Dielectric Studies of Amino Acid Conformation mation between ethanol and chloroform molecules exceeds the heat of dissociation of hydrogen bonding between ethanol molecules, which results in a negative heat of solution in the ethanol-chloroform system. It has been known from infrared spectral analyses that a few alcohol molecules form associated complexes, although their structures and populations have not been completely established yet. Fletchers studied the absorption spectra of the n-decane solution of ethanol-dl in the region of 1.9-2.2 km. He concluded that there exist monomers, acyclic tetramers, and cyclic tetramers with the relative population of 1:3.4:10.9, respectively a t 25 "C.He also studied the absorption spectra of methanol at 40,80, and 120 0C.9He found the coexistence of monomers, dimers, and tetramers in the gas phase. In the chloroform-ethanol system also, the associated complex structures may be rather complicated. In the present work, however, a single value, 1, is assumed for the number of ethanol
2777
molecules which form an associated complex. This theoretical treatment is certainly oversimplified, but the present results of 1 = 3 -2.5 are not unreasonable if we consider that 1 is an averaged value of association numbers which correspond to various types of polymer ethanols.
References and Notes (1) K. Iwasaki, M. Tanaka, and T. Fujiyama, Bunko Kenkyu, 25, 134 (1976). (2) K. Iwasaki, M. Tanaka, and T. Fujiyama, Bull. Chem. SOC.Jpn., 49, 2719
(1976). (3) T.Fujiyama, M. Kakimoto, and T.Suzuki, Bull. Chem. SOC.Jpn., 49, 606 (1976). (4) K. Iwasaki. Y. Katayanagi, and T. Fujiyama, Bull. Chem. SOC.Jpn., in press. (5) "International Critical Tables", McGraw-Hill, New York, N.Y., 1926. (6) G. Scatchard and C.L. Raymond, J. Am. Chem. SOC.,60, 1278 (1938). (7) J. A. Barker, I. Brown, and F. Smith, Discuss. Faraday SOC., 15, 142 (1953). (8) A. N. Fletcher, J. Phys. Chem., 76, 2562 (1972). (9) A. N. Fletcher, J. Phys. Chem., 75, 1808 (1971).
Dielectric Studies of Amino Acid Conformation Joseph A. Walder Depaitment of Chemistry, Northwestern University, Evanston, illinois 6020 1 (Received February 19, 1976) Publication costs assisted by the National lnstitute of General Medical Sciences
The dielectric properties of a number of structurally rigid aqueous amino acids have been reexamined in terms of the Kirkwood theory for the dielectric polarization of polar liquids. Those in which the charged groups are not enclosed in a common hydration sphere have an effective dipole moment, as defined by Kirkwood, substantially less than the true molecular moment calculated on the basis of charge separation. Thus molecular moments and mean intercharge distances for aqueous amino acids cannot be calculated directly from the dielectric properties. Nonetheless, the pattern of the dielectric behavior in a structurally homologous series of amino acids may still provide conformational information. It is shown on this basis, contrary to previous interpretation, that long chain a,w-amino acids (greater than C,) have allowed internal rotational motion in aqueous solution. The lower members in this series appear to exist in the extended configuration.
Among the methods that have been used to gain insight into the structure of small molecules in solution, dielectric measurements have been particularly suitable for the aqueous amino acids. Such investigations provided the principal evidence that in water the neutral form of these species existed as a dipolar or zwitterion.1,2With this result, Wyman was able to apply dielectric studies to the conformational analysis of a variety of dipolar ion^.^,^ Based on an empirical treatment of the data he interpreted the dielectric behavior of the a , w amino acids to indicate that these species existed in water as the freely rotating chains.2 Later Kirkwood gave theoretical support to the empirical approach of Wyman and made direct calculations of the root-mean-square intercharge distances for these specie^.^ The calculated values were in very good agreement with those calculated on the assumption of free rotation about carbon-carbon bonds with either the methods of Kuhnj or Eyring.6 Recently Edward et al. have extended these studies of the
a,w-amino acids to higher members in the ~ e r i e s .In ~ ,contrast ~ to previous findings their observations led them to conclude that these species adopt the fully extended conformation in water. It can be shown, however, that the pattern in the dielectric behavior of this series is not consistent with the extended configuration and in fact indicates the presence of allowed rotational motion although not to the extent of free rotation as was previously thought. In addition their studies of certain structurally well-defined amino acids require that there be given an altered interpretation of the measured dipole moments of dipolar ions from that of Kirkwood.8 Extending the approach of Onsager, Kirkwoodg developed the theory for the dielectric behavior of polar liquids to a stage that remains the most applicable form to this day. From this it becomes apparent that the dipole moment of a molecule, when in a polar solvent, cannot be obtained from dielectric measurements alone. Rather the dislectric properties are related to the moment ji, equal to (,&p)*/2 where ii is the dipole The Journal of Physical Chemistry, Vol. 80, No. 25, 1976
2770
Joseph A. Walder
Pa
-
lp I = e R b
(11
16.2
14.9
(11)
14.6
14.9
TABLE I: Dipole Moments for Rigid Amino Acids Amino acid H, +NCH CO 0 -
(9
--f
(IV)
15.9
21.4
(V)
27.9
32.2
coo-
a Calculated from the data of Edward et a1.O b Intercharge distances calculated using the bond lengths and angles given in Table I1 with the aid of CPK models.
