Apparent molal volumes of amino acids, N-acetylamino acids, and

Sep 21, 1982 - Chem., 75, 1120 (1971). (10) R. B. ... Soc., 75, 5139 ...... 152.47. 164.9. 140.0b. 139.6= 0 V*(dipeptide) = V°(amino acid, 1) + V°(a...
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86

J . Phys. Chem. 1984,88, 86-92

Apparent Molal Volumes of Amino Acids, N-Acetylamino Acids, and Peptides in Aqueous Solutions' Awadhesh K. Mishra and Jagdish C. Ahluwalia* Department of Chemistry, Indian Institute of Technology Delhi, New Delhi 110016, India (Received: September 21, 1982; In Final Form: April 11, 1983)

The apparent molal volumes of 24 a-amino acids, 6 N-acetylamino acids, and 9 peptides in aqueous solutions have been determined at 298.15 K from precise density measurements. Limiting partial molal volumes, P, have been also evaluated from the apparent molal volumes at various solute concentrations. Group additivity relationships were examined from the P data of these solutes as well as from those of several homologous series of compounds available in the literature. It has been shown that the presence of hydrophilic groups in close proximity in a-amino acids and N-acetylamino acids decreases the functional-groupcontribution as well as the contribution due to hydrophobic hydration toward P relative to those observed in the monofunctional compounds. It is also found that the v" values of the peptides estimated from the P values of the constituent amino acids, with a proper consideration of change in the electrostrictionvolume due to separation of the charged centers, agree with the experimental values. Concentration dependence of the apparent molal volumes of the solutes has been explained on the basis of combined effects of hydrophilic and hydrophobic solute-solute interactions mediated through the typical structure of water.

Introduction The partial specific volume of a protein is a characteristic parameter that has been used to elucidate several processes which depend on the protein conformation or during which the protein conformation changes, e.g., protein aggregation or polymerizat i ~ n , ~conformational -~ transitions of protein^^-'^ and polyp e p t i d e ~and , ~ ~antigen-antibody rea~ti0ns.l~ The changes in the partial specific volume of the macromolecules during such processes depend on the intra- and intermolecular interactions as well as on the electrostriction of the solvent due to the charged moieties present in the macromolecule and on the charge-neutralization processes.15 However, due to the structural complexities, it is extremely difficult to separate the various contributions that give rise to the observed volume changes in macromolecular reactions. Volume changes in such reactions have been explained by using volume data on small model compounds.16-ls Furthermore, the model-compound data are also known to elucidate the various effects which give rise to the observed partial specific volume of a macromolecule.16-'8 Since the early volumetric studies of small organic solutes by TraubeI9 there have been numerous investigations on the partial or apparent molal volumes of these solutes in aqueous solutions.2h55

(1) A major portion of this work is from A. K. Mishra, Ph.D. Thesis, Indian Institute of Technology, New Delhi, India, 1981. (2) J. M. Cassell and R. G. Christensen, Biopolymers, 5, 431 (1967). (3) R. Josephs and W. F. Harrington, Biochemistry, 7, 2834 (1968). (4) B. R. Gerber and H. Noguchi, J . Mol. Biol., 26, 197 (1967). (5) T. lkkai, T. Ooi, and H. Noguchi, Science, 153, 1756 (1966). (6) W. Kauzmann, Adu. Protein Chem., 14, 1 (1959). (7) S.Lapanje, M. Lunder, V. Vlachy, and J. Skerjanc, Biochim. Biophys. Acta, 491, 482 (1977). (8) S.Katz and T. G. Ferris, Biochemistry, 5, 3246 (1968). (9) S. Katz and J. E. Miller, J . Phys. Chem., 75, 1120 (1971). (10)R. B. Simpson and W. Kauzmann, J . Am. Chem. Soc., 75, 5139

(1953). (11) H. Noguchi and J. T. Yang, Biopolymers, 1, 359 (1963). (12) Y.Ohta, T. J. Gill, and C. S. Leung, Biochemistry, 9, 2708 (1970). (13) C.L. Stevens and M. A. Lauffer, Biochemistry, 4, 31 (1965). (14) R. Jaenicke and M. A. Lauffer, Biochemistry, 8,3083 (1969). (15) M. A. Lauffer, "Entropy Driven Processes in Biology", SpringerVerlag, West Berlin, 1975. (16) J. Rasper and W. Kauzmann, J . Am. Chem. Soc., 84,1771 (1962). (17) W. Kauzmann, A. Bodansky, and J. Rasper, J . Am. Chem. Soc., 84, 1777 (1962). (18) L. M. Krausz and W. Kauzmann, Arch. Biochim. Biophys., 139, 80 (1970). (19) J. Traube, Samm. Chenz. Vortr., 4, 255 (1899).

