The partial molar volumes of some tetra- and pentapeptides in aqueous solution: A test of amino acid side-chain group additivity for unfolded proteins

Article abstract of DOI:10.1039/b003034l

Ten new peptides with the amino acid sequences glycyl-X-Y-glycine and glycyl-X-Y-Z-glycine, where X, Y and Z are amino acids with neutral side-chains, have been synthesized and the partial molar volumes at infinite dilution, V₂/(o), have been determined for all these peptides in aqueous solution at 298.15 K. For several of the peptides, V₂/(o) data have also been obtained over the temperature range 283.15 to 363.15 K using a scanning densimetric method. The V₂/(o) results obtained are compared with those calculated using the principle of group additivity and the group partial molar volumes we have derived in earlier work. We have shown that our group partial molar volumes can be used to reliably predict the partial molar volumes over a wide temperature range of polypeptides that have neutral amino acid side-chains.

Full text of DOI:10.1039/b003034l

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The partial molar volumes of some tetra- and pentapeptides in
aqueous solution: a test of amino acid side-chain group additivity for
unfolded proteins¤
Marko Hackel,a Hans-Jurgen Hinza and Gavin R. Hedwig*b
a Institut fur Physikalische Chemie der W estfalischen W ilhelms-Universitat Munster,
Schloplatz 4-7, D-48149 Munster, Germany. E-mail: hinz=uni-muenster.de
b Institute of Fundamental Sciences È Chemistry, Massey University, Private Bag 11222,
Palmerston North, New Zealand. E-mail: G.Hedwig=massey.ac.nz
Received 14th April 2000, Accepted 24th May 2000
First published as an Advance Article on the web 6th July 2000
Ten new peptides with the amino acid sequences glycyl-X-Y-glycine and glycyl-X-Y-Z-glycine, where X, Y and
Z are amino acids with neutral side-chains, have been synthesized and the partial molar volumes at inÐnite
dilution, V ¡ , have been determined for all these peptides in aqueous solution at 298.15 K. For several of the
2
peptides, V ¡ data have also been obtained over the temperature range 283.15 to 363.15 K using a scanning
2
densimetric method. The V ¡ results obtained are compared with those calculated using the principle of group
2
additivity and the group partial molar volumes we have derived in earlier work. We have shown that our
group partial molar volumes can be used to reliably predict the partial molar volumes over a wide temperature
range of polypeptides that have neutral amino acid side-chains.
that the group contributions are based on partial molar
volume data for the zwitterionic amino acids. In these mol-
Introduction
Protein hydration plays a crucial role in the structure and
function of proteins in aqueous solution. For example, the
interactions of water with the various functional groups of
proteins are important factors in determining the conforma-
tional stability of proteins.1h4 In recent years, there has been
considerable interest in the determination of various ther-
modynamic properties of proteins that can provide some
insight into protein hydration. In this regard, volumetric
properties of proteins such as the partial speciÐc volume, and
more signiÐcantly the pressure and temperature derivatives of
the partial speciÐc volume (the partial speciÐc compressibility
and the partial speciÐc expansibility respectively) are macro-
scopic properties that have received attention because these
are particularly sensitive measures of hydration e†ects.3,5h9
To develop a complete understanding of the role of hydra-
tion in protein folding/unfolding transitions, it is necessary to
study both the native and denatured states of a protein. The
denatured state of some globular proteins in aqueous solution
still retains extensive residual structure10,11 so in these cases
the random coil form of the protein, which is the ideal refer-
ence state in discussions of the thermodynamics of protein
folding, is not accessible by experiment. One method to esti-
mate a particular thermodynamic property, e.g. the partial
molar (or speciÐc) volume, for this random coil state is to use
an additivity scheme in which the property is given by a
simple summation of the partial molar properties of the
various constituent groups of the protein. Such empirical
additivity schemes for the calculation of the partial molar
volumes of proteins have been in use for many years, as
reviewed recently by Kharakoz.12
ecules the charged NH ` and CO ~ groups will interfere with
3
2
the hydration of the adjacent amino acid side-chain. Thus, the
calculation of the side-chain group contributions based on
partial molar volume data for the amino acids will not neces-
sarily be appropriate for a polypeptide. Several years ago we
proposed15 the use of small peptides of sequence glycyl-X-
glycine (gly-X-gly), where X is one of the amino acids, as com-
pounds to model the amino acid side-chains of proteins. For
these tripeptides, the single side-chain is in the central position
within the molecule and is Ñanked by two peptide groups,
which is structurally analogous to that found in proteins. The
assumption made in using these peptides as model com-
pounds is that the ionic end-groups are far enough away from
the central side-chain not to a†ect its hydration to a signiÐ-
