Kinetics and mechanism for the reaction of cysteine with hydrogen peroxide in amorphous polyvinylpyrrolidone lyophiles

Article abstract of DOI:10.1007/s11095-006-9052-z

Purpose. Peroxide impurities play a critical role in drug oxidation. In metal-free aqueous solutions, hydrogen peroxide (H₂O₂) induced thiol oxidation involves a bimolecular nucleophilic reaction to form a reactive sulfenic acid intermediate (RSOH), which reacts with a second thiol to form a disulfide (RSSR). This study examines the reaction of cysteine (CSH) and H₂O₂ in amorphous polyvinylpyrrolidone (PVP) lyophiles to explore the possible relevance of the solution mechanism to reactivity in an amorphous glass. Materials and Methods. Amorphous PVP lyophiles containing CSH and H₂O₂ at varying initial 'pH' and reactant concentrations were prepared by methods designed to minimize reaction during lyophilization. Kinetic studies were conducted anaerobically at 25°C and reactants and products were monitored by HPLC. Products were characterized and the kinetic data were fit to models adapted from the solution mechanism. Results. Key differences in the reactions in aqueous solution and amorphous PVP are: (1) while only cystine (CSSC) forms in solution, three degradants-cysteine sulfinic acid (CSO₂H), cysteine sulfonic acid (CSO₃H) and cystine (CSSC)-form in amorphous PVP; (2) simple bimolecular kinetics govern the solution reaction while initial rates in amorphous PVP suggested more complex kinetics (i.e., non-unity values for reaction order); and (3) heterogeneous (i.e., biphasic) reaction dynamics are evident in amorphous PVP. The differences in product formation and apparent reaction orders in the solid-state could be rationalized by partitioning of the same reactive intermediate to multiple products in the solid-state due to the restricted mobility of CSH. Beyond the initial rate region, the kinetics in amorphous PVP could be described by the Kohlrausch-Williams-Watts (KWW) stretched-exponential equation or by assuming two populations of reactant molecules having different reactivities. Conclusions. When reactive intermediates are involved, differences in degradant profiles and other characteristics (e.g., rate constants, apparent reaction order) in the amorphous-state may simply reflect altered rates for individual reaction steps due to glass-induced changes in relative reactant mobilities rather than a change in overall mechanism.

Full text of DOI:10.1007/s11095-006-9052-z

#
Pharmaceutical Research, Vol. 23, No. 10, October 2006 ( 2006)
DOI: 10.1007/s11095-006-9052-z
Research Paper
Kinetics and Mechanism for the Reaction of Cysteine with Hydrogen Peroxide
in Amorphous Polyvinylpyrrolidone Lyophiles
Dayong Luo1 and Bradley D. Anderson1,2
Received January 29, 2006; accepted May 5, 2006; published online September 2, 2006
Purpose. Peroxide impurities play a critical role in drug oxidation. In metal-free aqueous solutions,
hydrogen peroxide (H2O2) induced thiol oxidation involves a bimolecular nucleophilic reaction to form
a reactive sulfenic acid intermediate (RSOH), which reacts with a second thiol to form a disulfide
(RSSR). This study examines the reaction of cysteine (CSH) and H2O2 in amorphous polyvinylpyrro-
lidone (PVP) lyophiles to explore the possible relevance of the solution mechanism to reactivity in an
amorphous glass.
Materials and Methods. Amorphous PVP lyophiles containing CSH and H2O2 at varying initial FpH_
and reactant concentrations were prepared by methods designed to minimize reaction during
lyophilization. Kinetic studies were conducted anaerobically at 25-C and reactants and products were
monitored by HPLC. Products were characterized and the kinetic data were fit to models adapted from
the solution mechanism.
Results. Key differences in the reactions in aqueous solution and amorphous PVP are: (1) while only
cystine (CSSC) forms in solution, three degradantsVcysteine sulfinic acid (CSO2H), cysteine sulfonic
acid (CSO3H) and cystine (CSSC)Vform in amorphous PVP; (2) simple bimolecular kinetics govern the
solution reaction while initial rates in amorphous PVP suggested more complex kinetics (i.e., non-unity
values for reaction order); and (3) heterogeneous (i.e., biphasic) reaction dynamics are evident in
amorphous PVP. The differences in product formation and apparent reaction orders in the solid-state
could be rationalized by partitioning of the same reactive intermediate to multiple products in the solid-
state due to the restricted mobility of CSH. Beyond the initial rate region, the kinetics in amorphous
PVP could be described by the Kohlrausch<Williams<Watts (KWW) stretched-exponential equation or
by assuming two populations of reactant molecules having different reactivities.
Conclusions. When reactive intermediates are involved, differences in degradant profiles and other
characteristics (e.g., rate constants, apparent reaction order) in the amorphous-state may simply reflect
altered rates for individual reaction steps due to glass-induced changes in relative reactant mobilities
rather than a change in overall mechanism.
KEY WORDS: amorphous solids; chemical kinetics; cysteine; drug stability; hydrogen peroxide;
lyophilization; nucleophilic substitution; poly(vinylpyrrolidone); solid-state kinetics; thiol oxidation.
INTRODUCTION
produce each formulation being considered and test its
stability. In contrast, a comprehensive mathematical and
Despite the fact that most commercial drug products are conceptual framework does exist for the analysis of kinetic
solid dosage formsVparticularly tablets, capsules, and lyoph- data for drug degradation in solution formulations, from
ilized productsVfew formal methodologies are currently which it is possible to determine reaction order, characterize
accepted or widely employed to treat drug degradation reactive intermediates, determine rate constants for various
kinetics in solid formulations. Moreover, one method which reaction steps and their pH and temperature dependence,
is routinely utilized, the application of the Arrhenius and identify the contributions of various ionizable species to
equation to extrapolate accelerated stability data to lower the overall reaction rate (4,5).
temperatures, may have uncertain reliability for reactions
Amorphous solid pharmaceutical formulations are be-
occurring in solids, particularly near a phase transition (1Y3). coming increasingly important due to a rising interest in
Beyond the Arrhenius model, predictive models for relating amorphous oral formulations with improved bioavailability
solid-state stability to various formulation and storage profiles (6,7) and an increase in the number of peptide,
conditions are seldom applied, making it necessary to protein, and other biomolecule drug products being formu-
lated in freeze-dried form for reconstitution prior to their use
(8Y10). The contributions of Zografi and his coworkers
(11Y17) in particular, have drawn the attention of the
pharmaceutical community to the physical characteristics
and significance of the amorphous state and the influence
1 Department of Pharmaceutical Sciences, University of Kentucky,
ASTeCC Bldg., Room A323A, Lexington, Kentucky 40506, USA.
2 To whom correspondence should be addressed. (e-mail: bande2@
email.uky.edu)
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2239
0724-8741/06/1000-2239/0
2006 Springer Science+Business Media, Inc.