0022-3654/84/2088-0086$01.50/0

The effects of hydrogen bonding,2&22e l e c t r o ~ t r i c t i o n , ioni~~-~~ z a t i ~ n , ~hydrophobic ~-~' i n t e r a ~ t i o nand , ~ ~zwitterion formation,33 (20)J. T. Edward, P. G. Farrell, and F. Shahidi, J . Chem. Soc., Faraday Trans. I , 73, 705 (1977). (21) F. Shahidi, P. G. Farrell, and J. T. Edward, J . Chem. Soc., Faraday Trans. 1, 73, 715 (1977). (22)S. Terasawa, H. Itsuki, and S. Arakawa, J . Phys. Chem., 79, 2345 (19isj. (23) E. J. King, J . Phys. Chem., 73, 1220 (1969). (24) F. Shahidi and P. G. Farrell, J . Chem. Soc., Faraday Trans. 1,74, 858 (1978). (25) F. Shahidi and P. G. Farrell, J . Solution Chem., 7, 549 (1978). (26)S. Cabani, V. Mollica, L. Lepori, and S. T. Lobo, J . Phys. Chem., 81, 982 (1977). (27)S . Cabani, V. Mollica, L. Lepori, and S. T. Lobo, J . Phys. Chem., 81, 987 (1977). (28) H. Hoiland, J . Chem, Soc., Faraday Trans. I , 71, 797 (1975). (29)H. Hoiland and E. Vikingstad, J . Chem. Soc., Faraday Trans. 1 , 71, 2007 (1975). (30)S.Cabani, G. Conti, and L. Lepori, J . Phys. Chem., 76, 1338 (1972). (31) S.Cabani, G. Conti, and L. Lepori, J . Phys. Chem., 78, 1030 (1974). (32) F.Franks, J . Chem. Soc., Faraday Trans. I , 73, 830 (1977). (33) S.Cabani, G. Conti, E. Matteoli, and M. R. Tine, J . Chem. Soc., Faraday Trans. I , 77, 2371 (1981). (34) F. J. Millero, A. L. Surdo, and C. Shin, J . Phys. Chem., 82, 784 (1978). (35) C.Jolicoeur and J. Boileau, Can. J . Chem., 56, 2707 (1978). (36) J. C. Ahluwalia, C. Ostiguy, G. Perron, and J. E. Desnoyers, Can. J . Chem., 55,3364 (1977). (37) M. E. Friedman and H. A. Scheraga, J. Phys. Chem., 69, 3795 (1 965). (38) C. Jolicoeur and G. Lacroix, Can. J . Chem., 54, 624 (1976). (39) M. Manabe and M. Koda, Bull. Chem. Soc. Jpn., 48,2367 (1975). (40) T. Nakajima, T. Komatsu, and T. Nakagawa, Bull. Chem. SOC.Jpn., 48, 783 (1975). (41) M. Sakurai, T. Komatsu, and T. Nakagawa, Bull. Chem. Soc., Jpn., 48, 3491 (1975). (42) H. Hoiland, Acta Chem. Scand., Ser A , 28,699 (1974). (43) J. E. Desnoyers and M. Arel, Can. J . Chem., 45,359 (1967). (44) R. Zana, J . Phys. Chem., 81, 1817 (1977). (45)F. J. Millero in "Water and Aqueous Solutions: Structure, Thermodynamics, and Transport Processes", R. A. Horne, Ed., Wiley-Interscience, New York, 1972. (46) J. Kirchnerova, P. G. Farrell, and J. T. Edward, J . Phys. Chem., 80, 1974 (1976). (47) E. J. Cohn and J. T. Edsall, "Proteins, Amino Acids and Peptides as Ions", Reinhold, New York, 1943. (48) G. DiPaola and B. Belleau, Can. J . Chem., 56, 1827 (1978). (49) H. D.Ellerton, G. Reinfelds, D. E. Mukahy, and P. J. Dunlop, J . Phys. Chem., 68, 398 (1964). (SO) F. T. Gucker, Jr., W. L. Ford, and C. E. Moser, J . Phys. Chem., 43, 153 (1939). (51)H . F. Tyrrell and M. Hennerby, J . Chem. Soc. A., 2724 (1968). (52)W. Devine and B. M. Lowe, J . Chem. SOC.A , 2113 (1971). (53) F. T. Gucker and T. W. Allen, J . Am. Chem. Soc., 64, 191 (1942).

0 1984 American Chemical Society

Molal Volumes of Aqueous Amino Acids and Peptides

The Journal of Physical Chemistry, Vol. 88, No. I , 1984 87

I

I v

u , k1-

r2y

1-31

CL+

1-54

C61

1-71

m, position of methylene group in alkyl chain

Figure 1. Limiting partial molal volume contribution of the mth methylene group in the alkyl chains of several homologous series of compounds: (1) n-alkylammonium ions, ref 43; (2) n-alkylamines, ref 31; (3) n-alkyl carboxylates,ref 42; (4) n-alkyl carboxylic acids, ref 41 and 42; ( 5 ) n-alkyl alcohols, ref 22, 37-40; (6) a-amino acids (this work); (7) w-amino carboxylic acids, ref 24; (8) dipeptides (this work); (9) Nacetylamino acids (this work); (10) n-alkyl amides, ref 60 and 61; (1 1) n-alkylureas, ref 62.

N-acetylamino acids may represent a value close to that in polypeptides or proteins.

Experimental Section The a-amino acids, N-acetylamino acids, and peptides were procured from either Sigma or Merck. N-acetyl-a- and y-amino-n-butyric acids were prepared by the acetylation of a- and y-amino-n-butyric acids, respectively, with acetic anhydride and were recrystallized twice from water-methanol mixture. Purity of the solutes was checked by high-performance liquid chromatography. Since the solutes were chromatographically homogeneous, they were used without further purification. Before we made the solutions for density measurements, the solutes were dried for about 48 h under vacuum over P,Os at room temperature. All the solutions were made by weight with deionized water, which was obtained by passing the distilled water through Barnstead mixed bed ion exchanger and then distilling from alkaline permanganate. Density measurements were performed immediately after making the solutions. The densities were measured at 298.15 K with an Anton Paar vibrating tube digital densitymeter Model DMA 602/60. Thermal stability of the liquid flowing through the jacket around the density measuring cell was maintained within fO.OO1 K by a Tronac PTC-40 proportional temperature controller. The temperature of the thermhtated bath system was set at 298.15 f 0.002 K with a platinum resistance thermometer (certified by National Bureau of Standards) and a G-2 Mueller bridge. The densitymeter was calibrated with the known densitiess6 of air and water every day. Reproducibility of the density measurements was better than 3 PPm.

