Solid-state stability studies of cholecystokinin (CCK-4) peptide under nonisothermal conditions using thermal analysis, chromatography and mass spectrometry

Article abstract of DOI:10.1016/j.ejps.2009.12.010

The solid-state stability of cholecystokinin (CCK-4) peptide under nonisothermal conditions was studied by differential scanning calorimetry (DSC), chromatography and mass spectrometry, identifying and schematizing the degradation products. To model the degradation mechanism of the peptide using the combined Kissinger and direct-differential methods, the observed degradation process was characterized by decomposition temperature (T_m), reacted fraction (α_m), activation energy (E_a), and pre-exponential factor (A). Results obtained by the two calculation methods were similar. The cleavage reaction on both N- and C-terminal sides of aspartic acid was the principal degradation pathway, although the reaction can occur consecutively and/or in parallel. Therefore to determine the relative importance of the different degradation pathways, a system of differential equations relevant to each degradation reaction was analysed using the R statistical program. The results obtained show that the consecutive reaction was the less plausible, whereas a slightly better fit was obtained for the reaction with both processes than for the in-parallel reaction. In this situation, the F-test was applied to discriminate between the models, indicating that the simpler model is the most probable. In conclusion, the results demonstrate for the first time that, in solid-state, n - 1 cleavage occurs in parallel to n + 1 cleavage at aspartic acid residues and not consecutively.

Full text of DOI:10.1016/j.ejps.2009.12.010

European Journal of Pharmaceutical Sciences 39 (2010) 263–271
Contents lists available at ScienceDirect
European Journal of Pharmaceutical Sciences
journal homepage: www.elsevier.com/locate/ejps
Solid-state stability studies of cholecystokinin (CCK-4) peptide under
nonisothermal conditions using thermal analysis, chromatography and mass
spectrometry
Alexis Olivaa,∗, David Sánchez Ashena, Mario Salmonab, José B. Farin˜aa, Matías Llabrésa
a Departamento Ingeniería Química y Tecnología Farmacéutica, Facultad de Farmacia, Universidad de La Laguna, 38200 La Laguna, Tenerife, Spain
b Istituto di Ricerche Farmacologiche “Mario Negri”, Via Giuseppe La Masa 19, 20156 Milano, Italy
a r t i c l e i n f o
a b s t r a c t
Article history:
The solid-state stability of cholecystokinin (CCK-4) peptide under nonisothermal conditions was stud-
ied by differential scanning calorimetry (DSC), chromatography and mass spectrometry, identifying and
schematizing the degradation products. To model the degradation mechanism of the peptide using the
combined Kissinger and direct-differential methods, the observed degradation process was characterized
by decomposition temperature (Tm), reacted fraction (˛m), activation energy (Ea), and pre-exponential
factor (A). Results obtained by the two calculation methods were similar.
Received 8 October 2009
Received in revised form
16 December 2009
Accepted 22 December 2009
Available online 5 January 2010
The cleavage reaction on both N- and C-terminal sides of aspartic acid was the principal degradation
pathway, although the reaction can occur consecutively and/or in parallel. Therefore to determine the
relative importance of the different degradation pathways, a system of differential equations relevant
to each degradation reaction was analysed using the R® statistical program. The results obtained show
that the consecutive reaction was the less plausible, whereas a slightly better fit was obtained for the
reaction with both processes than for the in-parallel reaction. In this situation, the F-test was applied to
discriminate between the models, indicating that the simpler model is the most probable. In conclusion,
the results demonstrate for the first time that, in solid-state, n − 1 cleavage occurs in parallel to n + 1
cleavage at aspartic acid residues and not consecutively.
Keywords:
Solid-state stability
DSC
Nonisothermal kinetic analysis
Peptide cleavage
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
pharmaceutical science, making the topic of solid-state kinetics
important. Solid-state reactions have many forms; however, those
Peptides and proteins may exhibit both chemical and physical
degradation also in the state solid (Lai and Topp, 1999), present-
ing challenges to the pharmaceutical industry during the process
of protein purification, formulation, storage and delivery. Under-
standing peptides and protein degradation pathways is essential
for the success of a biopharmaceutical drug. Chemical instability
of peptides and proteins can be investigated by different analytical
techniques: chromatography, electrophoresis, spectroscopy, ther-
mal analysis, light-scattering and mass spectrometry (Capelle et al.,
2007). It is important that these techniques be complemented with
methods to assess the biological activity (outside the focus of this
article).
that involve weight or enthalpy change are of great interest as their
kinetics can be studied by thermal analytical methods (Vyazovkin,
2004; Khawam and Flanagan, 2006a).
DSC has long been applied widely in the pharmaceutical indus-
try and offers a useful means of predicting the solid-state stability
of drugs. The DSC experiment can be used to compute the Arrhenius
pre-exponential factor, activation energy and order of the reaction
(Ford and Timmins, 1989; Beezer et al., 1999; Abd-Elrahman et al.,
2002; Pikal et al., 2008).
Kinetics in the solid-state show certain similarities to those in
homogeneous phases like solution or gases. In fact, many of the
basic mathematical principles are shared among all three phases.
However, solid-state reactions differ substantially from those in
the homogeneous state regarding the experimental procedures
used for their study and computation methods for analysing data
(Vyazovkin and Wight, 1999; Giron, 2002; Khawam and Flanagan,
2006b; Sánchez-Jiménez et al., 2008).
Many transformations may occur when a solid sample is
heated, such as melting, sublimation, polymorphic transformation,
or degradation. These solid-state reactions are quite common in
The many methods used to study solid-state kinetics may be
grouped into two categories: experimental and computational
∗
Corresponding author.
E-mail address: amoliva@ull.es (A. Oliva).
0928-0987/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.ejps.2009.12.010

264
A. Oliva et al. / European Journal of Pharmaceutical Sciences 39 (2010) 263–271
Table 1
(Khawam and Flanagan, 2006b). In the first case, there are two
approaches used to obtain solid-state kinetic data: isothermal and
nonisothermal methods. To analyse data from both of these, model-
fitting and model-free methods can be used. Khawam and Flanagan
(2006a) have proposed a complementary approach that uses both
the latter methods for kinetic data analysis, which allows one to
select models that might otherwise be indistinguishable, based on
quality of regression fit alone.