cant extent. This assumption seems reasonable based on the
results from volumetric studies16,17 of two homologous
series of compounds, the a,x-aminocarboxylic acids,
`NH (CH ) CO ~, n \ 1È7, and the oligoglycines, (gly) ,
3
2 n
2
n
n \ 1È5. For the a,x-amino acids the charged end-groups
have no e†ect on the central position in the molecule when
separated by Ðve or more carbon atoms,16 and similarly for
the oligoglycines when there are two or more peptide groups
present.17 In previous work over several years, we have used
these tripeptides of sequence gly-X-gly to derive the partial
molar volumes15,18h20 and heat capacities18,21,22 of all 20
amino acid side-chains over a wide temperature range, and
also to derive the partial molar compressibilities of several
amino acid side-chains at 298.15 K.23
Although the concept of group additivity of partial molar
volumes in aqueous solution is well established for a range of
di†erent solute types,24,25 to our knowledge the group addi-
tivity of amino acid side-chain volumes for small peptides has,
hitherto, not been veriÐed experimentally. To achieve this
objective, we have carried out the syntheses of Ðve tetra-
peptides of sequence gly-X-Y-gly and Ðve pentapeptides of
One of the limitations of previous additivity schemes12h14
used to calculate partial molar volumes of unfolded proteins is
¤ Electronic Supplementary Information available. See http://
www.rsc.org/suppdata/cp/b0/b003034l/
DOI: 10.1039/b003034l
Phys. Chem. Chem. Phys., 2000, 2, 4843È4849
This journal is ( The Owner Societies 2000
4843

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sequence gly-X-Y-Z-gly where X , Y and Z are amino acids
with neutral side-chains. As these peptides have at least two
adjacent amino acid side-chains, they can be used to verify the
concept of group additivity in polypeptides. Included in this
selection of peptides are three with just a single side-chain.
Using volumetric results for these peptides, the assumption
that end-group e†ects are indeed absent in the peptides of
sequence gly-X-gly can also be tested. In this paper we report
the syntheses of these peptides and the partial molar volumes
Alpha Plus 4151 amino acid analyser. Elemental analyses
gave: C, 53.2; H, 6.1; N, 16.7%; cf. calculated for
C
H
O N : C, 53.6; H, 6.0; N, 16.7%. Analysis by alka-
15 20
5 4
limetric titration28,29 gave
a relative molar mass of
332.7 ^ 4.3, which is in reasonable agreement with that for the
anhydrous compound (M \ 336.35).
r
Valylglycylglycine benzyl ester p-toluenesulfonate. The ester
was prepared by azeotropic distillation using the general pro-
cedure described by Greenstein and Winitz.26 Valylglycylgly-
cine (2.5 g, 0.0108 mol, Sigma) and p-toluenesulfonic acid
monohydrate (2.1 g, 0.0110 mol) were suspended in a mixture
of benzene (60 cm3) and benzyl alcohol (6 cm3). The mixture
was reÑuxed for ca. 10 h. On cooling and the addition of
diethyl ether, a white solid crystallized from the mixture.
There was no evidence of any unreacted starting material in
the product as shown by TLC. An infrared spectrum of the
product indicated that the sample was a crystalline hydrate.
Yield 4.8 g, 87%; mp 76È77 ¡C. Elemental analyses gave: C,
at inÐnite dilution, V ¡ , for the peptides at 298.15 K. For
2
several of the peptides, V ¡ data have also been obtained
2
across the wide temperature range 283.15 to 363.15 K.
Experimental
Preparation and puriÐcation of the peptides
Peptides of general formula (gly) -X-Y-(gly) , where X and Y
m
n
are amino acids, were synthesized using the standard carbo-
diimide method.26 The procedure used was to couple the
benzyl ester of the peptide Y-(gly) to the peptide (gly) -X,
54.0;
H,
6.4;
N,
8.3%;
cf.
calculated
for
n
m
which was protected at the N-terminal using the benzyl-
oxycarbonyl group. Dicyclohexylcarbodiimide was used to
e†ect peptide bond formation and N-hydroxysuccinimide was
used as a trapping agent.27 The protecting groups on the
peptide were then removed by catalytic hydrogenation using a
Paar low-pressure shaker-type hydrogenator with 5% Pd/C as
the catalyst. Since this carbodiimide method is a routine syn-
thetic procedure in peptide chemistry, the preparative details
for only a few of the peptides are given below. However, as
each synthesis is somewhat idiosyncratic, the experimental
details of any particular synthesis are available on request
from one of the authors (GRH).
C
H O N S É 1.0H O: C, 54.0; H, 6.5; N, 8.2%.
23 31
7
3
2
N-Benzyloxycarbonylglycylphenylalanylvalylglycylglycine
benzyl ester. N-Benzyloxycarbonylglycylphenylalanine (1.43 g,
0.004 mol, Sigma) was dissolved in dichloromethane (30
cm3) ] DMF (1.5 cm3) to which was added N-
hydroxysuccinimide (0.49 g, 0.0042 mol) dissolved in dichloro-
methane (5 cm3) ] DMF (1 cm3). To this mixture was added
a
solution containing valylglycylglycine benzyl ester p-
toluenesulfonate (1.97 g, 0.004 mol) and triethylamine (0.41 g
0.004 mol) followed by N,N@-dicyclohexylcarbodiimide (0.88 g,
0.0042 mol) dissolved in a little dichloromethane. The mixture
was stirred overnight and then treated using the same pro-
cedure as described above for the glypheglygly protected
peptide. The product obtained was recrystallized from
methanol ] diethyl ether. Overall yield 1.83 g, 69%; mp 175È
176 ¡C. Elemental analyses gave: C, 64.0; H, 6.4; N, 10.8%; cf.
