Drug Metabolism and Pharmacokinetics in Drug Discovery: a Primer for Bioanalytical Chemists, Part II

Drug Metabolism and Pharmacokinetics in Drug Discovery: A Primer For Bioanalytical Chemists, Part II

Chandrani Gunaratna, Ph.D. The rapidly evolving drug discovery process requires the analytical Bioanalytical Systems, Inc. chemist to design new analytical procedures that maximize the efficiency 2701 Kent Avenue West Lafayette, IN of lead compound selection. Pre-clinical pharmacokinetics studies are an 47906-1382 essential tool to weed out failures early on in the discovery process. Part I

Email: of this two-part series described the fundamentals of drug metabolism. [email protected] This article, Part II of the series introduces the analytical chemist to the pharmacokinetics aspects and prediction of pharmacokinetic parameters from in vitro drug metabolism data.

The first in this series of articles ex- design and establishing the dosage absorption needs to be considered. amined general aspects of drug me- interval. Pharmacodynamics (PD) of When the drug reaches the systemic tabolism (1). In Part II we will a drug describes the relationship be- circulation it can undergo both discuss the general pharmacokinet- tween the dose and the pharma- elimination and distribution. Elimi- ics principles and parameters and cological effect at the site of action. nation can be by metabolism or by how some of those parameters can be When a drug is administered, it excretion. Elimination processes are estimated from the in vitro drug me- distributes rapidly from its admini- irreversible and responsible for the tabolism data we discussed in Part I. stration site into the systemic blood removal of the drug from the body. Pharmacokinetics (PK) is the circulation. The drug is distributed Each of these processes is associated quantitative study of the time course between plasma and red blood cells with a rate constant. Rate constants of drug absorption, distribution, me- in the blood. Low molecular weight associated with distribution are tabolism and elimination (ADME). drugs can easily reach the extracel- much greater than the elimination This also includes the relationship of lular fluid of every organ in the body rate constants. Rates of these proc- ADME to the intensity and time rather quickly. Most lipophilic drugs esses govern the plasma drug con- course of therapeutic and toxicologi- cross cell membranes into the intra- centrations at any given time. A plot cal effects of drugs or chemicals. cellular fluid and distribute in vari- of plasma drug concentration versus Pharmacokinetic data is very useful ous tissues. Since distribution of a time is known as a pharmacokinetic in optimization of the dosage form drug is rapid and reversible, changes profile. An example is shown in F1. in the concentration of a drug in Elimination of a drug at equilib- F1 plasma reflect the changes in the rium generally follows first order ki-

Schematic representation ) concentration of the drug in other netics. The elimination rate

of pharmacokinetic / profiles for intravenous Oral tissues. decreases as the drug concentration

µg and oral doses. ( decreases and this relationship is on Pharmacokinetic Profile given by Eq.1, where K is the first IV order rate constant. Intravenously administered drugs

oncentrati

C distribute very rapidly throughout dCp/dt = -KCp (1) the body without an absorption step. Time (hour) For other routes of administration, Integration of Eq.1 gives

87 Current Separations 19:3 (2001) F2 100

) Area under the first moment drug. When drugs are highly bound

Estimation of AUC for a / 80 curve (AUMC) to plasma proteins, V is small and

first order PK profile. µg AUC ( AUMC is the total area under the results in high plasma concentra- n 60 AUC segment first moment curve. First moment tions of the drug. For basic drugs that 40 AUC curve is obtained by plotting concen- are preferentially bound to extravas- tration-time versus time. AUMC can cular sites, V is large and plasma 20

