Download Heat capacity changes in carbohydrates and protein–carbohydrate

Biochem. J. (2009) 420, 239–247 (Printed in Great Britain)
239
doi:10.1042/BJ20082171
Heat capacity changes in carbohydrates and protein–carbohydrate
complexes
Eneas A. CHAVELAS1 and Enrique GARCÍA-HERNÁNDEZ1
Instituto de Quı́mica, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México 04510, DF, Mexico
Carbohydrates are crucial for living cells, playing myriads of
functional roles that range from being structural or energy-storage
devices to molecular labels that, through non-covalent interaction
with proteins, impart exquisite selectivity in processes such as
molecular trafficking and cellular recognition. The molecular
bases that govern the recognition between carbohydrates and
proteins have not been fully understood yet. In the present
study, we have obtained a surface-area-based model for the
formation heat capacity of protein–carbohydrate complexes,
which includes separate terms for the contributions of the two
molecular types. The carbohydrate model, which was calibrated
using carbohydrate dissolution data, indicates that the heat
capacity contribution of a given group surface depends on its
position in the saccharide molecule, a picture that is consistent
with previous experimental and theoretical studies showing that
the high abundance of hydroxy groups in carbohydrates yields
particular solvation properties. This model was used to estimate
the carbohydrate’s contribution in the formation of a protein–
carbohydrate complex, which in turn was used to obtain the heat
capacity change associated with the protein’s binding site. The
model is able to account for protein–carbohydrate complexes that
cannot be explained using a previous model that only considered
the overall contribution of polar and apolar groups, while allowing
a more detailed dissection of the elementary contributions that
give rise to the formation heat capacity effects of these adducts.
INTRODUCTION
abundance and proximity of these groups in carbohydrates
yield solvation characteristics, such as the total number of
water molecules and the way they are shared inside the first
hydration shell, which might depart significantly from individual
hydroxy groups. In fact, heat capacities for saccharides in dilute
aqueous solutions are significantly larger than values calculated
from the sum of their individual chemical constituents [11].
Moreover, despite the highly polar character of carbohydrates,
Raman scattering experiments have identified them as waterstructure enhancers [12]. These properties must be relevant for
determining how carbohydrates interact with proteins, imparting
unique characteristics to the adducts they form [13,14]. Thus
the study of carbohydrate and P–CH (protein–carbohydrate)
complexes represents an excellent opportunity to expand our
knowledge of the role that the solvent plays in biomolecular
recognition processes. In the present study, a model for the
heat capacity formation of P–CH complexes (CpP−CH ) was
developed. This model performs better than an ad hoc model
previously obtained [15], allowing a more detailed dissection of
the elementary contributions that give rise to the formation heat
capacity effects of these adducts.
Heat capacity effects have long been recognized as key to
understanding the molecular principles that underpin noncovalent driven processes [1–4]. The absolute heat capacity of
a system is determined by dispersion of the enthalpy distribution,
which in turn is related to the number of vibrational, rotational and
translational ‘soft’ modes susceptible to absorbing thermal energy.
Changes in these soft modes are particularly large in processes
that take place in aqueous solutions, due to the rearrangement
of solvent molecules around solutes. The way the solvent
restructures, and the consequent impact of this restructuring on
the solution’s heat capacity, is highly dependent on the solute’s
chemical nature. The analysis of a large body of thermodynamic
data for the hydration of small organic compounds has shown
an increase in heat capacity as a thermodynamic signature for
the solvation of apolar groups, whereas the opposite effect is
characteristic of polar groups. These distinct effects have been
rationalized in terms of different restructuring responses of water
molecules, depending on the surface polarity [5]. Hydrophobic
solvation is thought to increase the number of energy reservoirs,
by forming water–water hydrogen bonds at the first solvation layer
that are stronger than at the bulk phase. In contrast, the stronger
interactions occurring between solvating water molecules and
polar groups prevent these interactions from being excited
significantly at ordinary temperatures. Thus Cp (change in heat
capacity) constitutes a powerful sensor for revealing the types and
amounts of solute surfaces involved in processes such as protein
folding and binding [6,7].
Carbohydrates have particular hydration characteristics which
are crucial for dictating the structure and functionality of
these biomolecules [8–10]. Hydroxy groups are thought to
behave similarly to solvent water molecules. Nevertheless, the
Key words: carbohydrate, hydration, lectin, molecular recognition, structural energetics, surface area model.
THEORY
Surface-area-based models for the formation heat capacity of
protein–carbohydrate complexes
Simple additivity models have proved to be very useful for
estimating heat capacities from structural information for many
classes of small non-ionic compounds. Among the different
additivity schemes developed and calibrated with model
compounds, those based on solvent-accessibility surface area
changes (A) became widely used in the analysis of
Abbreviation used: A , change in surface area; Cp, change in heat capacity; CBM9, family 9 carbohydrate binding module; 3D, three-dimensional;
P–CH complex, protein–carbohydrate complex; VIF, variance inflation factor.