N-Benzyloxycarbonylglycylphenylalanylglycylglycine benzyl
ester. N-Benzyloxycarbonylglycylphenylalanine (1.96 g, 0.0055
mol, Sigma) was suspended in hot dichloromethane (50 cm3)
and freshly distilled dimethylformamide (DMF) (3 cm3) was
slowly added until dissolution was complete. To this solution
calculated for C
H
O N : C, 63.7; H, 6.3; N, 10.6%.
35 41
8 5
was added
a solution of glycylglycine benzyl ester p-
toluenesulfonate (2.17 g, 0.0055 mol, Sigma) and triethylamine
(0.56 g) in the solvent mixture dichloromethane (50
cm3) ] DMF (4 cm3). N-Hydroxysuccinimide (0.67 g, 0.0058
mol) dissolved in dichloromethane (30 cm3) ] DMF (1 cm3)
was then added to the reaction mixture along with N,N@-dicy-
clohexylcarbodiimide (1.20 g, 0.0058 mol) dissolved in
dichloromethane (5 cm3). The reaction mixture was stirred
overnight at room temperature. The precipitated dicyclohexy-
lurea (DCU) was removed by Ðltration following the addition
of a small amount of glacial acetic acid (1 cm3). The Ðltrate
was washed successively with 100 cm3 portions of water, 3 M
Glycylphenylalanylvalylglycylglycine. N-Benzyloxycarbonyl-
glycylphenylalanylvalylglycylglycine benzyl ester (0.9 g) was
dissolved in hot methanol (130 cm3). The hydrogenation pro-
cedure used was similar to that outlined above for the tetra-
peptide glypheglygly. The white products from two batch
hydrogenations were combined and recrystallized from
water ] ethanol. A gel-like product was obtained which was
thoroughly dried under vacuum to remove the adsorbed
solvent. The material was chromatographically pure as shown
by TLC. The relative molar mass determined by alkalimetric
titration was 438.8 ^ 5.3, which is in good agreement with
HCl, water, a half-saturated aqueous solution of NaHCO
that expected for the anhydrous compound (M \ 435.48).
3
r
and water. The solution was evaporated to dryness to give a
Elemental analyses gave: C, 54.2; H, 7.0; N, 16.1%; cf. calcu-
white solid. The product was recrystallized from hot
ethanol ] light petroleum; bp 60È80 ¡C. The overall yield was
2.68 g, 87%; mp 165È167 ¡C. Elemental analyses gave C, 64.3;
H, 5.7; N, 10.1%; cf. calculated composition for
lated for C
H
O N : C, 55.2; H, 6.7; N, 16.1%.
20 29
6 5
Serylglycine benzyl ester p-toluenesulfonate. Serylglycine
(1.57 g, 0.0097 mol, Bachem) and p-toluenesulfonic acid mono-
hydrate (1.90 g , 0.01 mol) were suspended in benzene (90 cm3)
and a 20-fold mole excess of benzyl alcohol (20 cm3). After ca.
8 h of azeotropic distillation the reaction was judged to be
complete as indicated by TLC. Diethyl ether (40 cm3) was
added to the mixture which was cooled to 6 ¡C overnight. The
product was collected by Ðltration and recrystallized from
ethanol ] diethyl ether. Overall yield 3.84 g, 86%; mp 175È
177 ¡C. Elemental analyses gave: C, 53.9; H, 5.7; N, 6.6%; cf.
C
H
N O : C, 64.3; H, 5.8; N, 10.0%.
30 32
4 7
Glycylphenylalanylglycylglycine.
N-Benzyloxycarbonyl-
glycylphenylalanylglycylglycine benzyl ester (1.2 g) was dis-
solved in 100 cm3 of hot ethanol. On cooling, water (5 cm3)
was added along with the catalyst suspended in a small
amount of water. As the peptide product formed during the
hydrogenation is not soluble in ethanol, water was added
during the course of the hydrogenation. On completion of the
hydrogenation, the Pd/C catalyst was removed by Ðltration
and the Ðltrate was evaporated to dryness to give a white
solid. The products from several batch hydrogenations were
combined and recrystallized from water ] ethanol. The
peptide was chromatographically pure as determined by TLC
and by ion-exchange chromatography using a Pharmacia
calculated for C
H
N O S: C, 53.8; H, 5.7; N, 6.6%.
