomb and I. Tinoco, Jr., Biopolymers, 3 , 121 (1965). (8) M.N. Lipsett, L. A. Heppel, and D. F. Bradley, J. Biol. Chem., 236,857 (1961). (9) L. B. Clark, G. G. Peschel, and I. Tinoco, Jr., J . Phys. Chem., 6 9 , 3615 (1965). (10) J. Brahms, A. M. Michelson, and K. E. VanHolde, J . Mol. Biol., 15, 467 (1966). (11) K. E. VanHolde, J, Brahms, and A. M. Michelson, ibid., 12, 726 (1965). (12) M. Leng and G. Felsenfeld, ibid., 15, 220 (1966).
565
CALORIMETRIC STUDY OF 6-AIETHYL PURINE
eters. In either case one starts with the assumption that all heat effects upon dilution are due to dissociation of complex species, Furthermore, every complex is assumed to obey dilute solution laws. Both of these conditions are met at increasing dilution. Uncharged molecular species also obey dilute solution laws over a wider range of concentration than do ionic materials. The various reaction equilibria are characterized by equations of the form
A
+ An-l = A,
(1)
with equilibrium constants K , and enthalpies of reaction AH,". If the reaction stops with dimerization then n equals 2. If an unlimited number of reaction species is permitted then n can have all integer values from 2 on. The heat of infinite dilution, -napL, is defined as the heat obtained when an na molal solution (1 kg of solvent) is diluted with an infinite amount of solvent. With the above assumptions we may write 7 1 Z p ~=
(A2)AHZ"
+ (A3)(AHZ0+ AH3") +
,
. . (2)
where (A,) is the molality of species A, and the plus sign arises because the dilution process reverses the direction of the reaction of eq 1. With knowledge of the equilibrium constants K,, mpL can be expressed as
mpL
+
= Kz(A)~AH~'
+
KzK3(A)a(AHzo AH3")
+ ...
(3)
The molality of the solution is given by
m = (A) = (A)
+ ~ ( A z +) 3(A3) + . . . + 2Kz(A)' + ~ K z & ( A )+~ . . .
AH" -
(AH'/K)'/~(~L/~)'/~
' p ~ =
(AHo/2) - 1/Z(AH"/K)"'(pL/~)1'2 (6)
where the only difference is the appearance of the factor of '/z in the slope and intercept. Thus it is necessary t o have auxillary information, such as that given by the osmotic coefficient, to assess whether a particular equation is applicable. To avoid sign problems in eq 5 or 6 it is simplest to use the absolute magnitude of c p and ~ AH" and then recognize that the signs of c p and ~ AH" are the same. When osmotic coefficient data (p) are available, as in the case of 6-methylp~rine,~ an alternate procedure is a~ai1able.l~For either of the two special cases of the preceding paragraph the value of AH " is given by AH"
-
(7) This result has been obtained before by Schellman13 for the limiting case of polymer formation. With the availability of two procedures for evaluating AH" values it should be possible to apply a test of the consistency of the assumptions upon which the equations are based, provided experimental data for heats of dilution and osmotic coefficients is available. In general one would expect the application of eq 7 to be more valid, particularly if an extrapolation can be made to very low concentrations, where dimerization becomes predominant. = (PL/(~
cp)
Experimental Section
(4)
If the equilibrium constants are known then in principle these equations provide the means for obtaining AH," values from a sit of p L measurements at various values of m. The practical difficulty of obtaining several equilibrium constants forces consideration of simpler cases. We are particularly interested in the case of unlimited values on n where all equilibrium constants have the same value ( K , = K ) and all enthalpies have the same value (AH," = AH'). The combination of eq 3 and 4 subject to these conditions yields the following result pL =
tion occurs. For if one considers the case of simple dimerization, then one finds the following result
(5)
The arrangement of this equation shows that upon plotting ' p us. ~ ('p~/m)'" a straight line should result. From the value of the slope and intercept both K and AH" can be determined. It is of some interest to note that a straight-line plot of the parameters of eq 5 does not necessarily mean that a polymerization reac-
( a ) Materials. Grade I G-methylpurine was obtained from Cyclo Chemical Corp., Los Angeles, Calif. Tests by D. Lorusso on this material have shown that its spectroscopic properties remained unchanged upon sublimation. Solutions were prepared with distilled water in a series of dilutions of equal volumes of a given solution and water. These solutions correspond to the way in which dilutions within the calorimeter are performed. ( b ) Density Determinations. In order to convert molarity t o molality for the prepared solutions, density measurements were made using a 2-ml pycnometer with precision-bore (1-mm) side arms. Table I shows the solution densities along with concentrations of molality (m) and molarity ( M ) . (c) CalorimetricDeterminations. Dilution measurements were made mixing equal volumes (0.1000 ml) of solution with water at 25" within a flow microcalo(13) J. A. Schellman, Compt. Rend. Trail. Lab. CarZsberg, 29, No. 14 (1955).
