that R is constant for each polymer, eq 5 can be expected
to hold when T ) Texp and W ) W so that
9. Geiger, T.; Clarke, S. Deamidation, isomerization and race-
mization at asparaginyl and aspartyl residues in peptides.
Succinimide-linked reactions that contribute to protein
degradation. J . Biol. Chem. 1987, 262, 785-794.
g
g
o
Tg - Texp
10. Patel, K.; Borchardt, R. T. Chemical pathways of peptide
degradation. II. Kinetics of deamidation of an asparaginyl
residue in a model hexapeptide. Pharm. Res. 1990, 7, 703-
R )
(6)
Wg
7
11.
1
1. Bergren, M. S. An automated controlled atmosphere mi-
crobalance for the measurement of moisture sorption. Int.
J . Pharm. 1994, 103, 103-114.
g
where W is the water content needed to induce the glass
transition at Texp ) 50 °C. Substituting this value for R
(i.e., the slope) into eq 5 yields:
12. Guggenheim, E. A. Applications of Statistical Mechanics;
Clarendon: Oxford, 1966.
o
13. Anderson, R. B. Modifications of the Brunauer, Emmett and
Teller equation. J . Am. Chem. Soc. 1946, 68, 686.
14. van den Berg, C.; Bruin, S. Water activity and its estimation
in food systems: Theoretical aspects. In Water Activity:
Influences of Food Quality; Rockland, L. B.; Stewart, G. F.,
Eds.; Academic: New York, 1981; pp 1-61.
Tg - Tg
W
Wg
)
(7)
o
Tg - Texp
This equation states that the degree of plasticization
needed to induce a glass transition is related to water
content, the experimental temperature, and the dry in-
of the polymer. A convergence of the deamidation
rates in PVA and PVP was also observed when the rate
constant (kobs) was plotted against W/W
- Texp)] may be useful in correlat-
ing reaction rates in other systems, its utility in these
studies (Figure 8) may be due to the near linear relation-
1
5. Hancock, B. C.; Zografi, G. The use of solution theories for
predicting water vapor absorption by amorphous pharma-
ceutical solids: A test of the Florry-Huggins and Vrentas
models. Pharm. Res. 1993, 10, 1262-1267.
o
trinsic T
g
1
6. Gordon, M.; Taylor, J . S. Ideal copolymers and the second-
order transitions of synthetic rubbers. I. Noncrystalline
copolymers. J . Appl. Chem. 1952, 2, 493-500.
g
. Although this
o
parameter [(T - T
g
)/(T
g
17. Hancock, B. C.; Zografi, G. The relationship between the glass
transition temperature and the water content of amorphous
pharmaceutical solids. Pharm. Res. 1994, 11, 471-477.
1
8. Nyquist, H. Saturated salt solutions for maintaining specified
g
ship between T and water content observed for PVA and
relative humidities. Technol. Prod. Mfr. 1983, 4, 47-48.
PVP under these experimental conditions (Figure 2).
The results of this study suggest that several factors,
including water content and mobility, may affect the
chemical reactivity of Asn-hexapeptide in lyophilized poly-
mer formulations. Isolating a single dominant mechanism
driving deamidation is difficult because water content,
g
are coupled. Future studies will
attempt to vary T and water content independently with
the use of a separate plasticizer to deconvolute their effects
on deamidation in the solid state.
19. Connors, K. A.; Amidon, G. L.; Stella, V. J. Chemical Stability
of Pharmaceuticals, 2nd ed.; J ohn Wiley & Sons: New York,
1
986; pp 115-133.
2
0. Sperling, L. H. Introduction to Physical Polymer Science;
J ohn Wiley & Sons: New York, 1986; p 278.
21. In Polyvinyl Alchohol-Developments; Finch, C. A., Ed.; J ohn
Wiley & Sons: New York, 1992; pp xix-xx.
2
2. Peyser, P. Glass transition temperatures of polymers. In
Polymer Handbook, 3rd ed.; Brandrup, J .; Immergut, E. H.,
Eds.; J ohn Wiley & Sons: New York, 1989; p VI-211.
water activity, and T
g
23. Williams, M. L.; Landel, R. F.; Ferry, J . D. The temperature
dependence of relaxation mechanisms in amorphous poly-
mers and other glass-forming liquids. J . Am. Chem. Soc.