19 24
2 7
N-Benzyloxycarbonylglycylphenylalanylserylglycine benzyl
ester. N-Benzyloxycarbonylglycylphenylalanine (1.25 g, 0.0035
mol, Bachem) was dissolved in dichloromethane (30
cm3) ] DMF (1 cm3) to which was added N-
hydroxysuccinimide (0.43 g) dissolved in a little dichloro-
4844
Phys. Chem. Chem. Phys., 2000, 2, 4843È4849

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methane. Serylglycine benzyl ester p-toluenesulfonate (1.48 g,
0.0035 mol) was dissolved in dichloromethane (50
cm3) ] DMF (8 cm3). The two solutions were mixed and
N,N@-dicyclohexylcarbodiimide (0.77 g) was added. The
mixture was stirred at room temperature overnight. The pre-
cipitated DCU was removed by Ðltration. The Ðltrate was
extracted only once using water because of poor separation of
the aqueous and nonaqueous phases. The predominantly non-
aqueous layer was evaporated to dryness and the solid
obtained was recrystallized from ethanol ] diethyl ether. A
determination of the melting point of the product indicated
that the material was contaminated with DCU.
Glycylprolylalanylalanylglycine. The sample was rec-
rystallized from water ] ethanol. The relative molar mass
determined by alkalimetric titration was 408.5 ^ 3.0 which is
excellent agreement with that expected for a peptide dihydrate
(M \ 407.42). Elemental analyses gave: C, 44.1; H, 7.1; N,
r
17.3%; cf. calculated for C
H
N O É 2.0H O: C, 44.2; H,
15 25
5
6
2
7.2; N, 17.2%.
Glycylglycylserylglycylglycine. The peptide was rec-
rystallized from water ] ethanol. Alkalimetric titration gave a
relative molar mass of 370.4 ^ 2.6, which is in good agreement
with that expected for a peptide dihydrate (M \ 369.33). Ele-
r
mental analyses gave: C, 36.0; H, 6.1; N, 18.8%; cf. calculated
for C
H
N O É 2.0H O: C, 35.8; H, 6.3; N, 19.0%.
Glycylphenylalanylserylglycine.
The
crude
N-
11 19
5
7
2
benzyloxycarbonylglycylphenylalanylserylglycine benzyl ester
(1.69 g) was dissolved in ethanol (80 cm3) and hydrogenated as
described above. Following removal by Ðltration of the cata-
lyst and any unreacted material, the Ðltrate was evaporated to
dryness and the solid obtained was recrystallized from
water ] ethanol. The relative molar mass obtained by alka-
limetric titration was 363.9 ^ 4.0, which is in good agreement
Solution preparation
All anhydrous peptides were routinely dried under vacuum
before the preparation of solutions. The water used to prepare
solutions and as the reference solvent was deionized, twice
glass distilled and thoroughly degassed immediately prior to
use. All solutions were prepared by mass.
with that for the anhydrous compound (M \ 366.37). Ele-
mental analyses gave: C, 52.2; H, 6.20; N, 14.8%; cf. calcu-
r
Apparatus and methods
lated for C
H
O N : C, 52.5; H, 6.1; N, 15.3%.
16 22
6 4
Density measurements at 298.15 K were made at Massey Uni-
versity using an Anton Paar digital density meter (model
DMA 60/602). Details of the apparatus and procedures used
have been described in previous work.15,30 The repro-
ducibility of an individual density measurement was to better
than 3 ] 10~6 g cm~3. Density measurements over the tem-
perature range 283.15 to 363.15 K were determined at WWU
Munster using a di†erential scanning densimetric system
(DSD) comprising two matched Anton Paar DMA 602HT
cells coupled to a DMA measuring unit. Details of the appar-
atus and operational procedures used have been described in
previous papers.31,32
Characterization of other peptides
Glycylserylthreonylglycine. The peptide was recrystallized
twice,
Ðrstly
from
water ] methanol
then
from
water ] ethanol. The product was chromatographically pure
as determined by TLC and by ion-exchange chromatography.
Analysis by ES-MS gave m/z \ 321.3 for the peptide
[M ] H]`. The relative molar mass determined by titration
was 317.5 ^ 3.2 so the peptide is anhydrous. However, the
sample is very hygroscopic which is probably why we were
unable to obtain satisfactory elemental analyses.
Results
Densities of aqueous solutions of the various tetra- and penta-
peptides determined at 298.15 K are given in Table S1¤. These
density data were used to calculate the apparent molar
Glycylasparagylalanylglycine. The peptide was recrystallized
from water ] ethanol. The relative molar mass of the peptide
determined by ES-MS was 317.3 and that obtained by alka-
limetric titration was 316.1 ^ 2.5, which is in excellent agree-
ment with that expected for the anhydrous compound.
Elemental analyses gave: C, 41.5; H, 6.0; N, 22.3%; cf. calcu-
volumes of the solutes, V , using the equation
Õ
V \ (M /o) [ (o [ o0)/moo0),
(1)
Õ
2
1
1
where M is the solute molar mass, m is the solution molality
lated for C
H
O N : C, 41.6; H, 6.0; N, 22.1%.