The most popular representative of the so-called “model-free”
methods is that of Kissinger, which allows the effective activation
energy to be determined from the dependence of the peak temper-
ature (Tm) on the heating rate (ˇ). This method provides a single
value of the activation energy related to the conversion fraction
(˛m) at the peak temperature, and does not require any modelistic
assumptions to calculate Ea. However, it is not an isoconversional
method because it does not generate Ea at progressive ˛ values but
rather assumes a constant Ea.
Algebraic expression for the f(˛) functions for the most common mechanisms in
solid-state reactions.
Model
Symbol
f(˛)
Zero-order
First-order
Second-order
Third-order
Power law
Avrami–Erofeev
Prout–Tompkins
1-D diffusion
2-D diffusion
F0
F1
F2
F3
P2
A2
B1
D1
D2
1
(1 − ˛)
(1 − ˛)2
(1 − ˛)3
2˛(1/2)
2(1 − ˛)[−ln(1 − ˛)]1/2
˛(1 − ˛)
1/2˛
[−ln(1 − ˛)]−1
2. Theory
Kinetic analysis of solid-state decomposition is usually based on
a single-step kinetic equation:
The Kissinger method can be only applied to the kinetic
analysis of rising temperature experiments obtained under any
heating schedule when two requirements are fulfilled: a first-
d˛
dt
= k(T)f (˛)
(1)
order kinetic model is involved and the reacted fraction (˛m
at the maxima remains unchanged (Sánchez-Jiménez et al.,
2008).
)
where t is time, T is absolute temperature, ˛ is the extent of conver-
sion, and f(˛) is the reaction model. Table 1 includes the function for
the most commonly used mechanisms in solid-state reactions. The
explicit temperature dependence of the rate constant is introduced
by replacing k(T) with the Arrhenius equation, which gives:
The choice of isothermal or nonisothermal experiments
depends on the requirements of the study, whether one wishes
to study reaction kinetics over wide temperature ranges (i.e.
up to melting) or if a narrow range is enough. The applica-
tion of such results to predicting solid-state stability of a drug
also affects the choice of the most appropriate reaction condi-
tions.
Calculation methods have also raised many controversies,
because there are so many and their range of application and valid-
ity is unclear. Results obtained from several of them are often
different, even when applied to the same data set. A critical evalu-
ation of these methods was initiated in the ICTAC “kinetic project”
(Burnham, 2000; Roduit, 2000).
While the solution reaction of small peptides has been reason-
ably well characterized (Mu-Lan and Stavchansky, 1998; Joshi and
Kirsch, 2002; Oliva et al., 2006a,b), their reactions in the solid-
state have attracted scant attention. With the increasing use of
small peptides as pharmaceuticals, it is important to understand
the solid-state behavior of this type of compounds. The tetrapep-
tide CCK-4, which constitutes the 30–33 segment of the hormone
cholecystokinin, is used in nuclear medicine for the diagnosis of
CCK-B receptor-expressing tumors (Gotthard et al., 2004). CCK-4
is a suitable candidate for solid-state studies because of its rela-
tively low cost, but in particular, given its size and structure it can
help gain better knowledge of the degradation mechanism of small
peptides in the solid-state.
In this study, DSC was used to study the solid-state stability of
CCK-4 peptide under nonisothermal conditions. For this, the CCK-4
degradation processes in solid-state, including separation, identi-
fication of degradation products, determination of rate constants
and degradation pathway were characterized. Kissinger and direct-
differential methods were used to analyse the data and estimate the
kinetic parameters.
d˛
dt
= Ae−E /RT f (˛)
(2)
a
where A (the pre-exponential factor) and Ea (the activation energy)
are the Arrhenius parameters and R is the gas constant.
Under nonisothermal conditions in which a sample is heated
at a constant rate, the explicit temporal dependence in Eq. (2) is
eliminated through the trivial transformation:
d˛
dT
A
ˇ
a
=
e−E /RT f (˛)
(3)
where ˇ = dT/dt is the heating rate, and Eq. (3) represents the differ-
ential form of the nonisothermal rate law. The direct-differential
method uses Eq. (3) to numerically calculate the differential
(d˛/dT ≈ ꢀ˛/ꢀT). Rearranging the variables and using logarithms
in Eq. (3) gives:
ꢀ
ꢁ
d˛/dT
f (˛)
A
ˇ
Ea
ln
= ln
−
(4)
RT
By plotting the left side of Eq. (4) (including the model f(˛)) against
1/T, the Ea can be obtained from the slope and A from the intercept.
The model that gives the best linear fit is usually chosen as the
model (Khawam and Flanagan, 2006a). The universality of Eq. (4) is
supported by Ozawa (2000) who previously found it can be applied
to data obtained via all modes of temperature change.
Kissinger proposed a kinetic analysis method for reaction-order
models (f(˛) = (1 − ˛)n based on the derivative of Eq. (3), generating
d2˛/dT2. Accordingly, the maximum reaction rate occurs when the
second derivative is zero, from which the following equation can
be obtained:
Eaˇ
RTm2
n−1
/RT
a
m
= A · (n(1 − ˛m
)
) · e−E
(5)
Various models were evaluated and compared to determine the
relative importance of the different degradation pathways. Since
these models contain more than one kinetic constant that depends
on temperature, the number of parameter correlations is larger.
To diminish this, the reparameterization of the Arrhenius equation
and the proper choice of a reference temperature are of benefit. To
estimate the latter, a new norm based on the asymptotic properties
of the correlation matrix of a multinormal random variable was
proposed.
where Tm is the temperature and ˛m is the conversion fraction at
the maximum reaction rate, which represents the peak (i.e. inflec-
tion point) of a DSC curve. Taking the natural logarithm of Eq. (5)
and rearranging gives:
ꢀ
ꢁ
n−1
ˇ
Tm2
AR(n(1 − ˛m
)
Ea
ln
= ln
−
(6)
Ea
RTm

A. Oliva et al. / European Journal of Pharmaceutical Sciences 39 (2010) 263–271
265
The activation energy (Ea) is obtained by plotting the left-hand side
of the equation versus 1/Tm for a series of runs at different heat-
ing rates. Eq. (6) has been generalized to any reaction model (f(˛))
(Elder, 1985).
