3.2. Isothermal titration calorimetry (ITC)
ITC is an emerging and powerful technique that is widely used
to measure the thermodynamic properties of any chemical reaction
initiated by the addition of a binding component. Heat is
either generated or absorbed when substances bind. Modern titration
nano-calorimeters are able to accurately measure very small
amounts of heat change (<0.2 lJ) in aqueous solution upon the
delivery of a ligand. In a single experiment, the binding constant
(K), reaction stoichiometry (n) and enthalpy (DH0) can be accurately
determined via appropriate models. Generally, most fitting
models are based on the combination of single set of identical sites
(SSIS) model. Let us introduce the SSIS model as follows (Freire
et al., 1990; Kim, Yamasaki, & Kataoka, 2006). The binding constant
K and the relationship of the total and free ligand concentrations
([L]t and [L]) can be represented by Eqs. (1) and (2), respectively,
K ผ
u
๐1 _ uฝL_
๐1
ฝL_t ผ ฝL_ nฝMLn_ ผ ฝL_ nuฝM_t ๐2
where n is the number of binding sites, [M]t is the total concentration
of macromolecular, and u is the fractional sites occupied by ligand.
Combining Eqs. (1) and (2) gives Eq. (3),
u2 _ u 1
ฝL_t
nฝM_t
1
nKฝM_t
_ _
ฝL_t
nฝM_t
ผ 0: ๐3
Solving the quadratic Eq. (3) for u gives Eq. (4),
uผ
1
2
1
ฝL_t
nฝM_t
1
nKฝM_t
_
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
๐1ฝL_t=nฝM_t 1=nKฝM_t2 _4ฝL_t=nฝM_t
_ q _
:
๐4
Fig. 2. UV–Vis spectra for gallic acid (GA), methyl gallate (MEGA), protocatechuic
acid (PCA) in the absence and presence of iron(III)–citrate. Conditions: [GA or MEGA
or PCA] = 375 mM, [Fe(III)] = 125 lM, in Hepes buffer (30 mM, 100 mM citrate, pH
7.40).
304 S. Yang et al. / Food Chemistry 157 (2014) 302–309
In an ITC experiment, the heat evolved from each reaction after
a single injection will be proportional to the changes in [MLn] and
the binding enthalpy. So, the observed heat, DQ, for the ith injection
will be:
DQ ผ nDHV0DฝMLn_ ผ nDHV0ฝM_t๐ui _ ui_1; ๐5
where DH is the molar heat of ligand binding and V0 is the cell
volume.
Since V0 is constant, a small volume of the reaction solution corresponding
to the injection volume is displaced with each injection,
leading to dilution of the molecular species in the cell. It is
necessary to correct for this effect. If the injection volume for the
ith injection is called Vi, then the change d[X] in the concentration
of a molecular species, X, in the calorimeter cell upon an infinitesimal
change dVi in Vi will be:
dฝX_ ผ _
dVi
V0
ฝX_ ๐6
and integration of this differential equation with [X] between the
limits [X]i_1 and [X]i and Vi within 0 to Vi gives:
ฝX_i ผ ฝX_i_1 exp _
Vi
V0
_ _
๐7
The exponential factor in Eq. (7) is thus the dilution factor for a
single injection:
fi ผ exp _
Vi
V0
_ _
๐8
and the total dilution factor after i injections is:
ft;i ผ exp _
1
V0
Xi
jผ1
Vj
!
๐9
when ligand L is the injectant and the concentration of L in the
injection syringe is called [L]s, and then it is easily shown that the
total concentration of L in the calorimeter cell after the ith injection
is given by:
ฝL_t;i ผ ฝL_s๐1 _ ft;i ๐10
and the total concentration of macromolecular [M]t in the calorimeter
cell after the ith injection is:
ฝM_t;i ผ ft;iฝM_0; ๐11
where [M]0 is the initial concentration of M in the calorimeter cell
before titration.So, Eq. (5) can now be rewritten as:
DQ ผ nDHV0ฝM_t๐ui _ fiui_1 qm ๐12
Eq. (12) is the regression function for the least squares fitting of
the binding isotherms of the ITC experiments where the concentrations
and occupied fractions are calculated from Eqs. (11), (12), and
(4). The last term in Eq. (12), qm, is the heat of mixing or dilution,
which can be determined in separate blank titrations of ligand into
buffer. So, with the different values of DQ measured directly via ITC
after each injection, we can fit the heat plot to obtain the thermodynamic
parameters, n, DH and K. Because K is related to the Gibbs
free energy of binding (DG0) by the equation of DG0 = _RTln K, the
entropy (DS0) of the reaction can be easily calculated from the relationship
DG0 = DH0 TDS0.
ITC experiments were performed using a Nano-ITC II Instruments
with the normal cell (190 ll) at 25 _C. Three hundred microlitre
of MEGA solution (2.67 mM in 30 mM Hepes, 100 mM citrate,
pH 7.40) was poured inside the cell after three rinses with the
above solution. The solution of Fe(III) (10 mM in 30 mM Hepes,
100 mM citrate, pH 7.40) in syringe was titrated into the sample
cell with 32 sequential 1.5 ll injections at 360 s intervals. Fig. 3A
shows the raw ITC data for a titration of MEGA with Fe(III) in Hepes
buffer, pH 7.40. The integrated heats for each injection are shown
after subtraction of the control injection in buffer alone. The positive
peaks seen in Fig. 3A correspond to an exothermic reaction for
Fe(III) binding to MEGA. The heats for each injection begin to decrease
with an increase in the molar ratio of the Fe(III) to the
MEGA, and there is little heats change in the end, indicating that
the reaction is complete. The ITC data fitted well to an independent
binding model (Fig. 3B), giving an apparent equilibrium constant
Kapp = 9.97 _ 103 M_1 with the reaction MEGA/Fe(III) stoichiometry
of 0.31 ฑ 0.03 (Table 1), indicating that one Fe(III) ion can coordinate
up to three MEGA molecules in the presence of excessive citrate,
producing an Fe(III)–MEGA3 complex with an octahedral
geometry. Other experimental thermodynamic parameters are also
compiled in Table 1.
