Partial molar volumes and adiabatic compressibilities of glycyl

J. Phys. Chem. 1987, 91, 967-971

967

Partial Molar Volumes and Adiabatic Compresslbilities of Glycyl Peptides at 25 OC Mohammad Iqbal and Ronald E. Verrall* Department of Chemistry, University of Saskatchewan, Saskatoon, Canada S7N 0 WO (Received: May 6, 1986; In Final Form: August 14, 1986)

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on August 27, 2015 | http://pubs.acs.org Publication Date: February 1, 1987 | doi: 10.1021/j100288a039

Partial molar volumes (P) and adiabatic compressibilities (k") of di-, tri-, and tetraglycine have been calculated from high precision density and sound velocity measurements carried out at 25 "C. The contributions (V",o(gly)and K,"(gly)) of the glycyl unit, in a peptide of hypothetical infinite length, are estimated by four different techniques. Final values, obtained by averaging the concordant data, are 37.51 i 0.07 cm3 mol-' and (-8.50 k 0.01) X cm3 mol-' bar-' for V-"(gly) and kmo(gly),respectively. These values are required for use in a revised additivity scheme for calculating partial specific volumes and compressibilitiesof proteins. Contributions of the peptide group (-CONH-) to P and P are also estimated by comparing with data of o,w-amino acids. The values of i"(-CONH-) and R"(-CONH-) estimated in this way are 20.61 cm3 mol-' cm3 mol-' bar-', respectively. Some plausible modes of peptide solvation also are discussed. and -12.4 X

Introduction Amino acids and peptides are the fundamental structural units of proteins, depsipeptides, certain types of hormones and antibiotics, and many other compounds of biological relevance. It is generally recognized that in the absence of experimental thermodynamic data for these macromolecules, amino acids and peptides can serve as useful models in estimating their Even in situations where experimental data are available, the properties of these smaller units are still found applicable in exploring various aspects of structural organization in the larger biomolec~les.~ Studies of organization and thermal stability of proteins have been the focus of investigations in biochemistry for decade^.^,^ Structural details revealed by high-resolution X-ray crystallography, neutron diffraction, spectroscopy, and thermodynamic methods have contributed a great deal toward our understanding of protein function. Nevertheless, the important concepts concerning stability and folding are not fully understood at this stage and a great deal of fundamental information is still required in order to solve many key questions. The most reliable information about the phenomenon of folding would obviously be obtained by observing the process under in vivo conditions, where it is believed to take place almost instantaneously during the ribosomal synthesis. However, the limitations of the experimental techniques in studying such fast in vivo processes turn out to be a major impediment to obtaining such direct information. The focus of study thus shifts to consideration of indirect methods of investigation. In the past, several indirect methods have been used to investigate the folding of proteins. Most common among them include the determination of amino acid sequence and its correlation with structure,6 the study of refolding experiments using denaturants,' theoretical modeling using computer simulations,* and thermodynamic analysis of conformations involved in the folding p r o ~ e s s . ~Results ,~ obtained from these methods have provided a fairly general understanding of the phenomenon, but some concepts of fundamental importance still remain to be explored. Often, the validity of some of these methods has been ( I ) Shrier, M. Y.; Ying, A. H. C.; Ross, M. E.; Shrier, E. F. J . Phys. Chem. 1971, 81, 674. (2) Lapanje, S.; Skerjanc, J.; Glavnik, S.; Zibret, S. J . Chem. Thermodyn. 1978, 10, 425. (3) Octav, E.; Jolicoeur, C. J . Phys. Chem. 1982, 86, 3870. (4) Schulz, G. E.; Schirmer, R. H. Principles of Protein Structure; Springer Verlag: New York, 1979; Chapter 8. (5) Lumry, R.; Biltonen, R. L. In "Structure and Stability of Biological Macromolecules; Timascheff, S . , Fasman, G. D., Ed.; Marcel Dekker: New York, 1969; Chapter 2. (6) Anfinsen, C. B.; Scheraga, H. A. Adu. Protein Chem. 1975, 29, 205. (7) Lapanje, S. Physicochemical Aspects of Protein Denaturation;Wiley Interscience: New York, 1978; Chapter 6. ( 8 ) Levitt, M.; Warshel, A. Nature (London) 1975, 253, 694. (9) Jolicoeur, C.; Boileau, J. Can. J . Chem. 1978, 56, 2707.

