Accelerated Stability Modeling
for Bioproducts
2013 MBSW, Muncie, Indiana
May 21, 2013
Kevin Guo
Examples of Bioproducts
Amgen/Pfizer
Eli Lilly
Genentech
Genentech
Genentech
Eli Lilly
Slide 2
Merck
Abbott Labs
Company Confidential
Copyright© 2013 Eli Lilly and Company
What is Bioproduct
Bioproducts are proteins produced from recombinant DNA and grown in an
expression system such as bacteria, yeast, or eukaryotic systems
Slide 3
Company Confidential
Copyright© 2013 Eli Lilly and Company
Background
• One of the key objectives in developing bioproduct is to find a
commercial formulation prototype that has an acceptable stability
profile throughout a desired shelf-life of 18 months or more, under
typical storage condition of 2-8°C
• To expedite the decision process of selecting the optimal formulation
prototype, a short-term accelerated stability is usually conducted by
subjecting the formulation candidates to elevated multi temperature
exposures (typically 15°C and higher)
• Based on this short-term multi temperature stability study, a prediction
model is then developed to estimate the long-term stability profile of
the formulation candidates under the intended long-term storage
condition
Slide 4
Company Confidential
Copyright© 2013 Eli Lilly and Company
Why Stability Testing
•
•
•
•
•
•
Slide 5
Safety point of view from patient
Critical quality attribute (CQA)
Establish shelf life of the drug
Study the storage conditions
Study the container closure system
Provide evidence how the quality of the drug product changes over
time
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Copyright© 2013 Eli Lilly and Company
What’s so Special about Bioproduct Stability?
Common problems with stability of proteins
• Usually sensitive to light, heat, air, and trace metal impurities
• Small or large stress factors can disrupt protein folding
• Numerous physical degradation routes, including agitation, freezing,
interaction with surfaces and phase boundaries
• Possible Non-Arrhenius behavior
• One type of degradation can facilitate other types of degradation
leading to a cascading effect
• Possibility of different degradation mechanisms appearing depending
on the age of the product
• Limited formulation options
Reference: Handbook of Stability Testing in Pharmaceutical Development.
Anthony Mazzeo and Patrick Carpenter, Ch17, Stability Studies for Biologics
Slide 6
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Copyright© 2013 Eli Lilly and Company
Bioproduct Stability
• Why accelerated stability studies work despite the problems listed on
the previous slide?
– Degradation is often reasonably Arrhenius below 40°C
– Information from pre-formulation studies and other one-off studies
Slide 7
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Copyright© 2013 Eli Lilly and Company
Challenges in Accelerated Stability Modeling
• When developing the prediction model from the short-term
accelerated stability study:
– Bioproducts typically degrade in a nonlinear fashion, numerous
chemical degradation routes possible, much more so than the
small molecule compounds
– The underlying degradation mechanism is often very complex and
a characterization study to understand the degradation kinetic is
prohibitively expensive
– Limited resources to execute the accelerated study that minimal
number of temperatures and testing time-points can be
incorporated in the study design
• This presentation describes a proposal on how to develop
the prediction model. Some key features:
– Leveraging Arrhenius principle of the temperature dependence of a
chemical reaction
Slide 8
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Copyright© 2013 Eli Lilly and Company
Accelerated Stability Study Design
• Key features of the stability design
– Short-term, should be completed in 3 months or less
– Typically utilize 4 temperatures at minimum: long-term storage
condition of 5°C + 3 elevated temperatures (15 – 40°C)
– Highest temperature is chosen such that it is representative of
lower temperature stability profiles (e.g. elevated temperature
degrades in the same pathway as the lower ones)
– Utilize materials (e.g. Drug Substance) that are representative of
those for commercial use
– May incorporate other factors of interests besides temperature (e.g.
pH, concentration of drug substance, choice of excipient, etc)
Slide 9
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A Typical Accelerated Stability Study Sampling
Scheme
Slide 10
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Copyright© 2013 Eli Lilly and Company
Fixed Time-points vs. Fixed Amt of Change
•
•
•
Fixed Schedule
•
Months
Advantages:
•
• platform-wide approach (doesn’t need
to vary with molecule)
• requires little prior knowledge
• provides stability profile
•
Disadvantages:
• labor intensive
• different levels of degradation at
different storage conditions – can bias
rate coefficient estimates
Slide 11
Fixed Degradant
Months
Advantages:
• efficient
• same level of degradation (rate coefficient
bias does not depend on storage condition)
Disadvantages:
• requires Ea estimate to design correct
storage temperature / time-point
combinations
• target degradant level must be selected apriori
Company Confidential
Copyright© 2013 Eli Lilly and Company
Arrhenius Equation
• Rate constant k of a chemical reaction depends on the
temperature (Kelvin) and activation energy Ea according to
the following equation:
 Ea RT
 Ea 1
ln k 
  ln( k R , 0 )
R,0
k k e
 