etc., on the partial molal volumes of the solutes have been estimated. Recently, many authors have investigated the aqueoussolution volumetric properties of some protein constituents, viz., the amino acids and p e p t i d e ~ , ~for , ~different ~ - ~ ~ reasons. Apparent molal volumes of several a-amino acids were determined by Millero et al.,34who calculated the number of water molecules Results bonded to the charged centers of the a-amino acids. They also The apparent molal volumes, 4” of the solutes were calculated estimated various group contributions toward limiting partial molal from the densities of the aqueous solutions by using the equation volumes. Jolicoeur and B o i l e a ~have ~ ~ measured the apparent = M / d - 1000(d - do)/mddo (1) molal volumes, &, of several peptides and examined the group additivity relationships in those compounds. Ahluwalia et al.36 where, do is the density of water (0.997 0429 g ~ m - ~M) is, ~ the~ have shown that rather poor group additivity for the apparent solute molecular weight, m is the molality of the solution in units molal volumes of several a-amino and a-amino w-carboxylic acids of mol kg-’ (of H,O), and d is the solution density. The densities is due to the charged end groups, NH3+ and COO-, of the amino and dtiof the solutes at various concentrations are given in Table acids which interfere with each other when they are separated Iss7 Ionizations of the a-amino acids and peptides in aqueous by less than three methylene groups. An examination of the solutions, where these solutes exist mainly in the zwitterionic form, P m ( C H 2 ) ,the partial molal volume contribution of the mth are reporteds8 to be little, and hence no correction for the volume methylene group, in various homologous series of s o 1 ~ t e s ~of ~ionization ~ ~ ~was ~ considered ~ ~ ~ ~necessary ~ ~ ~in the values of 4”. The (vide Figure 1) reveals that P,(CH2) tends to attain a constant limiting partial molal volumes, P, were obtained by least-squares value of ca. 16 cm3 mol-’ only for m > 4. Further, the deviations values to the equation fitting of the in the P,(CH,) values from the average value of 16 cm3 mol-’ 4u = P Sum (2) are prominent in ionic species such as RCO, or RNH3+and have been attributed to the effect of electrostriction in such comwhere S , is the experimental slope. P and S , values together p o u n d ~ .In~ ~ the light of these findings it would be worthwhile with their standard errors are given in Table 11. to measure the aqueous-solution molal volumes of a large number The pK, valuess9 of the N-acetylamino acids and aspartic and of the naturally occurring amino acids and examine the limiting glutamic acids suggest that these compounds undergo a considpartial molal volume contributions of the amino acid side chains erable degree of ionization in aqueous solutions. The contribution and peptides in order to check the applicability of a group adof volume of ionization, 4K,,, can be approximated as ditivity scheme. Besides, it would be interesting to see the changes 4Kon= P ( A - ) P(H+) - P ( H A ) in the group contributions of limiting partial molar volume upon transferring the side chains from the a-amino acid to other amino = P(NaA) - P(HA) - P(Na+)- P(H+) (3) acid derivatives, e.g., N-acetylamino acids or peptides. The where P ( A - ) , P ( N a + ) , P ( H + ) , P ( H A ) , and P ( N a A ) are contributions of the peptide group (CONH), the peptide backbone the limiting partial molal volumes of acid anion A-, Na+, and H+ unit (CH,CONH), and the alkyl side chains toward P,could ions, undissociated acid, and its sodium salt, respectively. P ( N a + ) furnish a fundamental set of data for predicting the partial molal and V ( H + ) were taken from miller^^^ and are -6.6 and -5.4 cm3 volumes of proteins or polypeptides in aqueous solutions. The mol-’, respectively. P ( N a A ) for the sodium salts of N-acetylN-acetylamino acids constitute a ciass of compounds in which the glycine, N-acetyl-DL-alanine,and N-acetyl-y-amino-n-butyric acid electrostriction effect would not be present to perturb the partial were measured (vide Tables I and 11) and used to compute the molal volume contribution of the peptide or alkyl groups. In proteins or polypeptides the majority of the alkyl side chains are situated in the environment of dipolar CONH groups. Thus, the (56) J. P. Elder, Methods Enzymol., 61, 12 (1979). partial.mola1 volume contribution of the alkyl side chains in the (57) Available as supplementary material. See paragraph at end of text

+

+

(54) E. J. Cohn, T. L. McMeekin, J. T. Edsall, and M. H. Blanchard, J . Am. Chem. Soc., 56 784 (1934). (55) S. Cabani, G. Conti, E. Matteoli, and M. R. Tine, J. Chem. SOC., Faraday Trans. 1 , 77, 2385 (1981).

reearding sumlementarv material. -(58) 1 P.’Greensteinand M. Winitz, “Chemistry of the Amino Acids”, Wiley-Interscience, New York, 1961. (59) R. M. Izatt and J. J. Christensen, “CRC Handbook of Biochemistry and Molecular Biology”, Vol. 1, G. D. Fasman, Ed., CRC Press, Cleveland, OH, 1976.