2240
Luo and Anderson
of residual water on molecular mobility and the solid-state cysteic acid, and polyvinylpyrrolidone K90 (PVP, Mr õ360,000)
degradation of drugs. Nevertheless, better tools are urgently were purchased from Sigma Chemical Co. (St. Louis, MO).
needed to predict drug stability in amorphous dosage forms. Sodium phosphate dodecahydrate (Na3PO4 12H2O) was pur-
I
Bearing in mind Angell’s characterization of amorphous chased from Aldrich Chemical Company, Inc. (Milwaukee,
glasses as liquids that have lost their ability to flow (18), one WI). Sodium dihydrogen phosphate monohydrate (NaH2
might reasonably expect that certain attributes of the solution PO4 H2O), dibasic sodium phosphate heptahydrate (Na2
I
kinetics of a given drug molecule may carry over to reactions HPO4 7H2O), and H2O2 (30% aqueous solution) were ob-
I
of the same compound occurring in amorphous matrices. tained from Mallinckrodt Baker Inc. (Phillipsburg, NJ). All
Unfortunately, reaction kinetics in amorphous solids are much reagents were analytical grade and used as supplied. Deion-
more complex for a number of reasons. Most importantly, ized ultra-filtered (DIUF\) water used to prepare CSH and
while diffusion-controlled decomposition reactions seldom H2O2 solutions and HPLC grade acetonitrile were purchased
need to be considered in pharmaceutically relevant solution from Fisher Scientific Co. (Pittsburgh, PA). Water used to
formulations, molecular mobility plays a critical role in prepare mobile phases was deionized and further purified
amorphous solid-state reaction kinetics (14,16). Although through a Milli-Q\ UV Plus Ultra-pure Water System,
amorphous glasses are highly viscous, molecular motion is Millipore Ltd. (Billerica, MA).
not completely suppressed. As a result, amorphous systems
continue to undergo relaxation toward their equilibrium state
over time, with corresponding changes in properties (e.g.,
density) that may affect chemical reactivity. Spatial heteroge-
neity in these dynamic relaxation processes (19,20) and their
separate phosphate buffered (50 mM, pH 4.0 or pH 6.0) stock
time dependence (21,22) as well as possible heterogeneity in
the distribution of drug molecules, water, and other formula-
H2O2 (10, 20, 40, and 50 mM) with the same buffer to produce
tion components even in amorphous glass excipients such as
PVP (2,23,24) may also be important.
Lyophile Preparation and Storage
Lyophiles for kinetic studies were prepared by mixing
solutions of PVP (100 mg/ml), CSH (10, 20, and 40 mM) and
final solutions containing 10 mg/ml PVP, 1Y8 mM CSH, and
1Y8 mM H2O2 in 50 mM phosphate buffer. Stock solutions of
While such factors undoubtedly complicate reaction
CSH and H2O2 were prepared immediately prior to their use.
kinetics and may result in changes in both rate-determining
steps and preferred reaction pathways for a given compound,
some knowledge acquired in solution studies may be transfer-
able to amorphous systems. In this study, we explored the
phosphate buffer necessary to achieve a final volume of 0.5 ml.
reaction of cysteine (CSH) and H2O2 as a function of their
concentrations in amorphous polyvinylpyrrolidone (PVP)
added, mixed rapidly on a vortex mixer for 5 s, then quick-
lyophiles prepared at a fixed FpH_ in order to ascertain the
extent to which an understanding of the reaction mechanism
in aqueous solution might provide guidance in rationalizing
held in the liquid N2 bath for another 5 min after they were
the reaction kinetics and product formed in an amorphous
glass. Previously we and others have demonstrated (25Y28)
that, in the absence of metal ions, thiol oxidation by hydrogen
peroxide (H2O2) in aqueous solutions involves a two-step
bimolecular nucleophilic substitution mechanism, in which
before breaking the vacuum and placed in the controlled
the rate-determining formation of a reactive sulfenic acid in-
termediate (RSOH) is followed by reaction with a second
For DSC and powder X-ray diffraction analyses, larger
thiolate to form a disulfide (RSSR), the only product ob-
served in aqueous solutions except at extremely high ratios of
mg/ml PVP in 50 mM phosphate buffer (pH 4.0 or 6.0) either
H2O2:RSH.
Then 50 or 100 ml aliquots of the H2O2 stock solution were
transferred to 2 ml glass vials already containing 50 ml of the
PVP stock solution and a pre-calculated amount of 50 mM
Finally, 50 or 100 ml aliquots of the CSH stock solution were
frozen by immersion of the vial in liquid nitrogen to minimize
the extent of reaction prior to lyophilization. The vials were
frozen then transferred to a tray freeze dryer (FTS Systems,
Inc., Stone Ridge, NY) pre-cooled to a shelf temperature of
j45-C. The shelf temperature was maintained at j45-C
throughout the drying cycle time of 24 h. Vials were capped
temperature chamber to begin the kinetic studies.
lyophile batches were prepared from solutions containing 20
with or without 5 mM CSH and 5 mM H2O2.
The amorphous solid-state reaction produces multiple
degradation products and exhibits a decidedly more complex
rate law governing the reaction (which was shown to be first
Lyophile Characterization
order with respect to each reactant in solution). In this paper
we characterize these differences and explore the hypothesis
Water Content
that such dramatic differences between the solid-state and
solution reactions can be rationalized by invoking the same
The amount of lyophile in each sample was obtained by
subtracting the empty vial weight from the total weight of
reaction mechanism (i.e., involving the formation of the same
sample plus vial. Samples (n = 3) from each batch of lyophile
produced were dissolved by adding 1 ml DMSO and the
sulfenic acid intermediate) once molecular mobility consid-
erations are taken into account.
exact amount of DMSO/lyophile was obtained by weight.
Residual moisture was measured by Karl Fischer titration
MATERIALS AND METHODS
Reagents
with a Metrohm 684 KF coulometer (Brinkmann Instru-
ments, Inc., Westbury, NY) and Hydranal reagents (Sigma-
Aldrich Company, St. Louis, MO). Each titration consisted
of injecting õ100 ml of either blank DMSO or a DMSO/
Cysteine (>98% purity by TLC), cystine (SigmaUltra, lyophile solution into the titrator with constant stirring by
>99% purity by TLC), cysteine sulfinic acid (monohydrate), using a 1 ml disposable plastic syringe (Becton, Dickinson

Cysteine and Hydrogen Peroxide in Amorphous PVP
2241
and Company, Franklin Lakes, NJ). The exact amount High-Performance Liquid Chromatography (HPLC)
injected was determined by the difference in weight between
the syringe before and after transferring the solution. The
The analyses of cysteine (CSH), cystine (CSSC), cysteine
total amount of moisture in the lyophile was calculated by sulfinic acid (CSO2H), cysteine sulfonic acid (CSO3H) and
subtracting the amount of water in the DMSO from that hydrogen peroxide (H2O2) were carried out by reversed phase
measured in the DMSO/lyophile solution and calibrated high performance liquid chromatography (HPLC). The system
using a standard curve obtained by adding known quantities consisted of a Beckman 110A Solvent Delivery Module
of water to the Karl Fischer media. The percent of water (Beckman Coulter, Fullerton, CA), a Waters 717 Plus
content was calculated by multiplying by 100 the ratio of the Autosampler (Waters Corp., Milford, MA) and a Hewlett-
amount of water determined to the amount of lyophile.
Packard 1040M Series II HPLC detector (Hewlett-Packard
Company, Palo Alto, CA) operating at 214 nm which was
connected to a PC for data acquisition and analysis using HP
LC/MSD ChemStation software. Two Supelcosil ABZ+Plus, 5
mm (250 ꢀ 4.6 mm) analytical columns (Supelco, Bellefonte,
PA) in tandem and a 5 mm (2 cmꢀ2.1 mm) guard column were
employed. Elutions were performed isocratically at a flow rate
0.8 ml/min using a mobile phase consisting of 50 mM
phosphoric acid, 2.5 mM Sodium 1-nonanesulphonate (99%,
Lancaster Synthesis, Inc., Windham, NH), and 2.5% (v/v)
acetonitrile in water adjusted to pH 2.15 with NaOH. The
retention times for CSO3H, CSO2H, H2O2, CSH, and CSSC
were õ6.5, õ6.8, õ7.5, õ17 and õ27.5 min, respectively.
Powder X-ray Diffraction (PXRD)
Powder X-ray diffraction analyses of lyophiles produced
from 20 mg/ml PVP solutions in 50 mM pH 4.0 and 6.0
phosphate buffer and lyophiles from solutions containing
5 mM CSH and 5 mM H2O2 in 20 mg/ml PVP with 50
mM pH 6.0 phosphate buffer were conducted to confirm
their amorphous nature. Powder X-ray diffraction patterns
of solid samples were determined at ambient temperature
using a SIEMENS D500 X-ray powder diffractometer with
Bragg<Brentano optics to accomplish focusing (Bruker AXS
Inc., Madison, WI). Samples of amorphous solids were
packed as a thin layer into an aluminum sample holder. General Procedure for Kinetic Studies
Crystalline solids (Na3PO4 12H2O, Na2HPO4 7H2O, and
I
I
NaH2PO4 H2O) were ground into fine powders using a
Vials containing lyophiles sealed under vacuum were
I
mortar and pestle, transferred to the top of a quartz holder, placed in a controlled temperature chamber at 25-C. Initial
and several drops of acetone were added to facilitate powder (t0) samples and samples at later time points were either
adhesion after the evaporation of acetone. Samples were assayed immediately after reconstitution or immediately
exposed to CuYKa radiation at 40 kV and 30 mA. The frozen in liquid N2 after reconstitution and stored under
scanning range of 2q was from 10- to 60- with a step size of liquid N2 prior to their analysis. Lyophiles were reconstituted
0.05- and scanning rate of 1-/min.
by first dissolving them in 0.5 ml of a quench solution (50 mM
phosphoric acid, 5 mM sodium 1-nonanesulphonate, and 5%
acetonitrile in water) and then adding 0.5 ml DI water.
Assays were carried out by HPLC as described above.
For the initial rate studies, samples were taken in the
early stage of the reaction between CSH and H2O2.
Typically, the initial rate region was considered to include
the time frame during which less than 5% change in the
concentration of CSH had occurred.
Modulated Temperature Differential Scanning
Calorimetry (MTDSC)
MTDSC analyses were carried out using a TA Instru-
ments DSC2920 (TA Instruments Inc., New Castle, DE) with
MTDSC capacity and refrigerated cooling system under a dry
nitrogen purge. The samples (õ5 mg) were hermetically sealed
in aluminum sample pans and analyzed versus an empty pan in
the reference oven. Samples were first equilibrated at 5-C,
then heated from 5 to 260-C at 5-C/min. At the end of the
heating process, the samples were cooled to 5-C at 10-C/min
then reheated to 260-C at 5-C/min and thermal data were
collected. During the heating and cooling processes, a
modulation amplitude of T0.5-C and a period of 40 s was used
for each sample.
Data Analysis
Concentrations of CSH, H2O2, CSSC, CSO2H, and
CSO3H in quenched lyophiles determined at different
reaction times by HPLC analysis were converted to solid
state concentrations (M). The volume of the solid was
estimated from the calculated McGowan volumes (29) of all
solid phase components. The McGowan volume of a single
molecule is obtained from individual atom contributions
using the following equations:
pH and Initial Reactant and Product Concentrations
After Reconstitution
X
X
The pH of samples from several lyophile batches was
measured immediately after reconstitution in 0.5 ml deion-
ized water. Initial concentrations of both reactants (CSH and
H2O2) and products were determined immediately after
freeze drying by dissolving samples in 0.5 ml of a quench
Vx ¼
atom contributions ꢁ
6:56B
ð1Þ
B ¼ N ꢁ 1 þ Rg
ð2Þ
solution (50 mM phosphoric acid, 5 mM sodium 1-non- where Vx is the calculated McGowan volume of a molecule,
anesulphonate, and 5% acetonitrile in water) and then adding B is the total number of bonds (single, double, or triple bonds
0.5 ml DI water. Assays were carried out by HPLC as each count as one), N is the total number of atoms, and Rg is
described below.
the total number of ring structures. The primary contribution