(recovery mean < 101.2%), precise (repeatability < 1%), and reliable
(inter-assay precision < 4.0%). The LOD was calculated by statisti-
cal methods using a ratio of 3ꢁ/s (ꢁ: the standard deviation of
response; s: slope of the calibration curve). The LOQ was also cal-
culated with a ratio of 10ꢁ/s. In all cases, the limits were lower
than the smallest concentration in the linearity range. Acceptable
robustness was also observed, indicating that the analytical method
remains unaffected by small but deliberate variations in mobile
phase composition and flow rate, as described in the ICH Q2-R1
guidelines (2005).
3. Materials and methods
3.1. Materials
Cholecystokinin fragment 30–33 amide (CCK-4, Trp-Met-Asp-
Phe-NH2, WMDF-NH2) was purchased from Sigma Chemical
Company (St. Louis, MO, USA). Trp-Met (WM) and Trp-Met-Asp
(WMD) peptides were synthesized using Fmoc solid-phase chem-
istry with a 433A instrument (Applied Biosystems, Foster city, CA)
at the Istituto di Ricerche Farmacologiche “Mario Negri”, Milan,
Italy, under GMP conditions. Purity was checked by RP-HPLC and
MALDI-TOF mass spectrometry. Endoproteinase Glu-C and Modi-
fied Endoproteinase Asp-N were purchased from Sigma Chemical
Company (St. Louis, MO, USA). Trifluoroacetic acid (TFA: peptide
synthesis grade) and acetonitrile (HPLC grade) were obtained from
Merck (Darmstadt, Germany). Deionized water was purified in a
MilliQ plus system from Millipore (Molsheim, France), prior to use.
3.4. MALDI-TOF mass spectrometry
Mass spectra were measured on an Autoflex MALDI-TOF Mass
Spectrometer (Bruker Daltonics, Bremen, Germany), equipped with
a 337 nm nitrogen laser, delayed extraction, a reflectron and a
hydrophobic coating sample target (Anchor Chip 600/384, Bruker
Daltonics, Bremen, Germany). The spectra were obtained using
positive ion mode and the accelerating voltage was set to 20 kV.
The external calibration of the mass spectrometer was performed
with a commercial standard proteins mixture (Bruker Daltonics)
and the standard mass deviation was less than 10 ppm. The mass
spectra were accumulated for approximately 500 shots per prepa-
ration in total, 30 shots each. All reported masses are monoisotopic
[M+H]+ unless otherwise noted.
3.2. Differential scanning calorimetry (DSC)
DSC experiments were performed in a Mettler Toledo calorime-
ter, model DSC821e, with liquid nitrogen cooler and equipped with
the Star® evaluation program. Calibration of both temperature and
enthalpy was made with a standard sample of indium. CCK-4 sam-
ples (3–4 mg) were placed in non-hermetically crimped aluminium
pans (standard 40 ␮L type). The heating rates (ˇ) used for kinetic
analysis were 20, 15, 10, 7.5, 5, 2.5 and 1 ◦C/min under nitrogen
purge at 30 mL/min. Measurements were carried out on five sepa-
rate samples (replicates) and reported as averages.
The matrix used was 2,5-dihydroxybenzoic acid (DHB; Sigma)
in a saturated solution (0.16 mg/mL in acetonitrile and 0.1% TFA).
Samples were deposited on MALDI targets by spotting 0.5 ␮L of
matrix solution, dried and followed by 0.5 ␮L of sample.
3.5. Proteolytic digestion
3.5.1. Sample treatment
CCK-4 peptide (0.1 mg) was dissolved in 100 ␮L of DMSO, and
afterwards 900 ␮L of sodium phosphate (pH = 7.8) was added to
obtain a final concentration of 100 ␮g/mL.
The temperature at maximum rate (Tm) and the conversion
fraction (˛m) for each analysis were calculated using the Star®
software. The ˛m value at any temperature is calculated from:
AUCT0
m
˛
m
=
(7)
3.5.2. Endoproteinase Glu-C digestion
AUC∞0
One 25 ␮g vial of endoproteinase Glu-C sequencing grade was
reconstituted in 100 ␮L double-distilled water. The CCK-4 sample
was digested with endoproteinase Glu-C at an enzyme–substrate
ratio of 1:100 (w/w) at 25 ◦C for 2 h. Then, 20 ␮L of the digested
sample was mixed with 180 ␮L of mobile phase and analysed by
RP-HPLC, the injection volume being 50 ␮L.
where AUCT0 is the sample peak area from 0 to Tm, and AUC∞0 is
m
the total sample peak area.
3.3. RP-HPLC method
The chromatographic system used was a Waters apparatus
(Milford, MA, USA) consisting of a pump (600E Multisolvent Deliv-
ery System), an auto sampler (700 Wisp Model) and a UV–vis
detector (2487 programmable multi-wavelength model). Elution
was performed at room temperature in a Nova pack C-18 col-
umn (150 mm × 3.9 mm, 60 Å, 4 ␮m particle size, Waters). The data
collection and analysis were performed using the Millennium32®
chromatography program (Waters).
The mobile phase was an acetonitrile–water (30:70, v/v) mix-
ture with 0.05% TFA, the flow rate 1.0 mL/min, and the injection
volume 25 ␮L. The detection wavelength was set at 280 nm. All
solvents were filtered with 0.45 ␮m (pore size) filters (Millipore)
and degassed.
The analytical method for the three compounds, WMDF-NH2,
WMD, and WM, was validated by selectivity, linearity, limit of
detection (LOD), limit of quantitation (LOQ), accuracy, preci-
sion and robustness according to the International Conference
on Harmonization (ICH) guidelines (2005). The results obtained
indicate that the method is specific, linear over a range of con-
centrations of 2–12 ␮g/mL for the three compounds, accurate
3.5.3. Endoproteinase Asp-N
Modified Asp-N (Pseudomonas fragi, mutant) was supplied
lyophilized in a 2 ␮g vial, which was reconstituted with 20 ␮L
double-distilled water, yielding a final enzyme concentration of
0.1 ␮g/␮L. For peptide fragmentation, the enzyme was added to
the CCK-4 sample to be digested at a ratio of 1:100 (w/w) at 25 ◦C
for 3 h. The peptides obtained by Asp-N digestion were analysed by
RP-HPLC using the same conditions as above.