0022-3654/87/2091-0967$01.50/0

questioned. For example, a considerable redundancy in the rules relating amino acid sequence and protein structure has been described.1° Also, the process of reversible denaturation as a useful representation of the folding process can be seriously questioned on a number of grounds." The method of computer simulation appears to be promising but is quite cumbersome in terms of dealing with the very large number of conformational possibilities, even in the case of simple proteins. The thermodynamic method is in a developmental stage, as the techniques for observing thermodynamic properties with higher accuracy are continually evolving. The present study focuses on the use of this particular method to obtain information about the folding process. Like any well-defined thermodynamic system, two distinct states are believed to be involved in this process: the unfolded and the folded state. The former state is considered to be a completely unfolded, mutually noninteracting polypeptide chain, which is virtually a hypothetical state except for the early stages of biosynthesis. The folded state, on the other hand, is the native protein conformation or a subset of conformations having a certain span of thermal stability with an optimum free energy minimum. Thermodynamic information about both states is necessary in order to estimate relevant changes accompanying the folding process. The native-state properties can be readily measured with some degree of accuracy, although there often is disagreement between the results obtained from different studies. These discrepancies are due primarily to different sources of proteins and variations in the techniques employed. Strictly speaking, the unfolded state is experimentally inaccessible and its thermodynamic properties must be estimated from data of model compounds such as amino acids and peptides. Given the absence of higher structures in the unfolded state, the thermodynamic properties of this state can be determined by the application of simple additivity schemes using the data from these model compounds. This approach has already been used in the studies of partial specific volumes of certain proteins.'* The data used in such studies are the partial specific volumes of amino acid residues, Le., when they are within the polypeptide chain and not when they are simple monomeric zwitterions in solutions. These studies have shown that there is a considerable difference between the magnitudes of thermodynamic properties of amino acids in these two states which is attributed primarily to the dependence of hydration effects on steric and electrostatic charge factors. The results of additivity calculations to estimate volumes of proteins have shown good agreement with experimental data.'* As a consequence, it can be concluded that either there is no volume change associated with the process of folding or there is some kind of compensation resulting from the phenomenon. (10) Creighton, T. E. J . Phys. Chem. 1985, 89, 2459. ( 1 1 ) Brandts, J. F.; Hunt, L. J . A m . Chem. S o t . 1967, 89, 4826. (1 2) Cohn, E. J.; Edsall, J. T. Proteins, Amino Acids and Peptides; Hafner: New York, 1965; Chapters 7 and 16

0 1987 American Chemical Society


968

The Journal of Physical Chemistry, Vol. 91, No. 4 , 1987

Another reason for the agreement could arise from a greater degree of uncertainty in the experimental and calculated data used in these early investigations. While there has been some improvement in the accuracy of partial molal volume data obtained for amino acids and proteins, it is felt that a more useful approach is to consider whether other thermodynamic properties can be used to better quantify the folding phenomenon. Recently, we have been examining the utility of the adiabatic compressibility property for such a purpose. The compressibility of the unfolded state is generally negative by the application of any simple additivity scheme. Consequently, the larger differences expected between the compressibilities of the unfolded and native protein state^'^,^^ could allow for a more meaningful interpretation of the folding phenomenon. Since there has been no previous reports of the use of compressibility data to examine this possibility, we have started a systematic investigation of the volumetric properties of some native proteins and polypeptides. We report in this work the partial molal volumes and adiabatic compressibilities of three glycyl peptides, Le., di-, tri-, and tetraglycine at 25 OC. These data and those reported elsewhere for glycine1"' are used to obtain standard values for a single glycyl residue. These values, in conjunction with the side-group contributions of amino acids, can be used in an improved additivity scheme for calculating the partial molal volumes and adiabatic compressibilities of the unfolded state of proteins. These results will be presented in a manuscript currently in preparation. Experimental Section