2242
Luo and Anderson
different reactivities (ki). Models based on Eqs. (3)Y(7)
assuming either homogeneous (i.e., a single reactant popula-
tion) or heterogeneous kinetics (i.e., two reactant populations
having different reactivities) were evaluated.
CSH
CS- + H+
Mechanism
in Solution
Ka
Thiolate anion
k1
H2O2
r. d. s.
d½CSHꢂi
CS-
¼ ꢁk1i½CSHꢂi½H2O2ꢂi ꢁ k2i½CSHꢂi½CSOHꢂi
ð3Þ
dt
CSOH
CSSC
k2
Cysteine sulfenic acid
Cystine
d½H2O2ꢂi
dt
k3
¼ ꢁk1i½CSHꢂi½H2O2ꢂi ꢁ k3i½CSOHꢂi½H2O2ꢂi
ꢁ k4i½CSO2Hꢂi½H2O2ꢂi
H2O2
ð4Þ
CSO2H
Cysteine sulfinic acid
d½CSOHꢂi
dt
¼ k1i½CSHꢂi½H2O2ꢂi ꢁ k2i½CSHꢂi½CSOHꢂi
ꢁ k3i½CSOHꢂi½H2O2ꢂi
k4
H2O2
ð5Þ
ð6Þ
CSO3H
d½CSSCꢂi
dt
¼ k2i½CSHꢂi½CSOHꢂi
Cysteine sulfonic acid
(Cysteic acid)
Scheme I. Proposed mechanism for the reaction of CSH and H2O2
in amorphous PVP lyophiles. The outlined portion represents the
mechanism established for the reaction in aqueous solutions.
d½CSO2Hꢂi
dt
¼ k3i½CSOHꢂi½H2O2ꢂi ꢁ k4i½CSO2Hꢂi½H2O2ꢂi ð7Þ
to the total volume of solid in the amorphous lyophiles is
from PVP {(C6H9NO)n where n = 3,243}. Initial rates of
product formation were obtained from the initial slopes RESULTS
of product concentration versus time curves. Reactant and
product concentrations versus time in the initial rate region in Preparation and Characterization of Amorphous PVP
lyophiles at each pH were also fit to a mathematical model Lyophiles containing CSH and H2O2
(Eqs. 3Y7), which was derived from Scheme I, using non-
linear least squares regression analysis (SCIENTIST\, Micro-
Shown in Table I are the initial and final compositions of
math Inc., Salt Lake City, UT). Equations (3)Y(7) were the various lyophiles produced for the kinetic studies.
constructed to allow for the existence of two (or more) sub- Because CSH and H2O2 react rapidly in aqueous solution
populations of reactants (i subscripts in Eqs. (3)Y(7) having under the conditions employed in preparing solutions for
Table I. Composition of CSH and H2O2-Containing PVP Lyophiles used in Kinetic Studies
[CSH]:[H2O2] (CxHy)a pH C4H6
C4H3
C4H2
C4H1
C1H3
C2H3
C8H3
C4H4c
CSH initial (mM)
H2O2 initial (mM)
%CSH
4.0
8.0
4.0
4.0
4.0
2.0
4.0
1.0
1.0
4.0
2.0
4.0
8.0
4.0
4.0
5.0
4.0 96 T 1b
6.0 89
96 T 1
90
98 T 2
92
100 T 5
95
92 T 0.4
84
91 T 1
87
97 T 1
92
Y
93 T 3
remaining
%H2O2
4.0 74 T 3
6.0 88
76 T 1
94
78 T 4
101
75 T 6
113
72 T 4
90
74 T 2
92
74 T 2
89
Y
80 T 1
remaining
%CSSC formed
4.0 1.5 T 0.1
6.0 6.4
4.0 7.3 T 0.5
1.5 T 0.3
3.7
0.9 T 0.2
2.8
0.9 T 0.1
2.3
2.5 T 0.6
7.7
1.7 T 0.3
4.4
1.3 T 0.1
5.1
Y
4.0 T 0.5
Y
7.1 T 0.7
%H2O (w/w)
8.2 T 1.1
Y
97 T 2
94
7.4 T 1.3
Y
99 T 2
95
6.4 T 0.7
Y
101 T 5
97
9.4 T 1
Y
95 T 0.1
92
8.6 T 2
Y
93 T 2
91
8.3 T 0.3
Y
99 T 1
97
6.0 Y
4.0 98 T 1
6.0 95
Mass balance (%)
[CSH]lyophile (M)
[H2O2]lyophile (M)
Y
97 T 3
Y
0.32 T 0.01
Y
0.34 T 0.01
4.0 0.31 T 0.004 0.31 T 0.004 0.32 T 0.005 0.34 T 0.015 0.08 T 0.001 0.15 T 0.002 0.61 T 0.006
6.0 0.29 0.29 0.3 0.32 0.07 0.14 0.58
4.0 0.48 T 0.02 0.25 T 0.004 0.13 T 0.006 0.06 T 0.005 0.24 T 0.014 0.24 T 0.008 0.23 T 0.002
6.0 0.57 0.31 0.17 0.09 0.3 0.3 0.28
a CxHy reflects composition (mM) of reconstituted lyophiles (to their original volumes)
b T Values reflect standard deviations (n = 3); otherwise n = 1
c All formulations but C4H4 were used for initial rate studies. The C4H4 formulation was used to generate complete concentration versus time
data over 100 h.