oncentratio

C be expressed as concentrations are low, making 0 0246810 quantitative examination of the drug Time (hour) more difficult. When drug binding to plasma proteins or tissues is negli- F3 Half-life gible, V approximates the true vol- Schematic illustration of Half-life (t½) of a drug is the time ume of distribution which is related organ clearance. C - A required to reduce the drug concen- to the amount of body water. Arterial drug Q, C Q, C concentration, CV - A v tration by half. This can be estimated venous drug Organ concentration. from Eq. 3 for a first-order process Bioavailability and can be expressed as Bioavailability (F) of a drug re- Metabolism or fers to the rate and extent of absorp- Excretion t½=0.693/K (6) tion. Essentially it is the fraction of a dose that reaches the systemic cir- Since half-life is a quantitative pa- culation. Bioavailability of an intra- rameter of the presence of the drug -Kt venously administered drug is Cp(t) = Cp(0)*e (2) in the body, it is generally used as a considered as unity because there is log Cp(t) = logCp(0)-Kt/2.303 (3) guide to determine the dosing inter- no absorption. For a drug adminis- val of a drug. The common practice tered by any other route, for example A semi-logarithmic plot of LogCp(t) is to administer a drug once every orally, bioavailability is given by Eq. vs. time will be linear. Extrapolation half-life. 8. to time, t=0 will give the initial plasma concentration Cp(0) and the Volume of Distribution slope will correspond to the elimina- The drug distribution is certainly tion rate constant. not even throughout the body at When drugs are administered repeti- From the PK profile several im- equilibrium. Some sites such as cen- tively, the average plasma concen- portant pharmacokinetic parameters tral nervous system or brain are tration depends on the amount such as area under the curve (AUC), weakly accessible to a certain drug, absorbed from each dose and is in- bioavailability, clearance, and ap- whereas some tissues may have dependent of the rate of absorption. parent volume of distribution can be strong affinity for the drug. Regard- However, the rate affects the time estimated. less of this uneven distribution, at course of plasma concentration at equilibrium the drug concentration steady state. Drugs that are used for Pharmacokinetic Parameters in plasma (Cp) is proportional to the acute conditions such as pain must amount of the drug administered be absorbed rapidly to reach the sys- Area under the curve (AUC) (dose) intravenously. When plasma temic circulation and be effective Estimation of AUC is required to concentration changes linearly with immediately. Extent of absorption is determine some pharmacokinetic the dose, the drug is known to have a more important factor for drugs parameters. AUC is the area under a linear pharmacokinetics. The rela- that are used for chronic conditions. plot of drug concentration vs. time tionship between the dose and the and given by Eq. 4 as follows. plasma concentration can be ex- Clearance pressed by the simple equation, Eq. Clearance (Cl) is one of the most 7. useful pharmacokinetic parameters. Clearance of a drug from the body The most common method of esti- V = IV dose/Cp(0) (7) depends on the intrinsic ability of the mating AUC is to use the trapezoidal organs such as the liver and kidneys rule where the concentration-time The proportionality constant V is to metabolize or excrete. Also, clear- curve is considered as a series of called the apparent volume of distri- ance is a function of the blood flow trapezoids and estimate the total area bution. It is independent of the drug rate (Q) to these organs. Clearance of all the trapezoids (F2). concentration and is a characteristic by definition represents the volume of the drug. The parameter V is not a of blood cleared through an organ in true physiological volume but is a a unit time and can be expressed as measure of protein binding of the www.currentseparations.com 88 F4 Drug In Drug Out To estimate clearance, the drug is time can be expressed by Eq. 2. All One-compartment model Cp given intravenously. Clearance can- the PK parameters can be obtained after an intravenous administration. not be estimated after an oral dose as described before using the appro-

80 since the total dose doesn’t reach the priate equations. systemic circulation.

60 For certain drugs that get meta- Extravascular Administration bolized completely, renal clearance Administration of a drug by all 40 is negligible. In this case systemic routes other than the IV route will clearance can be approximated to involve an absorption step. The 20 hepatic clearance (ClH) by liver. He- change in plasma drug concentration

Concentration (µg/ml) patic clearance is given by: will now be a function of both the 0 0246810 absorption rate and elimination rate. Time (hour) ClH =QH * ERH (13) (F5) The relationship between F5 plasma concentration Cp and time is Drug In K Drug K Drug a where QH is the hepatic blood flow given by Eq. 14 Schematic representation in Gut in Body of one compartment Cp rate and ERH is the hepatic extrac- model with absorption tion ratio. Hepatic clearance can be step after oral 100 administration. estimated approximately from in vi- 80 tro metabolism kinetics data. This where F is the fraction of the admin- process of estimating in vivo PK pa- istered dose, D, that is absorbed after 60 rameters from in vivo data is dis- extravascular administration, Ka is 40 cussed in detail in a later section. the absorption rate constant and K is