2
11 19
6 5
and o and o0 are, respectively, the densities of the solution
1
and pure solvent (0.997 047 g cm~3 at 298.15 K33). The V
Õ
Glycylphenylalanylalanylglycine. The sample, which was
recrystallized from water ] ethanol, was chromatographically
pure as shown by TLC and ion-exchange chromatography.
The mass of the peptide [M ] H]` determined by ES-MS
was 351.3 and the relative molar mass obtained by alka-
limetric titration was 346.9 ^ 3.8, which is in agreement with
values, together with their uncertainties estimated using the
propagation of errors method outlined earlier,30 are given in
Table S1¤. The molality dependence of V for dilute solutions
Õ
of zwitterionic peptides is represented by the linear equation
V \ V ¡ ] S m,
(2)
Õ
2
V
that for the anhydrous compound (M \ 350.38).
where V ¡ is the partial molar volume of the solute at inÐnite
dilution and S is the experimental slope. For almost all the
peptide systems studied, either the low solubility of the solute
r
2
V
Glycylglycylleucylglycylglycine. The sample was rec-
rystallized from water ] methanol. Chromatographic purity
was conÐrmed by TLC and by ion-exchange chromatography.
or the limited amount of the material available for study
restricted the molality range that could be used. Analyses of
the V data using eqn. (2) gave values for S that were sta-
Alkalimetric titration gave M \ 361.3 ^ 2.9 which is in excel-
r
Õ
V
lent agreement with that for the anhydrous peptide (M \
tistically not di†erent from zero. If the molality dependence of
r
359.38). Elemental analyses gave: C, 46.7; H, 6.0; N, 19.3%;
V is ignored, a value of V ¡ can be estimated by averaging the
Õ
2
cf. calculated for C
H
N O : C, 46.8; H, 7.0; N, 19.5%.
V results. As outlined previously,19 any error associated with
14 25
5 6
Õ
assigning the mean V value as V ¡ is unlikely to be greater
than, at most, a few tenths of 1 cm3 mol~1. The means and
standard deviations of the V data are given in Table 1. For
Õ
2
Glycylglycylserylalanylglycine. The peptide was rec-
rystallized from water ] methanol. Alkalimetric titration gave
a relative molar mass of 349.3 ^ 2.5, which is in good agree-
Õ
the peptides glyglyleuglygly and glyglyseralagly, the molality
ment with that expected for the anhydrous peptide (M \
dependences of V were discernable. The values of V ¡ and S
given in Table 1 were obtained from weighted least-squares
r
Õ
2
V
347.33). Elemental analyses gave: C, 41.2; H, 6.4; N, 20.0%;
cf. calculated for C
H
N O : C, 41.5; H, 6.1; N, 20.2%.
analyses of the V data using eqn. (2). The weighting factors
12 21
5
7
Õ
Phys. Chem. Chem. Phys., 2000, 2, 4843È4849
4845

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Table 1 Partial molar volumes at inÐnite dilution for some tetra- and pentapeptides in aqueous solution at 298.15 K
V ¡ (calc)/cm3 mol~1
2
Peptide
V ¡/cm3 mol~1
(gly) a
(gly) b
2
3
4
glypheglygly
glyphealagly
glyphesergly
glyasnalagly
230.12(0.06)c
247.8(0.2)
247.0(0.2)
202.08(0.08)
201.7(0.1)
251.08(0.08)
201.32(0.05)
314.98(0.07)
220.9(0.2)
229.5(0.4)
247.3(0.4)
247.5(0.7)d
201.3(0.3)
200.4(0.7)d
249.8(0.4)
202.3(0.7)d
314.2(0.5)
220.1(0.7)d
252.4(0.4)
230.4(0.3)
248.2(0.3)
248.4(0.7)d
202.2(0.2)
201.2(0.6)d
250.6(0.4)
203.2(0.7)d
315.1(0.4)
221.0(0.7)d
253.3(0.4)
glyserthrgly
glyglyleuglyglye
glyglyserglygly
glyphevalglygly
glyglyseralaglyf
glyproalaalagly
255.4(0.2)
a Calculated using eqn. (6). b Calculated using eqn. (7). c Estimated uncertainties are in parentheses. d Using V ¡(ser) \ 18.0(0.6) cm3 mol~1 from
ref. 19. e S \ 4.5(2.1) cm3 kg mol~2. f S \ 7.0(6.0) cm3 kg mol~2.
V
V
Table 2 Coefficients from the Ðtting of eqn. (3) to the partial molar volumes of the peptides
Peptide
a/cm3 mol~1
b/cm3 mol~1 K~1
104 c/cm3 mol~1 K~2
R2 aa
m/mol kg~1
glypheglygly
glyphealagly
glyphesergly
glyserthrgly
glyasnalagly
glyglyleuglygly
glyglyseralagly
222.8 (0.1)b
242.6 (0.2)
238.7 (0.1)
197.3 (0.1)
196.4 (0.1)
244.5 (0.1)
214.6 (0.1)
0.302 (0.003)
0.255 (0.007)
0.353 (0.004)
0.256 (0.002)
0.271 (0.005)
0.245 (0.004)
0.284 (0.003)
[11.6 (0.3)
[3.7 (0.7)
[15.0 (0.4)
[12.1 (0.2)
[13.1 (0.6)
[6.1 (0.4)
[13.7 (0.3)
0.99
0.94
0.99
0.99
0.96
0.98
0.99
0.021È0.044
0.021È0.041
0.020È0.029
0.023È0.033
0.0095È0.0103
0.020È0.030
0.014È0.025
a Correlation coefficient. b Standard deviations are in parentheses.
used in the analyses were taken as 1/(dV )2,where dV is the
tides could not be detected, the V (T ) data for all the solutions
were combined and analysed using an equation of the form
Õ
Õ
Õ
estimated uncertainty for V .