1
Correspondence may be addressed to either of these authors (email [email protected] or [email protected]).
c The Authors Journal compilation c 2009 Biochemical Society
240
E. A. Chavelas and E. Garcı́a-Hernández
Table 1 Heat capacity parameterizations based on polar and apolar surface
area changes
−1
−1
−2
Values are means +
− S.D. and are in units of cal · K · mol · Å . S.D. is only given where
available.
cppol
Garcı́a-Hernández et al. [15]
The present study
Spolar et al. [18]
Murphy and Freire [19]
Makhatadze and Privalov [20]
Myers et al. [21]
Robertson and Murphy [22]
Madan and Sharp [23]
cpap
0.23 +
− 0.04
0.24 +
− 0.09
− 0.14 +
− 0.04
− 0.27 +
− 0.03
− 0.21
− 0.09 +
− 0.30
0.12 +
− 0.08
0.17
0.07 +
− 0.03
0.06 +
− 0.09
0.32 +
− 0.04
0.45 +
− 0.02
0.51
0.28 +
− 0.12
0.16 +
− 0.05
0.17
System
Seven P–C complexes
14 P–C complexes
Liquid amides
Dipeptide crystals
Protein unfolding
Protein unfolding
Protein unfolding
Nucleic acid fragments
conformational changes in macromolecules. Accessible surface
area is a geometrical parameter considered to be proportional to
the amount of water in contact with the solute. Therefore A
models allow us to take into account a partial exposition/burial
of the interacting chemical groups. A widely used A model
for Cp considers this thermodynamic parameter as a simple
function of the solvent-accessibility changes of polar (Apol ) and
apolar (Aap ) areas [6]:
Cp = cppol Apol + cpap Aap
(1)
Using thermodynamic and structural information for a database
of seven P–CH complexes, Garcı́a-Hernández et al. [15] derived
an ad hoc parameterization of eqn (1) for these adducts (Table 1).
According to this parameterization, both polar and apolar
surfaces elicit a decreasing effect on heat capacity upon complex
formation. This result is at variance with several results obtained
previously for eqn (1), where typically a negative coefficient for
polar groups was obtained (Table 1). Furthermore, the absolute
contribution of apolar surfaces, although of the sign expected,
is relatively small. The structural–energetic behaviour of P–CH
complexes is in qualitative agreement with both experimental and
theoretical studies, which indicate that carbohydrates bear unique
Table 2
Figure 1 Heat capacity changes for the formation of protein–carbohydrate
complexes as a function of changes in polar (A pol ) and apolar (A ap )
surface areas
Normalization of eqn (1) by A ap yields a straight-line model where A pol /A ap and
Cp/A ap are the independent and dependent variables respectively and the slope
and y -intercept correspond to cppol and cpap respectively.
solvation properties imparted by the large abundance of hydroxy
groups mounted on the sugar-ring scaffold [11,12,16,17].
Table 2 shows the seven P–CH complexes originally used to
calibrate eqn (1), along with another seven complexes of a known
3D (three-dimensional) structure for which CpP−CH has been
measured calorimetrically. Figure 1 shows CpP−CH as a function
of Apol and Aap . In this plot, eqn (1) was normalized by Aap to
obtain a 2D (two-dimensional) representation of eqn (1). Thus the
slope and the y-intercept correspond to the values of cppol and
cpap respectively. It can be seen that the new P–CH complexes
(numbers 8–14 in Figure 1) show the same trend as that seen
for the original complexes (numbers 1–7), yielding cppol and
cpap values close to those obtained originally with the reduced
set of seven P–CH complexes (see the first and second data rows
Heat capacity and surface area changes in protein–carbohydrate complexes
Values for –CpP−CH are means +
− S.D. S.D. is only given where available. Hev-GlcNAc2 : hevein-quitobiose (GlcNAcβ1-4GlcNAc), Hev-GlcNAc3 : hevein-quitotriose (GlcNAcβ1-4GlcNAcβ14GlcNAc), Lisoz-GlcNAc2 : lysozyme-quitobiose, Lisoz-GlcNAc2 : lysozyme-quitotriose, ConA-mMan: concanavalin A-methylmannose, ConA-Man2 : concanavalin A-trimannoside core
(Manα1-6[Manα1-3]Man), CBM9-Glc2 : CBM9 from Thermotoga maritima xylanase 10A-cellobiose (Glcβ1-4Glc); ConA-mMan: concanavalin A-methylglucose, ConA-Man2 : concanavalin
A-mannobiose (Manα1-3Man), DGL-Man3 : Dioclea grandiflora lectin-trimannoside core, CBM9-Glc: CBM9 from Thermotoga maritima xylanase 10A-glucose (Glc), CVIIL-mFuc:
Chromobacterium violaceum lectin-methylfucose, Cf CBM4-Glc5 : CBM4 from Cellulomonas fimi β1-4-glucanase-cellopentaose (Glcβ1-4Glcβ1-4Glcβ1-4Glcβ1-4Glc), TmCBM4-Glc6 : CBM4
from Thermotoga maritima β1-3-glucanase-laminarihexaose (Glcβ1-3Glcβ1-3Glcβ1-3Glcβ1-3Glc1-3Glc). Structure-based calculations of water-accessible surface areas were performed with the
NACCESS program [32], using a probe radius of 1.4 Å and a slice width of 0.1 Å. Total changes in surface area (A t ) were estimated from the difference between the complex and the sum of free
molecules. Polar area changes (A pol ) were obtained from the change in accessible area of nitrogen and oxygen atoms, while the apolar area change (A ap ) was computed from the contributions
of carbon atoms.
–A pol
–A ap
–A t
–CpP−CH
PDB
Reference(s)
HevGlcNAc2
1
HevGlcNAc3
2
LisozGlcNAc2
3
LisozGlcNAc3
4
ConAmMan
5
ConAMan3
6
CBM9Glc2
7
ConAmGlc
8
ConAMan2
9
DGLMan3
10
CBM9Glc
11
CVIILmFuc
12
Cf CBM4Glc5
13
Tm CBM4Glc6
14
162
313
475
64 +
−6
–
[13]
237
345
582
83 +
−8
–
[13]
276
309
545
83 +
−5
1lzbm
[15]
404
384
788
119 +
−3
1lzb
[15]
162
186
348
52 +
− 11
5cna
[24,25]
364
245
609
109 +
−5
1cvn
[24,26]
239
301
540
67 +
−2
1i82
[27]
145
185
330
37 +
−5
1gic
[25]
246
205
451
67 +
−2
1i3h
[28]
364
253
617
96
1dgl
[24,29]
208
175
383
34 +
− 16
1i8a
[27]
157
152
309
80
2boi
[30]
341
522
863
50 +
− 10
1gu3
[31]
407
490
897
172 +
− 14
1gui
[31]
c The Authors Journal compilation c 2009 Biochemical Society
Heat capacity changes in carbohydrates and protein–carbohydrate complexes
Table 3
241
Heat capacity and accessible surface area changes for the dissolution of carbohydrates
Surface areas were classified according to the heteroatom type and the configurational location within the carbohydrate molecule in terms of the distance (number of covalent bonds) from the sugar
ring (see Figure 2). Surface areas were calculated using the NACCESS program [32]. Cp values were determined at 25 ◦C.
