Calculus in Real-World Biopharmaceutical Development

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?


PART I

Bleeding disorder, rFVIII and the Bayer Perfusion Process


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


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


The Bayer Berkeley Site


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


PART II

Biopharmaceuticals Overview and Drug Development


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


The San Francisco Bay Area

>800 Companies


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


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


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.


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


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!)


Logistic Modeling


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


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.


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 − + =


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

− =


PART IV

What does all of this mean to you?


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!


Thank You!

Questions?

Calculus in Real-World Biopharmaceutical Development

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