Cysteine and Hydrogen Peroxide in Amorphous PVP
2243
lyophilization (28) and because H2O2 has a significant vapor in 50 mM pH 6.0 phosphate buffer either with or without
pressure (30), special precautions were necessary to minimize CSH and H2O2 (each at 5 mM) to those for several
degradant formation and loss of H2O2. First, solutions of crystalline powders of phosphate salts (Na3PO4 12H2O,
I
CSH and H2O2 had to be prepared separately, mixed rapidly, Na2HPO4 7H2O, NaH2PO4 H2O) revealed no evidence of
I
I
and quick-frozen in a liquid N2 bath. Secondly, the primary crystallization of phosphate salts either initially or during
drying process was conducted at j45-C and secondary drying storage for 7 days at 25-C, which is consistent with previous
was eliminated to prevent degradation prior to the initiation evidence that the presence of various glass-forming exci-
of kinetic studies at 25-C and to minimize loss of H2O2. pients inhibits the crystallization of phosphate salts (31).
These precautions enabled the production of lyophiles at pH
MTDSC was employed to detect the glass transition
4.0 containing <5% CSSC formation (Table I). Since CSSC temperatures (Tg) of both pure PVP and an amorphous
does not participate significantly in the reactions investigated PVP lyophile prepared from 20 mg/ml PVP in 50 mM pH
in Scheme I (vide infra), such formulations were considered 6.0 phosphate buffer containing 5 mM CSH and 5 mM
suitable as model formulations for kinetic studies. Generally, H2O2. The value of Tg estimated for pure PVP was 183.6-C
a lower pH (i.e., pH 4.0) produced formulations with less on heating and 179-C on cooling, which is consistent with
initial CSSC formation. Consequently, formulations at pH 4.0 the literature values (16,32). The value of Tg estimated for
were emphasized in the initial rate studies. Lower reactant an amorphous PVP lyophile prepared from 20 mg/ml PVP
concentrations also provided formulations with reduced in 50 mM pH 6.0 phosphate buffers containing 5 mM
degradant formation, but lower concentrations increased the CSH and 5 mM H2O2 and stored at 25-C for 1 week was
time required for kinetic studies and made the analyses of 182.3-C on heating and 180.4-C on cooling, indicating that
initial rates of product formation more difficult.
the glass transition temperature of the amorphous PVP
The drying procedure employed also enabled the lyophile was similar to that of pure PVP and well above the
retention of most of the H2O2 initially added (õ75%) while temperature (25-C) at which solid-state kinetic studies were
removing most of the water. Since the concentrations of conducted. No evidence of other phase transitions was found
H2O2 present in lyophiles at t0 were determined by HPLC, by the MTDSC analyses.
some loss during freeze-drying was inconsequential. Average
moisture contents determined by Karl Fischer titration HPLC Analysis of Reactant Disappearance and Product
ranged from õ6Y10% and were independent of the Formation in the Reaction of CSH and H2O2
[CSH]:[H2O2] ratio.
The pH values of reconstituted solutions from several
lyophile batches indicated no change in pH from the
in Amorphous Solids
Previously, an HPLC method was developed to simulta-
solutions that were lyophilized (pH of reconstituted lyophiles neously monitor the disappearance of CSH and H2O2 and the
averaged 4.01 T 0.01 (n = 2) and 6.00 T 0.01 (n = 15), appearance of CSSC, the primary solution degradant, in a
respectively). In this paper, the term FpH_ refers to a lyophile kinetic study in aqueous buffers as a function of reactant
property. It is the pH that lyophiles produce after reconsti- concentrations and pH (28). Although UV detection at 214
tution, which may not be the same value as the effective pH nm is less sensitive than electrochemical detection for H2O2
in the amorphous solid.
(33) and for CSH and CSSC (34) it is more stable and
Comparisons of the powder X-ray diffraction patterns of convenient. Cysteine sulfinic acid CSO2H and sulfonic acid
lyophiles prepared from solutions containing 20 mg/ml PVP CSO3H were not observed in the solution reaction except at
Fig. 1. HPLC chromatograms (214 nm) generated at various times during the reaction
of CSH with H2O2 in amorphous PVP lyophiles at 25-C. Lyophiles were prepared from
solutions containing 10 mg/ml PVP, 2 mM CSH, and 4 mM H2O2 in 50 mM pH 6.0
phosphate buffer.

2244
Luo and Anderson
very high ratios of H2O2 to CSH, but they were detected in CSH and H2O2 versus time in amorphous PVP lyophiles
amorphous PVP lyophiles, necessitating the development of stored at 25-C while Fig. 2B shows the concentrations of
an HPLC method that would allow the simultaneous analysis CSSC, CSO2H, and CSO3H forming in the same lyophiles,
of CSO3H, CSO2H, CSH, H2O2 and CSSC. Separations of which were prepared from 10 mg/ml PVP, 4 mM CSH and 5
CSO2H from CSO3H required two Supelcosil ABZ+Plus mM H2O2 in 50 mM pH 6.0 phosphate buffer solutions.
columns connected in series and a flow rate of 0.8 ml/min. Qualitatively, Fig. 2 illustrates the increased importance of
Under these conditions, retention times for CSO3H and reaction pathways leading to the formation of CSO3H and
CSO2H were õ6.5 and õ6.8 min, respectively.
CSO2H in the amorphous solid-state reaction.
Linearity in the HPLC response factors was established
over the concentration ranges of 100 mMY10 mM for CSH and
H2O2, 4 mMY3 mM for CSSC, 0.5 mMY2.5 mM for CSO2H,
and 150 mMY90 mM for CSO3H with intraday coefficients of
variation of <1.5% for all analytes except H2O2 for which the
coefficient of variation was 3.3%. The response factor for
CSO3H was only 1.4% of that for CSO2H, which limited the
ability to monitor the formation of CSO3H in the early stages
of the reaction.
Figure 1 displays typical HPLC chromatograms for
reconstituted amorphous PVP lyophiles containing CSH
and H2O2 (prepared from pH 6.0 phosphate buffer) versus
lyophile storage time at 25-C. A comparison of these
chromatograms with those generated for the same reactions
in solution revealed the formation of two new product peaks
corresponding in their retention times and UV spectra to
CSO3H (peak eluting earlier) and CSO2H in addition to the
peak for CSSC.
Kinetic Studies of the Reaction of CSH with H2O2
in Amorphous PVP
To ensure that the products forming in the amorphous
lyophiles involve only the reaction of CSH with H2O2,
preliminary experiments were carried out to determine the
stability of CSH and H2O2 alone in amorphous PVP. Both
were found to be stable (no significant change in concentra-
tion) in PVP at 25-C over the time frame (100 h) of the
longest kinetic studies. The stability of CSSC in amorphous
PVP both in the presence and absence of H2O2 at 25-C was
also determined. While no reaction occurred in the absence
of H2O2, a gradual decline in CSSC could be detected over
several hundred hours in the presence of H2O2 which could
be fit to a linear equation (% of CSSC remaining = j0.0492*t +
99.823, R2 = 0.9997, where t is time (h)). While this reaction
would have a negligible effect on the initial rate studies,
which were typically conducted over a 30-min time frame, it
could impact long-term kinetic studies such as that shown in
Fig. 2. However, the extent of decomposition of CSSC in the
presence of H2O2 was <5% at 100 h, so even in the time
frame explored in Fig. 2 this reaction would have only a
minor contribution. Two well-resolved product peaks were
observed from this reaction, both eluting at retention times of
õ15 min. These product peaks were not significant in
chromatograms generated in the kinetic studies of the
reaction of CSH and H2O2.
Initial rate studies of the reaction between CSH and
H2O2 were conducted at 25-C in amorphous PVP lyophiles
prepared from 10 mg/ml PVP in 50 mM pH 4.0 (n = 3) or pH
6.0 (n = 1) phosphate buffer as described in Table I. These
formulations varied either in their initial concentration of
CSH ([CSH]0 = 1, 2, 4, 8 mM (after lyophile reconstitution))
at constant H2O2 concentration (3 mM) or in their initial
concentration of H2O2 ([H2O2]0 = 1, 2, 3, and 6 mM (after
lyophile reconstitution)) at a constant CSH concentration (4
mM). Also listed in Table I are the calculated molar
concentrations of CSH and H2O2 in the lyophiles. The
concentrations of the two major degradants forming in the
initial rate region, CSSC and CSO2H, are plotted versus time
in Fig. 3. Initial rates of formation of each product for
each set of reactant concentrations were generated from the
slopes of the concentration versus time curves in the region
corresponding to <5% change in CSH concentration at pH
4.0 (<10% change in CSH at pH 6.0).
Reconstituted samples in quench solution were suffi-
ciently stable to enable analyses of both reactant disappear-
ance and product formation simultaneously using this HPLC
method. Figure 2A displays plots for the disappearance of
0.40
A
0.30
0.20
0.10
0.00
0
25
50
75
100
Time (hr)
0.12
0.09
0.06
0.03
0.00
B
0
25
50
75
100
Several significant features are evident in Fig. 3. First,
the initial rates of formation of both products increase with
an increase in CSH concentration at fixed H2O2 concentra-
tion or with an increase in H2O2 concentration at a fixed
concentration of CSH, indicating that the rate determining
step in the reaction depends on the concentrations of both
reactants. Second, the rate of CSSC formation exceeds that
Time (hr)
Fig. 2. Reactant (CSH, r; H2O2, ) disappearance and degradant
Í
(CSSC, q; CSO H, Ì; and CSO H, ) formation in amorphous PVP
)
2
3
lyophiles at 25-C. Lyophiles were prepared from solutions containing
10 mg/ml PVP, 4 mM CSH, and 5 mM H2O2 in 50 mM pH 6.0
phosphate buffer. Solid lines reflect the best fit using Eqs. (3)Y(7)
with i = 2 (see also Table IV).