Cpdiss
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11
12.
13.
14.
Ai (Å2 )
−1
Carbohydrate
(cal · mol
Arabinose (Ara)
Fructose (Fru)
Galactose (Gal)
Glucose (Glc)
Mannose (Man)
Ribose (Rib)
Xylose (Xyl)
Sucrose (Suc)
Maltotriose (Mtri)
Maltotetrose (Mtet)
Methyl-mannose (mMan)
Methyl-glucose (mGlc)
dGlc
GlcNAc
24
33
31
33
32
22
29
51
55
80
48
44
35
36
−1
·K
−2
·A )
A ap (Å )
A pol (Å )
C0
115
126
116
117
126
118
114
191
277
364
187
200
150
188
156
182
188
186
178
152
158
258
357
429
144
141
137
182
115
38
75
70
82
118
114
81
190
236
66
69
103
62
2
2
C1
C2,3
O0,1
75
83
0
80
156
108
147
151
139
152
158
175
248
303
109
105
101
101
88
41
47
44
110
87
128
46
48
47
46
O2
NCO
74
41
35
39
83
109
126
35
36
36
38
43
Reference
[11]
[11]
[11]
[11]
[11]
[11]
[11]
[11]
[35]
[35]
*
*
*
*
*Dr Aaron Rojas and Dr Luis A. Torres, Departamento de Quı́mica, CINVESTAV, IPN. Dr Ángeles Olvera and Dr Miguel Costas, Facultad de Quı́mica, UNAM, personal communication.
in Table 1). Nevertheless, it is also evident that for several of
the new complexes, the dispersion with respect to the fitting
line is wider. In particular, complexes 11, 12 and 13 show the
widest dispersion in Figure 1. Since the binding heat capacities
for these complexes seem to have been measured carefully (for
instance, at least nine different temperatures were sampled to
obtain CpP−CH in each instance) [27,30,31], the divergences
observed are presumably related to particular stereochemical
features at their binding interfaces. Complex 11 is made of glucose
and a CBM9 (family 9 carbohydrate binding module) from
Thermotoga maritima xylanase 10A [27]. Notably, the complex
of the same protein module binding cellobiose (complex 7) is
clearly better explained by the model. A comparison between
the two CBM9-complex crystal structures shows that glucose is
bound with an orientation that deviates significantly from that
of cellobiose [27], yielding quite different contact patterns. For
instance, although the disaccharide buries more polar areas at
the binding interface than the monosaccharide, the latter buries
a larger amount of the secondary hydroxy’s area. Complex 12
(fucose bound to a calcium-dependent tetrameric lectin from
Chromobacterium violaceum) shows the widest dispersion in
Figure 1. An inspection of the crystal structure reveals that
none of the fucose’s primary hydroxy groups makes contact with
the protein’s binding site, whereas the calcium ion is directly
mediating the binding [30]. These features are not observed in
any other complex in Table 2. Finally, complex 13 corresponds
to cellopentaose bound to the CBM4 from Cellulomonas fimi
β1-4-glucanase [31]. Surprisingly, the CpP−CH value of this
oligosaccharide complex is unusually small, falling in the range
observed for monosaccharide complexes. In contrast, the complex
made of an evolutionarily related CBM4 from T. maritima β1-3glucanase and laminaripentaose (complex 14) shows the largest
CpP−CH value in Table 2.
Overall, the above observations draw attention to the limited
utility of the model in eqn (1), which only considers the global
contributions of polar and apolar surface areas. An improved
model is needed, which can more finely capture the molecular
determinants of Cp in P–CH complexes. In the present study,
we aimed to develop a refined model that considers separately
the contributions from carbohydrate (CpCH ) and protein (CpP )
chemical groups:
CpP−CH = CpCH + CpP = (cpi · Ai )CH + (cpi · Ai )P
(2)
Where cpi and Ai are the specific heat capacity and surface
area changes of group type i respectively.
The validity of this term separation follows from the evidence
that, once corrected for protonation/deprotonation effects, heat
capacity effects in the formation of P–CH complexes are mostly
dictated by changes in the hydration extent of the interacting
groups [15]. Following the same approach as that used with
model compounds [33], the transfer of a sugar molecule from
an aqueous medium to a solid (pure) state may be used to mimic
the incorporation of free sugar into the highly ordered and packed
environment of a P–CH interface [34]. Accordingly, dissolution
data of carbohydrates may be taken advantage of to generate and
calibrate a model for the CpCH term in eqn (2). Once the CpCH
model has been parameterized, the carbohydrate contribution
to the formation of a given P–CH adduct can be estimated by
using the corresponding area changes of the ligand upon binding
to its protein counterpart. This contribution can then be subtracted
from the experimental CpP−CH to obtain the heat capacity change
associated with the protein’s binding site.
Surface-area-based model for the dissolution heat capacity
of carbohydrates
Table 3 shows a dataset of carbohydrates for which the dissolution Cp (Cpdiss ) has been determined calorimetrically.