Õ
Peptide solution densities determined over the temperature
range 283.15 to 363.15 K using the DSD method were
analysed using eqn. (1) to obtain apparent molar volumes. The
density of water as a function of temperature used in the data
analysis was taken from the work of Kell.33 For each peptide
studied, densityÈtemperature scans were carried out on a
minimum of four solutions with molalities in the range shown
V \ a ] b(T [ 273.15) ] c(T [ 273.15)2,
(3)
Õ
where a, b and c are the coefficients obtained from least-
squares Ðtting using unit weights. Values of these coefficients
for the various peptides studied are given in Table 2. The
analysis using eqn. (3) gives, at any temperature, an average
value for V over the molality range used. As outlined above
Õ
in Table 2. The V Ètemperature curves for the peptide glyp-
for the V results at 298.15 K, an average value of V at any
Õ
Õ
Õ
heglygly are shown in Fig. 1. All four curves are coincident
temperature T will be a good estimation of the partial molar
within the experimental uncertainties. This is typical for solu-
tions of any given peptide in the low molality range used in
volume of the peptide at inÐnite dilution.
A comparison is given in Table 3 of the V ¡ results obtained
2
this study. Since the molality dependences of V for the pep-
from density measurements at the temperature 298.15 K with
Õ
the results derived using the polynomial coefficients given in
Table 2. For each peptide, the V ¡ results are concordant
2
within the combined experimental uncertainties.
Discussion
Using the principle of group additivity,34 the partial molar
volume of any solute can be obtained from a summation of
Table 3 A comparison of the partial molar volumes of the peptides
at 298.15 K derived using density data obtained isothermally and by
DSD
V ¡/cm3 mol~1
2
Peptide
Isothermal
DSD
glypheglygly
glyphealagly
glyphesergly
glyserthrgly
glyasnalagly
glyglyleuglygly
glyglyseralagly
230.12(0.06)a
247.8(0.2)
247.0(0.2)
229.6(0.4)
248.7(1.3)
246.6(0.7)
202.9(0.4)
202.4(0.3)
250.3(0.8)
220.8(0.4)
201.7(0.1)
202.08(0.08)
251.08(0.08)
220.9(0.2)
Fig. 1 Temperature dependence of the apparent molar volume for
the peptide glypheglygly. One DSD scan is shown for each of four
solutions at m \ 0.020 75, 0.028 21, 0.036 82 and 0.043 46 mol kg~1.
a Standard errors are in parentheses.
4846
Phys. Chem. Chem. Phys., 2000, 2, 4843È4849

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the contributions of the various constituent groups of the mol-
ecule. For polypeptides it is convenient to use as constituent
groups the amino acid side-chains, the backbone glycyl unit
presence of the charged end-groups in the molecules39 or
because the tripeptides with bulky amino acid side-chains may
fold.40 The results at 298.15 K presented in Table 1 suggest
that these e†ects are not at all signiÐcant in the present
context and certainly do not detract from the suitability of
these gly-X-gly tripeptides as compounds to model the amino
(CH CONH) of the peptide chain and the ionic end-groups
2
(`NH and CH CO ~). The partial molar volume of an
3
2
2
amino acid side-chain, V ¡(R), was derived in our earlier
work18,19 using the equation
acid side-chains of proteins. Moreover, the V ¡(T ) results
2
obtained in this work suggest that the gly-X-gly peptides are
V ¡(R) \ V ¡(gly-X-gly) [ V ¡(glyglygly),
(4)
2
2
suitable models for the amino acid side-chains not only at
298.15 K but also over a wide temperature range.
A comparison is given in Fig. 2 of the temperature depen-
dences of the leucyl and phenylalanyl side-chain partial molar
volumes derived using di†erent methods. For each side-chain,
the solid line represents the V ¡(R)Ètemperature curve obtained
where V ¡(gly-X-gly) and V ¡(glyglygly) are, respectively, the
2
2
partial molar volumes at inÐnite dilution of the peptides
gly-X-gly and triglycine. The quantity V ¡(R) gives the contri-
bution to the volume on replacing a methylene H atom of the
glycyl group by the side-chain R. The partial molar volume of
the glycyl unit, V ¡(CH CONH) was derived previously35
using eqn. (4), i.e. based on V ¡ data for tripeptides. The side-
2
2
using the V ¡ results for the peptides of sequence ala(gly) ,
chain volumes based on the V ¡(T ) results obtained for the
2
n
2
n \ 2È4. As the derivation of the ionic end-group contribution
given in earlier work35 was based on V ¡ data for triglycine,
peptides glypheglygly and glyglyleuglygly are also shown in
Fig. 2. The dashed curves, which are based on triglycine as the
reference compound, were derived using the equation
2
viz.
