ASSOCIATION OF DIKETQPIPERAZINE IN WATER
3065
~ C ~ ~ o ~ iStudy ~ e tof r Association i ~ ~ of Diketopiperazine in Water
ill* and Leo No11 Department of Chemistry, University of Colorado, Boulder, Colorado 80308 (Received June 16, 1973)
An estimate of -2.1 & 0.5 kcal/mol for the enthalpy of hydrogen bond formation of -CO . .HW-in water at 25’ was determined from heats of dilution measurements on diketopiperasine. This cyclic dipeptide was chosen as a model compound for the study of hydrogen bond interactions of the type found in proteins. The results agree with spectroscopic studies by Susi on 6-valerolactam in water but disagree with studies by Klots and coworkers on N-methylacetamide. The influence of these specific compounds on the structure of the water solvent in the region of potential hydrogen bond formation is advanced as the key factor in the difference of these results. I
Introdaction The thermodynamics of hydrogen bond formation in model compounds which contain carbonyl and amide groups has been of particular interest in interpreting i,he stability of protein structures. The model compound istudies which have been made for aqueous solutions are not in satisfactory agreement. Gucker’s datal for heats of solution for urea in water have been analyzed in various ways assuming self-association of urea, in water by hydrogen bonding. Schellman2 arrived at -2160 cal for AH of dimerization of urea in water with an equilibrium constant of K z = 0.041 m-l. Kresheek and Scheraga3 examined the temperature dependence of the nonidealit,y of urea-water solutions and found similar values. Schellman also re,tlsoned that the urea dimer could consist of structures with a single hydrogen bond and of a cyclic form with Lwo hydrogen bonds. He concluded that both structures were present giving an average of about 4/3 hydrogen bonds per dimer. Thus Schellman concluded that the enthalpy of formation of an amide carbonyl hydrogen bond for urea in water was about - 1.7 kcal. The enhanced solubility of diliehopiperazine in urea solutions as a function of temperature was studied by Gill, et aL4 The results were interpreted to mean that urea and diketopiperazine interact in water to form complex species, the simplest being a dimer. A rough estimate of the enkhalpy of complex formation was determined as -3.4 kcal with a maximum number of I,WQ hydrogen bonds in the structure. A spectroscopic study of N-methyla,cetamide (1) in various
w
H\p I
solvents including water was made by Klotz and Franzen5 and led to the conclusion that the enthalpy of dimerization of this material was essentially zero in water. They could detect no particular infrared bands that might confirm self-association of urea in urea water solutions. A calorimetric study of various acetamides in different solvents by Kresheek and Klotz6b7revealed that heats of dilution for N-methylacetamide were of opposite sign (exothermic) from heats of dilution of urea which are endothermic. Thus a positive heat of association is estimated for dimerization of N-methylacetamide. Hydrogen bonding ideas are not used in explaining these results.? Susi and coworkers8-’l examined 6-valerolactam, which gives two amide-carbonyl hydrogen bonds in a, simple dimer structure, by means of infrared qectroscopy in various solvents, including water. They report a value of AH = -2.8 kcal/rnol for the formation of the amide hydrogen bond in water. In view of this general lack of agreement of such model compound studies in water we have been interested in performing additional. experiments which might give some hope of clarifying the situation. Since diketopiperazine (2) has a rigid ring structure, with carbonyl and amide groups directed in the same direc(1) F. Guclter and W.Pickard, J . Amer. Chem. Soc., 62, 1464 (1940). (2) J. A. Schellman, C. R. Trav. Lab. Carlsberg, Ser. Chim., 29, 230 (1955). (3) G. C. Kresheck and H. A. Scheraga, J . Phys. Chem., 69, 1704 (1965). (4) S. J. Gill, J. Hutson, J. R. Clopton, and N.Downing, ibid., 6 5 , 1432 (1961). (5) I. M. KlotE and J. S.Franzen, J . Amer. Chem. Soc., 84, 3461 (1962). (6) C . C. Kresheck and I. M. Klotz, Biochemistry, 8 , 8 (1969). (7) G. C. Kresheck, J . Phys. Chem., 73, 2441 (1969).
H. Susi, S. N. Timasheff, and J. S. Ard, J . B i d . Chem., 239, 3051 (1964). (9) H. Susi and J. S. Ard, Arch. Biochem. Biophys., 117, 147 (1966). (10) H. Susi, J . Phys. Chem., 69, 2799 (1965). (11) H. Susi in “Structure and Stability of Biological Macromole(8)
cules,” S. N. Timasheff and G. D. Fasman, Ed., Marcel Dekkcr, New Y o r k , N. Y . , 19ti9.