Cysteine and Hydrogen Peroxide in Amorphous PVP
2245
Fig. 3. Initial rates of formation of CSSC (q, r) and CSO2H (Ì, ) in lyophiles prepared from pH 4
Í
(q, Ì) or pH 6 (r, ) buffers. Left panel: [H2O2]0 fixed at 3 mM and [CSH]0 = 8, 4, 2, 1 mM (A1YA4).
Í
Right panel: [CSH]0 fixed at 4 mM and [H2O2]0 = 6, 3, 2, 1 mM (B1YB4). Dash lines are the model fitted
(Eqs. 3Y7, i = 1) curves for FpH 6_ data and solid lines are the fitted curves for FpH 4_ data. Here Ct and
C0 are the concentration in the lyophiles at time t and time 0 respectively.
for the formation of CSO2H at low [H2O2]:[CSH], while trations of either CSH or H2O2. From the slopes of these
CSO2H formation becomes more significant at high logYlog plots, the apparent reaction order with respect to
[H2O2]:[CSH] concentration ratios. This is more clearly each reactant could be determined. Also shown in Fig. 5 are
illustrated in Fig. 4, where the percent of CSSC or CSO2H the log (initial rate) versus log (concentration) plots obtained
in the total product are plotted versus the initial concen- for CSSC formation in aqueous solutions containing CSH
trations of CSH at fixed [H2O2] (upper panels) or versus the and H2O2 generated in a previous study (28). Whereas the
initial concentrations of H2O2 at fixed [CSH] (lower panels). solution reaction exhibited apparent reaction orders (i.e.,
Finally, the initial rates of degradant formation (Fig. 3) slopes) very close to 1.0 with respect to both CSH and H2O2,
appear to be nearly independent of pH between 4.0 and 6.0 Fig. 5 suggests more complex relationships in amorphous
while percent of CSSC in the total decomposition product PVP. Linear regression analyses of the data at FpH 4_
mixture (Fig. 4) increased modestly at pH 6.0 (right panel) generated Eq. (8), which again suggests a more complex
compared to pH 4.0 (left panel).
dependence of the initial rates on reactant concentrations in
Recognizing that in solution the reaction of CSH with amorphous PVP, at least with respect to H2O2 concentration,
H2O2 produces a reactive intermediate (CSOH), the forma- than in solution. Similar reaction orders were observed at
tion of which is rate-determining, the apparent reaction order FpH 6._
was examined by summing the initial rates of CSSC and
CSO2H formation rather than considering each product
individually. Shown in Fig. 5 are plots of log (d[CSSC]/dt +
d[CSO2H]/dt) versus the logarithms of the initial concen-
fd½CSSCꢂ=dt þ d½CSO2Hꢂ=dtg
1:27
0:76
¼ kCSO2HþCSSC ꢀ ½CSHꢂ0 ꢀ ½H2O2ꢂ0
ð8Þ

2246
Luo and Anderson
'pH' 4.0
'pH' 6.0
100
80
60
40
20
0
100
80
60
40
20
0
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
Lyophile [CSH]0 (M)
Lyophile [CSH]0 (M)
100
80
60
40
20
0
100
80
60
40
20
0
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
Lyophile [H2O2]0 (M)
Lyophile [H2O2]0 (M)
Fig. 4. Percent of total degradant accounted for by CSO2H (Ì, ) and CSSC (q, r) formation in the
initial rate region of the reaction of CSH and H2O2 as a function of initial lyophile concentration of CSH
Í
or H2O2 in amorphous PVP lyophiles at FpH 4.0_ (open symbols) and FpH 6.0_ (closed symbols) and
25-C.
Kinetic Modeling of the Initial Rate Data Generated
in Amorphous PVP
CSO3H in the initial rate region) were used to fit each set
of reactant and product concentration versus time profiles
shown in Fig. 3. Although this approach produced excellent
The appearance of CSO2H and CSO3H as significant fits, the parameter values k2 and k3 were highly correlated
degradants in addition to CSSC in the reaction of CSH with with each other, resulting in large 95% confidence limits for
H2O2 in amorphous PVP suggested that the mechanism each. Significantly reduced correlation between the param-
previously established for the reaction in aqueous solution, eter values was obtained by substituting for k2 and k3
which produced only CSSC, had to be modified. Scheme I transforms reflecting the sum of k2 + k3 (i.e., ktotal) and the
represents the proposed mechanism that was tested in this fraction of CSOH converting to CSSC (i.e., fd = k2/(k2 + k3)).
study. Initially, Eqs. (3)Y(7) (ignoring the formation of This approach provided identical fits and clearly indicated
Fig. 5. LogYlog plots of the initial rates of total product formation versus the starting
concentrations of CSH (A) or H2O2 (B) in amorphous PVP lyophiles (left panels) or
aqueous solution (right panels) at 25-C. Lyophiles were prepared from pH 4 (VV, n =
3) or pH 6 ( - - -, n = 1) buffers while aqueous solutions were at pH 6.0.