3.6. Identification of degradation products
A sample of CCK-4 was heated up to 210 ◦C, temperature
of the maximum rate at 5 K/min, then the sample was quickly
cooled to 30 ◦C, and analysed by RP-HPLC. The degradation prod-
uct peaks were collected by making repeated 200 ␮L injections of
the degraded sample. Collected fractions were pooled and con-
centrated in a Speed-Vac® before analysis by MALDI-TOF mass
spectrometry.

266
A. Oliva et al. / European Journal of Pharmaceutical Sciences 39 (2010) 263–271
Fig. 2. Degradation scheme proposed for cleavage reaction at aspartic acid residue
for the CCK-4 peptide in solid-state. The full model involved the parallel and con-
secutive pathways of n + 1 and n − 1 cleavage reaction.
products and the proposed degradation routes are shown in
Fig. 2.
Fig. 1. Chromatograms of CCK-4 sample. (A) Standard sample. (B) Sample hydrol-
ysed using the endoproteinase Glu-C and Asp-N (C), respectively. (D) Sample
degraded at 210 ◦C, two degradation products detected, identified as WMD (II) and
WM (III).
4.2. DSC data
Fig. 3 shows the DSC curve for heating rates of 1, 5 and 10 K/min,
which reveals two endothermic peaks in the 190–240 ◦C. Also
clearly visible was the shifting of endothermic peaks to a higher
temperature by increasing the heating rate. To identify these two
characteristic phenomena, the melting point of CCK-4 was deter-
mined using a Buchi instrument (Model B-540, Delaware, USA),
obtaining a value of 222.5 0.5 ◦C (n = 3) for a heating rate of
5 K/min. Hence, the second DSC endotherm could correspond to
the melting point. The first DSC endotherm required more detailed
study, so the effects of heating CCK-4 to the different tempera-
tures were compared. A sample of CCK-4 was heated in the DSC
up to 175 ◦C at 5 K/min, before the first DSC endotherm, removed,
and then cooled to 30 ◦C and analysed by RP-HPLC, detecting the
3.7. Direct-differential method
Various samples of CCK-4 (2.4–2.6 mg) were analysed by DSC
at a heating rate of 5 K/min from 175 to 220 ◦C at intervals of 5 ◦C.
The rest of the conditions were as described earlier. Each sample
was diluted with the mobile phase to obtain concentration values
within the calibration range, and analysed by RP-HPLC the same
day in duplicate.
In this case, the conversion fraction “˛” for the WMDF-NH2
product was calculated from the following expression:
m0 − mT
˛ =
(8)
m0 − m
∞
where m0 is the initial sample weight, mT is the sample weight at
temperature T, and m is the final sample weight. However, the
∞
determination of m is problematic since the residues are totally
∞
carbonized above 220 ◦C. For this reason, m was taken as zero.
∞
For the WMD and WM derivatives, the conversion fraction “˛” is
obtained directly as the sample weight at temperature T.
4. Results and discussion
4.1. Degradation product identities
Degradation products were separated by RP-HPLC and identi-
fied by proteolytic digestion and MALDI-TOF mass spectrometry.
Chromatographic separation of a degraded CCK-4 sample shows
three peaks (I–III, Fig. 1). Peak I was found to have a mass of
596.25, which corresponds to the parent peptide (WMDF-NH2),
while II was found to have a mass of 450.51 (WMD). The differ-
ence in mass between peaks I and II was 145.47, which corresponds
to the loss of phenylalanine-amide (Phe-NH2). In addition, the
difference in mass between peaks II and III was 115.37, which
corresponds to the loss of an aspartic acid residue (WM). This
result suggests that the degradation pathway of this peptide in
solid-state involves the cleavage reaction on the n − 1 and n + 1
sides of aspartic acid. To verify this, CCK-4 samples were hydrol-
ysed using two endoproteinases, Glu-C and Asp-N, and analysed
by RP-HPLC. The results confirm that peaks II and III correspond
to the WMD and WM fragments, respectively. The degradation
Fig. 3. DSC curves for the CCK-4 peptide at different heating rates (ˇ = 1, 5 and
10 K/min), where the corresponding decomposition temperature, Tm, increases with
the heating rate.

A. Oliva et al. / European Journal of Pharmaceutical Sciences 39 (2010) 263–271
267
Table 2
4.3. Estimation of the activation energy (Ea), pre-exponential
factor (A), and the reaction model
The peak temperature (Tm) and conversion fraction at peak temperature (˛m) at
different heating rates obtained in the decomposition of CCK-4 by DSC.
Heating rate (◦C/min)
Peak temperature
(Tm
◦C)
%Conversion at peak
temperature (˛m)
It is clear that in the case of a first-order reaction (F1 model),
the Kissinger plot is a straight line whose slope gives the activa-
tion energy, independently of both the heating schedule used to
reach the maximum reaction rate and the value of the reacted frac-
tion ˛m at this point, whereas the pre-exponential factor can be
determined from the intercept. If the reaction does not follow a
first-order kinetic model, the slope of the plot of ln(ˇ/Tm2 ) versus
1/Tm would only lead to the activation energy if ˛m is independent
of the heating schedule used. Various authors (Criado and Ortega,
1986; Budrugeac and Segal, 2007) have shown the dependence
between the ˛m values of the different kinetic models (Table 1)
resulting from linear heating experiments and the actual value of
Ea/RT. However, the error in the determination of the activation
energy from the Kissinger plot has been clearly demonstrated to
be lower than 5%, for values of Ea/RT higher than 10.
At first, ˛m can be considered constant and independent of
the linear heating rate used, and assuming first-order kinet-
ics, the Ea obtained from Kissinger plot was 300 kJ/mol, the
uncertainty being given as 95% confidence intervals calculated
from the residual standard deviation by the standard expression
(Draper and Smith, 1981) of 295 and 306 kJ/mol, respectively.
These confidence intervals are narrow due to the large num-
ber of experimental points used. The estimated pre-exponential
factor was 3.03 × 1032 min−1, the 95% confidence intervals being
6.92 × 1031 min−1 and 1.32 × 1033 min−1, respectively. These inter-
vals are relatively small despite coupling of the uncertainty of the
prediction, due to fit of the rate constants (ˇ) at each temperature
(Tm) and their dependence on the kinetic model used.