The Journal of Physical Chemistry, VoE. 76, N o . 21, 1972
Q=C
--N
/ \
I
effects minus solvent mixing heat effects. The error range is regarded here as an approxi~ationto the standard deviation. The most accurate determinations occur a t dilution fractions near ' / z ~ A value of q = 20 cal/mol at f = for a solutioii of 13.1M means that upon mixing equal volumes of solution with water there will be a temperature rise of 0.0Olo
N-I3
1
c=o
~
2
tion, as compared to the possible existence of various structural forms possible in urea and N-methylacetamide, it afiords one the opportunity of studying a specific rigid configuration. Crystallographic studies also indicate the fcrmation of linear hydrogen-bonded polymers in the i?olid structure.l2 Unfortunately the solubility of DMP is too low (1.66 % at 25") to permit extensive calorimetric or spectroscopic studies without special procedures. With the recent development of a high-sensitivity flow micr~calorirneter'~we found that the dikc topiperazine water-system could be studied by heats of drlution measurements.
Table I : Heats of Dilution of Diketopjperazine with Water, Initial Concentration 0.131 M Dilution fraction,
J, 10/Zl
6/6
"7 "/a
'/z '/a 2 / ~
'/e
xperimental S
e
~
~
~
~
caI/mol (200)
3.110.2 7.41t0.3 10.4k0.3 12.110.2 17.3 f 0 . 2 23.9 1t 0 . 4 27.4i0.9 32.3rtO.Fj
q,
cal/mol (25')
q,
oai/moi (30')
q,
cai/mol (35")
3.3rt0.3 2,510.4 2.110.3 6.2rt0.3 4.fif0.4 4.210.4 1 0 . 8 1 0 . 5 8.9k09 6 . 2 1 1 . 0 11.54~0.4 9.2f0.4 9.110.5 16.8 f 0 . 6 1 4 . 3 f 0 . 6 13.6 10 . 4 22.8 f 0 . 5 19.4 =J= 0 . 5 1 7 . 1 i: 1 . 0 22.9rtl.4 21.4i1.1 17.211.9 2 5 . 6 r t 2 . 8 1 9 . 6 4 ~ 2 . 32 0 . 0 f 2 . 0
~
The diketopiperazine used in this work was obtained from Eastnian Chemicals. Similar results were obtained on both unrecrystallixed and recrystallized material. Solutions were prepared using distilled tvater to a concentration of 0.131 M . It was the highest concentration thak could be used over the range of temperatures studied without the occurrence of precipitation. T tie flow- ~ a l o r i r n e t e r used ~ ~ in this investigation can be operated conveniently a t several temperatures. Temperatures were chosen near to room temperature to allow io-r maximum stability. The calorimeter can be calibrated electrically and the accuracy of the unit had been veri6ed t o 1% by sucrose dilution experiment~.'~The flow. of two solutions to be mixed in the calorimeter i s regulated by synchronous motor driven precision syringes. Various rates of flow are accessible by different gear ratios. The viscous hea,t effect of mixing mater with water was determined for the different rakes of mixing used and at the various temperatures of the different experiments. This water\ d e r correction was applied Lo each solution measurement ~
he heat of dilution was determined for various fractions of dilution f, where f times the initial concentration (0.131 A I ) gives the final solution concentration. The heat effect per mole of solute is denoted by q (cal/rnol). In Table I we have summarized the results of a number of dilution experiments at temperatures of 20, 25, 30, and 35". The heat effects are quite small. h range of values is indicated for each temperature anti dilution fraction as determined from ten repetitive measurements on solution mixing heat The Journal oj Physical Chemistry, Vol. 76, N o . 81, 1978
q-
The data in Table I can be expressed in terms of JLL, the relative apparent heat content. In principle the concentration dependence of $L can then be used to obtain the thermodynamic parameters of the self-association of the material.14 An alternate explanation involving a model based on solute-solvent interaction^'^-^^ might also be used to interpret the heat effects observed. The question of this second approach was raised by a referee and is highly pertinent. The choice of which model should be used has generally depended upon the chemical nature of the solute and solvent. Where very weak solutesolute interactions occur as in aqueous sucrose solutions then the solutesolvent model works quite well.15 When strong solute-solute interactions are possible as in urea then the solute-solute model is adequate.2 When a sufficient range of concentrations is possible for accurate determinations of osmotic coemcients as a function of molality, then one can show from the forms of the power series which model provides the most suitable representation of the system. In the case of diketopiperazine the solubility is not suficient for accurate osmotic coefficient data. The choice of the solutesolute model in this case is then governed by the presence of amide carbonyl hydrogen bonds as found in systems such as urea. The geometry of dilietopiper(12) R. B. Corey, J . Amer. Chem. Soc., 60, 1598 (1938). (13) S. J. Gill and V. Chen, Rev. Sci. Instrum., 43, 774 (1972). (14) S. J. Gill and E. L. Farquhar, J . Amer. Chem. Soe., 90, 3039 (1968). (15) R. H. Stokes and R. A. Robinson, J. f h y s , Chem., 70, 2126 (1966). (16) R. A. Robinson and R. H. Stokes, ibid., 65, 1924 (1961). (17) G. Scatchard, J. Amer. Chem. Soe., 43, 2387 (1921).