V ¡(`NH and CH CO ~) \ V ¡((gly) ) [ 2V ¡(CH CONH)
V ¡(R) \ V ¡(peptide)
3
2
2
2
3
2
2
(5)
[ MV ¡(glyglygly) ] ; V ¡(CH CONH)N,
(8)
2
2
it is convenient in the context of the present study to use tri-
glycine as the reference compound for group additivity. The
partial molar volumes of the tetra- and pentapeptides used in
this study can then be derived using the expression
where V ¡(peptide) is the partial molar volume at inÐnite dilu-
2
tion of either glypheglygly or glyglyleuglylgy. The dotted
curves were obtained using an analogous equation but with
tetraglycine as the reference compound,
V ¡(calc) \ V ¡((gly) )
V ¡(R) \ V ¡(peptide)
2
2
3
2
] ; V ¡(CH CONH) ] ; V ¡(R).
(6)
[ MV ¡(glyglyglygly) ] V ¡(CH CONH)N.
(9)
2
2
2
The results obtained for 298.15 K are given in Table 1. With
the exception of the seryl side-chain, the V ¡(R) values used in
the calculations were taken from earlier work18,20 in which
density data were determined isothermally. The recent mea-
surement of V ¡(ser) at 298.15 K obtained by DSD22 is 1.2 cm3
mol~1 smaller than that determined in a previous study.15
From comparisons of these V ¡(ser) results with that obtained
It follows, of couse, that for the peptide glypheglygly there will
be no contribution from the glycyl group in eqn. (9). Values
for V ¡(glyglygly), V ¡(CH CONH) and V ¡(glyglyglygly) used
2
2
2
in the calculations were obtained from the V ¡(T ) polynomials
2
reported in earlier work.19,35 The uncertainties shown in Fig.
2 were calculated using propagation of errors relationships.
For both side-chains the V ¡(R)Ètemperature curves based
using amino acid V ¡ data,36 and also based on the results of
on V ¡ data for the tripeptides are in excellent agreement,
2
2
calculations of the changes in side-chain volumes on protein
within the combined estimated uncertainties, with those
folding,19 it would appear that the V ¡(ser) result obtained by
DSD is more reliable than the earlier result.15 Consequently,
we have used herein the more recent V ¡(ser) result. As shown
in Table 1, there is excellent agreement between the V ¡ results
calculated using eqn. (6) and those obtained experimentally.
obtained using eqn. (8). The results obtained using eqn. (9) are
also in agreement with the side-chain results based on the V ¡
data for the gly-X-gly peptides, within the admittedly larger
uncertainties, which arise because of the low solubility of
tetraglycine, as discussed previously.35 The results presented
in Fig. 2 conÐrm that any interactions between the phe or leu
2
2
With the exception of the peptide glyproalaalagly, the di†er-
ences between the calculated and experimental values range
side-chains in the gly-X-gly peptides and the charged `NH
3
and CO ~ groups must have a negligible e†ect on the partial
2
between 0.2 and 0.6% of V ¡ . Even for glyproalaalagly the dif-
2
ference is only 1.2%, which is still small considering the quan-
molar volume of the side-chain. If such interactions were sig-
titative limitations of the principle of group additivity.34,37,38
An alternative method of calculating the partial molar
volumes of the peptides using group additivity is to use tetra-
glycine instead of triglycine as the reference compound, i.e.
niÐcant, then V ¡(R) values derived from V ¡ data for tetra- and
pentapeptides in which the ionic end-groups are further
2
V ¡(calc) \ V ¡((gly) )
2
2
4
] ; V ¡(CH CONH) ] ; V ¡(R).
(7)
2
The V ¡ (calc.) values obtained using eqn. (7) and the V ¡ .
result for tetraglycine at 298.15 K that we reported in a recent
2
2
paper35 are also given in Table 1. There is excellent agreement
between the calculated and experimental V ¡ . values for all the
2
peptides. The di†erences are small, in the range 0.04 to 1.0%
of V ¡ . The V ¡ (calc.) results presented in Table 1 clearly show
2
2
that a general additivity scheme, using our group partial
molar volumes of the amino acid side-chains derived using the
tripeptides of sequence gly-X-gly19 and the group partial
molar volume of the backbone glycyl unit,35 is able to reliably
predict the V ¡ . values of the tetra- and pentapeptides at
2
298.15 K.
It has been reported in the literature that peptides of
sequence gly-X-gly may not be appropriate compounds to
model the amino acid side-chains of proteins because of the
Fig. 2 Partial molar volumes of the phenylalanyl and leucyl side-
chains as a function of temperature: (ÈÈ) experimental results, (È È È)
calculated using eqn. (8), (É É É É) calculated using eqn. (9).