The combined analysis of experimental data by means of the
logarithmic expression of the general differential equation (Eq. (4))
is thus shown to be a suitable method for determining the kinetic
model and its parameters. Therefore, any set of T − ˛ or (d˛/dt)
data should fit the equation, regardless of the experimental pro-
cedure used (Pérez-Maqueda et al., 2002). In order to check this,
the differential method described in Section 3 was used for the
kinetic analysis of data obtained from the thermal decomposition
of CCK-4 at a heating rate of 5 K/min and to determine the model
that best fits the data. The ˛ (or d˛/dt) − T data were analysed by
the differential method after applying the f(˛) function proposed
in the literature for describing solid-state reactions, as shown in
,
1.0
2.5
5.0
7.5
10
199.3 0.26
204.7 0.36
209.0 0.16
211.6 0.18
212.9 0.36
216.1 0.24
218.0 0.42
75.5 0.26
75.6 0.87
74.4 0.98
74.7 1.11
73.8 0.62
74.1 0.96
74.2 1.13
15
20
peak corresponding to pure CCK-4. Another sample of CCK-4 was
heated to 210 ◦C, temperature of the maximum rate at 5 K/min,
and was similarly analysed. In this case, the degradation products,
WMD and WM, were detected. Therefore, the first DSC endotherm
is attributed to the solid-state decomposition of CCK-4 according
to the diagram shown in Fig. 2. The second endotherm, attributed
to the melting of CCK-4, could actually correspond to the melting
of both products.
This fact was also observed in other samples of CCK-4 analysed
at different heating rates (1, 2.5 and 10 K/min), both degrada-
tion products were also detected, indicating that the degradation
mechanism can be the same, independently of the heating
rate.
The corresponding decomposition temperature, Tm, and the
conversion fractions (˛m) obtained for different heating rates are
shown in Table 2. Low relative standard deviation values of the Tm
and ˛m properties support their excellent reproducibility. The Tm
was highly dependent on the scan rate, indicating that the ther-
mal decomposition process was, at least in part, under kinetic
control and reflects a unique thermal decomposition reaction of
the drug. In contrast, the results clearly show that ˛m is con-
stant and independent of the heating rate as is well established
in literature (Criado and Ortega, 1986; Sánchez-Jiménez et al.,
2008). The mean ˛m value obtained using the Star® software was
0.746. 0.70 (n = 35) whereas that calculated using Eq. (8), with
different samples analysed at 1, 2.5 and 5 K/min, was 0.725 0.013
(n = 7). These results confirm the validity of both procedures to
determine ˛m
.
Table 3
Arrhenius parameters and 95% confidence intervals for nonisothermal decomposition of WMDF-NH2 and its derivatives, WMD and WM, determined using the direct-
differential method.
Product
Model
Ea (kJ/mol)
ln A (min−1
)
r
WMDF-NH2
D1
F1
F2
F3
B1
P2
306 [237 to 376]
270 [220 to 321]
276 [170 to 383]
349 [193 to 505]
62.4 [5.58 to 119]
58.6 [0.88 to 116]
74.7 [56.9 to 92.5]
66.9 [54.0 to 79.9]
69.3 [41.8 to 96.8]
88.4 [48.2 to 129]
15.7 [1.12 to 30.2]
12.6 [−2.17 to 27.4]
0.9751
0.9869
0.9180
0.8943
0.7390
0.7121
WMD
WM
D1
F1
F2
F3
B1
P2
218 [98.4 to 337]
230 [142 to 317]
159 [49.9 to 268]
200 [83.6 to 315]
−22.0 [−109 to 64.7]
−7.41 [−86.6 to 101]
51.1 [20.7 to 81.5]
55.6 [33.4 to 77.8]
37.9 [10.1 to 65.6]
48.5 [19.0 to 78.1]
−6.61 [−28.7 to 15.5]
−1.10 [−25.0 to 22.9]
0.8525
0.9495
0.7935
0.8385
0.2215
0.0702
D1
F1
F2
F3
B1
P2
377 [241 to 513]
245 [213 to 276]
271 [236 to 306]
297 [256 to 338]
−33.3 [−56.4 to 123]
109 [93.1 to 125]
90.0 [55.5 to 125]
61.0 [53.0 to 69.1]
67.9 [59.0 to 76.7]
74.7 [64.2 to 85.1]
−9.20 [−31.9 to 13.5]
27.2 [23.1 to 31.3]
0.9405
0.9917
0.9917
0.9905
0.3480
0.9892

268
A. Oliva et al. / European Journal of Pharmaceutical Sciences 39 (2010) 263–271
Table 1. Table 3 includes the resulting activation energies, the pre-
exponential factors, and the correlation coefficient for the kinetic
models included in Table 1. The results demonstrate that when an
F1 kinetic model is assumed, all the experimental data fit by a single
straight line whose slope and intercept lead to an activation energy
of 270 kJ/mol and a pre-exponential factor 1.17 × 1029 min−1 with
a correlation coefficient r = 0.9869. On the other hand, for a F2
kinetic model, the apparent values of Ea and A obtained are very
similar to those obtained for the F1 model, although the correla-
tion coefficient found was lower (r = 0.9180). The results obtained
indicate that the calculated kinetic parameters were comparable to
the values estimated by the Kissinger method, but the 95% confi-
dence intervals were higher: 220–321 kJ/mol for activation energy
and 2.78 × 1023 to 4.87 × 1034 min−1 for the pre-exponential factor.
This discrepancy could be due to differences in the data analysis
method and the lower number of degrees of freedom.
4.4. Kinetics and degradation mechanism of WMD and WM
degradation products
Fig. 4 shows the reacted fraction, ˛, for each degradation prod-
uct as a function of time. The shape of the curve is sigmoidal, as
is common for solid-state decompositions; it is characterized by
an induction period followed by a growth period, and finally, a
decay period. In this case, the formation processes of WMD and
WM have similar profiles, although the induction period for WM
was slightly higher, whereas the growth period takes place at a rela-
tively faster rate for the WMD product. This result is consistent with
the observations made by Inglis (1983), since the n − 1 cleavage is
slower than n + 1 because the former proceeds via a six-member
ring intermediate rather than a five-member ring. However, the
decay period was not observed for the WMD product, since the
samples are totally carbonized from 220 ◦C, making it impossible
to detect any products.
The ˛ (or d˛/dt) − T data were analysed by means of the differen-
tial method as described earlier for CCK-4. For both products, the F1
kinetic model was found to provide the best fit to the kinetic profile.