3067 azine also allows for the convenient formation of two hydrogen bonds on each side, thus giving the possibility of even stronger solute-solute interactions than found in [ m a , We shall then assume that the solute-solvent equilihria are of lesser importance than the solutes d u t e equilibria II in Table I the values of #L are experimental error) directly proportional t o th+ concentration. This means that the degrer of self-whociation ii so small that the process of dilution alters the concentration of dimers in direct propohon to the fraction of dilution. I n terms prepiously developcd14 the heat of infinite dilution #L of a sdutlon at coneentration m will be related to q by the apparent relative heat content $'L, for a solution of concentration f j t bv q = 4/L - $'I,. Where the extent of dimerization is very small one finds that -#t = nzMAH, so one obtajins the result that q = -m(1 - f ) K A M , where 777 is the initial solution concentration, ie., 0.132 34 in our pa~ticular case. The values of q/ (4 - j ) as determined from the dilution experiments with factors 2/a. I / a 1 and give average values of 36.3, 33.7, 28.3, and 26.1 al/mol with an approximate standard deviation of f .B cai/mol for the temperatures of 20,23,30, and 35". Thr important property of the factor y / ( l - f) is that it is direcity proportional to the equilibrium constant for the dimerization process. Thus from the temperature dependence of K given by
H
w
H
13
s
d lnM/d(l/l')
=
-AH/R
(1)
we can use the fact that q/(1 - f) is proportional to K t o obtain
d I n [ g / ( l - f)1/d(l/T) = - A H / R
(2)
Jvhere we have assunied that AH and in are essentially constmt over the range o f temperature of interest. '@hen the values of q/(l - f ) are inserted into the integrated form of eq 2 at the respective applicable iernpt~aturesp-e find that A H has a value of -4.2 f 0.9 kcal/mol where the error is the standard deviation. .4plo t of q/(1 -- f ) us. LIT is shown in Figure 1. A talue of PI: can now be calculated from q / ( l - j = --mKAH, and a t 25",db' i s found to equal 0.06 f 0.01 M-1.
The values of AH and K determined by this analysis of course rely .m the assumption that the calorimetric data can be treated by a description of self-associated complexes in iiolution. The approximation that the pelf-association ie small is verified by the calculated equilibrium constant, for with nz = 0.13 and K = 3 X 10P, the fraction of monomer which dimerizes is aboui 0.008. At thew low concentrations we would expect these uncharged solutes to behave ideally, which 1s another necessary condition for the above analysis. If we assume that the diketopiperazine is forming a cyclical hydrogen bonded dimer in solution as
then a value of AH(NH. .OC) for cis hydrogen bond formation in water would be -2.1 I: 0.4 kcal/mol. This value is slightly more exothermic than the estimate made by Schellman2 of -1.5 kcal/mol but in reasonable agreement with the value of -2.8 kelal/mol given by Susi.ll
I
3.40
U
2 3.20
I
3.00 3.20
I
3.25
I
1
3.30
3.35 xi03
(IIT)
I 3.40
I 0.45
Figure 1. This figure represents a plot o f h [q/l - f ] us. 1 / T . The slope gives - AH/R, where R is the gas constant.