(14) S. J. Gill, G. F. Sheats, and M. Downing, in preparation.
Volume 7 1 , Wumber 3 February 1967
P. R. STOESSER AND S. J. GILL
566
Table I: Concentrations 25” m,
.+!f,
Density, g/cc
moles/l.
moles/kg of solvent
1.0155 1.0072 1.0028 1.0007 1.0004 0.9994 0.9980 0.9979 0.9978
0.4758 0.2381 0.1194 0.0597 0.0299 0.01495 0.00748 0.00374 0.00187
0.5000 0.2442 0.1210 0.0602 0.0300 0.01500 0.00750 0.00375 0.00188
rimeter.16 The endothermic heat of dilution was measured by electrical heating through calibrated resistors by means of a digital readout electronic controller. l6 The calibration of the electronic controller by both standard electrical calibration and calorimetric comparison with a direct current standard was accurate to 0.01%. Rlechanical heats of mixing pure water (0.1000 ml) with itself were found to average 15 f 2 pcal. This value was subtracted from actual dilution runs to give a corrected heat of dilution. At least 30 runs were made for each solution. The reason for making so many runs on a given solution was to eliminate heat conduction errors by extrapolation to infinite loop gain of the servo system controller used.16
Results The average heats, qt, of equal volume dilution per number of moles of solute, nil are shown with the range of variation in Table 11.
Table 11: Heats of Dilution of 6-Methylpurine Solution with Water at 25’
i
Initial oonon, m
Final ooncn, m
1 2 3 4 5 7 8 9 10
0.5000 0.2442 0.1210 0.0602 0.0300 0.01500 0.00750 0.00375 0.00186
0.2442 0.1210 0.0602 0.0300 0.01500 0.00750 0.00375 0.00186 0.00093
Dilution,
dni,
oal/mole
617 f 1 671 f 2 653 f 3 553 f 6 402 f 3 257 f 7 158 f 3 80 zk 14 48 It 16
Since the values of q J n f decrease linearly with concentration at the highest dilutions, the correction to The Journal of Physieal Chemistry
infinite dilution is given by the last reliable dilution value. If we base this value on the ninth dilution step, then a heat of 80 f 14 cal/mole would be expected for the process of going from 0.00186 to 0.00000 m. The relative molal enthalpy, PL, is given by summing the terms qi/nf from the infinite dilution step to the step of the concentration that is applicable for (PL. These values along with the factor (qJrn)”~are tabulated at various concentrations in Table 111. Table 111: Relative Molal Enthalpies of 6-Methylpurine in Water at 25” m
- QL, cal/mole
0.5000 0.2442 0.1212 0.0602 0.0300 0.01500 0.00750 0.00375
3471 i.52 2854 i.51 2183 k 49 1530 f 46 977 f 41 575 f 38 318 f 31 160 f 28
(~~/rn)l‘Z
(Ts’o) 1
AHo (W 7)t kcal/mole
83f 1 108 f 1 135 i: 2 159 f 3 180 i: 4 196 f 7 205 f 10 207 f 18
0.543 0.452 0.346 0.242
-6.4f0.1 - 6 . 3 f0 . 1 -6.3 f0 . 1 - 6 . 3 i0 . 2
1--(o
A plot of the values given in Table I11 is shown in Figure 1. Within the range of errors indicated values of AHo = -5.6 f 0.2 kcal/mole and K = 8.6 f 1.1m-l are found.