The estimated activation energies were 230 kJ/mol for WMD and
245 kJ/mol for WM, respectively. The selection of the kinetic model
and calculation of the constant rates do not require knowledge of
the degradation mechanism, because even complex degradation
pathways involving multiple consecutive or parallel reactions can
be represented by combinations of zero, first- and second-order
reactions. For example, Inglis (1983) points out that n + 1 cleavage
would always precede n − 1 cleavages; i.e. the two cleavage mech-
anisms occur consecutively and not in parallel. However, Joshi and
Kirsch (2002) have reported for the first time that the n − 1 cleav-
age can occur consecutively and in parallel to n + 1 at Asp-residues
using the polypeptide hormone glucagon as model, in acidic aque-
ous solution. At first, the experimental data suggest that CCK-4
degradation does not undergo a consecutive reaction, perhaps a
parallel reaction; although the presence of both pathways cannot
be ruled out. To investigate this, the different degradation pathways
can be expressed by a system of ordinary differential equations.
If the reaction is composed of two parallel steps according to the
diagram in Fig. 2, then:
ꢂ
ꢂ
ꢂ
ꢃꢃ
Ea
dX1
dt
1
1
12
= −(k12 + k13)X1 = − kTref12 exp B12
+
−
Tref T(t)
R
ꢀ
ꢁꢁ
ꢂ
ꢃ
Ea
1
Tref
1
T(t)
Fig. 4. Variation of the reacted fraction (˛) for the products WMDF-NH2 (open
circle), WMD (triangle), and WM (black circle), respectively, vs temperature, con-
sidering a linear heating rate of 5 K/min, for the different models given in Fig. 2:
consecutive reaction (A), parallel (B) and both pathways (C). Data were fitted using
the R® statistical program through the odesolve ( ) package.
13
+ kTref13 exp B13
+
−
X1
(9)
R
ꢂ
ꢂ
ꢃꢃ
Ea
dX2
dt
1
1
12
= k12X1 = kTref12 exp B12
+
−
X1
(10)
R
Tref
T(t)

A. Oliva et al. / European Journal of Pharmaceutical Sciences 39 (2010) 263–271
269
ꢀ
ꢁ
ꢂ
ꢃ
the norm proposed was performed, obtaining an optimum refer-
ence temperature of 479.6 K. With this reference temperature and
assuming a parallel reaction, the parameter correlation, expressed
as log(det(V)), was equal to −0.572, while for Tref = 470.2 K, the
parameter correlation was equal to −4.18. For the rest of mod-
els, the parameter correlations were always lower than the ones
obtained with the average temperature of the experimental range.
Although it is not possible to eliminate all the parameter cor-
relations, the proper choice of the reference temperature can
significantly reduce the final one. Similar results were obtained
using the empirical norm proposed by Schwaab et al. (2008).
Fig. 4 shows the fitted curves for the different degradation path-
ways shown in Fig. 2. The estimated parameters and respective 95%
confidence intervals obtained are presented in Table 4. The results
indicate that CCK-4 degradation does not follow a consecutive reac-
tion since the activation energy obtained for step 23 is negative and,
therefore, this value lacks physical sense. However, when the data
fit a parallel reaction or both consecutive and parallel process do
not differ, the residual sum of squares (RSS) is slightly higher for the
parallel reaction (3.714 × 10−3 vs 3.429 × 10−3), but the increased
number of parameter does not produce a significant improvement
in fit. In this situation, the F-test can be used to choose between
models that are hierarchical (i.e. one is the full model, and all the
rest can be expressed as restricted cases of that full model), but
for which there is no a priori reason to prefer one over another
(Mannervik, 1981). When two models j and k with pj and pk (pj < pk)
parameters, respectively, are fitted to the same data set and yield
residual sums of squares RSSj and RSSk (RSSj > RSSk), the signifi-
cance of the improvement in RSS by using the model (k) containing
more parameters can be found by comparison of the quotient:
Ea
dX3
dt
1
Tref
1
T(t)
13
= k13X1 = kTref13 exp B13
+
−
X1
(11)
R
where Xi is the amount of each product expressed as reacted frac-
tion and ki are rate constants with an Arrhenius-type dependence
on the temperature. To reduce the strong dependence between the
parameters A and Ea, the Arrhenius equation can be reformulated
by introducing a reference temperature in the form:
ꢄ
ꢂ
ꢃꢅ
Ea
R
1
Tref
1
T
k = exp B +
−
(12)
where the parameters of the reparameterized equations can be
related to the parameters of the traditional Arrhenius equation as:
B = ln(kT
)
(13)
ref
where kT is the specific reaction rate at the reference temperature
ref
Tref. For the rest of the schemes, the same procedure was used.
To resolve the differential equation, and estimate the kinetic
parameter, the odesolve package from R® statistical program
(version 2.9.0, 2009) was used, which allows a direct nonlinear
estimation of the activation energy and the rate constants through
nlme ( ) function. This generic function fits a nonlinear mixed-
effects model in the formulation described in Lindstrom and Bates
(1990). The initial estimated values for Ea and the rate constants
obtained by the direct-differential method were used as starting
values in order to converge much faster to a solution.
Introduction of the reference temperature into the Arrhenius
equation leads to reduction of the parameter correlation, con-
sequently, less computational effort required for estimating the
model parameters (Espie and Macchietto, 1988). The reference
temperature is usually defined as the average of the analysed
experimental data. For instance, Veglio et al. (2001) suggested that
the reference temperature should be calculated as the reciprocal of
the average value of the reciprocal of all the experimental temper-
atures. However, little attention has been given in the literature
to establishing the optimum value of the reference temperature.
Schwaab and Pinto (2007) showed that it is possible to determine
an optimum reference temperature in order to eliminate parameter
correlation and minimize the relative errors of model parameters
with a single kinetic constant. The problem is more complicated
when there is more than one Arrhenius equation in the model, since
it then becomes necessary to define some criterion for optimization
of reference temperature. Schwaab et al. (2008) used an empirical
norm to resolve this problem. We propose to use the following cri-
terion: the logarithm of the determinant of the correlation matrix
of parameter estimates (log(det(V)) must be minimum. This norm
is based on the asymptotic properties of correlation matrix of a
multinormal random variable (Morrison, 1976).
ꢀ
ꢁ ꢀ
ꢁ
RSSj − RSSk
n − pk
pk − pj
F =
x
(14)
RSSk
with the F-statistic F(pk − pj, n − pk) at the appropriate significance
level (˛ = 0.05).