The lack of agreement with the studies on N-methylacetamide5-' raises a number of questions. In the case of N-methylacetamide the amide group is presumed t o be in the trans configuration in solution, whereas in diketopiperasine it is definitely cis. One might therefore look for an explanation for the differences in the difference of cis and trans structures. Tsuboil8 studied N-methylacetamide in GC14 and determined a AH = -3.8 kcal/mol for hydrogen bond association. This trans value compares well with determinations of the cis form in CC14 by Susi and h r d g of -3.5 kcal/mol. So it would not appear that the effect of cis and trans is important in the nonaqueous solvent CCl,. One 4s left with the idea that the overall structure of the model compound used plays 8 sensitive role in the self-association process when water is the soivent. Susi" has suggested that the bifunctional nature of water, i e . , a proton-donating and a. proton-accepting molecule, is the basis for forming relatively stable hydrogen bonded complexes of the 6-vaierolactam type. The difference observed with N-rnethyla~et~amide might be due to the effect of the N-methyl group on the Rtructure of the water solvent. (18) M. Tsuboi, YNippon Kagaku Zasshi, 7 6 , 376 (1955) The Journal of Physical Chemistry, Vol. 76, N o . 21, 2978
ANDREFEILLOLAY AND MICHEL LUCAS
3068 Heats of dilution measurements were also made by Mreslzeck on ilr,N.-tlfmethylacetamide in water and he found them to be even more exothermic than N-methylacetamide? Since B bonding is ruled out for the dimethyl compoiind some other form of interaction is implied such as hydrophobic interactions. These solvent-typ3 interrrctions -vvou!d be expected to give an exothermic effect on dilution. In the case of Nmeth,vlacctarr,ide both H bonding and methyl hydrophobic effects would be present. The N-methyl group in this molecule possibly affects the water structure in the wvironmcnt of' the carbonyl group where an H bond could form. En the ca3e of the ring structures, diketopiperaxine b,n d 6-vderolactam, the C Hz groups at-
tached to the NH are farther removed from the sensitive H bonding region and the effect of them groups on the solvent would presumably be much less. The overall conclusion from these arguments is that hydrogen bond strengths in proteins will depend on the hydrophobic groups adjacent to tho amide and carbonyl groups. When hydrophobic groups are small we can expect, the formation of hydrogen bonds in water to have entlialpies of - 2 to -3 kcallrnol,
Acknowledgment. We wish to thank the National Institutes oi Health and Xational Science Foundation for making grants available for the support of this work.
elium and Methane in Aqueous Tetrabutylammonium tioms at 25 and 350
y Andre Feillolay and Michel Eucas* Dipartcment de G6nie Radioactif, 92-Fontenay-auz-Roses, France
(Receiced March 3, 1979)
PubEica.iion costs assisted by the Commissariat a' t'energie atomique
The solubility of helium and methane in aqueous BudNBr solutions has been determined at 25 and 35". The saltingout constant and the enthalpy of solution have been calculated according to the scaled-particle theory neglecting the influence of dispersion forces, and these values are compared to experimental values. For helium the fit between the calculated and experimental dependence of enthalpy and salting-out constant on salt concentrations is good. For other solutes the agreement decreases as the polarizability of the solute is increased.
~~troducti~n The scaled-particle theory has been used rather successfu'ily by Pierotti' to predict the values of the free energy and enthalpy of solution for nonpolar molecules in pure water. Lebowitz and Rowlinson2 extended the Percus-Yevick theory to mixtures of hard spheres, thus a!lo.ci-ing the extension of the calculations to aqueous salt solutions. We have compared previously experimental and calculated thermodynamic data for the process of solution of gaseous hydrocarbons in aqueous teiraatlcylammonium bromide mixture^.^^^ lt has been found that the fit between the two sets of data was only qualitative. This was ascribed to the existence of dispersion forces, as the scaled-particle theory does not take them in account. Thus the need arises for measuremen ts of the solubility ol a less polarizable gas in aqueous salt solution in order to reduce the Importance of the dispersion forces. I n the present paper we report the solubility of The Journal of Physical Chemistry, Vol. 76, N O .21, 19'72
helium in aqueous tetrabutylammonium bromide solutions at 25 and 35" and we compare the enthalpy and salting out constant calculated from experimental solubility data and from theory. Some measurements of methane solubility are also given in order to extend the literature measuremexit~.~
Experimental Section Chemicals. BupNBr (South Western Analytical Chemical), polarographic grade, was used without lurther purification. Helium and methane were obtained from 1'Air Liquide and stated l o be at least 99.99% purity. (1) R. A. Pierotti, J . Phys. Cham., 69, 281 (1965). (2) J. 1,. Lebowitz and J. S . Rowlinson, J . Chem. Phys., 41, 133 (1964). (3) M. Lucas and A. de Trobriand, J . Phys. Chew., 75, 1803 (1971). (4) M.Lucas and A. Feillolay, ibid., 75, 2330 (1971). (5) W. Y . Wen and J. Hung, ibid., 74, 170 (1970).