Cp (mg/ml) the elimination rate constant. 20 The basic equations described so far to estimate PK parameters cannot The rate constants can be esti- 0 04812 be applied to all drugs. When a drug mated by fitting concentration-time Time (hour) absorbs slowly, a significant fraction data to Eq. 14 using a non-linear least could be eliminated before reaching squares regression program. Several Cl = Elimination rate/ CA (9) distribution equilibrium. Then the compartmental as well as non-com- data cannot be expressed by a simple partmental pharmacokinetic soft- where, CA is the input concentration exponential relationship. In these ware packages that fit the of the drug. Elimination rate is a situations complex mathematical concentration-time data to various function of the blood flow and the models are required to express the models are commercially available. difference between input (arterial) PK profiles. PK data analysis using For most drugs the absorption and output (venous) concentrations mathematical models is known as constant is considerably larger than of the drug. (F3) Elimination rate can compartmental pharmacokinetics. the elimination constant. When Ka be expressed as In compartmental analysis the body >> K, e-kat approaches zero and Eq. is represented as a system of com- 14 becomes, Elimination rate = Q (CA - CV) (10) partments. These compartments Therefore, Cl = Q (CA -CV)/CA (11) have no anatomical meaning. The rate of transfer between these com- The quantity, (CA -CV)/CA is de- partments and the rate of elimination fined as the extraction ratio (ER) of are assumed to be following first-or- the organ. The single organ clear- der kinetics. The simplest PK mod- ance can be extended to the total els are briefly explained below. This equation describes the elimina- body clearance. Total or systemic tion phase of the PK profile. A plot clearance is the sum of all individual One-Compartment Model of Log C versus time is linear and organ clearances that contribute to p elimination rate constant can be ob- the overall elimination of the drug. Intravenous administration tained from the slope. The only organ clearance that can be The one-compartment model is measured experimentally is the renal the simplest and it represents the Two-Compartment Model clearance, clearance through the kid- body as a single unit (F4). This model neys. Therefore, total clearance is is applicable to drugs that distribute Intravenous administration evaluated from the PK data as shown through the body rapidly. Following an intravenous injec- in Eq. 12. According to this model, after an tion, a drug will distribute rapidly IV administration the drug is elimi- into the peripheral tissues. During Cl = Dose/AUC (12) nated by first-order kinetics and the this distributive phase the drug con- plasma concentration at any given centration in tissues will decline

89 Current Separations 19:3 (2001) F6 K12 Also from these constants, PK pa- MRT is the mean residence time. Peripheral Schematic representation Central rameters AUC, Cl and Vss (volume AUC and AUMC respectively can be of a two-compartment K21 model after an of distribution at steady state) can be obtained from Eq. 4 and Eq. 5. The intravenous dose. estimated as shown. first order rate constant and half-life can be estimated from MRT as Kel 100 shown below. A a>b 10 K = 1/MRTiv (25)

)

L B / t½ = 0.693 MRTiv (26) 1 slope(ln) = b

(

p a C slope(ln) = Apparent volume of distribution at .1 steady state, Vss is one of the impor- .01 tant PK parameters and is given as 061218 Time (hour) The models described above are the F7 ) simplest pharmacokinetic models

ml AUC and AUMC are /

µg and are for single dose administra- Other PK parameters, volume of dis- obtained from the ( First-moment

n~time concentration versus time n tions. tribution, clearance and bioavailabil- curve and the The most common method of ity etc. can be estimated from AUC concentration-time versus time curve. Zero-moment (µg~hr/ml) maintaining therapeutic plasma con- and AUMC as same as for the com-

oncentratio centration of drugs is through the

Concentratio partmental treatment of data.