The F-test results suggest that the model with both processes
offers no significant improvement over the model with the parallel
reaction, since the calculated value (F = 0.997) is lower than the
tabled value (F = 3.40).
Also, the confidence intervals of the estimated parameters kT
ref
and Ea for step 23 corresponding to the full model include the
value 0, which indicates that these parameters are not significant
(p > 0.05) and that the consecutive reaction can be effectively dis-
regarded. All these results indicate that the simpler model should
be adopted. In this case, activation energies of 289 and 361 kJ/mol
were obtained for the WMD and WM products, higher values than
those obtained by the direct-differential method, but the confi-
dence intervals of the estimated parameters are narrower. Thus,
this approach gives a reliable estimate of all parameters, and this
Starting from the reference temperature of 470.2 K, calcu-
lated in accordance with Veglio et al. (2001), the application of
Table 4
Estimated parameter and 95% confidence intervals using an optimized reference temperature of 479.6 K for the different degradation pathways proposed for the CCK-4
peptide shown in Fig. 2.
Parameter
Step 12
Step 13
Step 23
Both processes
kT (min−1
)
0.246 [0.180–0.312]
291 [265–318]
0.108 [0.075–0.142]
354 [309–400]
0.0016 [−5.10 to 5.09]a
312 [−572 to 1196]a
ref
Ea (kJ/mol)
Consecutive reaction
kT (min−1
Ea (kJ/mol)
)
0.352 [0.345–0.359]
303 [279–327]
0.234 [0.221 to 0.249]
−81.6[−28.7 to−134]
ref
Parallel reaction
kT (min−1
Ea (kJ/mol)
)
0.244 [0.237–0.251]
289 [262–316]
0.110 [0.100–0.120]
361 [299–424]
ref
a
Probability > 0.05.

270
A. Oliva et al. / European Journal of Pharmaceutical Sciences 39 (2010) 263–271
fact is reflected in the goodness of fit between experimental data
and the kinetic model adopted.
n
R
T
t
m
k
Tm
Tref
Xi
RSS
reaction order
gas constant (J/mol K)
absolute temperature (K)
time (min)
To evaluate the effect of heating rate on degradation mechanism
of CCK-4 peptide, a second experiment was conducted under a lin-
ear heating rate of 2.5 K/min. The results obtained seem to confirm
that the in-parallel reaction is the most probable, and therefore, the
degradation pathway is independent of the heating rate.
sample weight
rate constant (min−1
)
temperature at maximum rate (K)
optimum reference temperature (K)
amount of each product expressed as reacted fraction
residual sum of squares
5. Conclusions
The DSC analysis of CCK-4 peptide showed two endothermic
peaks, attributed to the decomposition and the melting, respec-
tively. Degradation products, WMD and WM, were identified by
proteolytic digestion and MALDI-TOF mass spectrometry. This
result suggests that the degradation pathway involves the cleavage
reaction on the n − 1 and n + 1 sides of aspartic acid.
Greek letters
˛
˛
ˇ
reacted fraction
reacted fraction at maximum temperature
linear heating rate (K/min)
m
The nonisothermal kinetic analysis was carried out using the
Kissinger method, which requires two conditions: a first-order
kinetic model and that the reacted fraction at the maxima remains
unchanged. At first, both requirements are fulfilled, obtaining acti-
vation energy of 300 kJ/mol. However, this method provides little
data on reaction complexity.
Acknowledgments
The authors would like to thank Laura Colombo (Istituto di Ris-
erche Farmacologiche “Mario Negri”, Milan, Italy) for providing
the WMD and WM peptides for this study. This research has been
financed by the Fondo de Investigación de la Seguridad Social, Spain
as part of project PI 061804.
The direct-differential method can offer an alternative approach
for determining kinetic parameters and the reaction model since
it can be used to analyse experimental data obtained under the
same or different conditions. For this, the kinetics of CCK-4 degra-
dation were also studied from a data set generated under linear
heating at a constant rate of 5 K/min. The activation energy and
pre-exponential factor determined by the differential method were
found to be in good agreement with the results of Kissinger’s
method. In any case, the activation energy for the solid-state reac-
tion is much greater than that in solution (102 kJ/mol) (Oliva et al.,
2006a), reflecting the greater energy required for rearrangement
within the confines of a crystal lattice.
The cleavage reaction at the Asp-residue occurs on both N- and
C-terminal sides, but the mechanism can occur through consecu-
tive or parallel reactions, or both. To investigate this, a system of
differential equations appropriate for each scheme was analysed
using the R® statistical program. In this case, the reparameteriza-
tion of the Arrhenius equation and the proper choice of a reference
temperature are crucial to improve the precision of the estimated
parameters. A slightly better fit was obtained for a scheme involv-
ing both processes, since the RRS was lower; however, the F-test
results suggest that this scheme offers no significant improvement
over the parallel reactions. In view of the results, pharmaceutical
researchers are challenged to gain a better understanding of the
models, statistical and mathematical tools and software that can
be applied in studying solid-state reaction kinetics.
References
Abd-Elrahman, M.I., Ahmed, M.O., Ahmed, S.M., Aboul-Fadl, T., El-Shorbagi, A., 2002.
Kinetics of solid state stability of glycine derivatives as a model for peptides
using differential scanning calorimetry. Biophys. Chem. 97, 113–120.
Anonymous, 2005. International Conference on Harmonization (ICH) of Technical
Requirements for the Registration of Pharmaceuticals for Human Use, Validation
of Analytical Procedures: Text and Methodology (ICH-Q2-R1), November 2005.
Beezer, A.E., Gaiford, S., Hills, A.K., Wilson, R.J., Mitchell, J.C., 1999. Pharmaceutical
microcalorimetry: application to long-term stability studies. Int. J. Pharm. 179,
159–165.
Budrugeac, P., Segal, E., 2007. Applicability of the Kissinger equation in thermal
analysis revisited. J. Therm. Anal. Calorim. 88, 703–707.
Burnham, K., 2000. Computational aspects of kinetic analysis. Part D: the ICTAC
kinetics project-multi-thermal-history model-fitting methods and their rela-
tion to isoconversional methods. Thermochim. Acta 355, 165–170.
Capelle, M.A.H., Gurny, R., Arvinte, T., 2007. High throughput screening of pro-
tein formulation stability: practical considerations. Eur. J. Pharm. Biopharm. 65,
131–148.