Discussion The linear behavior shown in Figure 1 indicates that the assumptions used in deriving eq 5 or 6 are consistent with experimental findings. The use of the polymerization equation, eq 5, is based on the findings of TS’O.~It might be noted that the determination of A H o by eq 5 is not as sensitive to error as is the value of K . The range of error which we have assigned to our determination of K (8.6 f 1.1) does not quite reach the value of 6.7 m-l for K found by Ts’o. A range of error is not assigned by Ts’o. It is possible that if osmotic coefficients could be determined over a range comparable to the range of heats of dilution data, a higher value of K might be found. From the nature of the experimental technique TS’O’Smeasurements were limited to approximately 0.05 m concentration. In view of these considerations the K values seem quite plausible. A calculation of AHo by the second approach, combining osmotic coefficient with heats of solution (15) P. R. Stoesser and S. J. Gill, Rev. 6%. Inatr., in press. (16) H. B. Albert and S. J. Gill, in preparation.
567
CALORIMETRIC STUDY OF 6 - ~ E ' I " Y L P U R I N E
-
4000
I
-e+!
'
2000
IOOOt
0 0
I
I
100
I
150
, 200
250
Figure 1.
data, can be made using eq 7. Ts'o has fitted his osmotic coefficient data to a sixth-degree polynomial which can be employed to calculate values of (a or 1 (a at concentrations given in Table 111. Since the OSmotic coefficient data were taken on solutions above 0.05 m we shall apply TS'O'S equation only to concentrations above this range. The values of 1 - cp (Ts'o) are given in Table I11 along with the calculation of AH" by eq 7. Whereas the application of eq 5 yields a value of AH" = -5.6 f 0.2 kcal/mole, the application of eq 7 in conjunction with osmotic and calorimetric data yields a value of -6.3 f 0.1 kcal/mole. This differenceappears to be beyond experimental error and more likely reflects the different weight that each of the methods places upon the assumption of ideal solution behavior. The application of eq 7 should become increasingly accurate for more and more dilute solutions
where ideal solution behavior always occurs. Unfortunately osmotic coefficient data are most difficult to obtain at these low concentrations and so it seems the best that can be done at present is to assign a value for the heat of self-association of 6-methylpurine in water at 25" as -6.0 f 0.4 kcal/mole. With this value and TS'O'Svalue2 of -1.1 kcal/mole for AGO, the value of AS" is -16 f 1eu. A value of AH" in the range of -6 kcal/mole indicates that the strength of the stacking interaction between these bases is relatively large. This is in at least qualitative agreement with studies on adenylic acid oligomers"-12 which provide an estimate in the range of -8 to -10 kcal/mole. A variety of factors such as steric effects and differences in electronic distribution are undoubtedly the cause of these differences. A number of theoretical calculations have been made of the interaction energies between purine and pyrimidine molecules using different basic assumption^.^^^^ A calculation by Vande Vorst and A. Pullmanla on 6methylpurine assuming vertical overlap of the K electron clouds has given a value of 0.37-0.43 in terms of P"" Hiickel units.l8 With a conversion factor of 16.5 kcal/P"" unit19 the stabilization energy is between -6.1 and -7.1 kcal/mole. It is difficult to assess the precise effect of solvent on these values. The theoretically calculated interaction energies are of a similar magnitude as those observed experimentally and the stacking picture offers a satisfactory explanation of the experimental observations.
Acknowledgments. We wish to acknowledge the assistance from the National Institutes of Health in the form both of research grant support and of fellowship support for one of us (P. R. S.). We also wish to acknowledge the many helpful discussions about this work with H. B. Albert and M. Downing. ~
~
~
(17) B. Pullman, P.Claverie, and J. Caillet, Compt. Rend., 260,5387 (1965). (18) A. Vande Vorst and A. Pullman, ibid., 261, 827 (1965). (19) R.Daudel. R. Lefevore. and C. Moser. "Quantum ChemistwMethods and Applications,'" Interscience. Phblishers, Inc., New York, N. Y.,1961, p 177.
Volume 71, Number 3 February 1967