moment of the molecule and the sum of the dipole moment of the molecule and the moment which it induces in its neighbors by hindering their rotation relative to itself. For aqueous dipolar ions the relationship between ,iiand the dielectric constant, t, assumes a particularly simple form:4
where c is the molar concentration of the dipolar ion, EO the dielectric constant of the pure solvent, and 6 the so-called dielectric increment. Although fi is formally a function of composition, saturated aqueous solutions of all aliphatic amino acids correspond to a mole fraction of less than 0.05. Accordingly, for these species 6 is generally constant throughout their entire range of solubility. For structural information 1fi1 is the moment of interest but unfortunately it cannot in practise be obtained from the value of 2. Kirkwood showed, however, that for glycine fi differed by less than 5% from 151, calculated on the basis of charge separation.1° Hence, he concluded that for the aliphatic amino acids, 1fi1 is to a close approximation equal to ,ii itselfa4With this assumption and eq 1 we have
a
where e is the elementary charge and the root-mean-guare dipole separation. Using eq 2 we may then calculate R in a straightforward fashion from dielectric measurements. Recently several other amino acids have been studied in which the intercharge distance is structurally fixed (Table I).s In agreement with Kirkwood's assumption ,ii is approximately equal to (fit for compounds I(glycine), 11, and 111. However for IV and V, ,iiis considerably less than JfiI.The differences beand (fi1 for IV and V, 5.5 and 4.3 D, respectively, are tween ,ii too large to be explained by any factors that might effect such as dipole-dipole interactions or dipole induction in bonds neighboring charged groups. The values of lfiI calculated on the basis of charge separation according to the first relation in eq 2 are to a close approximation correct. Consequently the differences between ,ii and for IV and V must reflect the effects of interactions with neighboring water molecules upon the effective moment E. Thus there must be some aspect of the hydration of IV and V that is not shared by glycine, €1,and 111. One possibility suggests itself. Solvating water molecules will surround the charged ends of these dipolar ions as shown The Journal of Physical Chemistry, Vol. 80,No. 25, 1976
Figure 1. The planar projection of 8-aminooctanoic acid in the extended configuration. Water molecules are depicted hydrating the charged ends of the dipolar ion. Those water molecules labeled B provide backsided hydration. End-to-end distances are shown for the C4, C5, and CB a,w-amino acids to demonstrate the stepwise increase in extended chain length.
in Figure 1.Those water molecules labeled A are oriented in such a way that their moments add to the moment of the molecule. Those labeled B, providing backsided hydration, are so oriented that their moments detract from that of the molecule. For glycine, 11, and I11 the intercharge distance is too small to permit backsided hydration; both the amino and carboxyl groups are encased in a common hydration sphere. Hence fi will more nearly equal ; 1 I for these compounds than for IV and V in which backsided hydration can take place. From the definition of ,ii we may write
fi = ( ) k ) 2t b'fimd)1'2
(3)
where filnd is the moment induced in neighboring molecules. Knowing, fi and lfil we can calculate the component of fiind along the direction of ,G. For IV and V this is approximately 9.6 and 8.0 D, respectively, equivalent to the moment of four-five water molecules.This is not too large to be accounted for by backsided hydration if one considers that both charged groups are subject to this hydration and that the effect extends beyond the first hydration sphere. The argument of course assumes that hydrating water molecules on the backside of the charged groups are more rigidly oriented than those hydrating the outer faces. This is not unreasonable since the hydrocarbon portion of the dipolar ion should result in an ordering of the surrounding water. In any case, it is clear that for the amino acids in which the charged groups are sufficiently far apart to be separately hydrated, fi is substantially less than li~l. Thus the approximate equivalence of fi and JfiI found for glycine cannot be expected for all aliphatic amino acids. Generally the intercharge distance is sufficient to permit separate hydration of both charged groups in which case ,ii will be considerably less than I;I. As such a direct calculation of from eq 2, as performed by Kirkwood, will usually be in serious error. In the series of a,w-amino acids, glycine is the only member in which the charged groups are enclosed in a common hydration sphere. Its value of ,ii then is expected to be disproportionately large. That this is so is reflected in the fact that - ,iigly is far smaller than for any other adjacent homologues in the series (Table 11). Although eq 2 cannot be considered valid, the relationship between 1fi1 and ,ii should remain relatively constant for those members in a homologous series of dipolar ions which present similar structural features. Accordingly the pattern in the dielectric behavior of such a series may provide conformational information even though the precise intercharge distances cannot be calculated. Based on an approximately linear relationship between 6 and R,,,2, the square of the extended chain length, Edward and co-workers have proposed that the aqueous dipolar ions of the a,o-amino acids adopt the fully extended configuration.s However, as shown in Figure 2, this