88

The Journal of Physical Chemistry, Val. 88, No. 1, 1984

Mishra and Ahluwalia

TABLE 11: Limiting Partial Molal Volumes of @-AminoAcids, Peptides, and N-Acetylamino Acids in Aqueous Solutions at 298.15K no. concn range. S,, cm3 mol-' of mol (kg of ' compd v",cm3 mol-' (kg of H,O)-l data H,O)-I Vo(lit.), cm3 mol-' a-Amino Acids DL -alanine ( Ala)a 60.42F 0.02 0.74i 0.07 12 0.02-0.49 60.61,b 60.6,c 61,d 60.47,e 60.45,f60.62,fi 60.3,h, 60.47' 75.50i 0.02 0.67A 0.10 12 0.03-0.36 DL-a-aminobutyricacid (Abu) 75.54,'75.635 2.8i 0.4 L-arginine (Arg) 123.86i 0.09 8 0.07-0.45 127.34" 140.06i 0.06' 2.8 i 0.9' L-arginine hydrochloride (Arg.HC1) 9 0.01-0.14 74.8?- 0.2m -4 i 8" L-aspartic acid (Asp) 7 0.01-0.03 73.83" 95.63F 0.05 1.1i 0.5 L-asparagine hydrate (Am-H, 0 ) 6 0.04-0.14 L-glutamic acid (Glu) 89.85i O . l O m 1.1i 0.1" 7 0.02-0.08 85.88e L-glutamine (Gln) 93.61t 0.07 2.4i 0.6 7 0.01-0.20 43.19 0.02 glycine (Gly) 0.90i 0.04 16 0.01-1.01 43.2,b 43.5,c44,d 43.19,e 43.25,,f 43.39,g 43.5,h43.22,"43.20.'' 43.29,P42.9Q L-histidine (His) 98.3i 0.1 10 i 3 98.79,"99.3r 7 0.02-0.06 L-hydroxyproline (Hyp) 84.49I0.01 0.73i 0.03 8 0.09-0.43 Laisoleucine (Ile) 105.80i 0.07 -0.5 1 9 0.02-0.10 L-leucine (Leu) 107.83i 0.05 -1.3i 0.8 10 0.01-0.12 107.5,b 108,d107.74,e 107.75' L-lysine hydrochloride (Lys.HC1) 2.3i 0.8' 124.76t 0.08k 7 0.01-0.21 L-methionine (Mst) 105.57i 0.02 -0.4i 0.2 10 0.02-0.14 105.35" norleucine (Nle) 107.93t 0.05 -1.2t 1.2 9 0.01-0.07 norvaline (Nva) 91.70t 0.02 0.49t 0.08 8 0.05-0.41 L-phenylalanine (Phe) 122.2?- 0.1 -8 t 4 8 0.01--0.06 121.2,b 121.3,d121.48" L-proline (Pro) 82.63t 0.05 0.5i 0.2 9 0.06-0.45 81.0,b3C81,d 82.83" L-serine (Ser) 60.62t 0.03 1.3i 0.2 9 0.04-0.34 60.62,f60.3h L-threonine (Thr) 76.83i 0.04 1 . 2 i 0.2 7 0.06-0.27 DL-tryptophan (Trp) 143.8i 0.2 9 0.007-0.014 144.1.c143.91" 5 2 19 143.7I0.3s OS L-tyrosine (Tyr) 124.4t 0.2 -6 i 28 7 0.004-0.01 124.3I0.ls 0 8 L-valine (Val) 90.65i 0.03 0.4F 0.2 11 0.02-0.20 91.3,b91.05,c91,d 90.78",O Peptides diglycine (Gly,) 76.23I 0.03 3.2i 0.1 10 0.01-0.17 76.27,f76.34,"77.2f triglycine (Gly,) 112.11F 0.03 5.4I0.4 8 0.02-0.11 111.81,f 113.5t tetraglycine (Gly,) 149.6i 0.1 23 i 11 15 0.003-0.016 149.7f glycyl-DL -alanine (Gly-Ala) 92.37i 0.02 2.9i 0.2 8 0.04-0.15 glycyl-DL-a-amino-n-butyricacid (Gly-Abu) 107.81t 0.05 2.6I0.8 10 0.02-0.10 glycyl-L -valine (Gly-Val) 121.99t 0.02 1.7I 0.4 10 0.01-0.10 glycyl-L-leucine (Gly-Leu) 139.70I 0.07 0.9i 1 10 0.02-0.10 L-leucylglycine (Leu-Gly) 145.34i 0.04 0.6i 0.4 6 0.04-0.16 2,5-diketopiperazine (Dkp) 76.73i 0.07 1 i 1.5 10 0.02-0.09 76.70' N-Acetylamino Acids N-acetylglycine ( AcGly) 88.39i 0.05m -0.14i 0.1" 7 0.07-0.24 N-acetylglycine sodium salt ( AcGlyNa) 75.14i 0.04k 0.2t 0.2' 9 0.04-0.20 N-aCetyl-DL -alanine ( AcAla) 105.78i 0.05m -0.54 I0.08" 7 0.11-0.37 N-acetyl-DL-alaninesodium salt (AcAlaNa) 92.46i 0.01' -0.48i 0.11' 8 0.03-0.22 N-acetyl-DL-a-amino-n-butyricacid 121.44i 0.05m -0.54i 0.08" 9 0.08-0.39 (Ac-a-Abu) N-acetyl-7-amino-n-butyric acid (Ac-7-Abu) 120.55i 0.03, -2.7i 0.5" 8 0.03-0.12 N-acetyl-7-amino-n-butyric acid sodium salt 108.94i 0.03" -1.8I 0.2' 8 0.02-0.19 (Ac-7-AbaNa) N-acetyl-DL-valine (AcVal) 136.63i 0.03m 0.6i 0.3n 6 0.07-0.13 N-acetyl-DL-leucine ( AcLeu) 152.47t 0.04In -0.1i 0.1" 8 0.03-0.08 a Abbreviations of the compounds are given in the arentheses. Reference 46. Reference 47. Reference 48. " Reference 34. Reference 35. LReference 48. ?Reference 24. Reference 36. Reference 49. 7value obtained = V' + b,c, where c is the solute concentration in units of mol dm-' and b , is an empirical from the equation @, - 1.86821'2 constant. Value of b,. V' value obtained from eq 4 with AVlon = -11.5 cm' mol-'. " S, value of eq 4. O Reference 50. Reference 51. Reference 52. Reference 53. ' Since errors in S , values in these cases are very large, concentration dependence has been assumed to be zero; hence, v" values are the averages of the Q, values. Reference 54. Reference 55. ' P value from eq 4 with A V l o n = -9.7cm3 mol-'. J

Q

AV,,, values for the corresponding acids. The AVO, for Nacetylglycine, N-acetyl-m-alanine, and N-acetyl-y-amino-nbutyric acid are -1 1.3, -1 1.6, and -9.6 cm3 mol-', respectively. For other N-acetyl-a-amino acids and L-aspartic and L-glutamic acids an average value of -1 1.5 cm3 mol-' for AVO, was assumed since ca. 10-15% error in AV,,, was found to produce not more than 0.1-0.2% errors in P ( H A ) values. The P ( H A ) values,

(hereafter to be referred to simply as P)were obtained, with corrections for ionization volume by King's equationz3 r$L - CUAV,,,= P + S,C (4) where, S , is an empirical constant, C is the molar concentration, and cy is the degree of dissociation, which was estimated from the pK, values.59 The values of the solutes available in the lit-

Molal Volumes of Aqueous Amino Acids and Peptides

The Journal of Physical Chemistry, Vol. 88, No. 1, I984 89

120-

jl

2 1

IO0

-l_l___

80

60

LO

20

r

OL

0

I

20

I

40

I

60

TABLE 111: Limiting Partial Molal Volume Contributions of Various Functional Groups in Aqueous Solutions at 298.15 K functional v",om3 mol-' method group -COOH 34.8 from CH,(CH,),COOH' 25.2 from (CH,),(COOH),b 25.3 from ~O,C(CH,),COOHb -coo28.8 from CH,(CH,),COO19.9 from ~O,C(CH,),CO,- and from -O,C( CH,),COOHb --NH,' 14.0 from CH,(CH,),NH,+ ' 0.0 from (CH,),(NH,+),d -NH, 25.0 from CH,(CH,),NHZe -NH, + -NH,+ 17.6 from H,N(CH,),NH,+ -CONH, 38.9 from CH,(CH,),CONH,f -NHCONH, 44.3 from CH,(CH,),NHCONH,g --OH 21.4 from CH,(CH,),OH" 12.0 from mono- and dialkylamino alcoholsi >CH, 15.9 in several homologous series of compounds -CH, 18.lr 3 CH 12.0: -H 3.01 a Data from ref 4 1 and 42. Data from ref 42. Data from ref 43. Data from ref 25. e Data from ref 3 1 Data from ref 60 and 61. g Data from ref 62. Data from ref 22 and 37-40. Data from ref 27. Taken from the compilations of Millero et al., ref 34.