Cysteine and Hydrogen Peroxide in Amorphous PVP
2247
Table II. Parameter Values Generated from Fitting Scheme I to the Initial Rate Data* in Amorphous PVP at FpH 4.0_ and FpH 6.0_
k1 (Mj1minj1) T 95% conf. limits k2 + k3 (Mj1minj1) T 95% conf. limits
k2/(k2 + k3) T 95% conf. limits
Formulation
FpH 4_
FpH 6_
FpH 4_
FpH 6_
FpH 4_
FpH 6_
2.4 T 1.8
C8H3
C4H3
C2H3
C1H3
C4H6
C4H2
C4H1
0.0061 T 0.0001
0.0049 T 0.0001
0.0041 T 0.0004
0.0034 T 0.0003
0.0039 T 0.0001
0.0048 T 0.0002
0.0067 T 0.0007
0.0056 T 0.0002
0.0045 T 0.0003
0.0044 T 0.0002
0.0042 T 0.0013
0.0061 T 0.0003
0.0080 T 0.0002
0.0092 T 0.0006
0.65 T 0.01
0.68 T 0.01
0.78 T 0.02
0.82 T 0.01
0.75 T 0.01
0.57 T 0.01
0.47 T 0.03
0.76 T 0.004
0.81 T 0.01
0.85 T 0.004
0.92 T 0.03
0.83 T 0.001
0.72 T 0.004
0.67 T 0.01
1.6 T 0.2
1.4 T 0.2
3.3 T 1.6
1.7 T 0.3
2.5 T 0.6
2.8 T 0.8
3.4 T 2.3
2.7 T 2.6
1.8 T 0.4
13.9 T ND**
1.3 T 0.4
1.4 T 0.2
1.3 T 0.5
*Actual reactant and product molar concentrations in lyophiles rather than concentrations in reconstituted solutions were used to generate the
above values.
**NDV95% confidence limits equal or exceed the parameter value.
that the uncertainty in parameter estimates was mostly should be first order with respect to both CSH and H2O2
associated with the overall rate of conversion of CSOH to concentrations. Contrary to this expectation, as illustrated in
products, ktotal, while the ratios of products forming as Fig. 5, apparent reaction orders of 0.76 and 1.27 (FpH 4_) and
reflected in k2/(k2 + k3) were well determined. The solid 0.72 and 1.17 (FpH 6_) were obtained for the dependence of
and dashed lines shown in Fig. 3 represent these best fits. the initial rates on H2O2 and CSH, respectively.
Values of the parameters generated for each formulation
A closer inspection of the parameter values in Table II
are listed in Table II along with statistical information for reveals additional quantitative inconsistencies. The mean
each parameter. Clearly, the model was capable of fitting values (T SD) for k1, k2/(k2 + k3), and k2 + k3 from Table II
each data set when treated separately, supporting the at pH 4.0 were 0.0048 T 0.0012 Mj1minj1, 0.67 T 0.14, and
hypothesis that Scheme I is an appropriate model for the 2.4 T 0.8 Mj1minj1, respectively. While the overall variability
solid-state reaction.
in these parameters does not seem large, the 95% confidence
Because the formation of the reactive intermediate limits for k1 and k2/(k2 + k3) for each formulation indicated
(CSOH) is the slow step in amorphous PVP, indicated in significant differences between formulations. Bar graphs
Table II by the fact that ktotal exceeds k1 by at least two comparing the values of k1 and k3/(k2 + k3) (= 1 j k2/(k2 +
orders of magnitude, the model based on Scheme I predicts k3)) in different formulations along with error bars reflecting
that the overall initial reaction rate in amorphous PVP their 95% confidence limits at both FpH 4_ and FpH 6_ are
Fig. 6. Systematic variation in k1 (upper panels) and k3/(k2 + k3) (lower panels) at FpH_ 4 (left) and FpH_ 6 (right) as the ratio of CSH and
H2O2 in lyophile formulations is varied.

2248
Luo and Anderson
shown in Fig. 6. These comparisons clearly indicate Heterogeneous Dynamics Exhibited in Amorphous PVP
significant and similar trends in the parameter values with
varying CSH:H2O2 concentration ratios in the formulations
The reaction of CSH and H2O2 at 25-C in amorphous
at both pH values. A further analysis of the parameter values PVP lyophiles containing (after reconstitution to their
at pH 4 suggested linear relationships between these original volume) 4 mM CSH and 4 mM H2O2 in 50 mM pH
parameter values and XHOOH, where XHOOH is the mole 6.0 phosphate buffer along with 10 mg/ml PVP was compared
fraction of H2O2 relative to the total moles of reactant in Fig. 7 to the same reaction in aqueous solutions also
(i.e., XHOOH = [H2O2]/([H2O2] + [CSH]). Thus, at pH 4, k1 = containing 4 mM CSH and 4 mM H2O2 in 50 mM pH 6.0
j0.0051*XHOOH + 0.0072 (r 2 = 0.8412) and k2/(k2 + k3) = phosphate buffer. Figure 7 demonstrates that the disappear-
0.5538*XHOOH + 0.4202 (r 2 = 0.9424). These empirical ance of the reactants and formation of products for the
relationships between the rate constant parameters and reaction of 4 mM CSH and 4 mM H2O2 is more rapid in
formulation composition with respect to H2O2 provided an aqueous solution at this pH than in amorphous PVP (at the
empirical model that could fit the entire data set (i.e., all same concentrations after reconstitution), despite the fact
compositions) at each pH.
that the concentrations in amorphous PVP prior to reconsti-
tution are significantly higher (õ100-fold, Table I). In the
solution reaction, two molecules of CSH are consumed for
each molecule of H2O2 resulting in a rapid depletion of CSH
from the solution (lower panel), producing CSSC as the only
product (upper panel), and leaving unreacted H2O2 in
solution. As noted previously, CSSC is only one of several
products forming in amorphous PVP, though it is the only
one shown in Fig. 7. The most remarkable difference
between the solution and amorphous solid reactions illus-
trated in Fig. 7 is the nearly complete arrest of the decline in
CSH after an initially rapid phase lasting approximately 5 h,
leaving õ40Y50% unreacted CSH which then gradually
declines over the remaining reaction time to less than 25%
remaining after 100 h. At the start of this slow decline phase
in the decomposition of CSH approximately 1/2 of the
original H2O2 concentration remains. The sudden slowing in
the rate of decomposition of CSH (lower panel) is ac-
companied by a similar abrupt slowing in the rate of for-
mation of CSSC (upper panel).
Two models were explored to fit the apparent biphasic
character of the reaction in amorphous PVP. Each of the
concentration versus time curves can be described individu-
ally by the Kohlrausch<Williams<Watts (KWW) stretched
exponential equation (35Y37) (Eq. 9):
h
i
ꢁ
ꢀkwwðtÞ ¼ exp ꢁðt=tÞ
ð9Þ
where ꢀkww (t) is a relaxation function (e.g., [CSH]/[CSH]o,
etc.), t (> 0) is a relaxation time and b is a stretching pa-
rameter between 0 and 1 necessary to describe non-mono-
exponential behavior. The parameters generated from fits of
each concentration-time profile, shown in Fig. 8, are dis-
played in Table III. Understandably, different parameter
values are obtained depending on the probe selected to
monitor the process.
Alternatively, the simplest model that can account for
the apparent biphasic character of the reaction in PVP that is
also consistent with Scheme I assumes the existence of two
populations of reactants having different kinetics (i.e., i = 2 in
Eqs. 3Y7). For first-order decay this would lead to a bi-
exponential equation. This model has the advantage of en-
abling all of the reactant and product concentration versus
time curves to be fit simultaneously. The solid lines in
Figs. 2A and 2B were generated from this model and values
for the reaction parameters are shown in Table IV. As judged
by the excellent fit of the data in Fig. 2, a simple two
population model with approximately 50Y50 populations of
Fig. 7. Comparison of the reactions of cysteine and hydrogen
peroxide in aqueous solution and in amorphous PVP (concentrations
expressed are after reconstitution) at 25-C. Aqueous solutions
contained 4 mM CSH and 4 mM H2O2 in 50 mM pH 6.0 phosphate
buffer solutions. Amorphous PVP lyophiles contained (after recon-
stitution to their original volume) the same concentrations of CSH
and H2O2 in 50 mM pH 6.0 phosphate buffer along with 10 mg/ml
PVP. Upper panel, CSSC ( , Ì); middle panel, H2O2 (P, ); and
)
Í
lower panel, CSH (r, q)-aqueous solutions (open symbols); amor-
phous PVP (closed symbols).