2779
Dielectric Studies of Amino Acid Conformation
TABLE 11: Increments in Rma, and (~,,W-Amino Acids.Q ARmax,
cn-cn+l
C,-C, C,-C, C,-C,
between the
ab
1.54
~ i iDC ? 1.2
3.2 4.7 5'6 -' 3.2 6'7 -' 3.4 C,-C, 2.6 c*-c, 1.36 3.2 C,-C,Ll 1.14 3.1 UR, and; for glycine are 3.10 and 16.2 D, respec. tively. bThe negative charge was taken to lie between the oxygen atoms along the line of the C,-C, bond. The positive charge of the ammonium group was assumed to lie 0.25 8 beyond the nitrogen atom on the C,-N bond. All C-C-C and C-C-N bond angles were assumed t o be 109.5'. The C,-C, bond length was taken to be 1.52 8, all other C-C bond lengths 1.54 and the C,-N bond length 1.4 8. CCalculated from data in ref 8. 0.98 1.49 1.06 1.42 1.10
a
a,
Repeating these measurements (Table 11)we have found: (1) that the amplitude of the variation is less than given by Edward and co-workers, and (2) that the variation does in fact dampen with increasing chain length. If the aqueous a,wamino acids existed in the extended configuration a similar variation would be expected for the increments in (Table II).ll This appears to hold through Cg. Recall that the disproportionately small increment in ji between glycine and @-alanineis due to the abnormally large value of iifor glycine which is not representative of the series. The increment in ji between the C4 and C g amino acids is approximately 1.5 times that between the C3 and Cq amino acids in accord with the increments in R,,. After C g the increments in ji are essentially invariant12 and do not at all reflect the pattern in Rmax.13 Therefore, from a t least 7-aminoheptanoic acid through 10aminodecanoic acid some degree of rotational motion must be allowed. The forces responsible for limiting the internal rotation of the a,w-amino acids must in large measure be due to hydration, particularly of the charged end groups. For the lower members in the series (through CS-C~),these forces appear to be sufficient to freeze the molecules in the extended configuration. With increasing chain length, the effects of the end group hydration decrease, and the internal degrees of freedom increase, resulting in the development of rotational motion. Since an exact relationship between 1fi1 and ji cannot be obtained the precise extent to which internal rotation is allowed cannot be determined from these data alone.
Acknowledgment. This investigation was supported in part by Grant No. GM-09280 from the National Institute of General Medical Sciences, U.S. Public Health Service, to Professor I. M. Klotz. T h e author is grateful to Professor Klotz for helpful discussions. References and Notes 50
100
Rk,,
150
200
250
(i2)
Figure 2. Plot of 6 vs. Rmaxz,the square of the extended chain length (data from Edward et al.).8 The dotted line indicates the regular stepwise variation in 6.
interpretation neglects a striking stepwise variation in 6 as a function of Rmaxz.This pattern results from the fact that R,, increases in a stepwise fashion with the number of carbon atoms in the chain, n, whereas 6does not. The basis for the alternating pattern in R,,, can be seen in the planar projections of the extended structures (Figure 1).For the values of R,, given by Edward et al.7,s the increment in R,,, when proceeding from an even to odd carbon chain number is always 1.82 A while that from an odd to even carbon chain number is 0.69 A. A consideration of the geometry involved, however, indicates that the variation cannot be fixed but rather should dampen with increasing chain length.
J. Wyman, Jr., and T. L. McMeekin, J. Am. Chem. Soc., 55,908 (1933). J. Wyman, Jr., Chem. Rev., 19, 213 (1936). J. Wyman, Jr., J. Phys. Chem., 43, 143 (1939). J. G.Kirkwood in "Proteins, Amino Acids and Peptides", E. J. Cohn and J. T. Edsall, Ed., Reinhold, New York, N.Y., 1943, pp 294-296. W. Kuhn, Z.Phys. Chem., 175A, l(1935). H. Eyring, Phys. Rev., 2, 39, 746 (1932). J. T. Edward, P. G. Farrell, and J. L. Job, J. Phys. Chem., 77, 2191 (1973). J. T. Edward, P. G. Farrell, and J. L. Job, J. Am. Chem. Soc., 96, 902 (1974). J. G.Kirkwood, J. Chem. Phys., 7,911 (1939). For glycine the intercharge distance is structurally fixed. Other contributions to the moment are relatively small. The so-called even-odd effect found for the nematic to isotropic transition temperatures of certain liquid crystals is an example where such a pattern does result when aliphatic chains are in the extended configuration. See S. MarMia, J. Chem. Phys., 60, 3599 (1974). The dielectric increment of 1I-aminoundecanoic acid was also determined (see ref 8),but had to be done at 40 O C because of solubility problems. The increment in riL between the C T Oand C1l amino acids was unexpectedly large, probably reflecting aggregation of the C1 species. For this reason, the Cl0-C1i increment was not included in Table II. The pattern of increments in R,, after C5 is sensitive to the exact bond lengths and angles chosen. With variation of these parameters, however, we have found R, to always increase in a stepwise fashion and all increments in R,,, after Cs to be greater than the C J - C ~increment. Neither
of these relations are found in E,
The Journal of Physical Chemistry, Vol. 80, No. 25, 1976