3

Molecular weight of alkyl side chain

Figure 2. Limiting partial molal volumes of several solutes in water at 298.15 K as a function of the molecular weights of their alkyl side chains: (1) n-arkylammonium ions, ref 43; (2) n-alkyl alcohols, ref 22, 37-40; (3) n-alkylamines,ref 31; (4) n-alkyl carboxylates, ref 42; (5) n-alkyl carboxylic acids, ref 41 and 42; (6) n-alkyl amides, ref 60 and 61; (7)

n-alkylureas, ref 62. erature are also included in Table I1 for comparison and which in general show a good agreement. However, P values of Larginine, L-aspartic acid, and L-glutamic acid are not in agreement with those obtained by Millero et al.34 An independent measurement in our laboratory at a later date by another worker on the chromatographically homogenous samples of L-aspartic acid (74.3 cm3 mol-') and L-glutamic acid (89.7 cm3 mol-') gave a better agreement with the present reported values.

Discussion Limiting Partial Molal Volumes. The P value of any functional group, X, can be obtained from the volume data on the homologous series R-X by least-squares fitting of the P values of R-X vs. the molecular weight of the alkyl chain of the moleVolume data of the homologous series of monofunctional compounds RCOO-,42RCOOH,42RNH3+,43and RCONH260,61 were utilized to evalute the P ( X ) values of the corresponding functional groups, respectively. Excellent correlations have been observed in the linear curves for P values of R-X vs. molecular weight of the alkyl chain (Figure 2; correlation coefficients 0.9999). Estimates of P ( N H 3 + ) , P(COO-), P ( C O O H ) , and P ( C 0 N H ) by this procedure are given in Table 111. P(CO0H) = 34.8 and P ( N H 3 + )= 14.0 cm3 mol-' are in good agreement with those given by Millero et al.,34but P(COO-) = 28.8 cm3 mol-' is a little higher than the earlier estimate34of 26.3 cm3 mol-'. In these calculations P ( H + ) = 5.4, F'(Na+) = -6.6, P ( B r - ) = 30.1, P(Cl-) = 23.2 cm3 mol-' have been taken from miller^.^^ These group contributions have been utilized to estimate the limiting partial molal volumes of the amino acids, N-acetylamino are given in Table acids, and peptides. The estimated values (p) IV. It is observed that the p values are always higher than the experimental P values. This large difference in F'and P values can be rationalized in terms of the following equation: P = v, v, v,+ v, (5)

+ +

Thus, p(group) values contain the contributions due to intrinsic size of the group (V,) as well as the hydrophobic hydration ( Vh), free volume ( Vf), and solutesolute-solvent interactions ( Vs).For (60) T. T. Herskovits and T. M. Kelley, J . Phys. Chem.. 77, 381 (1973). (61) J. Daniel and D. J . Cohn, J . Am. Chem. SOC.58, 415 (1936).

J

TABLE V I: Estimated Limiting Apparent Molal Volumes, V*, of Some Amino Acids, N-Acetylamino Acids, and Peptides Calculated from Functional-Group Contributions a t 298.15 K -

v"-

-

v"-

I

compd Ala Abu ASP

(exptl), cm3 mol-' 60.42 75.50 74.8

V*, cm3 mol-' 72.9 88.8 105.5

AsnH,O Glu Gln GlY Ile Leu Lys.HC1

75.63 89.85 93.61 43.19 105.80 107.83 124.76

127.6 121.4 125.5 58.7 118.9 118.9 155.6

Nle Nva Ser Thr Val AcGly AcAla Ac-a-Abu Ac-7-Abu AcVal AcLeu

107.93 91.70 60.62 76.83 90.65 88.39 105.78 121.44 120.55 136.63 152.47

118.4 104.7 82.7 96.9 103.0 104.7 118.9 134.8 136.5 149.0 164.9

compd Gly,

Gly, Gly, Gly-Ala

Gly-Abu

Glv-Val

Gly-Leu

-

(exptl), v*, cm cm3 mol-' mol-' 76.23 110.5 68.4' 75.5b 7 5. 0' 112.11 162.3 109.9' 214.1 149.6 144.8' 92.37 124.7 85.6' 92.6b 92.2' 107.81 140.6 100.7' 107.7b 107.3' 121.99 154.8 116.0' 123.0b 122.5' 139.70 170.7 133.0' 140.0b

139.6' V'(amino acid, 2) - v"(H,O). These are the V* values corrected for the change in electrostriction (see text). ' V*(peptide) evaluated from the v" of corresponding amino acid, V'(C0NH) = 19.3, v"(CH,) = 15.9 and -3.4 cm3 mol-' for the increased electrostriction due t o separation of charges.

' V*(dipeptide) = v ( a m i n o acid, 1) +

the hydrophilic functional groups in monofunctional compounds, contributions toward V,,should be zero. The hydrogen bonding with the solvent molecules in these groups would give negative contribution of V, since hydrogen bonding is accompanied with a decrease in volume.20-22 Furthermore, the electrostriction of