Cysteine and Hydrogen Peroxide in Amorphous PVP
2249
intermediate may be instrumental in rationalizing and
ultimately predicting differences in reaction kinetics and
degradant profiles in amorphous solid-state reactions.
1.2
We and others have demonstrated (25Y28) that the
reaction between thiols and hydrogen peroxide in aqueous
solution (in the absence of metal ions) involves bimolecular
nucleophilic attack of thiolate to form a reactive sulfenic acid
intermediate (RSOH), ultimately producing a disulfide
(RSSR) via reaction of the intermediate with a second thiol
molecule as described in Scheme I (section outlined). An
alternative pathway for the sulfenic acid intermediate
through further reaction with H2O2 can occur (46), which is
also described in Scheme I, leading to a sulfinic acid
(RSO2H) and ultimately to a sulfonic acid (RSO3H) but in
aqueous solution these reactions appear to be unimportant
except possibly at extremely high ratios of H2O2 (25Y28).
Intuitively, one might expect that in an amorphous PVP
glass the bimolecular reaction between CSOH and CSH (or
CSj), the fast (i.e., non-rate-determining) reaction step in
solution, might be substantially reduced given the restricted
translational mobility in glassy polymers due to their high
viscosities below Tg (18). For a reaction which is molecular
mobility or diffusion controlled, relative rate constants are
often estimated by the Stokes<Einstein equation (Eq. 10)
which relates the translational diffusion coefficient, Dt, to the
inverse of viscosity (h) and molecular radius (r) (13,45,47):
0.9
0.6
0.3
0.0
0
25
50
75
100
Time (hr)
Fig. 8. Best fits of the KWW equation to each reactant (CSH (r)
and H2O2 )) and degradant (CSO H ( ) and CSSC(q))
concentration vs. time profile during the reaction of CSH and H2O2
in amorphous PVP lyophiles prepared from 50 mM pH 6.0 phosphate
buffer containing 10 mg/mL PVP, 4 mM CSH and 5 mM H2O2.
(
)
3
Í
reactants differing by õ one order-of-magnitude in reactivity
is adequate for this set of conditions.
DISCUSSION
kbT
Dt ¼
ð10Þ
6ꢂꢃr
Many important degradation pathways affecting phar-
maceutical products involve formation of a reactive interme-
diate along the reaction coordinate. Considering only
Recent molecular dynamics simulations of small mole-
reactions prevalent in peptide and protein formulations, cule diffusion in amorphous PVP glass suggest that the size
deamidation, isomerization, and racemization reactions at selectivity for solute diffusion may be significant (19,24). A
asparagine and glutamine residues proceed through a cyclic simulation of the diffusion coefficients of water and a
imide intermediate (38); peptide bond cleavage at aspartate tripeptide in both bulk water and in glassy PVP indicated
residues may involve a cyclic anhydride intermediate; in that whereas the self-diffusion coefficient for water in bulk
some instances cyclic anhydride formation may produce water was 370-fold greater than in PVP, the diffusion of the
covalent, amide-linked aggregates (39Y41); covalent aggre- tripeptide in water exceeded its value in PVP by 3,700-fold.
gates may also form from reactive free thiol intermediates
If the reactions in Scheme I become mobility-con-
which are generated from disulfide bond hydrolysis and can trolled in amorphous PVP, the substantially reduced diffu-
participate in thiol-disulfide exchange reactions (42Y44); sion coefficients for CSH and CSOH increase the likelihood
finally, the Maillard reaction between amine-containing for the alternate pathway for reaction of CSOH with the
molecules and reducing sugar excipients involves a Schiff smaller (and more mobile) molecule, H2O2. Indeed, this
base intermediate (45). The kinetics of such reactions, which anticipated outcome is observed, as demonstrated by the
involve multiple steps, may be more complicated in the solid- HPLC chromatograms in Fig. 1 and the product concentra-
state due to the more limited molecular mobility of the tion versus time profiles in Fig. 2, both of which dem-
participants in the various stages of a reaction. Because of onstrate the formation of three significant degradation
this and other complicating factors, kinetic models based on products in the reaction between CSH and H2O2 in
reaction mechanisms originally developed for solutions amorphous PVP. The disulfide, CSSC, the predominant
generally fail to account for reactivity in the solid-state product in aqueous solution is also the major decomposition
(1,45). Nevertheless, knowledge of the existence of a reactive product in amorphous PVP but significant quantities of
Table III. Parameter Values Generated from Fitting the KWW Equation (Eq. 9) to each Concentration vs. Time Profile in Fig. 8
Sum of squared deviations
Model selection criterion (MSC)
t (95% conf. limits)
b (95% conf. limits)
CSH
0.0297
0.0342
0.0266
0.0153
2.877
24.1 (12.9, 35.3)
21.7 (13.9, 29.5)
3.8 (2.4, 5.2)
0.37 (0.27, 0.47)
0.58 (0.44, 0.73)
0.51 (0.34, 0.68)
0.53 (0.42, 0.64)
H2O2
CSSC
CSO3H
3.2071
3.1517
3.4066
14.2 (9.8, 18.6)

2250
Luo and Anderson
Table IV. Parameter Values Generated by Simultaneously Fitting Eqs. (3)Y(7) (i = 2) to All of the Concentration* vs. Time Profiles in Fig. 2
k1 (Mj1minj1) T
95% conf. limit
k2/(k2 + k3) T
95% conf. limit
k2 + k3 (Mj1minj1) T
95% conf. limits
k4 (Mj1minj1) T
95% conf. limits
Fx = [a]/([a] + [b]) T
95% conf. limits
Population a
Population b
0.044 T 0.009
0.001 T 0.0001
0.8 T 0.01
0.25 T 0.06
0.31 T 0.06
0.009 T 0.003
0.06 T 0.01
0.015 T 0.002
0.52 T 0.023
*Molar concentrations of reactants and products in lyophiles.
CSO3H are also found. CSO2H formation is important in CSOH disappearance k2/(k2 + k3) were employed in the
the initial stages of the reaction but it degrades further to place of k2 and k3 due to a significant correlation between k2
CSO3H. This change in degradant profile is the first line of and k3. This provided excellent statistics for k1, the rate
evidence in support of the hypothesis that the reaction in constant for formation of reactive intermediate and for the
amorphous PVP proceeds through the same reactive inter- fraction of the intermediate going to either product, but poor
mediate but to produce a more diverse array of products due statistics for the sum of k2 + k3, as judged by the 95%
to the increased importance of translational (and possibly confidence limits. It is reasonable that the 95% limits for k2 +
rotational) diffusion in the solid-state reaction.
k3 should be large, because k1 reflects the rate-determining
Initial rate studies conducted at FpH 4.0_ and FpH 6.0_ step. (Due to the paucity of data at pH 6, confidence limits
and at varying ratios of [CSH]:[H2O2] provide further could not be determined for k2 + k3 in some cases.)
evidence for the hypothesis that the reaction in amorphous
Compared to the reaction in aqueous solution at pH 4.0
PVP is governed by Scheme I. The plots for the initial rates (28), the rate constant for the rate determining step, k1, in
of formation of CSSC and CSO2H illustrated in Fig. 3 show amorphous PVP is õ1Y2ꢀ105-fold smaller. However, the
the following features consistent with Scheme I: (1) the values in Table II are based on lyophile concentrations of
overall reaction rate and the rates of formation of both CSH and H2O2 which exceed the concentrations in the
degradants increase with increasing concentrations of either solutions from which the lyophiles were prepared by õ100-
CSH or H2O2 indicating that the rate law must include the fold. Thus, the actual initial rate of reaction is ~10-fold
concentrations of both; (2) CSSC and CSO2H formation rates slower in FpH 4_ lyophiles than in water at pH 4. In the
both increase with either an increase in CSH or an increase in amorphous state k1 is nearly the same at pH 4 and pH 6
H2O2, consistent with the initial formation of a reactive indicating that the overall reaction rate in this pH range is pH
intermediate (e.g., the rate of CSSC formation would not be independent (and therefore evidently involving CSH rather
expected to increase with an increase in H2O2 unless an than CSj as the reactant), in stark contrast to the situation in
intermediate were involved); (3) both degradants form in aqueous solution where k1 is first order in [OHj], indicating
parallel with no apparent lag time, suggesting that the that CSj is the nucleophile in the first reaction step. As a
reactive intermediate formation is rate-determining (i.e., no result, the initial reaction rate is slower in FpH 6_ lyophiles
significant build-up in concentration of intermediate); (4) the than in water at pH 6. The reaction at FpH 6_ produces a
ratios of initial rates of formation of CSSC and CSO2H vary modestly higher fraction of CSSC product, consistent with
in response to the initial concentrations of CSH and H2O2 in some contribution of CSj in the second reaction step.
the expected manner (qualitatively) for a reaction in which
Although most features of the reaction in amorphous
the two reactants are competing for the same intermediate, PVP are consistent with Scheme I, the mathematical model
as more clearly shown in Fig. 4 (i.e., the percent of total described in Eqs. (3)Y(7) could not adequately fit all of the
degradant accounted for by CSSC increases with increasing initial rate data in Table II simultaneously. An explanation
CSH/H2O2 while CSO2H accounts for a higher percentage of for the ultimate failure of this simple model seems to reside
the total with increasing H2O2/CSH); and (5) the absence of in a small but systematic dependence of the rate constants on
detectable levels of CSO3H suggests that CSO2H formation is the [CSH]:[H2O2] composition. This is explored in greater
indeed a precursor to this product (however, the HPLC detail in Figs. 7 and 8. In Fig. 5, logYlog plots of the initial
response factor for CSO3H is much lower than that for CSO2H rates of total product formation versus the initial concen-
making CSO3H difficult to detect at low concentrations).
trations [CSH]0 or [H2O2]0 are shown for the reaction in
As a more rigorous quantitative test, a mathematical aqueous solution and in amorphous PVP. In aqueous solution
model representing the reactions in Scheme I (Eqs. 3Y7) was the formation of CSSC is first-order in [CSH]0 and [H2O2]0
employed to fit each set of concentration versus time profiles and quantitatively consistent with Scheme I, while in
shown in Fig. 3 along with the reactant concentrations (not amorphous PVP the apparent reaction order is 0.76 (0.72)
shown). The solid lines in Fig. 3 reflect the best fits of this with respect to [H2O2] and 1.27 (1.17) with respect to [CSH]
model and the parameters generated are listed in Table II. at FpH 4_ (FpH 6_). This reduced sensitivity to [H2O2]0 and
The model was clearly capable of fitting each group of the heightened sensitivity to [CSH]0 are also revealed in the
concentration versus time data separately and generating systematic variation in both k1 and k2/(k2 + k3) (and
reasonable parameter values over the range of CSH:H2O2 therefore k3/(k2 + k3)) at FpH 4_ and also FpH 6,_ as shown
ratios, which provides further support for the model. Trans- in Fig. 6. At constant [CSH]0, increasing [H2O2]0 over an
formed parameters representing the overall rate constant for approximately six-fold range results in an õ37Y47% reduc-
disappearance of CSOH (k2 + k3) and the ratio of the rate tion in k1, thus reducing the slope in log (d[CSSC]/dt +
constant for CSSC formation to the overall rate constant for d[CSO2H]/dt) versus [H2O2]0 to a value less than one. At