Cpdiss values were obtained by subtracting the sugar’s
absolute heat capacity in the solid (anhydrous) state from
its absolute heat capacity in an aqueous solution (at infinite
dilution). The dataset is composed of 14 saccharides spanning
a wide range of chemical characteristics, including furanoses,
pyranoses, pentoses, hexoses, monosaccharide derivatives and
lineal oligosaccharides. The availability of these data was crucial
in the present study, as they allowed the inclusion of all the
c The Authors Journal compilation c 2009 Biochemical Society
242
E. A. Chavelas and E. Garcı́a-Hernández
Table 4 Heat capacity parameterization based on surface area changes for
the dissolution of carbohydrates
Values are in units of cal · K−1 · mol−1 · Å−2 .
cpC0
cpC1
cpC2,3
cpO0,1
cpO2
cpNCO
Value
Error
0.09
0.36
0.23
0.10
− 0.15
− 0.19
0.05
0.10
0.04
0.03
0.09
−
Figure 2 Schematic representation of a disaccharide molecule showing
the different sugar surface area types considered in the present study
Surface areas were classified according to the heteroatom type and the configurational location
in terms of the distance (number of covalent bonds) from the sugar ring. Atoms forming the
amide group were considered to form a single group (NCO). O0 and O1 surfaces were gathered
into a single group (O0,1), whereas C2 and C3 surfaces (excepting C2 for the NCO group) were
summed up to conform to another group (C2,3). See text for details.
carbohydrate chemical groups present in the P–CH complex
database (Table 2). Table 3 also shows surface area changes
for carbohydrate dissolution, assuming that in the solid state
the molecule is completely dehydrated, whereas in the aqueous
medium it is fully exposed to the solvent.
Since the heat capacity contribution of a given chemical surface
may depend significantly on the particular environment in which it
is immersed, the surface area-based CpCH model was partitioned
taking into account both the atom type (carbon, oxygen or
nitrogen) and the distance of the atom from the sugar’s ring (in
terms of the number of covalent bonds). The number of covalent
bonds separating a particular atom from the closest sugar ring
atom is indicated by numerical subscripts, where 0 corresponds
to atoms forming part of the ring skeleton. This classification
yields nine different surface area types, as shown schematically
in Figure 2. The areas of O0 and glycosidic O1 atoms are marginal
in relation to the total polar area exposed by a carbohydrate
molecule (∼ 5 % and ∼ 1 % respectively). So, to reduce the
number of independent variables, O0 and O1 were gathered into a
single group (O0,1). Furthermore, C2 and C3 atoms corresponding
to methyl groups were summed up to form another group (C2,3),
whereas atoms forming the amide group were also considered as
a single group (NCO). Thus the specific model for CpCH takes
the form:
CpCH = cpC0 · AC0 + cpC1 · AC1
+ cpC2,3 · AC2,3 + cpO0,1 · AO0,1
(3)
+ cpO2 · AO2 + cpNCO · ANCO
The complete set of parameters for eqn (3) was obtained through
three sequential steps. First, cpC0 , cpC1 , cpO0,1 and cpO2
were obtained from a multilinear regression fit of eqn (3) to data
in Table 3, but excluding data for mMan, mGlc and GlcNAc.
Secondly, cpC2,3 was then obtained from the analysis of mMan
and mGlc, as follows: using the respective surface area changes
in these methyl derivatives, the theoretical contribution of C0,
C1, O0,1 and O2 to the total Cpdiss was calculated. This quantity
was subtracted from the experimental Cpdiss value to calculate
the contribution of the methyl group (CpC2,3 ). cpC2,3 was then
obtained by dividing CpC2,3 by AC2,3 . Finally, cpNCO was
obtained in a similar way from the analysis of GlcNAc data.
Table 4 shows the fitting values obtained through this sequential
analysis. The associated errors given in this Table correspond to
standard errors of the regression analysis.
c The Authors Journal compilation c 2009 Biochemical Society
Figure 3 Calculated versus experimental Cp for the dissolution of
carbohydrates
Solid symbols were obtained using parameters obtained from the analysis of the 14 P–CH
complexes (the second row in Table 1). Open symbols correspond to calculated values obtained
with eqn (3) and parameters in Table 4. The solid line represents the best fitting of a straight line.
As can be seen in Figure 3, the early ad hoc Cp model for
P–CH complexes (Table 1) systematically overestimates Cpdiss
of saccharides (solid symbols), with a mean excess [=(Cpcalc –
Cpexp )/Cpexp ] of 53 +
− 23 %. This bias is not surprising, as
the parameters are weighted by the contributions of both protein
and carbohydrate chemical groups. In contrast, the CpCH model
(open symbols) satisfactorily accounts for the experimental
Cpdiss values (R2 = 0.98). As anticipated [36], results in Table 4
indicate that the thermodynamic behaviour of a given surface atom
type is influenced by the relative position of the atom in relation
to the saccharide ring. The contribution is larger for carbon atoms
located outside the ring (C1 and C2,3) than for those forming the
ring (C0). Oxygen surfaces located two covalent bonds away from
the ring (O2) show a negative value, whereas those closer to the
ring (O0,1) have a small positive value. The amide group has a
negative value, similar to that reported for liquid amides [18]
(Table 1).
Heat capacity changes of non-saccharide hydroxylated compounds
It has been typical to assume that the heat capacity effect for
the solvation of a given atom or chemical group surface is
constant, regardless of the covalent or non-covalent connectivity.