Materials. Diglycine (Sigma, Lot No. 102F-5037), triglycine (Sigma, Lot No. 87C3-0417),and tetraglycine (Sigma, Lot. No. 72F-0496) were recrystallized from ethanol-water mixtures and were dried under vacuum at room temperature. All water used in these experiments was distilled and deionized by using a Millipore Super-Q system and was degassed prior to making solutions. NaCl (BDH Aristar) used in the calibration of the densimeter and the sonic velocimeter was of the highest purity and oven dried at 130 O C prior to use. Apparatus and Procedure. Solution densities were measured with a high-precision digital densimeter (Model 02D, Sodev Inc.), details of which are described elsewhere.18 Thermostating of the densimeter was maintained by a closed-loop Sodev temperature controller, which maintained the temperature constant to better than fO.001 "C. The absolute temperatures of the solutions in the cavity were obtained by using a tissue implantation thermistor calibrated against a Pt resistance thermometer (Leeds and Northrup). They were found to be accurate to fO.O1 OC. The suggested technique for operating the densimeter was improved by developing several procedures to minimize possible experimental artifacts responsible for increasing the magnitude of the error in the density data. The instrument was calibrated with water," dry nitrogen (density calculated from the ideal gas equation), and NaCl solutions by using density data from the literature.20 The calibration constants obtained from all three reference systems agreed very closely. Short-term drifts in the instrument were taken into account by performing calibrations prior to every series of measurements. The density of each solution was obtained relative

Iqbal and Verrall TABLE I: Values of compd glycine' diglycine triglycine tetraglycine

(13) Gekko, K.; Noguchi, H. J . Phys. Chem. 1979, 83, 2706. (14) Gavish, B.; Gratton, E.; Hardy, C. J. Proc. Natl. Acad. Sci. U.S.A. 1983, 80, 750.

(15) Millero, F. J.; Lo Surdo, A.; Shin, C. J . Phys. Chem. 1978, 82, 784. (16) Ogawa, T.; Mizutani, K.; Yasuda, M. Bull. Chem. SOC.Jpn. 1984, 57, 2064. (17) Cabani, S.; Conti, G.; Matteoli, E.; Tine, M. R. J . Chem. Soc., Faraday Trans. 1 1981, 77. 2385. (18) Picker, P.; Tremblay, E.; Jolicoeur, C. J . Solution Chem. 1974, 3, 377. (19) Kell, G . S . J . Chem. Eng. Data. 1975, 20, 97. (20) Vaslow, F. J . Phys. Chem. 1966, 70, 2286.

43.19 f0.02 16.76 f0.03 112.51 f0.03 149.98 f0.40

0.864 2.35 f0.29 4.16 f0.50 23.14 f4.11

27.00 f0.44 35.91 f0.09 44.36 f0.80 53.14 f2.39

4.56 8.58 f0.84 9.84 f1.21 10.55 f1.09

"Units of cm3 mol-I. b u n i t s of cm3 mol-2 kg. 'Units of cm3 mo1-l bar-'. "Units of cm3 mol-2 bar-' kg. eData from ref 15; standard deviations for S, and Skwere not reported. Numbers below the values are standard deviations.

TABLE II: Comparison of Thermodynamic Data from This Work with Previous Studies at 25 O C -KO x 104, compd diglycine triglycine tetraglycine

v",cm3 mol-'

cm3 mol-' bar-'

76.76," 11.2,b 76.34: 16.21,d 16.23e 35.91,4 35.5; 32g 112.51," 111.81,d 112.11e 44.36h 149.98," 149.7,d 149.6' 53.14h

"This work. bReference 32. 'Reference 33. dReference 9. 'Reference 26. /Reference 17. gReference 34. hThis work with no comparative data available.