Criado, J.M., Ortega, A., 1986. Analysis of the shape index of DTG or DTA curves under
hyperbolic or logarithmic schedule. Thermochim. Acta 103, 317–323.
Draper, N., Smith, H., 1981. Applied Regression Analysis, second edition. Wiley, New
York.
Elder, J.P., 1985. The general applicability of the Kissinger equation in thermal anal-
ysis. J. Therm. Anal. 30, 657–669.
Espie, D.M., Macchietto, S., 1988. Nonlinear transformations for parameter estima-
tion. Ind. Eng. Chem. Res. 27, 2175–2179.
Ford, J.L., Timmins, P., 1989. Pharmaceutical Thermal Analysis, Techniques and
Application. Ellis Horwood, Chichester.
Giron, D.J., 2002. Applications of thermal analysis and coupled techniques in phar-
maceutical industry. J. Therm. Anal. Calorim. 68, 335–357.
In summary, these results indicate that the nonisothermal
methodology used in this study may be used to extrapolate pep-
tide and protein stability in the solid-state, saving time, samples
and experimental effort. Also, proteins in the dry state, even if
formulated with disaccharides, are thermodynamically unstable at
normal storage temperatures (Pikal et al., 2008), so they would be
a representative example to evaluate the practical potential of the
methodology applied in this study. This is a future research topic
in our laboratory.
Gotthard, M., Boermann, O.C., Behr, T.M., Behe, M.P., Oyen, W.J., 2004. Development
and clinical application of peptide-based radiopharmaceuticals. Curr. Pharm.
Des. 10, 2951–2963.
Inglis, A.S., 1983. Cleavage at aspartic acid. Methods Enzymol. 91, 324–332.
Joshi, A.B., Kirsch, L.E., 2002. The relative rates of glutamine and asparagines deami-
dation in glucagons fragment 22–29 under acidic conditions. J. Pharm. Sci. 91,
2332–2345.
Khawam, A., Flanagan, D.R., 2006a. Basics and applications of solid-state kinetics: a
pharmaceutical perspective. J. Pharm. Sci. 95, 472–498.
Khawam, A., Flanagan, D.R., 2006b. Solid-state kinetic models: basics and mathe-
matical fundamentals. J. Phys. Chem. B 110, 17315–17328.
Lai, M.C., Topp, E.M., 1999. Solid-state chemical stability of proteins and peptides. J.
Pharm. Sci. 88, 489–500.
6. Nomenclature
Lindstrom, M.J., Bates, D.M., 1990. Nonlinear mixed effects models for repeated
measures data. Biometrics 46, 673–687.
Mannervik, B., 1981. Design and analysis of kinetic experiments for discrimination
between rival models. In: Endrenyi, L. (Ed.), Kinetic Data Analysis: Design and
Analysis of Enzyme and Pharmacokinetic Experiments. Plenum Press, New York,
pp. 235–270.
Morrison, D.F., 1976. In: Arthur, A., Gardner, M. (Eds.), Multivariate Statistical Meth-
ods, second edition. McGraw Hill, New York.
A
Ea
f(˛)
pre-exponential factor (min−1
activation energy (kJ/mol)
reaction model
)

A. Oliva et al. / European Journal of Pharmaceutical Sciences 39 (2010) 263–271
271
Mu-Lan, L., Stavchansky, S., 1998. Isothermal and nonisothermal decomposition of
thymopentin and its analogs in aqueous solution. Pharm. Res. 15, 1702–1707.
Oliva, A., Llabrés, M., Farin˜a, J.B., 2006a. Data analysis of kinetic modelling used in
drug stability studies: isothermal versus nonisothermal assays. Pharm. Res. 23,
2595–2602.
Oliva, A., Hidalgo, M., Alvarez, C., Llabrés, M., Farin˜a, J.B., 2006b. Evaluation of chole-
cystokinin (CCK-8) peptide thermal stability for use as radiopharmaceutical by
means isothermal and nonisothermal approaches. Drug Dev. Ind. Pharm. 32,
947–953.
Sánchez-Jiménez, P.E., Criado, J.M., Pérez-Maqueda, L.A., 2008. Kissinger kinetic
analysis of data obtained under different heating schedules. J. Therm. Anal.
Calorim. 94, 427–432.
Schwaab, M., Pinto, J.C., 2007. Optimum reference temperature for reparameteriza-
tion of the Arrhenius equation. Part 1: problems involving one kinetic constant.
Chem. Eng. Sci. 62, 2750–2764.
Schwaab, M., Lemos, L.P., Pinto, J.C., 2008. Optimum reference temperature for repa-
rameterization of the Arrhenius equation. Part 2: problems involving multiple
reparameterizations. Chem. Eng. Sci. 63, 2895–2906.
Ozawa, T., 2000. Kinetic analysis by repeated temperature scanning. Part 1. Theory
and methods. Thermochim. Acta 356, 173–180.
Statistics Department of the University of Auckland, 2009. Statistical Data Analysis
R, version 2.9.0. Auckland, USA., www.r-project.org.
Pérez-Maqueda, L.A., Criado, J.M., Otor, F.J., Málek, J., 2002. Advantages of combined
kinetic analysis of experimental data obtained under any heating profile. J. Phys.
Chem. A 106, 2862–2868.
Veglio, F., Trifoni, M., Pagnanelli, F., Toro, L., 2001. Shrinking core model with variable
activation energy: a kinetic model of manganiferous ore leaching with sulphuric
acid and lactose. Hydrometallurgy 60, 167–179.
Pikal, M.J., Rigsbee, D., Roy, M.L., 2008. Solid state stability of proteins III: calorimet-
ric (DSC) and spectroscopic (FTIR) characterization of thermal denaturation in
freeze dried human growth hormone (hGH). J. Pharm. Sci. 97, 5122–5131.
Roduit, B., 2000. Computational aspects of kinetic analysis. Part E: the ICTAC kinetics
project-numerical techniques and kinetics of solid state processes. Thermochim.
Acta 355, 171–180.
Vyazovkin, S., 2004. Thermal analysis. Anal. Chem. 7, 3299–3312.
Vyazovkin, S., Wight, C.A., 1999. Model-free and model-fitting approaches to kinetic
analysis of isothermal and nonisothermal data. Thermochim. Acta 340, 53–
68.