Nevertheless, the above results paint a different picture. To
explore this issue in an alternative way, an analysis of simpler
Heat capacity changes in carbohydrates and protein–carbohydrate complexes
Table 5
243
Cp and A for the dissolution of simple hydroxylated compounds
Compound
Cpdiss * (cal · K−1 · mol−1 · Å−2 )
A C † (Å2 )
A OH ‡ (Å2 )
Methanol
Ethanol
1-Propanol
1-Butanol
1-Pentanol
1-Hexanol
Cyclohexanol
1,3-Propanediol
1,4-Butanediol
1,5-Pentanediol
1,6-Hexanediol
1,2-Ethanediol
1,2,3-Propanetriol
Arabinitol
Ribitol
Xylitol
Mannitol
Sorbitol
27
47
64
79
96
112
92
40
53
69
84
27
29
43
43
36
53
45
81
134
167
193
219
247
210
139
164
191
226
108
111
126
120
119
132
126
43
43
39
38
41
41
38
76
75
80
81
83
114
167
170
176
201
203
*Values were obtained by subtracting the absolute Cp of the solid from the absolute Cp of a
dilute aqueous solution of the same compound. Absolute heat capacities for the solid state were
estimated using eqn (4). Data for aqueous solutions were taken from [37,38].
†Accessible surface area of carbons.
‡Accessible surface area of oxygen atoms in hydroxy groups.
hydroxylated compounds was carried out. Table 5 shows transfer
heat capacity data and accessible surface areas for seven nalcohols, four diols with no contiguous hydroxy groups [i.e. HO(CH2 )n -OH, where n > 2], and seven polyols with contiguous hydroxy groups (including 1,2-ethanediol and 1,2,3-propanetriol).
Analysis of these dissolution data can be used to estimate the
specific heat capacity contribution of hydroxy and carbon surfaces
(cpOH and cpC respectively) in non-cyclic compounds with
varying densities of hydroxy groups. For mono-hydroxylated
and di-hydroxylated compounds with no contiguous hydroxy
groups, cpOH = –0.34 and cpC = 0.49 cal · mol−1 · K−1 · Å−2
(where 1 Å = 0.1 nm). In contrast, the analysis of polyols yields a
positive value for cpOH (= 0.17 cal · mol−1 · K−1 · Å−2 ), and
a significantly decreased value for cpC (= 0.13 cal · mol−1 ·
K−1 · Å−2 ). These results indicate that the elementary heat
capacity contributions in hydroxylated compounds indeed depend
on the density of hydroxy groups. As described in the
Introduction section, this behaviour should be related to different
characteristics of the solvent’s organization. It is worth noting that
cp values for O2 and C1 surfaces in carbohydrates (Table 4) are
similar both in sign and magnitude to cpOH and cpC values
in n-alcohols and diols. In contrast, cp values for O0,1 and C0
surfaces in carbohydrates are closer to cpOH and cpC values.
These concordances suggest that the contribution of a given atom
in a sugar molecule depends on its spatial position inside the
molecule: the further an atom is from the sugar ring, the closer its
solvation behaviour will be to that of simpler compounds.
Absolute heat capacity of carbohydrate crystals
Benson and Buss [39] found that absolute heat capacities of amino
acid crystals can be described adequately in terms of atomic or
covalent bond composition. For instance, the authors obtained
the following atom-based model from the analysis of amino acid
crystals:
Cpsolid = 0.85NH + 3.75NC + 3.4NO + 3.4NN
(4)
Figure 4
Calculated versus experimental Cpsolid for different carbohydrates
Solid bars were obtained using eqn (4), whose parameters were obtained from the analysis
of a dataset of amino acid crystals [39]. Open bars correspond to experimental Cpsolid values.
Numbers in the X -axis stand for the list position of the corresponding carbohydrate in Table 3.
where Cpsolid is the crystal’s absolute heat capacity, and Ni stands
for the number of type i atoms present in the amino acid. Almost
40 years later, Gomez et al. [40] used the parameters of Benson
and Buss to reproduce the absolute heat capacity of crystals of
anhydrous globular proteins, finding excellent agreement between
calculated and experimental values. Therefore it was concluded
that Cpsolid (or primary heat capacity, using Gomez et al.’s
terminology) is basically determined by the protein’s atomic
composition, whereas stereochemical contribution (including
the particular network of intra and inter non-covalent bonds in the
crystal) is negligible. Extending this argument, it would be
expected that models such as that of eqn (4) would account for
the Cpsolid of other kinds of compounds, including saccharide
crystals. As shown in Figure 4, this is, in fact, the case (mean
error = 2 +
− 4 %). This agreement is consistent with the picture
that Cpdiss is not determined by the compound’s covalent
architecture itself, but by the way the organization of solvating
water molecules is affected by the compound’s stereochemistry.
Heat capacity model for carbohydrate-binding sites in proteins
Once having parameterized the CpCH model, the carbohydrate
contribution to the formation of each P–CH adduct was estimated
using the corresponding ligand’s area changes upon binding
to its protein counterpart (Table 6). This contribution was
then subtracted from the experimental CpP−CH to obtain the
heat capacity change associated with the protein’s binding site
desolvation:
CpP = CpP−CH − CpCH = (cpi ∗ Ai )P
(5)
CpCH and CpP as long as A values for the different
surface types are shown in Table 6. In general, the two
binding counterparts contribute unequally to the overall CpP−CH .
However, although CpCH can be either significantly larger or
smaller than CpP , the carbohydrate tends to bury more surface
area (on average 60 % of At ) than the protein.
