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Protein Bioanalytics / Pharmacokinetics
Protein Therapeutics
Pharmacokinetics – a practical application of calculus
April 6, 2009
Elena Ho
Bayer Aspirin In 1897, Felix Hoffman, a research chemist employed by the "Farbenfabrikin vorm. Freidr. Bayer and Co." synthesized acetylsalicylic acid. On February 1, 1899, Aspirin® was registered as a trademark. On March 6th of the same year, this drug was registered with the Imperial Patent Office in Berlin. Aspirin quickly become popular worldwide, and remains an important drug today.
(Interestingly, it was not until 1971 that Sir John Vane discovered the mechanism of action of aspirin, a feat that earned him the 1981 Nobel Prize for Medicine.)
Business operations :
Bayer HealthCare makes an important contribution to human and animal health with its innovative products and by researching new therapeutic approaches. The subgroup has four operating divisions: Bayer Schering Pharma* (prescription medicines), Consumer Care (over-the-counter medicines and nutritional supplements), Medical Care (blood glucose monitoring systems and contrast injection systems), Animal Health (veterinary medicines and grooming products)
Bayer CropScience is a world leader in the areas of crop protection, pest control, seeds and plant biotechnology. As a partner in the production of high-quality food, feed and fiber, the company offers comprehensive solutions for modern, sustainable agriculture and non-agricultural applications.
Bayer MaterialScience is one of the world’s leading manufacturers of polymers and high-quality plastics. Apart from its polycarbonates and polyurethanes, this company’s offering also includes innovative developments in the fields of coatings, adhesives, insulating materials and sealants. Principal customers are the automotive and construction industries, the electrical/electronics sector and manufacturers of sports and leisure articles, packaging and medical equipment.
Products
The Bayer Group markets some 5,000 products. Best-sellers include:
in the health care field: Yasmin®/YAZ®/Yasminelle®, Betaferon®/Betaseron®, Kogenate®, Adalat®, Avalox®/Avelox®
in the nutrition field: Confidor®/Gaucho®/Admire®/Merit®, Flint®/Stratego®/Sphere®
in the field of high-tech materials: Makrolon®, Baydur®, Bayflex® Footwear, Desmodur®/Desmophen®
Workforce
On December 31, 2007, the Bayer Group had 106,200 employees worldwide (2006: 106,000). North America accounted for 16,800 of these employees, while 18,900 were based in Asia-Pacific, 14,300 in Latin America/Africa/Middle East and 56,200 in Europe. In Germany we had 39,100 employees, who made up 36.8 percent of the Group workforce.
106,200 employees worldwide (as of December 31, 2007), including:
56,200 in Europe16,800 in North America18,900 in Asia-Pacific14,300 in Latin America/Africa/Middle East
Bayer is seeking exceptional college students for summer internships at the Berkeley site. Help us spread the word.
Visit website for details...
http://www.bayerjobfair.com/interns
Application deadline is March 15, 2009.
Volume of Distribution
Half-life
ClearanceAbsorption
Oral bio-availability
How much ? How often ?
Metabolic Stability
Renal Excretion
Biliary Excretion
CNS Penetration
Protein Binding
Tissue Binding
Permea-bility
EffluxAqueous Solubility
Dosing Regimen
Typical Study Tools
Kerns & Li 2003, DDT 8:316-323
Barriers between Dose and Target
Interesting facts about a human body
Absorbing surface area of skin: 1.73 m2
Absorbing surface area of the lung: 70 m2
Absorbing surface area of GI tract: ~200m2
(1/2 basketball court) Small intestine is ~2” around, 22’ long Total length of capillaries is ~ 37,000 miles
Compartment models
A compartment is an entity which can be described by a definite volume and a concentration (of drug)
V
Concentration Dose
Dose (mg) = C (ug/ml) x V (ml)
V = Dose/Concentration
One compartment model: the drug enters the body, distributes instantlybetween blood and other body fluid or tissues.
Model
1. One compartment
2. Two compartment
3. Three compartment
central tissue
Tissue 1 Tissue 2central
Drug in
Drug out
Drug in
Drug out
Drug in
Drug out
__________________________
____________________________
Hydrodynamic analogy
centralTissue 1Tissue 2
Drug in
Drug out
Drug in
Drug outDrug recycle
The human body is a multimillion compartmentmodel considering drug concentration in
different organelles, cells, or tissues
We have access to only two types of body fluid – blood and urine
We will begin with the simplest model
Then : dA/dt = - kel A where kel = ke + km
rearrange to : dA/A = - kel dt
Integrate: ∫A0 dA/A = - kel ∫ t0 dt
Gives: ln A | A0= - kel t | t0 or ln A – ln A0 = - kel . t – t0
This yields the familiar exponential or logarithmic expressions
A = A0 e – Kel t
C = C0 e – Kel t
log C = log C0 – kel . t /2.3
Kel = 2.3/t . log C/C0
Single dose, IV, one compartment : dose of drug introduced rapidly and completely andquickly distributes into its homogenous volume of distribution. Drug is then eliminated by metabolism and excretion.