90

Mishra and Ahluwalia

The Journal of Physical Chemistry, Vol. 88, No. 1. 1984

the solvent molecules due to the charged NH3+and COO- groups gives rise to another negative component to V,. The sign of vh for alkyl side chains is supposed to be p0sitive.4~ From the bond lengths and atomic volume increments62a value of 10.23 cm3 mol-' is obtained for V, of the methylene group. Thus, 15.9 - 10.2 5.7 cm3 mol-' could be attributed to Vh V, of the methylene group. The effect of the charged group on Vh of the central CH2 moiety in glycine has been estimated to be -2.5 cm3 mol-' by Shahidi and Farre11.24 But the observed P values for amino acids are much smaller than the P values (P- P 10-50 cm3 mol-'; vide Table IV). Similarly the P - P values for N-acetylamino acids (15 2 cm3 mol-') are also much higher than one would expect from the effect of the hydrophilic groups on the hydrophobic hydration volume of the central methylene group. Smaller values of P ( X ) in the bifunctional compounds (such as amino acids or N-acetylamino acids) from those found in the monofunctional compounds may be another factor for the observed differences in P and P.Volume data of several a,w dicarboxylic acids,42their mono- and d i a n i o n ~and , ~ ~dialkylamine mono- and d i c a t i o n ~have ~ ~ been examined to estimate the effect of the presence of a second functional group on P ( X ) . Functional-group contributions in these compounds estimated by the same procedure as was done for the monofunctional compounds are given in Table 111. The effect of a second hydrophilic or charged functional group on P ( X ) value is seen to decrease considerably the latter. Cabani et al.27have also observed such effects. Thus, it can safely be concluded that for amino acids and peptides the difference in P and P values may be due to (i) the smaller P(NH3'), P(COO-), P ( C O O H ) , P ( O H ) , and P ( C 0 N H ) values than observed in the monofunctional compounds, and (ii) the decrease in hydrophobic hydration volume, V,, of the alkyl group when it is present in between the charged NH3+and COO- groups. In the case of N-acetylamino acids also the presence of the hydrophilic C O N H group at the a-carbon atom may result in a mutual decrease of P ( C 0 N H ) and P ( C O 0 H ) values just as it is observed in the case of a,w dicarboxylic acids, thereby increasing the difference in the values of P and P,At present, it seems impossible to estimate the reduction in P ( N H 3 + ) , P ( C O O - ) values (or other P(functiona1 group) values) when these groups are present together in a compound. Therefore, instead of predicting the P values from the P(group) values obtained from the homologous series of compounds, the limiting partial molal volumes of the amino acids, N-acetylamino acids, and peptides should be utilized to obtain the group contributions for CONH, CH,CONH, and other amino acid side chains, with which one can later predict the i;" values of larger solutes. In fact, for the dipeptides P can be assumed to be made up of the sum of the P of respective amino acids minus the molal volume of water (-18 cm3 mol-'). But the P values derived in this way are always smaller by 7 cm3 mol-' than the experimental F"' values (Table IV). Such a discrepancy may be due to the changes in the electrostriction volume ( Ve), originating from (i) loss of two charged moieties and (ii) separation of COO- and NH3+ by several atoms in a peptide molecule. The difference of 13 cm3 mol-' between v" values of glycine (43.2 cm3 mor-') and g l y ~ o l a m i d e(52.6 ~ ~ cm3 mol-') should represent the total electrostrictive volume, V,, in glycine. According to Shahidi nd Farre1124the combined effect of COO- and NH3+ on the hydrophobic hydration of the CH2 group of glycine results in a decrease of 2.5 cm3 mol-'. This leaves the decrease in P due to the charged centers alone in glycine = 13 - 2.5 = 10.5 cm3 mol-'.?It has been observed that separation of NH3+ and COO- groups by several methylene groups increases the electrostrictive effect compared to a-amino acids. The difference of v" values of norvaline (91.7 cm3 mol-') and 6-amino-n-valeric acid36(88.3 cm3 mol-'), i.e., 3.4 cm3 mol-', could be a reasonable estimate of the increased electrostriction effect in dipeptides due to separation of charged centers by four atoms. Thus, P(dipeptide) = P ( f i r s t amino acid) + P(second amino acid) + 10.5 (for decrease in electrostriction

due to removal of COz- and NH3+ groups) - 18 (for removal of 1 mol of water) - 3.4 (for the increase in electrostriction due to separation of charged centers) cm3 mol-'. The P values estimated in this way for several dipeptides are given in Table IV and show a relatively better agreement with the experimental P values. In an alternative approach, the P values of the glycyl peptides can be estimated from the P values of a-amino acids as follows. For the CONH portion of the peptide molecule P may be taken as P ( N H C O N H 2 ) - P ( N H 2 ) = 19.3 cm3 mol-'. Since the C O N H moiety is next to another hydrophilic group, NH,, in the group NHCONH2, this value may be a more reasonable representation of P ( C 0 N H ) in peptides. Further, as usual -3.4 cm3 mol-' may be included to compensate for the increasing electrostriction effect due to separation of charges by four atoms. Thus, P(dipeptide) = P ( a m i n o acid) P ( C H 2 ) P ( C 0 N H ) 3.4 cm3 mol-'. Excellent agreement between P values, obtained in this way (Table IV), and the experimental P values of the peptides is observed. Side-Chain Contributions. Various side-chain contributions to the T"' of amino acids, dipeptides, and N-acetylamino acids are given in Table V. The P ( s i d e chain) value in a-amino acids and N-acetylamino acids are in good agreement with the values obtained from various homologous series of compounds (Table 111), except in the cases where the side chains contain the hydrophilic groups. Side-chain contributions in dipeptides are found to be smaller than those in a-amino acids or N-acetylamino acids. In the series of N-acetylamino acids probably the absence of the charged centers gives rise to larger P ( s i d e chain) values than those observed in the dipeptides. In the dipeptides studied in this work the side chains are situated near the carboxylate group. The volume contribution of an alkyl group near a COO- moiety is found to be smaller than if it is near the NH3+ This difference in Po(side chain) at COO- and NH3+centers, according to Zana$4 comes from a larger decrease in the electrostriction of NH3+compared to that of COO- upon alkyl-group substitution and explains the smaller magnitude of P(side chain) in dipeptides. The decrease in electrostriction due to alkyl-group substitution at the charged NH3+ center is also reflected in the greater ?O' of leucylglycine (145.3 cm3 mol-') than that of glycylleucine (139.7 cm3 mol-'). Similar effects have been observed for other isomeric dipeptides also; viz., P(G1y-Ala) = 92.37 cm3 mol-' < P(Ala-Gly) = 95 cm3 mol-' and P of phenylalanylglycine (160 cm3 mol-') > that of glycylphenylalanine (155 cm3 mol-').58 Peptide-Group Contributions. i;"(CONH) and P(CH2CONH) values derived from the present results are given in Table VI. P ( N H C O N H 2 ) and P ( C O N H 2 ) obtained from ides, respectively (Table the P data on alkylureas and a1 (CONH) values. Thus, 111), can also be utilized to prod P ( C 0 N H ) = P ( N H C O N H 2 ) - P ( N H 2 ) = 19.3; and t"(CONH) = P ( C O N H 2 )- P ( H ) = 35.8 cm3 mol-'. The present estimates of P ( C 0 N H ) in N-acetylamino acids (20.5 I 0.3 cm3 mol-') and in alkylureas (19.3 cm3 mol-') are in good agreement with the value obtained by Cohn and E d ~ a 1 (20.0 1 ~ ~ cm3 mol-') from the early volume data. However, P ( C 0 N H ) values obtained from the difference of i" of dipeptides and amino acids (16 f 1 cm3 mol-]) are considerably smaller than the above value of -20 cm3 mol-'. On the other hand, P ( C 0 N H ) evaluated from alkyl amides (35.8 cm3 mol-') is significantly higher. It has been observed that P of a hydrophilic functional group decreases if another hydrophilic group is present in the neighborhood (vide supra). Probably this is the reason that P ( C 0 N H ) is lower in N-acetylamino acids, alkylureas, and dipeptides than in alkyl amides. This conjecture is also supported by the fact that P of NH2CONH2(45.1 cm3 is much smaller than one would expect from the group contributions of P ( N H 2 ) = 25.0 cm3 mol-' (in RNH2) and P ( C O N H 2 ) = 38.9 cm3 mol-' (in RCONH,). For P(CH,CONH) similar discrepancies are observed in the values obtained from different series. The average value of

(62) H Holland and E. Vikingstad, Acta Chem. Scand. Ser A, 30, 182 ( 1976).