Phys. Chem. Chem. Phys., 2000, 2, 4843È4849
4847

View Article Online
removed from the side-chain than they are in tripeptides
would be expected to di†er from those based on the gly-X-gly
tripeptides. As end-group e†ects are absent for the phe and leu
side-chains, which are intrinsically of large volume, it is a rea-
sonable assumption that such e†ects will also be negligible for
all amino acid side-chains over a wide temperature range.
The results presented in Table 1 establish categorically that
group additivity of amino acid side-chain partial molar
volumes is valid at 298.15 K. To verify that this group addi-
tivity holds across a wide temperature range, we have deter-
mined the partial molar volumes of glyglyseralagly and four of
the peptides of sequence gly-X-Y-gly over the temperature
range 283.15 to 363.15 K. The results obtained are shown in
Figs. 3 and 4. For comparison, the V ¡ values at 298.15 K that
2
are given in Table 1 have been included in the Ðgures. Figs. 3
and 4 also contain the V ¡Ètemperature curves for the peptides
2
calculated on the basis of group additivity using eqns. (6) and
(7). In general, there is good agreement, within the estimated
uncertainties, between the V ¡ results obtained experimentally
2
and those derived using the group partial molar volumes
reported in earlier papers.19,35
For the peptide glyasnalagly, the agreement between the
experimental and calculated V ¡ Ètemperature curves was ini-
tially rather poor, despite the excellent agreement between the
Fig. 4 Partial molar volumes of the peptides glyphealagly and gly-
2
serthrgly as a function of temperature: (ÈÈ) experimental results,
experimental and calculated V ¡ results at 298.15 K (see Table
(È È È) calculated using eqn. (6), (É É É É) calculated using eqn. (7), (…) V ¡
2
2
1). It transpired that the polynomial function for the asn side-
result at 298.15 K from Table 1.
chain that was derived in earlier work31 is erroneous. From
new DSD measurements over the temperature range 283.15 to
358.15 K on Ðve solutions (m \ 0.028È0.035 mol kg~1) of gly-
asngly, the polynomial coefficients of eqn. (3) are a \ 141.8
cm3 mol~1, b \ 0.249 cm3 mol~1 K~1 and 104 c \ [13.14
cm3 mol~1 K~2. As shown in Fig. 3, the agreement between
Although the V ¡ results as a function of temperature for the
peptide glyserthrgly are slightly larger than those predicted
using group additivity (see Fig. 4), the di†erences are neverthe-
less only about 1%. The anhydrous peptide glyserthrgly is
hygroscopic and, as such, it is not easy to handle. The slightly
2
larger V ¡ values observed may be a result of moisture
the calculated and experimental V ¡ data for the peptide glyas-
2
2
adsorbed from the atmosphere during the preparation of the
nalagly is good when the group partial molar volumes for the
solutions.
asn side-chain are derived using the polynomial coefficients
for glyasngly determined in this work. We have no satisfactory
explanation for the error in our earlier results for this peptide,
It should be noted that the peptides chosen for study have
combinations of amino acid side-chains that have di†erent
hydration characteristics. For example, the peptide glyphea-
lagly has two adjacent hydrophobic side-chains, the peptide
glyphesergly has one hydrophobic and one hydrophilic side-
chain and the peptide glyserthrgly has two side-chains that
each contains hydrophilic functional groups. The conclusion
that can be drawn from the results presented in Figs. 3 and 4
is that group additivity of side-chain partial molar volumes in
polypeptides, and by inference in unfolded proteins, is indeed
valid over a wide temperature range irrespective of the amino
acid sequence of the polypeptide. However, it should be
stressed that the assumption of group additivity has been vali-
dated in this work for only neutral side-chains. For complete-
ness, tetra- and pentapeptides with combinations of neutral
and ionic side-chains should be studied. These peptides, which
pose a greater challenge to the synthetic skills of a physical
chemist, will be the subject of future work.
other than to note that the higher V ¡ values observed in the
2
previous study31 are consistent with possible water adsorption
on the solid peptide sample.
Acknowledgements
We thank a summer student, James Stephenson, for his assist-
ance with the syntheses of some of the peptides. The Ðnancial
assistance from the NZ/FRG ScientiÐc and Technological
Cooperation Agreement and Westfalische Wilhelms-
Universitat Munster is gratefully acknowledged. M.H.
acknowledges support from the German Academic Exchange
Service in the form of a ““DAAD Doktorandenstipendium im
Rahmen des gemeinsamen Hochschulsonderprogramms III
von Bund und LandernÏÏ.
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Fig. 3 Partial molar volumes of the peptides glyphesergly, glygly-
seralagly and glyasnalagly as a function of temperature: (ÈÈ) experi-
mental results, (È È È) calculated using eqn. (6), (É É É É) calculated using
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4848
Phys. Chem. Chem. Phys., 2000, 2, 4843È4849

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Phys. Chem. Chem. Phys., 2000, 2, 4843È4849
4849