C 024 6 8 oral administration of multiple Non-compartmental analysis of Time (hour) doses. Many drugs like antibiotics the data allows the estimation of are given in multiple doses, although most of the basic kinetic parameters F8 CSS one important goal is to reduce that for characterizing the disposition of Drug accumulation after number to a minimum. Discussion of the drug. However, non-compart- multiple IV dosing. the complex pharmacokinetic mod- mental methods do not adequately

centration C max els applicable for these cases would treat non-linear cases. They do not

C be beyond the scope of this article. describe the time course of drug in (µg/mL) τ Cmin More advanced mathematical treat- the blood (different half-lives, rate ment of PK data can be found in constants, etc). Compartmental Plasma pharmacokinetic texts (2,3). methods partly depend on the ex- Time (hour) perimental design. They provide an Non-Compartmental Analysis insight into understanding the more rapidly than in the postdis- mechanism of drug kinetics and dy- tributive phase. A bi-exponential de- Non-compartmental methods can be namics. Both methods have their cline can be associated with a used to determine pharmacokinetic own merits. two-compartmental model as shown parameters without fitting the PK During multiple dosing the drug in F6. Plasma concentration in this data to any specific compartmental concentration in plasma will in- case is represented by the sum of the model, assuming the data follow lin- crease during the dosing interval (t) two exponential terms as in Eq. 17. ear pharmacokinetics. Non-com- and reach a constant level as the partmental methods are based on the number of doses increases. The -at -bt theory of statistical moments. AUC, Cp =Ae +Be (17) plasma drug concentration during a or the total area under the curve of a dosing interval in the steady state is The constants a and b are obtained drug concentration, versus time known as steady-state concentration from the slopes. The constants A and curve from time zero to infinity is (Css) as shown in F8. B are intercepts obtained by extrapo- called the zero moment. As men- Area under the curve and Css di- lating the linear portions to time t=0. tioned before, AUMC, or the first rectly affect the pharmacological The relationships of A, B, a and moment, is the area under the curve properties or side effects of a drug. b to the rate constants are shown of concentration-time (Cp*t) versus Since body clearance (Cl) and he- below. time curve from time zero to infinity patic bioavailability (FH) control (F7). AUC and Css, it is important to know The non-compartmental phar- Cl and FH values. Total body clear- macokinetic parameters are repre- ance is the sum of clearances from sented in the following equations. all organs that are connected through blood flow. The two major clearance terms are renal clearance and hepatic www.currentseparations.com 90 clearance (ClH). The only organ independent of other physiological of the liver and administration of clearance that can be determined di- factors such as the liver blood flow drugs that are cytochrome P450 en- rectly in humans is the renal clear- or drug binding in the blood. CLint, zyme inducers or inhibitors can ance. The hepatic clearance has to be is the proportionality constant be- therefore influence the systemic predicted from animal or in vitro tween rate of metabolism and the clearance. data. Scaling up of animal data to drug substrate concentration at the Once the CLint is obtained from predict human hepatic clearance has enzyme site (Cs) as shown in Eq. 28. Michaelis-Menten constants, CLint not been very successful because of can be scaled to in vivo clearance, the inherent species differences. The Rate of metabolism (V0)=CLint Cs (28) CLin vivo using scaling factors. The alternative is to use in vitro drug scaling factors depend on the in vitro metabolism data to predict the he- Rate of metabolism is generally de- system used. For liver microsomes patic clearance. fined by the Michaelis-Menten en- and hepatocytes, the scaling factors The process of obtaining in vivo zyme kinetics relationship, as in Eq. include microsomal protein content, pharmacokinetic data from in vitro 31 where Km is the Michaelis-Men- number of hepatocytes per gram of data is known as in vitro-in vivo ten constant and Vmax is the maxi- liver, liver weight and liver blood correlation. Hepatic microsomes mum rate of metabolism. Km is the flow. and hepatocytes are the main in vitro substrate concentration at half the The relationship between he- systems used for this purpose. maximum velocity (Vmax). patic clearance, hepatic blood flow and unbound fraction of the drug Enzyme Kinetics cannot be determined without know- ing the actual circulating drug con- The basis for the extrapolation of in centration and C . Since these cannot When the drug concentration is s vitro data to the in vivo case is the be quantitatively measured, a liver much smaller than K (K >>C )un- parameter intrinsic clearance m m s model is needed to estimate the in- der linear conditions CLint can be (CLint). Intrinsic clearance is solely trinsic in vivo clearance, CL . expressed as, in vivo a measure of enzyme activity and is From CLin vivo the hepatic clearance of the drug for a particular pathway CLint =V0 / Cs =Vmax/Km (30) F9 can be estimated. Essentially, the Vmax purpose of the liver model is to con- Dependence of reaction In this case CL is a constant and velocity on the substrate int vert the scaled kinetic data from liver concentration. independent of the drug concentra- concentrations to plasma/blood con- elocity tion. centrations. The extrapolation of in e V To calculate CL , enzyme activ- int vitro data to obtain in vivo data is ity should be measured at time points schematically outlined in F11. Enzym over the time period that V is line- 0 Several liver models have been K m [substrate] arly changing with concentration proposed (4). However, a discussion (F9). on liver models would be beyond the F10 Enzyme activity is measured by scope of this article. According to the Linweaver-Burk plot for measuring the increase in metabolite enzyme kinetics. ity most commonly used venous equili- and/or the decrease in parent drug.