(63) W. Y. Wen, A. Losurdo, C. Jolicoeur, and J. Boileau, J. Phys. Chem., 80, 466 (1976).

+

-

*

+

+

The Journal of Physical Chemistry, Vol. 88, No. 1 , 1984 91

Molal Volumes of Aqueous Amino Acids and Peptides

TABLE V: Amino Acid Side-Chain Contributions toward Limiting Partial Molal Volumes in Aqueous Solutions at 298.15 K -

amino acid side chain -CH,

-CH,CH,

-cH(CH3)2

-CHCH,CH, I

CH3 --( CH 2 ) 3 CH3 -CH,CONH,.H,O -CH,CONH,

V" , cm3 mol-' 17.2 16.1 18.4 17.3 32.3 31.6 33.1 34.0a 47.5 45.8 48.2 48.Za 48.5 49.9Q 64.6 63.5 64.1 64.1a 62.6 64.1a 64.7 65.8" 52.4 34.4 34.3 54.8a 50.4 70.7a 80.7

-

method

&-

Ala - Gly Gly-Ala - Gly, AcAla - AcGly AcAlaNa - AcGlyNa Abu - Gly Gly-Abu - Gly, Ac-a-Abu - AcGly

@.-

Q[ I

Leu - Gly Cily-Leu - Gly, AcLeu - AcGly Ile - Gly

I --(CH,),SCH, -CH,OH

Nle - Gly

-CH(OH)CH,

Asn.H,O - G& Gln - Gly - V"(CI-I,) Asn.H,O - Gly - V"(H,O)

-C H,COO H

Gln - Gly

--(CH,),COOH

Arg - Gly

Phe - Gly

81.1

Tyr - Gly

Trp - Gly

55.1

His - Gly

67.6

Pro - T ( H ) - p ( O H )

69.5 76.6

Hyp - p ( H ) - T ( 0 H ) Pro - 2 p ( H )

62.4 17.4 27.9" 35.lC 33.6 33.3 51.1d 31.6 50.7" 41.1e 46.7 47.5 66.6a 57.0e 73.7

Met - Gly Ser - Gly

method

I

Nva - Gly

Lys.HC1- Gly

V" , cm3 mol-' 100.5

I

Val - Gly Gly-Val - Gly, AcVal - AcGly

58.4 77.6a 79.0

achzmcH2-

amino acid side chain

-

Thr - Gly Ser - Gly + V"(CH,) ASP - Gly Glu - Gly Asp - Gly

+ V"(CH,)

Arg.HC1- Gly - 7(C1-)

P (C1-)

88.0b

HO

- Calculated by using the group contributions derived from monofunctional compounds, given in Table 111. V"(G1y) t p ( 0 H ) - B " ( H ) ; V " ( 0 H ) = 12.0 c m 3 mol-'. 25.2 c m 3 mol-', (as in a-amino w-carboxylic acids).

TABLE VI: Peptide Group Contributions toward Limiting Partial Molal Volumes in Aqueous Solutions at 298.15K V(CH,CONH), cm3 mol-' P ( C O N H ) , cm3 mol-' _ I I

--

--

N-acetylN-acetylamino glycine amino peptides acids oligomers peptides acids 33.0a 36.5g 33.0a 16.2" 20.5' 32.0b 37.gh 35.9" 16.gq 21.2" 32.3c 36.8' 37.5" 16.1' 20.9" 31.3d 36.0' 37.5O 14.2? 2O.lx 31.ge 36.1k 15.gt 20.55 38.4f 36.5l 20.62 a Gly, - Gly. Gly-Ala - Ala. G l y A b u - Abu. Gly-Val - Val. e GlLLeu - Leu. v"(Dkp)/2. K AcGly - CH,COOH; v" of acetic acid and other carboxylAcAla - C,H,COOH. ' Ac-aic acids are from ref 42. Aba - C,H,COOH. 1 Ac-Y-Aba - C,H,COOH. AcValC,H,COOH. AcLeu - C,H,,C_OOH. " Gly, - Gly,. " Gly, - Gly,. Gly, - Gly,; V ( G l y , ) from ref 35. P Gly, - Ala. q Gly-Ala - Aba. Gly-Aba - Nva. GlyVal - Leu. Gly-Leu - Leu - P ( C H , ) . ' AcGly C,H,COOH. lU Ac-a-Aba - C,H,,COOH. Ac-Y-Aba C,H,COOH. '-AcValC,H,,COOH. AcLeu C,H,,COOH - V(CH,). P ( C H , C O N H ) in N-acetylamino acids is 36.5 A 0.6 cm3 mol-', in good agreement with Cohn's value of 36.3 cm3 but

P(CH,OH) - V"(H).

V"(C,H,OH)

-

p(H).

e

p(Phe)V"(CO0H) =

P ( C H 2 C O N H ) = 32.1 f 0.06 cm3 mol-] obtained from the dipeptides (Table VI) is significantly smaller. It is found that the increase in electrostriction effect by separating the charged centers COO- and NH,+ by four atoms in dipeptides results in an additional decrease in volume by 3.4 cm3 mol-' compared to that in a-amino acids (vide supra). This increased electrostriction effect in the dipeptides seems to be responsible for the lower value of P ( C 0 N H ) and P(CH,CONH) derived from the dipeptides. This conclusion is supported by the P ( C H 2 C O N H ) values obtained from the P of glycine 01igorners.~~ ConcentrationDependence of & The concentration dependence of the thermodynamic properties of solutes in aqueous solutions has been explained in terms of the solute-solute interactions. The usual interpretation is that the solute species interact through the destructive overlap of their hydration spheres.64 For apolar species, V,, the positive volume component of the P, originating from the hydrophobic hydration, starts decreasing as the solute concentration is increased. The overlap of two hydrophobic hydration cospheres relaxes some water molecules from the solvation sphere to the bulk giving rise to a negative change in volume. For hydrophilic ionic species the volume of water molecules is smaller in the solvation shell due to (i) the effect of electr~striction~~ and (ii) a decrease in the hydrogen-bonded network of water molecules in the solvation sphere than in the bulk (the so-called structure(64) R. W . Gurney, "Ionic Processes in Solutions", McGraw-Hill, New York, 1954.

