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Calculus in Real-World Biopharmaceutical
Development
Chetan T. Goudar, Ph.D., P.E.
Cell Culture Development, Global Biologics Development
Bayer HealthCare, 800 Dwight Way
Berkeley, CA 94710
April 15, 2010 Calculus Lecture 2
Presentation Overview
I. Bleeding disorder, rFVIII and the Bayer Perfusion
Process
II. Biopharmaceuticals overview and drug development
III. Calculus examples
IV. What does all of this mean to you?
April 15, 2010 Calculus Lecture 4
Hemophilia: A Disease that Destroyed an Empire
Tsar Nicolas Queen Alexandra
Rasputin
TsarevichAlexis
Queen Alexandria was the
carrier of the disease. Her
grandmother, queen Victoria of
England passed on the gene to
her
April 15, 2010 Calculus Lecture 5
Bleeding Disorder and Factor VIII
• Hemophilia A (FVIII deficiency) is a hereditary disorder
• Blood clotting is impaired
• Incidence rate is 1 in 5,000 – 10,000 live male births (300,000
people worldwide)
• Treatment of Hemophilia A
• First generation: from donor plasma
• Current: Recombinant FVIII made from mammalian cells
• Treatment is very expensive
• $200,000/year for each patient
April 15, 2010 Calculus Lecture 7
The Bayer Perfusion Process
• 2003 Industrial Bioprocess Award of the American Chemical Society
• The most prestigious award in the Biotechnology community
• Awarded to Bayer HealthCare in 2003 for the perfusion process used to manufacture r-FVIII
• "The entire team at Bayer is
extremely honored to receive this award. We work every day to
enhance the manufacturing process for our Kogenate® products, and this
recognition for our continuous perfusion technology is both an
honor and a strong motivator to continue our efforts in this
area"……Konstantin Konstantinov, VP of R&D, Bayer HealthCare
April 15, 2010 Calculus Lecture 9
Modern Biotechnology
• Recombinant DNA technology has given rise to modern
biotechnology
• Gave us the ability to modify cellular DNA to produce the
desired product
• South San Francisco is the “Birthplace of Biotechnology”
• Genentech, the first Biotech company was formed in 1976
• There has been an explosive growth worldwide since
• US continues to be the leader
• Germany, Denmark, Netherlands, Switzerland and Sweden are major
players
April 15, 2010 Calculus Lecture 11
Biopharmaceuticals Overview
• What is a biopharmaceutical?
• Therapeutic product made using recombinant DNA
• It has to treat a medical condition, e.g., cancer
• History of Biopharmaceuticals
• Genentech’s human growth harmone: 1979
• Insulin: 1982
• 1982 – 2000: 84 new drugs (4.5 drugs/year)
• 2001 – 2003: 60 new drugs (20 drugs/year)
• Financial Perspective
• 2003 Global Market: ~$30 billion
• 2007 Global Market: At least 2 times more than in 2003
• It will only keep increasing in the near future
April 15, 2010 Calculus Lecture 12
The Drug Development Process
• Takes ~10 years and $1 billion
• 10,000 initial targets � 1 successful product
• Typically, only large established companies can do this all
by themselves
• Smaller companies do a part of it and enter into collaboration
with larger companies
April 15, 2010 Calculus Lecture 13
PART III
Calculus Example 1
Modeling Data from Cell Culture Bioreactors*
*Goudar, C.T., Joeris, K., Konstantinov, K. and Piret, J.M. (2005) Logistic Equations Effectively Model Mammalian
Cell Batch and Fed-batch Kinetics by Logically Constraining the Fit. Biotechnology Progress, 21, 1109-1118.