Under the similar experimental conditions, GA solution was titrated
against Fe(III) at pH 7.40. The results show that the chelation
between iron(III) and GA is also a exothermic reaction (Fig. 4A).
The experimental thermodynamic parameters, which were obtained
from the curve fitting of the integrated heats in Fig. 4B to
an independent binding model, are listed in Table 1. The stoichiometry
of 0.33 ฑ 0.05 (Table 1) was obtained by the curve-fitting.
Thus, one Fe(III) molecule can also bind with three GA molecules.
However, the apparent equilibrium constant of GA (Kapp = 6.98
_ 103 M_1) is significantly lower than that of MEGA (Kapp = 9.97
_ 103 M_1). Subsequently, a titration of PCA with Fe(III) resulted
in similar ligand/Fe(III) stoichiometry to that of GA (Fig. 5 and
Table 1), but markedly reduced apparent equilibrium constant
compared to GA (Kapp = 3.96 _ 103 M_1 for PCA versus Kapp =
6.98 _ 103 M_1 for GA).
The stoichiometry (n = 0.33) of MEGA/GA/PCA reacting with
Fe(III) is in good agreement with previous studies measured by
spectroscopy methods showing that three phenolic acids are
bound to one free ferric ion (Hider, Liu, & Khodr, 2001; Perron &
Brumaghim, 2009). And the ultraviolet spectrum shows that, even
in the presence of citrate, there is still a new absorption in the
range 450–700 nm with a maximum at 540–590 nm, which is
the characteristic absorption of polyphenol-–iron complexes. Coupled
with the consideration of the UV characteristic absorption and
the stoichiometry, the present results demonstrate that these three
species of phenolic acids can replace the citrate to form complexes
with Fe(III). So the displacement model can be used to calculate the
condition-independent binding constant.
The parameters that we gained directly from the ITC are apparent
thermodynamic parameters. However, the apparent thermodynamic
parameters are much dependent on the experiment
conditions, e.g., pH, or citrate concentration. These conditiondependent
values are only comparable to other values determined
under identical conditions. Hence, it will be meaningful to calculate
the condition-independent values from the apparent thermodynamic
parameters. In our conditions, the Fe(III) (represented
by M3+) can form 1:2 complexes with citrate (represented by
C3_), and the phenolic acids (represented by H2P, where P2_ represents
the ionized phenolic acids) mainly exist in three states
(P2_,HP_ and H2P) at the experimental pH. The stoichiometry we
gained from ITC means the Fe(III) can form 1:3 complexes (MP3_
3 )
with phenolic acids. Consideration of the low affinity, the interaction
between the Fe(III) and Hepes is negligible. The overall equilibrium
is given by Eq. (13),
๐1 _ aMC3_
2
M3 aMC3_
2
MC3_
2 3๐1 _ aHP_ _ aH2PP2_ 3aHP_HP_
3aH2PH2P $
MP3_
3 ๐3aHP_ 6aH2PHC2_ ๐2aMC3_
2
_ 3aHP_ _ 6aH2PC3_
๐13
S. Yang et al. / Food Chemistry 157 (2014) 302–309 305
where aMC3_
2
represents the mole percentage of MC3_
2 in all kinds of
M3+ species; similarly, aHP_ and aH2P represent the mole percentage
of HP_, H2P in the total of P species. The overall equilibrium includes
two main competing equilibria that could be found with iron complexation
in our experiment conditions. One is citrate competition
with the phenolic acids for the iron, and another is proton competition
with the iron for the phenolic acids. The fitting algorithm
for displacement model is derived from the following equations:
CM3 ผ ฝM3_ ฝMC3_
2 _ ฝMP3_
3_ ๐14
CP ผ ฝP2__ ฝHP__ ฝH2P_ 3ฝMP3_
3_ ๐15
KMC3_
2
ผ
MC3_
2
h i
ฝM3_ฝC3__
2 ๐16
KHP_ ผ
ฝHP__
ฝH_ฝP2__
ผ K_1
a1 ๐17
K2;H2P ผ
ฝH2P_
ฝHP__ฝH_
ผ K_1
a2 ๐18
where KMC3_
2
represents the stability constant of MC3_
2 ; Ka1 and Ka2
represent the first and second acid ionization constant of phenolic
acids.
In order to write conveniently, b2;H2P is introduced:
b2;H2P ผ KHP_K2;H2P ผ
ฝH2P_
ฝP2__ฝH_
2 ผ K_1
a1 K_1
a2 ๐19
The apparent equilibrium constant Kapp is calculated by Eq.
(20):
Kapp ผ
MP3_
3
h i
ฝM3_ITC ฝP2__
3
ITC
; ๐20
where [M3+]ITC and [P2_]ITC represent the concentration of t
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