6080 concentration analyser). The original glass vessel supplied with the instrument was replaced by a cell having a smaller volume (80 mL) fitted with a thermostating arrangement and a suitable lid for transferring material to and from the cell whenever required. The temperature was controlled by a Sodev temperature controller similar to the one used with the densimeter. The sound velocity, u , (m s-') at a given temperature, t , ("C) was calculated, using eq 1, from the pulse frequency,f(Hz) of the sound wave measured

by means of a frequency meter (Fluke 7261 universal counter), where I and b are the sonic path length (m) and electronic time delay constants (s), respectively, and a is the coefficient of expansion of the transducer metal. The velocimeter was calibrated by obtaining values of I and b using previously reported sound velocity data for water22and aqueous NaCl solutions.23 In the case of NaCI, the data were statistically analyzed and regression constants were obtained as a function of concentration. In order to minimize errors, calibrations were performed prior to every series of measurements. The precision in the sound velocity was found to be better than f0.15 cm s-'. Results

Apparent molal volume (4") and adiabatic compressibility (&) were calculated with the following equations: M 1000(do-d) i#J,=-+ (2) d mddo

to t h a t of solvent, which was measured immediately before a n d

after taking the solution density. The precision in the density data was found to be better than i 1.5 ppm. Sound velocity measurements were carried out by using the sing-around technique2' with a single transducer cell (Nusonic

Yo,S,, K,",and Sk for Peptides at 25 OC v"* s,b -kx io4' skx

(3)

where M is the relative molar mass of the solute and m, d, and

p, are the molality, density, and coefficient of adiabatic compressibility of the solution, respectively, at 25 'C. Variables subscripted with a zero refer to the solvent. Ps is calculated from sound velocity and density data according to eq 4. Data for all

P, = I/(u2d) (4) systems studied are presented in the Supplementary Material. (21) Gamey, R.; Mahoney, R.; Litovitz, T. A. J . Chem. Phys. 1964, 64, 2073. (22) Del Grosso, A.; Mader, C. W. J . Acoust. SOC.Am. 1972, 52, 1442. (23) Sakurai, M.; Nakajima, T.; Komatsu, T.; Nakagawa, T. Chem. Lett. 1975, 97 I .

The Journal of Physical Chemistry, Vol. 91, No. 4, 1987 969

Molar Volumes and Compressibilities of Glycines


- 0

I

3

2

4

20'

n

Figure 1. Partial molar volume, t",of glycyl peptides vs. n, the number of residues in the polypeptide.

Values of q5v and 4k,$ calculated with eq 2 and 3 were fit to the following equations: $v = 4 v " 4- Svm (5)

4k.s = 4k,so + Skm

(6)

of the apparent molal properties The limiting values, 4voand can be regarded as the infinite dilution partial molal volume, (P) and adiabatic compressibility ( K O ) of a given peptide. S, and S k are the slopes indicative of solute-solute interactions arising from solute concentration effects. The values of p, K O , s,, and Sk are given in Table I. Table I1 compares data obtained in this study with results reported from earlier studies.

Discussion Partial molal volumes (P) and adiabatic compressibilities ( K O ) of the peptides are plotted in Figures 1 and 2, respectively, as a function of n, the number of glycyl residues in a particular homologue. It is found that both p and K" increase linearly with the chain length of the molecules. An attempt was made to estimate the contribution of P and K" of the peptide group (-CONH-) by combining the present data with previous data on a,w-amino a ~ i d s . ' ~ ,It~is~found , ~ ~ that a comparison of peptides and a,w-amino acids of the same carbon chain length is often useful in deriving such information since both types of molecules are similar in structure except that in peptides the -CONH- group replaces the two methylene (-CHI-) groups of the a,w-amino acid. An overview of the data indicates that V" and K O values of the peptides are generally smaller than their a,o-amino acid analogues. This implies that the replacement of two -CHI- groups with one -CONH- group causes a considerable decrease in the volume and compressibility of the molecule. Before discussing this aspect further, however, we will show the calculation of the peptide group contribution. The differences between the magnitudes of either V" and K" of a,w-amino acids and peptides are taken as the values of t" and K" for the substitution -CHICHI-CONHAP(-CHZCHz-CONH-) = P(peptide) - V"(a,w-amino acid) (7) AKo(-CHzCH2-CONH-) = Ko(peptide) - K"(Lu,w-amino acid) (8)

