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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.

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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 Efflux Aqueous

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 1 Tissue 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 50time (hour)

Observed

Predicted

0

500

1000

1500

2000

0 5 10 15 20 25 30 35 40 45 50time (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

Plas

ma

Con

cent

ratio

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:

AUCDoseCL =

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 Lumen

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

Plas

ma

Con

cent

ratio

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

popoDAUC

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 0.29dose 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 SDgeo LOGSDgeo

Mari 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 5.872 0.083 2259 1888 2044 2163 2084 1.08 0.0336 2089 160 7.663 0.5 1045 978 1005 1095 1030 1.05 0.0214 1031 51.2 4.964 1 754 639 679 838 724 1.13 0.0519 728 87.9 12.15 2 519 445 513 416 471 1.12 0.0475 473 51.2 10.86 4 271 239 273 254 259 1.07 0.0276 259 16.3 6.277 7 252 196 177 210 207 1.16 0.0641 209 31.6 15.18 24 30.8 30.7 35.6 36.6 33.3 1.10 0.0405 33.4 3.12 9.329 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]

conc

. [µg

/L]

rat 1rat 2rat 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

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