92 The Journal of Physical Chemistry, Vol. 88, No. I , 1984 lo1 HYDROPHOBIC

HYDROPHOBIC

BULK

+ IbI

IONIC lor DIPOLAR1

IONIC

BULK

HYoRoPHoBIC

+ I C / lor DIPOLAR]

AV< 0

-c

AVtO

IONIC ~~~DIPOLARI

@+

BULK

AV>O

Figure 3. Solute-solute interactions through the overlap of hydration cospheres and the resulting volume changes in aqueous solutions.

breaking effect). The overlap of cospheres of two ionic species relaxes some solvation water to bulk so that overall structure is increased, giving rise to positive volume change. Further, if the ions are oppositely charged, this type of interadtion also causes an attraction since the orientation of water molecules by the cations leads to favorable anion-water dipole interactions (and vice versa). In this way even the electrostricted water molecules may be shared, resulting in a positive volume change. The structure-breaking influence of ionic species on the hydrophobic hydration sphere of apolar groups gives a negative volume effect. The changes in volume due to the various types of interactions elaborated above are summarized in Figure 3. Amino acids and dipeptides are nonelectrolytes; nevertheless, due to the zwitterionic nature of these compounds in aqueous solutions, interactions involving the charged centers COO- and NH3+ are also important. Thus, the concentration dependence of of these solutes can be interpreted in terms of the interactions involving the hydrophobic apolar moieties as well as the charged centers. For both the amino acids and the dipeptides the conLe., s, values, are positive except centration dependencies of those for leucine and its isomers, and methionine (vide Table 11). The positive sign of S, values thus indicates that interactions involving the charged moieties dominate the apolar group-apolar group and apolar group-charged center interactions. However, the negative volume contribution due to hydrophobic interactions causes the S, values to decrease as the side-chain length increases; consequently, for leucines negative values for S, are observed. Furthermore, separating the charged COO- and NH3+groups by several methylenes should enhance the intermolecular interactions involving the cospheres of the charged centers and suppress the hydrophobic interaction due to steric reasons. In this way more positive S, values for w-amino carboxylic acids should be expected than the isomeric a-amino acids. This is indeed seen if the present data are compared with the data of Ahluwalia et al.36 on 4" of w-amino carboxylic acids. In summary, the group additivity relationships have been examined from the P data on a-amino acids, N-acetylamino acids,

+,

+",

Mishra and Ahluwalia and peptides as well as from those of several homologous series of compounds. It has been found that P(group) values obtained from several monofunctional compounds give the estimates of limiting partial molal volumes of a-amino acids, N-acetylamino acids, and peptides much higher than the experimental values. Probably, the presence of many hydrophilic groups in close proximity in these compounds decreases the functional-group contributions as well as the contribution due to hydrophobic hydration of the alkyl groups from those observed in the monofunctional compounds. However, it has been shown that limiting partial molal volumes of the peptides estimated from the P values of a-amino acids with a proper consideration of the changes in the electrostriction volume due to separation of charged centers agree with the experimental values. Amino acid side-chain contributions toward i" are also evaluated from the P data on a-amino acids, N-acetylamino acids, and peptides. The P contributions of nonpolar side chains agree with those obtained from the group additivity. The influence of hydrophilic and charged centers on the P contribution of another hydrophilic group is reflected in the P values of C O N H and CH,CONH groups and other hydrophilic side chains. In general, these values of P of the peptide group or hydrophilic side chains are smaller compared to those obtained from additivity. Therefore, for the prediction of P values of higher peptides, the side-chain and peptide-group contributions obtained from the a-amino acids or N-acetylamino acids should be used. Finally, the concentration dependence of the apparent molal volumes of these solutes has been rationalized in terms of the combined effects of hydrophilic and hydrophobic solute-solute interactions mediated through the typical structure of water, though such an attempt may be an oversimplification.

Acknowledgment. We gratefully acknowledge the financial assistance from the Department of Science and Technology (HCS/DST/123/76), Government of India. Registry No. DL-Alanine, 302-72-7;DL-a-aminobutyric acid, 283581-6; L-arginine, 74-79-3;L-arginine hydrochloride, 11 19-34-2;L-aspartic acid, 56-84-8;L-asparagine,70-47-3; L-glutamic acid, 56-86-0;L-glutamine, 56-85-9; glycine, 56-40-6; L-histidine, 7 1-00-1;L-hydroxyproline, 5 1-35-4;L-isoleucine, 73-32-5; leucine, 61-90-5; L-lysine hydrochloride, 657-27-2; L-methionine, 63-68-3;norleucine, 327-57- 1; norvaline, 660040-4; L-phenylalanine, 63-91-2; p proline, 147-85-3;L-serine, 56-45-1; L-threonine, 72-19-5;DL-tryptophan, 54-12-6;L-tyrosine,60-18-4;L-valine, 72-18-4; diglycine, 556-50-3; triglycine, 556-33-2; tetraglycine, 926-77-2; glycyl-~~-a-amino-n-butyric acid, 637-84-3;glycyl-~~-alanine, 7369-76-8; glycyl-L-valine, 1963-21-9; glycyl- l leucine, 869-19-2, Lleucylglycine, 686-50-0; 2,5-diketopiperazine, 106-57-0; N-acetyl-yamino-n-butyric acid sodium salt, 543-24-8;N-acetylglycinesodium salt, 2494-04-4; N-acetyl-DL-alanine,1 115-69-1; N-acetyl-DL-alanine sodium salt, 87656-14-2; N-acetyl-DL-or-amino-n-butyric acid, 7682-14-6; Nacetyl-y-amino-n-butyric acid, 3025-96-5;N-acetyl-y-amino-n-butyric acid, 17756-65-9; N-acetyl-DL-valine, 3067-19-4; N-aCetyl-DL-kUCine, 99-15-0.

Supplementary Material Available: Table I, listing aqueous solution densities and apparent molal volumes of several a-amino acids, N-acetylamino acids, and peptides at 298.15 K (12 pages). Ordering information is given on any current masthead page.