April 15, 2010 Calculus Lecture 14
Mammalian Cell Bioreactor
• During protein production, the following things happen
• Cell growth
• Nutrient Consumption (Glucose, glutamine……)
• Protein (and waste material) production
Time (days)
0 2 4 6 8 10 12
Via
ble
Cel
l Den
sity
(1
06 cel
ls/m
L)
0
2
4
6
8
10
12
14
Time (days)
0 2 4 6 8 10 12
Glu
cose
(m
M)
0
20
40
60
80
April 15, 2010 Calculus Lecture 15
Mathematical Description of a Reactor
Description of a Batch System
Batch Systems are Transient
• Current Modeling Approaches
• Unstructured Kinetic Modeling
• Polynomial/Spline Approximations
• Functional Approximation
• Viable Cells
• Dead Cells
• Total Cells
• Glucose
• Glutamine
• Lactate
• Ammonia
• Product
( )Vd V
dXk X
dtµ= −
Dd V
dXk X
dt=
TV
dXX
dtµ=
G V
dGq X
dt= −
Gln
Gln
Gln
V
dq X
dtk
=−
−
Lac V
dLacq X
dt=
3
3
Gln
NH V
dNHq X
dtk
=
+
P V
dPq X
dt=
Cells NutrientsMetabolites
/Product
• Need accurate derivative (d/dt) estimation (not very easy!)
April 15, 2010 Calculus Lecture 17
Application of Logistic Modeling
Time (days)0 2 4 6 8 10 12
Via
ble
Cel
l Den
sity
(106
Cel
ls/m
L)
0
2
4
6
8
µµ µµ' (
1/d)
-0.4
-0.2
0.0
0.2
0.4
0.6
µµµµ'
Time (days)
0 2 4 6 8 10 12
Via
ble
Cel
l Den
sity
(106
Cel
ls/m
L)
0
2
4
6
8
10
µµ µµ' (
1/d)
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
µµµµ'
(1x)
(1.5x)
Time (days)0 2 4 6 8 10 12
Lact
ate
(mM
)
0
10
20
30
qLa
c (
pM/c
ell/d
)
0.0
0.2
0.4
0.6
0.8
1.0
Time (days)0 2 4 6 8 10 12
Glu
cose
(m
M)
0
20
40
60
80
qG
lc (
pM/c
ell/d
)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
(a) (b)qGlcqLac
Time (days)
0 2 4 6 8 10 12
Glu
tam
ine
(mM
)
0
2
4
6
8
10
12
14
16
qG
ln (
pM/c
ell/d
)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Time (days)
0 2 4 6 8 10 12
Am
mon
ia (
mM
)
0
5
10
15
20
25
qN
H4+
(pM
/cel
l/d)
0.0
0.1
0.2
0.3
0.4
0.5(c) qNH4+ (d)
qGln
Works well for cell density, nutrients
and metabolites
April 15, 2010 Calculus Lecture 18
PART III
Calculus Example 2
Explicit Solution of the Michaelis-Menten Equation*
*Goudar, C. T., Sonnad, J. R. and Duggleby, R. G. (1999) Parameter estimation using a direct solution of the
integrated Michaelis-Menten equation. Biochimica et Biophysica Acta, 1429, 377-383.
April 15, 2010 Calculus Lecture 19
The Michaelis-Menten Equation
• The most fundamental equation in enzyme kinetics
• Was proposed by Michaelis and Menten in 1913
• Did not have an explicit closed form solution until 1999
(86 years!)
m
m
V SdS
dt K S= −
+
00 lnm m
SS S K V t
S − + =
April 15, 2010 Calculus Lecture 20
Explicit Closed-form Solution
• Lambert W function based explicit solution first published in 1999
• Eliminates need for iterative calculations
• The kinetic parameters Vm and Km can now be determined very
easily
• Modeling of complex cellular systems is now possible
• Improved understanding of cell physiology
• Helps better engineer cells to enhance process robustness and protein
production
0 0exp mm
m m
S S V tS K W
K K
− =
April 15, 2010 Calculus Lecture 22
Why Mathematics Matters?
• Mathematics is the language of science
• The ability to quantify observations enhances our
understanding of the underlying process
• We can use this understanding to design better, faster, cheaper
products
• It will have an impact on job search and career
advancement
Pay attention in your calculus class!