-

-

For example, the difference between, the data for 5-aminopentanoic acid ( p = 87.65 f 0.64 cm3 K O = (-27.3 f 2.0) X cm3 mol-' bar-' 1 7 ) and that of diglycine gives A P (24) Shahidi, F.; Farrell, P. G.J . Chem. SOC.,Faraday Trans. 1 1978, 74, 858. (25) Cabani, S . ; Conti, G.;Matteoli, E.; Tine, M. R. J . Chem. SOC., Faraday Trans. 1 1981, 77, 2311.

b

I

I

I

I

I

2

3

4

n Figure 2. Partial molar adiabatic compressibility, K O , of glycyl peptides vs. n, the number of residues in the polypeptide.

a"

and values for one such substitution while a similar difference between the values of 8-aminooctanoic acidz4 and triglycine provides values for two such substitutions. From these two cases, an average value of A p for a single substitution was found to was obbe -1 1.39 cm3 mol-'. The corresponding value of tained from the only available comparison, that between 5aminopentanoic acid and diglycine, and was found to be -8.61 X cm3 mol-' bar-'. From these data the values of P(CONH-) and KO(-CONH-) were estimated with the following simple relations: AP(-CH2CH2-CONH-) = P(-CONH-) - P(-CHzCH,-) (9)

a"

+

AKo(-CH2CH2-

-+

-CONH-) = KO(-CONH-) - Ko(-CH2CH2-) (10)

With the widely accepted values of 16 cm3 mol-' 14,15 and -1.9 X cm3 mol-' bar-'I7 for p and K" of the -CHI- group, respectively, p and K" of the peptide group can be calculated. The values of p ( - C O N H - ) and R"(-CONH-) calculated in this cm3 mol-' bar-', way are 20.61 cm3 mol-' and -12.4 X respectively. The p (-CONH-) value derived, here, agrees with the previously reported values of 20,1222.3,25and 19.326cm3 mol-'. No comparative value for K"(-CONH-), however, was available. . These results point out some distinct aspects of peptide solvation. For example, it is seen that in spite of the larger intrinsic volume of the -CONH- group in peptides as compared to two -CHIgroups in the a,w-amino acid analogue the smaller values of P and K" for -CONH- indicate a more compact solvation sheath around this group than in the case of two -CHI- groups. It is expected that the presence of intermittent -CONH- groups in an otherwise continuous chain of hydrocarbon can perturb the homogeneous solvation sheath of hydrophobic hydration. The replacement of two methylene groups with one peptide group incorporates two hydrogen bonding sites in the peptide molecules which appears to create a relatively greater shrinkage of the hydration shell around the solute molecule. The observed decrease in the volume and compressibility of peptides can be attributed to this shrinkage as well as to the diminution of the solvation shells surrounding the peptide group and the adjacent methylene due to the vicinal perturbation. These types of steric effects have been noted in similar situations, e.g., regarding the estimation of true and apparent electrostrictive volumes,24where the adjacent groups have been found to affect the size of the neighboring solvation shells. The V" and K" data of these peptides were analyzed in a number of ways to derive the contribution of a single glycyl residue (26) Mishra,