Makhatadze and Privalov [41] developed a Cp model for
protein folding reactions, in which a fine dissection of protein
constituent groups was performed. It was used here to calculate
c The Authors Journal compilation c 2009 Biochemical Society
244
Table 6
E. A. Chavelas and E. Garcı́a-Hernández
A and Cp of carbohydrates and proteins upon complex formation
− A CH
Sugar
HevHevLisozLisozConA- ConA- CBM9- ConA- ConA- DGLCBM9- CVIIL- Cf CBM4- Tm CBM4- cp (Makhatadze
GlcNAc2 1 GlcNAc3 2 GlcNAc2 3 GlcNAc3 4 mMan5 Man3 6 Glc2 7 mGlc8 Man2 9 Man3 10 Glc11 mFuc12 Glc5 13
Glc6 14
and Privalov)*
O0,1
43
3
O2
NCO
47
58
C0
30
C1
85
C2,3
Total
266
− CpCH 32
Protein − A P
Cal
27
113
Car
Polar part of
Arg
Asn
Asp
Cys
Gln
Glu
24
His
Lys
Met
Ser
Thr
Trp
20
Tyr
22
-CONH3
Calcium
Total
209
32
− CpP
50
18
67
56
30
93
314
29
63
55
52
63
42
78
357
30
59
66
69
82
28
133
437
33
87
35
198
35
112
46
68
36
108
55
200
36
120
36
104
49
150
88
155
33
46
33
234
30
74
67
49
47
75
27
48
36
164
89
146
106
230
29
55
59
16
277
29
73
68
374
45
115
56
31
329
35
377
46
258
23
204
31
452
54
495
54
17
149
47
75
65
76
59
15
81
23
25
105
38
21
72
19
89
23
17
56
52
144
125
62
176
12
19
18
12
67
47
3
10
5
12
15
32
25
20
7
8
10
2
17
35
10
15
29
18
12
14
27
16
13
4
15
38
21
12
3
37
12
6
63
5
8
1
4
2
19
27
26
235
64
20
23
1
32
17
52
7
13
268
54
188
53
351
86
114
18
1
18
7
5
11
12
16
29
27
211
32
100
8
174
38
240
50
12
7
125
11
6
22
105
40
21
31
33
9
28
411
−4
402
118
0.53
0.29
− 0.05
− 0.23
− 0.32
− 0.93
− 0.05
− 0.12
− 0.31
− 0.38
− 0.93
− 0.31
− 0.30
0.90
0.02
− 0.39
− 0.39†
*Specific heat capacity coefficients (in units of cal · K−1 · mol−1 · Å−2 ) for protein chemical groups obtained by Privalov and Makhatadze [41] from the analysis of transference data of pertinent
model compounds.
†Hydration Cp for calcium was taken from Markus [42]. This value was corrected for volume effects by the method of Privalov and Makhatadze [41] and normalized by the total accessible
surface area to obtain the specific heat capacity coefficient.
CpP in the formation of P–CH complexes. The Makhatadze
and Privalov model includes terms for aliphatic and aromatic
carbons (Cal and Car respectively), the peptide group (-CONH-)
and the polar moiety of each of the side chains bearing a polar
chemical group. The parameters were obtained from the analysis
of heat capacity data for various organic model compounds used
to mimic the different protein constituent groups. This model
proved to estimate satisfactorily the absolute heat capacity of the
native and unfolded states of a number of globular proteins [20].
The set of parameters for the Makhatadze and Privalov model,
as long as the area changes for each of the proteins in Table 2,
are shown in Table 6. Figure 5(A) compares ‘experimental’ CpP
values, obtained through eqn (4), with the estimates obtained from
the Makhatadze and Privalov model [41]. The poor agreement
observed may suggest that protein-binding sites for carbohydrates
have also a distinct thermodynamic behaviour. Therefore an ad
hoc model for these binding sites was calibrated using CpP
values. To keep a moderate number of independent variables, polar
areas were separated only into neutral and charged polar areas
(Pneu and Pchg respectively), whereas apolar areas, following the
Makhatadze and Privalov scheme, were partitioned into aliphatic
and aromatic carbon areas.
CpP = cpCal ACal + cpCar ACar
+ cppneu Apneu + cppchg Apchg
c The Authors Journal compilation c 2009 Biochemical Society
(6)
As mentioned above, the Cf CBM4–Glc5 complex (complex 13
in Table 2) has an unusually small CpP−CH value (– 50 cal · K−1 ·
mol−1 ), comparable with those shown by monosaccharide
complexes. In contrast, the evolutionarily related TmCBM4–Glc6
complex (complex 14) shows a much more negative CpP−CH
value. In spite of this large difference, the two complexes bury
fairly similar amounts and kinds of areas at the binding interface
(Table 6). Even though detailed structural and thermodynamic
comparisons between these complexes have been performed,
the bases for this dissimilar behaviour are still unclear [31].
According to our CpCH model, ligands in complexes 13 and
14 contribute similar heat capacity changes, – 54 cal · K−1 · mol−1
(Table 6). Whereas for complex 14 this contribution represents
about one-third of the total CpP−CH , it exceeds the total change
in complex 13. Therefore a positive CpP value for Cf CBM4
is predicted. In view of this anomalous result, complex 13 was
excluded in parameterizing eqn (6).
Table 7 shows the parameterization obtained for eqn (6)
from a multilinear regression analysis of CpP and AP values
from Table 6. It is worth noting that both cpCal and cpCar values
for carbohydrate-recognition protein sites are similar to those
in other parameterizations (Table 1), with cpCal being larger
than cpCar , in agreement with that obtained by Makhatadze and
Privalov using model compounds [41]. Furthermore, the cppchg
value is comparable with the specific values for an aspartic acid
residue or lysine, although considerably more negative than those
for glutamic or arginine. In contrast, the large positive value
Heat capacity changes in carbohydrates and protein–carbohydrate complexes
245
the solution [43–45]. To test whether this factor is significant in the
formation of P–CH adducts, we performed a regression analysis,
in which a term for interface water molecules was included in eqn
(6): Cpw = cpw N w , where N w is the number of water molecules exchanged. By considering the crystallographic water
molecules located within 3 Å (1 Å = 0.1 nm) from both the protein
and the carbohydrate, the analysis yielded cpw = –5.8 +
− 11.0
cal · K−1 · mol−1 . This value is close to the difference between
the absolute heat capacities of liquid water and ice (approx.