R
T
k = Reaction rate
Slope 
Ea = Activation Energy (Kcal mol-1)
R = Gas constant (Kcal mol-1 K-1)
ln (k)
T = Temperature in Kelvin
kR,0 = Pre-exponential Factor
1/T
Slide 12
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Copyright© 2013 Eli Lilly and Company
 Ea
R
Double Regression Analysis
• Step 1. Estimation of the k
– Fit “Zero-order” regression of the concentration of an
analytical property vs. time, at each Temperature condition
• Step 2. Estimation of the Activation Energy
– Fit Arrhenius Regression, using fitted k(T) values [i.e.,
slopes] from regression in Step 1 as Ys:
Slope 
ln (k)
1/T
Slide 13
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Copyright© 2013 Eli Lilly and Company
 Ea
R
Double Regression Analysis
• High variability relative to degradation may lead to negative rate
constant estimates that become truncated at the logarithm scale
(e.g. increasing monomer  ln(-x)=NA)
• Insufficient resolution (high degree of rounding) that results in the
same value at each time-point can produce zero rate constant
estimates (k=0) that become truncated (ln(0)  -inf)
• Non-constant variance with the logarithmic form of Arrhenius
Slide 14
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Copyright© 2013 Eli Lilly and Company
Non-Linear Model Description
Therapeutic proteins are complex molecules that can degrade
(aggregate) via a variety of different physical/chemical mechanisms.
For simplicity, consider only two broad categories:
time
reactive
non-reactive
Only the ‘reactive’
monomer aggregates
Use first-order Arrhenius kinetics to describe the system
Parameters:
Mtotal – total monomer concentration
t – time
MNR – non-reactive monomer concentration
MR,0 – reactive monomer concentration at t = 0
kR – first-order rate constant
kR,0 – Arrhenius pre-exponential term
Ea – apparent activation energy
kR,0’ = ln( kR,0 ) – for numerical convergence
Slide 15
Mtotal t   M NR  M R,0 expkRt

kR  kR,0 exp Ea RT   exp kR,0  Ea RT

A good compromise between firstprinciples rigor and practical limitations
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Non-Linear Model Fitting
Mtotal
MNR + MR,0
MNR
time
Model parameter is a function of…
Parameter
Analytical
Property
Formulationa
Temperature
MNR
yes
yes
no
MR,0
yes
no
no
kR
yes
yes
yes
kR,0, kR,0’
yes
yes
no
Ea
yes
no
no
Formulation = unique set of pH, ionic strength, excipients; replicates of a given
formulation (different “runs”) were fit independently.
a
Parameters:
Mtotal – total monomer concentration
t – time
MNR – non-reactive monomer concentration
MR,0 – reactive monomer concentration at t = 0
kR – first-order rate constant
kR,0 – Arrhenius pre-exponential term
Ea – apparent activation energy
kR,0’ = ln( kR,0 ) – for numerical convergence
Slide 16
The nonlinear regression
platform in JMP 8.0.2 was used
to estimate unknown parameters
Company Confidential
Copyright© 2013 Eli Lilly and Company
Monomer
Double Regression vs. Non-Linear
99
TempC
98
5
97
25
30
96
40
95
94
93
92
91
0
1
2
3
Month
Nonlinear Model
Double Regression
1
-0.5
-1
-1.5
-2
91
1/T
0
1
2
3
Month
Ea=15.486
Slide 17
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Copyright© 2013 Eli Lilly and Company
90
Month
3
0.0036
0.0035
92
92
0.0034
93
0.0033
-2.5
0.0032
94
94
2
95
96
1
96
98
0
Monomer
L n (K)
97
Monom er
100
0.5
98
0
99
Concluding Remarks
• Summary
– An approach for modeling the accelerated stability data for
biomolecules are presented
– The nonlinear model based on the interplay between of reactive
and non-reactive species shown to fit the data quite well when
there is sufficient degradation
• Future work
– Evaluate alternative loss functions for better model selection (i.e.
goodness-of-fit)
– Evaluate alternative nonlinear models
– Find potential patterns from existing biomolecules that may provide
clues on how to better design and analyze data for future studies
Slide 18
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Copyright© 2013 Eli Lilly and Company
Acknowledgments
• Adam Rauk, inVentiv Health
• Will Weiss
• Suntara Cahya
Slide 19
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Copyright© 2013 Eli Lilly and Company