log C
time
C0
- Kel/2.3
A t
A t
Biological half-life (T1/2)
Consider again the rearranged expression
dA/A = - kel dt
Integrate between limits A and A/2
∫ A dA/A = - kel ∫ t0 dt
Gives: ln A – ln (A/2) = kel t1/2
ln 2 = kel t1/2 = 0.693
Therefore: t1/2 = 0.693 / kel
A/2 t/2
Area Under the Curve (AUC)
The integral of drug blood level over time from zero to infinity and a measure of quantity of drug absorbed in the body
Area = A o ∞
Sum of all concentration from t0 to t∞
i) Linear trapezoidal method: AUC t1t2 = Area of a trapezoid t1t2
= (t2 – t1). (C2+ C1)/2
ii) Log trapezoidal method: AUC t1t2 = (t2 – t1). (C2+ C1)/ln(C2/C1)
iii) Lagrange method: cubic polynomial equationiv) Spline method: piecewise polynomials for curve-fitting
0
500
1000
1500
2000
0 5 10 15 20 25 30 35 40 45 50
time (hour)
Observed
Predicted
0
500
1000
1500
2000
0 5 10 15 20 25 30 35 40 45 50
time (hour)
Observed
Predicted
T1, T2, T3, T4, T5, T6 T7
Advantages: Easy to use. Reliable for slow declining or ascending curves
Disadvantages: error-prone for data points with a wide interval; over or underestimate the true AUC; log 0 is not defined; not good for multiexponential curve
Linear and/or Log trapezoidal method
In vivo Pharmacokinetics in Rodents In vivo Pharmacokinetics in Rodents
Disposition kinetics:
Time
Pla
sma
Co
nce
ntr
atio
n
Distribution
Elimination
AUC(inf)kel
• single iv administration• repeated blood sampling• plasma concentration-time profile
kel
Tln 2
1/2=kel
CLVdss=
Plasma Half-life: Plasma Clearance:
Volume of Distribution at steady-state:
AUCDose
CL =
The clearance of compounds is evaluated in relation to the liver blood flow which is60 and 90 mL/min/kg in rat and mouse, respectively.
The volume of distribution should exceed that of total body water, i.e. 0.6-0.7 L/kg which indicates that the compound distributes freely into tissues.
T1/2 = 0.693 x Vd/CL
Absorption
• size MW
• aqueous solubility Sw
• lipophilicity logP
• polarity PSA
• ionization pKa
• ...
Compound properties controlling absorption:
Stomach: DissolutionStability at pH 1
Intestines: DissolutionStability at pH 3-8PermeabilityMetabolic stability
GI Tract
Absorption
Deriving Models of the Gastrointestinal Tract
Gut WallPorta
l Vein
Liver
Stability Solubility
PermeabilityATP-dependent EffluxDrug Metabolism
Hepatocellular Uptake, Drug Metabolism andBiliary Excretion
Oral Absorption Oral Absorption limited by:limited by:
In Vitro Models:In Vitro Models:
Gut Lum
en
Gastric andIntestinalJuice
Phys.-Chem. Descr.Caco-2Intest. Microsomes
Liver MicrosomesHepatocytesS9 mix, Cytosol
Oral bioavailability: Barriers and In vitro ModelsOral bioavailability: Barriers and In vitro Models
FA%
F%
Fraction ofdose absorbed:
Oralbioavailability:
In vivo Pharmacokinetics in Rodents In vivo Pharmacokinetics in Rodents
Oral kinetics:
Time
Pla
sma
Co
nce
ntr
atio
n
Cmax
Tmax
Absorption
Distribution
Elimination
AUC(inf)kel
• single po administration• repeated blood sampling• plasma concentration-time profile
Max. plasma conc. andTime of max. pl. conc. Oral Bioavailability:
Tmax Cmax
iviv
popo
DAUC
DAUCF
/
/= x 100%
There is no possibility to extrapolate the bioavailability in rodents to that in man. The sources of its limitation are oftenmore important than the actual value as this information may allow to study the corresponding mechanism using human invitro systems and to extrapolate the expected bioavailability .
Example of a pharmacokinetic study: single dose IV in the rat
Study designAnimal : Sprague-Dawley male rat, approximately 10 weeks old weighing ~250 g each
(n=4)
Compound : BAY xxxxxx supplied by AABBCC. Dissolve 0.7 mg in 10 ul of DMSO, bring it up to 1 mL with PBS.
Dosing : each animal will receive a dose equivalent to 0.7 mg/kg.