A. K.; Ahluwalia, J. C. J . Phys. Chem. 1984, 88, 86.

970 The Journal of Physical Chemistry, Vol. 91, No. 4, 1987

Iqbal and Verrall

44,

?23 i

m oc

, 0

IY


36 1

11 0

0.0 I

I

I

I

I

2

3

4

n

Figure 3. Partial molar volume of a glycyl residue, Un0(gly), vs. n, the number of residues in the polypeptide.

to these properties. This contribution, in conjunction with the estimates of P and Ko for side groups, can be used to develop an additivity scheme for calculating more accurate estimates of the unfolded state of proteins. Analyses of the data were carried out by using graphical and/or curve-fitting procedures. Although the validity of such procedures using smaller data bases may be questionable, we have shown that different methods of data analysis provide values that are in close agreement with each other. It is to be noted that the extremely low solubility of long-chain peptides precluded our obtaining experimental data for larger polyglycines. On balance, the results reported below are considered to be satisfactory for use in the additivity schemes. The data were analyzed as follows. i. The first method involved fitting the data shown in Table I to the following equations:

The values ( d P / d n ) , and ( d R o / d n ) T are considered as the representative contributions of a glycyl residue in a peptide of sufficiently long chain length. These values are 35.62 f 0.62 cm3 mol-' and (-8.69 f 0.01) X l o 4 cm3 mol-' bar-' for P and K O , respectively. ii. In another method, the volume and compressibility contributions of a glycyl residue were estimated for each peptide as a function of n. These values were referred to as vno(gly) and Kno(gly): respectively, and were obtained by dividing the individual p and K O values by the respective n values. The resulting data were then plotted in a way similar to Figures 1 and 2; Figure 3 is typical of these plots. It was found that each curve in these plots reached an asympototic value which was treated as the desired standard contribution for the glycyl residue in a long chain. These values were referred to as Vwo(gly)and F&,O(gly), assuming m, a polypeptide chain of infinite that they correpond to n length. The analogy with an infinitely long polypeptide chain is suitable and is adopted here because of the similarity of this state with the unfolded state of most proteins chains. Values of V",o(gly) and K,O(gly) estimated according to this method are 37.45 cm3 mol-' and -13.4 X IO4 cm3 mol-' bar-', respectively. A similar method has been reported previo~sly,~ where the incremental volume contributions of the glycyl residue (Ad,") were plotted as a function of n. The parameter Ad," was obtained by subtracting P of monomeric glycine from P of a particular peptide and then dividing the resulting number by n - 1. The values of Yno(gly)calculated from our results agree well with the dvodata previously r e p ~ r t e d except ,~ for the case of n = 2. The reasons

-

0.25

0.5 I

0.75

1.0

-n

Figure 4. Partial molar adiabatic compressibility of a glycyl residue, &"(gly), vs. l / n , n being the number of residues in the polypeptide.

for this discrepancy are apparent from the way this parameter was c a l ~ u l a t e d . ~ iii. The third method for estimating the glycyl residue contribution involved plotting Vn0(gly) and Kno(gly) data vs. l / n . A typical plot is shown in Figure 4. Estimates of the properties Vwo(gly)and K,O(gly) were obtained by extrapolating the curves to their limiting values, Le., I / n = 0. These values can also be derived by fitting the data to the following equations: rno(gly) = Vwo(gly)

+ a ( l / n ) + b(l/n)'

(13)

Rno(gly) = k 0 ( g l y )

+ a ( l / n ) + b{l/n]'