–8 cal · K−1 · mol−1 at 25 ◦C). However, it has a large regression
standard error associated. Furthermore, the inclusion of Cpw
does not affect significantly the cppneu value (= 0.37 +
− 0.24
cal · K−1 · mol−1 ), whereas the quality of the fitting decreases
slightly (R = 0.93 with Cpw versus R = 0.95 without Cpw ).
Heat capacity model for protein–carbohydrate complexes
Using values in Tables 4 and 7 in eqn (2), the final parameterized
model for protein–carbohydrate complexes derived here is:
CpP−CH = 0.09AC0 + 0.36AC1 + 0.22AC2,3 + 0.10AO0,1
− 0.15AO2 − 0.14ANCO + 0.35ACal
+ 0.16ACar + 0.43Apneu − 0.27Apchg
Figure 5 Heat capacity changes for dehydration of the protein-binding site
(A) and for formation of P–CH complexes (B)
In both panels, solid circles correspond to experimental values. In (A), open triangles
represent values calculated with the Makhatadze and Privalov model (see Table 6), and solid
triangles are values calculated with the ad hoc parameters for carbohydrate-binding sites in
proteins (eqn 6 and Table 7). In (B), open squares correspond to values calculated with eqn
(1) using parameters for P–CH complexes (the second row in Table 1), and solid triangles are
values calculated with the extended P–CH’s Cp model obtained in the present study (eqn 7).
Table 7 Specific heat capacity coefficients for surfaces on binding sites of
carbohydrate-recognition proteins
cpCal
cpCar
cppneu
cppchg
Value
Error
0.35
0.16
0.43
− 0.27
0.19
0.09
0.16
0.36
for cppneu differs significantly from most of the specific values
for neutral polar areas in the Makhatadze and Privalov model,
although it is smaller than the coefficient for the polar part of
tryptophan. It is worth mentioning that we tried grouping neutral
polar areas in different ways (for instance, separating the aromatic
and/or amide surface from the rest of neutral polar surfaces),
always obtaining positive values for the corresponding fitting
coefficients.
Among polar areas forming part of carbohydrate-binding sites
of proteins, neutral areas predominate over charged areas. Thus
the positive sign of cppneu could help rationalize why the
Makhatadze and Privalov model tends to underestimate CpP .
Nevertheless, other factors not considered hitherto could also be
responsible for such a discrepancy. One of these factors could
be the incorporation of water molecules into the P–CH interface.
The transference of a bulk water molecule to a highly ordered
protein environment is expected to decrease the heat capacity of
(7)
As shown in Figure 5(B), this new model performs better
for reproducing experimental CpP−CH than the original model,
which considers only total polar and apolar areas. Furthermore,
the refined model is able to explain quantitatively cppol and
cpap values for the complete dataset of P–CH complexes in
Table 2. By summing up the contributions of O0,1, O2, NCO, Pneu
and Pchg surfaces, the total heat capacity contribution for polar
groups (Cppol ) can be obtained for each complex. The slope of
Cppol versus Apol yields directly cppol (= 0.16 +
− 0.04). The
same approach yields cpap = 0.22 +
0.03.
The
values
obtained
−
in this way are, within statistical uncertainty, the same as those
obtained for eqn (1) using P–CH complexes in Table 2.
A co-linearity analysis of eqn (7) yielded values for VIF
(variance inflation factor) smaller than 10 for all the independent
variables, with exception of AC0 and AO0,1 . Although this indicates a low co-linearity degree in the model, it is clear that Cpdiss
data for additional (preferentially deoxy and other derivatized)
carbohydrates are required in order to further strengthen the model
statistically. In the meantime, we think that the co-linearity for
AC0 and AO0,1 is tolerable due to the following reasons: (i) none
has a VIF value larger than 30; and (ii) the exclusion of any of the
saccharides in Table 2 does not yield significant variations in
the regression parameters, showing therefore an acceptable
stability in the estimations. Additionally, the model is able to
account satisfactorily for Cpdiss of: (i) 2-deoxy-glucose, which
exhibits a significant variation between AC0 and AO0,1 in
relation to the other saccharides considered here and (ii) other
sugars not included in Table 3, namely α, β and γ cyclodextrins,
which are cyclic β1-4 oligosaccharides composed of six, seven
and eight glucose residues respectively (results not shown).
DISCUSSION
Carbohydrates have stereochemical properties that impart unique
thermodynamic behaviour to these molecules. Not surprisingly,
P–CH complexes bearing unique thermodynamic properties have
also evolved. Formation G and H, normalized per unit of
interface surface area, are significantly larger for P–CH complexes
than for other types of protein systems [14]. Furthermore,
c The Authors Journal compilation c 2009 Biochemical Society
246
E. A. Chavelas and E. Garcı́a-Hernández
models obtained for protein folding or protein–protein binding
processes perform poorly in accounting for CpP−CH [15].
This situation makes it imperative to obtain ad hoc structural–
energetic models for P–CH adducts. In the present study, we
have derived a refined model for CpP−CH , taking advantage of
dissolution thermodynamic data of sugars. The use of transference
data of model compounds has been recurrent in trying to
elucidate the molecular determinants of the thermodynamic
behaviour of macromolecules. Nevertheless, there is a question
always lingering in these kinds of studies, regarding the
appropriateness of extrapolating thermodynamic data derived
from small compounds to macromolecular systems. As stated by
Hedwig and Hinz [46], ‘ . . . to ensure the best quantitative success
of a group additivity scheme, it is preferable to choose model
compounds that reflect as closely as possible the size, surface
area, charge and hydrophobicity of the target moieties for which
the thermodynamic properties are to be evaluated.’ Following this
premise, the authors used data of oligopeptide molecules to mimic
the properties of unfolded proteins, obtaining an additivity scheme
that performed better than those calibrated using simpler model
compounds. To a large extent, our CpP−CH model achieves this
reliability in stereochemical representation, as the transference
data used to parameterize it correspond directly to one of the
counterparts involved in the macromolecular complex studied.