eloc Km bration model, the hepatic clearance Slope = —— Michaelis-Menten equation (Eq.

1/V is given as Vmax 29) can be rearranged to give

-—1 Lineweaver-Burk equation as shown K m 1 in Eq. 31. — Vmax where fu is the fraction of unbound drug in the blood (5). 1/[substrate] To obtain useful in vivo clear- The parameters Km and Vmax are ob- ance values, the in vitro data must be F11 tained from a plot of 1/V vs. 1/Cs as F10 obtained under proper conditions. Schematic illustration of in Metabolite shown below in . Profiles For example, the drug concentra- vitro-in vivo correlation Scaling process. Factors In Vitro In Vitro In Vivo In Vitro-In Vivo Correlation tions used for in vitro incubations Incubation CLint CLint must be physiologically relevant. Liver Model Rate of Drug Loss Systemic clearance of a drug that is Enzyme kinetics data must be ob- Hepatic CL eliminatedbymetabolisminthe tained under linear conditions with liver is a function of the hepatic respect to the enzyme concentration In Vivo Body Clearance blood flow and the intrinsic clear- and incubation time. ance of the liver. Disease conditions

91 Current Separations 19:3 (2001) Using in vitro models to study available, and drug discovery proc- References human drug metabolism as a part of ess continues to evolve due to the the drug discovery and drug devel- technological advances in synthesis 1. C. Gunaratna, Current Separations, 19, (2000) 17-23. opment process is expanding. The and screening of hundreds of thou- 2. Pharmacokinetics, M. Gibaldi, D. prediction of in vivo hepatic or me- sands of new drug candidates, the Perrier, Eds. 2nd edition, Marcel tabolic clearance based on drug me- analytical chemist will be chal- Dekker, Inc., New York, (1982). tabolism data using human lenged to keep up with the acceler- 3. Pharmacokinetic and recombinant cytochrome P450 ated pace of drug discovery. Pharmacodynamic Data Analysis: Concepts and Applications, J. isozymes seems to be possible. The Familiarization with the pharmacok- Gabbrielsson, D. Weiner, Eds. usefulness of in vitro systems will, inetics and drug metabolism princi- Swedish Pharmaceutical Press, however, depend largely on the ples will help prepare the analytical Stockholm, Sweden, (1994). availability and quality of the human chemist to face this challenge. The 4. G. R. Wilkinson, Pharmacol. Rev. 39 (1987) 1-47. in vitro systems. Cell culture sys- goal will continue to be to determine 5. J. B. Houston, Biochemical tems with single human drug-meta- the least desirable compounds and Pharmacology 47 (1994) bolizing enzymes expressed are cast them aside as soon as possible 1469-1479. commercially available and already to reduce R&D expenditure, allow- in wide use. ing more funding to support the most As a massive amount of informa- satisfactory candidates through to tion on the human genome becomes the market.