Time points: pre dose, 5 min, 30 min, 1, 2, 4, 7, 24, 28, 31 hours post dose
Blood sample : collect 225 ul of blood in 25 ul of 5% Na Citrate at each time point. Centrifuge blood at 5000 g for 5 minutes. Separate the plasma and keep at -80ºC until analysis
animal # rat 1 rat 2 rat 3 rat 4animal wt (kg) 0.278 0.296 0.295 0.29
dose volume(ml) 0.28 0.30 0.30 0.29
time (hr)
predose <LLOQ <LLOQ <LLOQ <LLOQ
0.083 2259.1 1888.1 2044.2 2162.70.5 1045.4 977.5 1005.3 1095.31 754.5 639.0 678.9 838.2
2 519.2 444.9 513.4 415.54 271.2 238.6 273.3 254.17 251.7 196.5 177.2 209.8
24 30.8 30.7 35.6 36.628 25.5 20.2 21.5 23.031 18.8 18.0 16.4 16.8
LLOQ = 15.6 ng/ml Retain = 866 ug/ml
SUMMARY OF RESULTS: Plasma concentration in ng/ml:
MW: fu [%]: 2/3 rule
Animal No. rat 1 rat 2 rat 3 rat 4 Mgeo SDgeoLOG
SDgeoMari SDari CV
orig. dose [mg/kg] 0.7 0.7 0.7 0.7
norm. dose [mg/kg] 1 1 1 1
[#] [h]
time point time
1 0 2258 1960 2093 2150 2113 1.06 0.0256 2115 124 5.87
2 0.083 2259 1888 2044 2163 2084 1.08 0.0336 2089 160 7.66
3 0.5 1045 978 1005 1095 1030 1.05 0.0214 1031 51.2 4.96
4 1 754 639 679 838 724 1.13 0.0519 728 87.9 12.1
5 2 519 445 513 416 471 1.12 0.0475 473 51.2 10.8
6 4 271 239 273 254 259 1.07 0.0276 259 16.3 6.27
7 7 252 196 177 210 207 1.16 0.0641 209 31.6 15.1
8 24 30.8 30.7 35.6 36.6 33.3 1.10 0.0405 33.4 3.12 9.32
9 28 25.5 20.2 21.5 23.0 22.5 1.11 0.0434 22.5 2.28 10.1
10 31 18.8 18.0 16.4 16.8 17.5 1.06 0.0270 17.5 1.09 6.24
[µg/L]
concentrations
orig. dose orig. doseorig. dose
norm. dose
Rat plasma concentration was determined using ELISA immunoassay method:
plasma conc. of BAY 877030 (Prep.No.= WANG1010-1-1) after iv bolus administration of 0.7mg/kg to male Sprague Dawley Rat, (n=4 of 4)
10
100
1000
10000
0 5 10 15 20 25 30time [h]
co
nc
. [µ
g/L
]
rat 1rat 2
rat 3rat 4
Xxxxxx
Animal No. rat 1 rat 2 rat 3 rat 4 Mgeo Sdgeo Mari Sdari CV
Dose [mg/kg] 0.700 0.700 0.700 0.700 0.700 1.00 0.700 0.00 0.00
AUC [µg·h/L] 5603 4819 5047 5299 5184 1.07 5192 337 6.49
AUCnorm [kg·h/L] 8.00 6.88 7.21 7.57 7.41 1.07 7.42 0.481 6.49
%AUC(tlast-∞) [%] 3.01 3.31 3.19 3.19 3.17 1.04 3.17 0.122 3.84
CLplasma [L/h/kg] 0.125 0.145 0.139 0.132 0.135 1.07 0.135 0.00873 6.45
Vss [L/kg] 0.945 1.12 1.05 1.02 1.03 1.07 1.04 0.0736 7.11
MRT [h] 7.56 7.73 7.58 7.73 7.65 1.01 7.65 0.0916 1.20
t1/2 [h] 6.63 6.85 6.79 6.81 6.77 1.01 6.77 0.0974 1.44
t1/2,a [h] 0.588 0.592 0.583 0.681 0.610 1.08 0.611 0.0469 7.67
Com1: BAY 877030 = HKB11-R338A-HG3 (HTI AHIX-5041 was used as capture antibody in the assay)
This compound represents a 2-compartment model.
Elimination T1/2 = 6.8 hours
Total plasma clearance = 135 ml/h/kg
Vss = 1.03 L/kg
This profile suggests a slow clearance compound with a moderate eliminationhalf life. The volume of distribution at steady state is high, suggesting thecompound distribution is beyond the plasma volume compartment
Pharmacokinetic parameters:
Summary
Remark
body weight
CLVdss
• Direct ScalingDirect Scaling of in vitro rate of metabolism to the CL in vivoof in vitro rate of metabolism to the CL in vivo
• Allometric ScalingAllometric Scaling of human PK based on animal data in vivo of human PK based on animal data in vivo
in vitroCL
in vivoCLc
t
Predicting Human PK
• physiologically based• metabolic CL only• first-pass effect• oral bioavailability
• empirical• total CL and Vss• requires mech. to be scalable• t1/2
Our job is to contribute to the understandingof our drug’s behavior and
save lives one day
Research and development at Bayer HealthCare focus on identifying and developing new active substances
to treat diseases with a high unmet medical need.