According to the lines of reasoning exposed in the Introduction
section of the present paper, the high positive Cp values
observed for the hydration of saccharides indicate predominance
of hydrophobic solvation effects. Nevertheless, the CpCH model
obtained here yields an alternative picture. Contrary to what has
been observed for polar groups in most of the previous studies,
hydroxy groups attached directly to carbon atoms forming the
sugar ring increase the solution’s heat capacity. Since secondary
hydroxy groups are abundant in saccharide molecules, their
positive contribution to the heat capacity is significant. Based on
molecular simulations, Lemieux [16,36] proposed that hydroxy
groups in sugars direct water molecules towards them, generating
‘gaps’ or ‘void’ spaces over carbon atoms forming part of the
sugar ring, i.e. they should have a diminished heat capacity
contribution due to an inefficient hydration. Therefore it would
be expected that the solvation thermodynamics of carbon atoms
forming the sugar ring would be altered in relation to the properties
of ‘fully’ solvated carbon atoms. In agreement with this, the
heat capacity contribution of the ring’s carbon atoms (cpC0 )
is significantly smaller than that of those located outside the ring
(cpC2,3 ). Furthermore, cpC0 is smaller than the corresponding
contribution of carbon atoms in simple hydroxylated compounds
(cpC ) or smaller than the cpap value of any of the previous
parameterizations for eqn (1) [18–23]. A corollary of Lemieux’s
hypothesis is that the more distant a chemical group is from the
sugar ring, the more ‘typical’ should its solvation be. This is
what is seen in the CCH model. Both primary hydroxy and
acetamide groups show the characteristic decreasing heat capacity
effect of polar groups, whereas the contribution of outer carbon
surfaces falls within the range of values observed in simpler model
compounds.
Surfaces at the binding sites of carbohydrate-recognition sites in
proteins presented similar specific heat capacity contributions to
those observed in model compounds and protein folding events.
Nevertheless, polar-neutral surfaces are a notable exception, as
they showed a large positive solvation heat capacity. Interestingly,
Madan and Sharp [23] also obtained a positive value (0.17
cal · K−1 · mol−1 · Å−2 ) for polar groups in nucleic acids. The
reason for this thermodynamic behaviour is still unclear, although
it is presumably related to the hydration properties elicited by the
spatial proximity of polar groups in these molecules.
c The Authors Journal compilation c 2009 Biochemical Society
Concluding remarks
P–CH complexes have unique properties that put them in a
separate energetic–structural class among protein complexes.
Accordingly, ad hoc structural–energetic correlations for these
heterocomplexes are required. Previously, we obtained a Abased model for heat capacity formation of P–CH adducts with
preformed protein-binding sites. This model, containing a single
term for each of the polar and apolar area changes, indicated that
both kinds of surfaces diminish the heat capacity upon binding,
with the apolar contribution being relatively small in comparison with other parameterizations obtained from protein
folding and model compound studies. These results are in
qualitative agreement with previous studies demonstrating that the
hydration behaviour of carbohydrates is atypical. In the present
study, a more sophisticated CpP−CH model was developed, in
which the contributions of the two binding counterparts were
dissected. No previous parameterizations are able to account for
desolvation heat capacity effects of carbohydrates or proteinbinding sites. The model obtained for saccharides shows that,
indeed, these molecules exhibit unique and rather complex
solvation behaviours. The specific heat capacity of a given
saccharide surface depends not only on the atom and group
type, but also on its configurational location. The further away
the surface is from the sugar ring, the closer is its solvation
behaviour to simpler model compounds. Carbohydrate-binding
sites of proteins, in particular neutral polar groups, seem also to
show unique solvation properties. Explicit consideration of these
stereochemical properties allows accounting for the energetics of
a larger variety of P–CH complexes.
Although these results are encouraging, it is to be anticipated
that the inclusion of other factors not considered in the present
study might lead to an improvement of predicted P–CH heat
capacities. For binding processes where solvation/desolvation
effects are predominant, A models are able to explain the
observed Cp satisfactorily. Nevertheless, large differences
between experimental and calculated Cp values have been
observed for an increasing number of protein complexes
[7,43]. In many of these instances, the occurrence of coupled
equilibria such as exchange of counterions, structural water
molecules, protonation/deprotonation of ionizable groups and
large conformational dynamics changes has been established.
These factors, which imply additional contributions to the simple
change in solvent exposition of the interacting surfaces, have been
named by Ladbury and Williams [47] as the extended interface.
Clear evidence for non-local effects in P–CH complexes has
appeared in the literature in the last few years [48]. As more
quantitative information about these effects accumulates, it will
be possible to elaborate more accurate semi-empirical models for
these kinds of biomolecular adducts.
ACKNOWLEDGEMENT
We thank Dr Miguel Costas for his critical review and valuable comments on this paper
prior to submission.
FUNDING
This work was supported by the CONACyT (Consejo Nacional de Ciencia y Tecnologı́a)
[grant numbers 47097 and 41328] and DGAPA [PAPIIT; IN204609-3]. E. A. C. received
fellowships from the CONACyT and DGAPA.
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Received 9 December 2008/23 February 2009; accepted 3 March 2009
Published as BJ Immediate Publication 3 March 2009, doi:10.1042/BJ20082171
c The Authors Journal compilation c 2009 Biochemical Society