(14)

where a and b are the coefficients of the least-squares fit. iv. The final method is based on the concept that the hydration of terminal groups and the intervening chain in peptides produce nonuniform volume and compressibility effects. In aqueous solutions, amino acids and peptides normally exist in the zwitterionic form. The end groups are solvated in an electrostrictive manner while the intervening chain experiences nonelectrostrictive interactions with the solvent, presumably hydrophobic and hydrogen bonding. Peptides of shorter length are also believed to be fully solvated because of the absence of secondary structure and a greater conformational flexibility which provides free access of solvent to all parts of the solute molecule. Previous studies of amino acids and short-chain peptides have shown that the electrostriction of end groups tends to interfere with the hydration of the intervening chain because of the overlap of solvation ~ h e a t h s . ~ , ' ~ , ' ~ This - ~ ~ ,interference, *' however, diminishes as the distance of separation between the end groups increases. The phenomenon is also observed in the case of certain model compounds, e.g., alkylammonium halides,'*J9 a,w-amino a ~ i d s , * ~ , * ~ and diaminoalkane m01cules~~ of varying chain length. It has been established from these studies that the end-group electrostriction and the hydration of the intervening chain become essentially constant and independent of each other as the separation between the the end groups exceeds five covalent bonds. In order to calculate the standard contribution of an intervening glycyl unit, for example V'(gly), the O'F of the entire peptide structure can be regarded as a composite of the separate conand the end-group tributions from the intervening chain ( Pint) electrostriction ( Pel), i.e.

t" = Pin, + Pel

(15)

The contribution of the intervening chain in this expression can (27) Shahidi, F.; Farrell, P. G. J . Chem. Soc., Faraday Tram. 1 1981, 77. 963. (28) Desnoyers, J. E.; Arel, M.; Perron, G.; Jolicoeur, C. J . Phys. Chem. 1969, 73, 3341. (29) Conway, B. E.; Verrall, R. E, J . Phys. Chem. 1966, 70, 3952. (30) Shahidi, F.; Farrell, P. G. .I Solution . Chem. 1978, 7 , 549

The Journal of Physical Chemistry, Vol. 91, No. 4, 1987

Molar Volumes and Compressibilities of Glycines TABLE 111: Estimated Values of Various Polyglycines at 25 O C

peptide length, n 1 2 3 4 ma

roand Iofor a Glycyl Residue in

vile (gly),

cm3 mor1, by method ii and iii iv 43.22 38.38 37.51 37.49 35.62: 37.45: 37.56d

30.19 30.28 32.10 33.44 38.86'

Kno(giy) x 104, cm3 mol-' bar-', bv method

ii and iii

iv

-27.00 -17.96 -14.79 -13.28 -8.69,b, -13.4,' -8.49d

+2.70 -3.10 -4.89 -5.86 -8.50'

a Derived values correspond to a peptide of infinite length; see text for details. bFrom method i. CFrom method ii. dFrom method iii. From method iv.


be viewed as the total contribution from all such glycyl residues, assuming that each residue contributes a constant factor, so that

Pint = nVno(gly) (16) Substituting the expression for pint from eq 15 into eq 16 and rearranging, one obtains Vno(gly) =

(t"- P e l ) / n

(17)

The same arguments can be extended to the compressibilities, as well, to obtain Kno(gly) =

(KO

- Koel)/n

In order to calculate the value of rno(gly)and Kno(gly),estimates of the electrostrictive components of these properties are required. were obtained from previous studies based on The values of Pel a comparison between data of the amino acids and their uncharged i s o m e r ~ . 'For ~ shorter molecules, these values were found to be a function of the chain length and increased with the length of the molecule. In monomeric amino acids, for example, Velwas estimated as 13 cm3 mol-' and was used for calculating Vlo(gly) in the present calculations. In solutes where the minimum separation between the end groups is five or more covalent bonds, it was found to reach a constant value24~30 of 16.2 cm3 mol-'. It follows that for diglycine and higher peptides, the value of 16.2 cm3 mol-' is a reasonable estimate of the volume of electrostriction and can be used in eq 17. With respect to compressibility data, the value of K O e 1 for monomeric amino acids was found to be -29.7 X lo4 cm3 mol-' bar-'.15 There appears to be no other data available regarding estimates of electrostrictive components of compressibilities of peptides or similar compounds. The value -29.7 X cm3 mol-' bar-', therefore, was used directly in eq 18 for all the peptides. Vno(gly) and Kno(gly) data calculated with eq 17 and 18 were plotted in a manner similar to Figure 4 and fit to eq 13 and 14, respectively, to obtain Vmo(gly)and Kmo(gly)values. Table I11 shows a comparison of the data obtained from the four methods. It is seen that there is generally good agreement between different data sets. A final value for each of these parameters was chosen on the basis of the extent of agreement between the individual methods. In the case of Vmo(gly),for example, the values from methods ii and iii showed better agreement and an average value of 37.51 f 0.07 cm3 mol-' was calculated. This value compares well with the previously reported values of 38.0 cm3 mol-' and 36.2 cm3 mol-'.I2 In the case of