1
955, 77, 3701-3707.
2
2
4. Angell, C. A. Formation of glasses from liquids and biopoly-
mers. Science 1995, 267, 1924-1935.
References and Notes
5. Hancock, B. C.; Zografi, G. Characteristics and significance
of the amorphous state in pharmaceutical systems. J . Pharm.
Sci. 1997, 86, 1-12.
1
2
. Hageman, M. J . Water sorption and solid-state stability of
proteins. In Stability of Protein Pharmaceuticals, Part A:
Chemical and Physical Pathways of Protein Degradation;
Ahern, T. J .; Manning, M. C., Eds.; Plenum: New York, 1992;
pp 273-309.
. Roy, M. L.; Pikal, M. J .; Rickard, E. C.; Maloney, A. M. The
effects of formulation and moisture on the stability of a
freeze-dried monoclonal antibody-vinca conjugate: A test of
the WLF glass transition theory. Dev. Biol. Standard. 1992,
2
2
2
2
3
3
6. Ota, I. M.; Clarke, S. Calcium affects the spontaneous
degradation of aspartyl/asparaginyl residues in calmodulin.
Biochemistry 1989, 28, 4020-4027.
7. Yoshioka, S.; Aso, Y.; Nakai, U.; Kojima, S. Effect of high
molecular mobility of poly(vinyl alcohol) on protein stability
of lyophilized insulin. J . Pharm. Sci. 1998, 87, 2, 147-151.
8. Hancock, B. C.; Zografi, G. Molecular mobility of amorphous
pharmaceutical solids below their glass transition temper-
atures. Pharm. Res. 1995, 12, 799-806.
7
4, 323-340.
3
4
. Constantino, H. R.; Langer, R.; Klibanov, A. M. Moisture-
induced aggregation of lyophilized insulin. Pharm. Res. 1994,
9. Inoue, T.; Cicerone, M. T.; Ediger, M. D. Molecular motions
and viscoelasticity of amorphous polymers near Tg. Macro-
molecules 1995, 28, 3425-3433.
0. Brennan, T. V.; Clarke, S. Spontaneous degradation of
polypeptides of aspartyl and asparaginyl residues: Effect of
the solvent dielectric. Protein Sci. 1993, 2, 331- 338.
1. Boyer, R. E. Effect of plasticizers on some physical properties
of polymers. Tappi 1951, 34, 357-362.
1
1, 21-29.
. Strickley, R. G.; Anderson, B. D. Solid-state stability of
human insulin. I. Mechanism and the effect of water on the
kinetics of degradation in lyophiles from pH 2-5 solutions.
Pharm. Res. 1996, 13, 1142-1153.
5
6
. Shalaev, E. Y.; Zografi, G. How does residual water affect
the solid-state degradation of drugs in the amorphous state?
J . Pharm. Sci. 1996, 85, 1137-1141.
. Levine, H.; Slade, L. The glassy state phenomenon in food
molecules. In The Glassy State in Foods; Blanshard, J . M.
V.; Lillford, P. J ., Eds.; Nottingham: Nottingham, 1993; pp
Acknowledgments
M.C.L. thanks Bob Dalga of Pharmacia & Upjohn, Inc. for his
help on the CAM and Pharmacia and Upjohn for the opportunity
of an industrial externship. This project was supported by the
Takeru Higuchi Predoctoral Fellowship (M.C.L.), a NIGMS Bio-
technology Training Grant (M.C.L.), Pharmacia & Upjohn, Inc.,
and by NIH Grant GM-54195.
3
5-101.
7
8
. Ahlneck, C.; Zografi, G. The molecular basis of moisture
effects on the physical and chemical stability of drugs in the
solid state. Int. J . Pharm. 1990, 62, 87-95.
. Oliyai, C.; Patel, J .; Carr, L.; Borchardt, R. T. Solid-state
stability of lyophilized formulations of an asparaginyl residue
in a model hexapeptide. J . Parenteral Sci. Technol. 1994, 48,
1
67-173.
J S980227G
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080 / Journal of Pharmaceutical Sciences
Vol. 88, No. 10, October 1999