Cysteine and Hydrogen Peroxide in Amorphous PVP
2251
constant [H2O2]0, increasing [CSH]0 over an eight-fold range heterogeneous reaction dynamics consistent with Scheme I
resulted in a near doubling of k1, giving rise to a slope >1 in that could be tested assumes two populations of reactants
log (d[CSSC]/dt + d[CSO2H]/dt) versus [CSH]0. Parallel having different reactivities (i.e., i = 2 in Eqs. 3Y7). This
influences were seen in the effects of [CSH]:[H2O2] compo- model has an advantage over the KWW equation in that it
sition on k3/(k2 + k3) (Fig. 6). While increasing [H2O2]0 has a conceptual basis, it is reasonable in light of the likely
increases the fraction of CSO2H degradant formed, the heterogeneous distributions of water, H2O2, and possibly
increase is less than the model in Eqs. 3Y7 predicts due to a cysteine in amorphous PVP, and it can be used in conjunction
reduction in k3/(k2 + k3). In contrast, increasing [CSH]0 with Scheme I to simultaneously fit both reactant disappear-
produces a greater fraction of CSSC degradant, but less than ance and product formation, as demonstrated by the solid
that predicted by the model because k3/(k2 + k3) increases.
lines in Fig. 2. The parameter values generated (Table IV)
The systematic variation in rate constants with indicate that the data in Fig. 2 can be described by two
[CSH]:[H2O2] composition may indicate that the distribution approximately equal reactant populations having reactivities
of these molecules is not uniform throughout the PVP that differ by more than an order of magnitude.
matrix. Rather, spatial heterogeneity in their distribution
may occur due to a preference of these solutes to localize in
pockets of high water content or due to their potential to
CONCLUSIONS
themselves form hydrogen bonded clusters. Previously,
molecular dynamics simulations (24) demonstrated that the
When reactive intermediates are involved, differences in
distribution of water in an amorphous PVP glass is highly
degradant profiles and other characteristics (e.g., rate con-
heterogeneous at 10% w/w water (comparable to the water
stants, apparent reaction order) in the amorphous-state may
content in the lyophiles in the present study), reflecting the
simply reflect altered rates for individual reaction steps due
formation of water strands or small clusters occupying the
to glass-induced changes in relative reactant mobilities rather
channels between polymer chains rather than complete phase
than a change in overall mechanism. Compared with the
separation. These water clusters gave rise to an enhanced
reaction in solution where a single degradant (CSSC) is
local mobility with increasing water content. Experimentally
produced, CSH reacts with H2O2 in amorphous PVP to
in PVP under ambient conditions, Lebedeva et al. (48)
generate CSSC, CSO2H and CSO3H. While simple bimolec-
identified clusters consisting of four water molecules associ-
ular kinetics govern the solution reaction, initial rates in
ated with two neighboring polymer units.
amorphous PVP suggested more complex kinetics (i.e., non-
H2O2 forms stronger hydrogen bonds than water be-
unity values for reaction order). These differences in
cause it is a stronger acid (pKa (H2O2) = 11.5 (28) versus
degradants and apparent reaction orders in the solid-state
15.75 for water). Panarin et al. (49) confirmed that H2O2
could be rationalized by a model that assumes that the same
molecules form stronger hydrogen bonds than water with the
reactive intermediate (CSOH) forms in the amorphous solid-
carbonyl oxygen atom in PVP and that strong self-association
state reaction as in solution, but partitions to multiple pro-
of H2O2 can occur in PVP, leading to extended ribbon
ducts in the solid-state due to the restricted mobility of CSH.
structures of H2O2 complexed with PVP carbonyl oxygen
Beyond the initial rate region, the kinetics in amorphous
atoms.
PVP could be described by the Kohlrausch<Williams<Watts
The reductions in rate constants observed in this study
(KWW) stretched-exponential equation or by assuming two
with increasing H2O2 ratios in PVP may reflect the formation
populations of reactant molecules having quite different
of H2O2 clusters having reduced reactivity. Further studies
reactivities.
will be needed to more thoroughly characterize these subtle
Future studies will focus on more rigorous tests of the
composition effects.
kinetic models suggested by the data in the present study.
Heterogeneous dynamics as manifested in non-mono-
exponential decay kinetics are often seen in amorphous
polymers (50Y52) and frequently described by the empirical
ACKNOWLEDGMENTS
KWW equation (Eq. 9) (35Y37). While this equation could
also be applied to fit each of the concentration versus time
curves generated in this study (Fig. 8), different parameter
values were obtained (Table IV) depending on which species
was monitored. This is understandable, given that the KWW
equation cannot readily take into account the detailed
chemistry and multiple reaction steps that are described in
Scheme I.
This work was made possible by a grant from Pfizer Inc.
The authors thank Dr. Paul Bummer for allowing use of his
DSC and Mr. Henry Francis for assistance in powder X-ray
diffractometry. The use of the powder X-ray diffractometry
facility in the Kentucky Geological Survey (KGS) of the
University of Kentucky is also gratefully acknowledged.
An alternative approach for describing local motions in
amorphous polymers assumes molecules residing in different
spatial locations have different rate constants and geometries
of motion, such that they can be treated as sub-ensembles of
mobile and less mobile components (53Y55). Bohmer et al.
(56) demonstrated in various glass-forming materials that
Bnon-exponential relaxation results from a superposition of
dynamically distinguishable entities,^ consistent with the
existence of spatial heterogeneity. The simplest model for
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