971

K,O(gly), the results from methods iii and iv were in closer agreement and an average value of (-8.50 f 0.0) X lo4 cm3 mol-' bar-' was obtained for the compressibility of a glycyl residue. In order to use these data for calculating properties of the unfolded state, further information about the side-group contributions is required. It appears that standard contributions for the specific side groups are not easy to obtain because peptides of irregular sequence are more difficult to characterize in terms of side-group contributions. In previous work on amino acids a simpler way of estimating side-group contributions has been shown,15Le., by subtracting the value of t" or K O for glycine from the same properties of the given amino acid. Other studies focusing on poly(amino acids)g have shown that the side-group contribution to the thermodynamic properties in these type of molecules is slightly larger (by about 7%) than the contribution derived from the difference method. This discrepancy is attributed to factors similar to those described earlier regarding end-group and intervening chain solvation. Some studies on small peptides of mixed sequence indicate no change in the volume of side groups.31 In view of the conflicting information and after a careful review of the literature, we conclude that at present the simple subtraction method is by far the most reliable for estimating side-group contributions. The data obtained in this way can be used in conjunction with the Vmo(gly)or Kmo(gly)to calculate the volumes and compressibilities of the unfolded state of proteins.

Conclusion Partial molar volumes and adiabatic compressibilities of glycyl peptides have been measured in this study. The contributions of the peptide group toward these properties have been calculated by comparison of the present data with previous results from cup-amino acids. The partial molar volume and adiabatic compressibility of the peptide group have been estimated to be 20.41 cm3 mol-' and -12.4 X lo4 cm3 mo1-I bar-', respectively. The data from mono-, di-, tri-, and tetraglycine are also used to derive the values of these properties for a glycyl residue in a polypeptide chain of an hypothetical infinite length. These values are regarded as standard parameters for calculating properties of unfolded proteins from additivity principles. Four methods for deriving these values have been described which provide satisfactory results. The calculated standard values of partial molar volume and adiabatic compressibility for a glycyl residue are 37.51 f 0.07 cm3 mol-l and (-8.50 f 0.01) X lo4 cm3 mol-' bar-', respectively. It is proposed that these values can be used in conjunction with the side-group contributions of individual amino acids to calculate the volumetric properties of the unfolded state of proteins. Acknowledgment. We thank the Natural Sciences and Engineering Research Council of Canada for financial support. Registry No. Gly, 56-40-6; diglycine, 556-50-3; triglycine, 556-33-2; tetraglycine, 637-84-3. Supplementary Material Available: Tables of m , &, and +k,s for di-, tri-, and tetraglycines (3 pages). Ordering information is given on any current masthead page. (31) Based on calculations performed with molality and density data from: Kumaran, M. K.; Watson, I. D.; Hedwig, G. R. Aust. J . Chem. 1983, 36, 1813. (32) Cohn, E. J.; McMeekin, T. L.; Edsall, J. T.; Blanchard, M. H. J . Am. Chem. SOC.1934. 784. 56. (33) Ellerton, H. D.'; Reinfelds, G.; Mulcahy, D. E.; Dunlop, J. P. J . Phys. Chem. 1964, 68, 398. (34) Yayanos, A. A. J . Phys. Chem. 1972, 76, 1783.

Partial molar volumes and adiabatic compressibilities of glycyl

Recommend Documents