November 2007 Metabolite Kinetics Theoretical Approach PHM324Y Guest Lecturer Dr. Jasmina Novakovic Apotex Inc, R&D

November 2007 Learning Objectives  Drug fate  Renal and hepatic elimination  Drug-metabolite relationships  Fundamentals of metabolite kinetics  Metabolite concentration versus time profile  Estimation of relevant rate constants

November 2007 Drug Fate  Elimination = clearance  How?  Unchanged or metabolized.  Where?  Excreta. Urine, bile, feces, perspiration…  Clearance renal, mainly unchanged drug  Clearance hepatic = metabolic clearance  Other clearances (e.g. bile)  Liver - the main site of biotransformation. More that one metabolite can be formed: CL h = CL m1 + CL m2 +…  CL total = CL h + CL r + CL other

November 2007 Drug-Metabolite Relationships Important Facts  Drug = precursor  Metabolite = successor  As long as precursor is in the body, the successor will be there  Half-life of a metabolite formed from the drug can not be shorter than parent drug’s half-life  Conc-time profile of a metabolite: One exponent more than conc-time profile of the parent drug  Metabolite is a chemically distinct entity and has its own volume of distribution and clearance

November 2007 Relationship Between Drug and Metabolite (A) i.v. Doses Given on Separate Occasions

November 2007 What Can We Learn from i.v. Data? Parameter D1D2MUnits Dose 100 μmoles Co μmoles/L Vd (Dose/Co) L K /h CL (Vd*K) L/h T1/2 (0.693/K) h AUC (Co/K) μmoles*h/L CL (Dose/AUC) L/h  The only way to determine Vd of metabolite.  Metabolite, when given individually, can have longer or shorter T1/2 than drug. What will be if the metabolite is formed in the body?

November 2007 Relationship Between Drug and Metabolite (B) Drug was given i.v., the metabolite is formed Analogy between oral absorption and metabolism Drug at absorption site ka Drug in the body Absorption K Elimination of Drug Drug in the body k fm Metabolism Metabolite in the body k me Elimination of Metabolite What would be Plasma Conc versus Time profile of metabolite? As long as the drug is in the body, the metabolite will be formed.

November 2007 A Drug V d Urine keke Metabolite V m k mf Bile k me IV Dose (A o ) dA/dt= -K A K = k e + k mf + k b A t = A o e -Kt /V d C t = C o e -Kt dM/dt = k mf A – k me M M t = k mf A o [ e -Kt – e- kmet ]/(k me - K) /V m C M(t) = k mf A o [ e -Kt – e- kmet ]/[V m (k me - K)] kbkb Drug: i.v. bolus, mono-exponential conc vs time profile Metabolite: Polar, no further metabolites

November 2007 (B) Drug Given i.v., Metabolite Formed in the Body  When K > Km, M terminal phase kinetics follows its own profile  When Km > K, M terminal phase kinetics follows the parent drug profile  The slowest step is rate-limiting  M T1/2 can’t be shorter than T1/2 of the parent drug

November 2007 C M = (e (-kmet) - e (-Kt) ) k mf Dose Drug i.v. V M (K-k me ) Metabolite Conc. versus Time Profile (B) Drug is given i.v., metabolite is formed in the body or K > k me (A) Metabolite is given i.v. C M = Dose Metab i.v. e -Km C M = (e (-kmet) - e (-Kt) ) k mf Dose Drug i.v V M ( k me - K) k me >K Note: Different Mol.Wt of parent drug and metabolite! Use MOLAR doses or correction to calculate C M : Dose Drug i.v. x (Mol.Wt.Met/Mol.Wt.Drug)

November 2007 C M = (e (-kmet) - e (-Kt) ) k mf Dose Drug i.v. V M (K-k me ) Metabolite Conc. versus Time Profile Drug is given i.v., the metabolite is formed in the body If K >> k me C M = (e (-kmet) - e (-Kt) ) k mf Dose Drug i.v V M ( k me - K) If k me >>K C M = e (-kmet) k mf Dose Drug i.v. V M (K-k me ) K>k me k me > K C M = e (-Kt) k mf Dose Drug i.v V M ( k me - K)

November 2007 The Impact of k fm on the Metabolite Profile C M and AUC of the metabolite are proportional to k fm

November 2007 How to Determine K, k me and k mf ? Knowledge on:  Oral absorption kinetics  Urinary data analysis Step 1: Terminal PhaseStep 2: Residual Analysis

November 2007 We have two exponents. Do we know which is K or k me ? Recall: The slowest step is rate limiting. Terminal slope is “K”. “Residual” slope is k me Terminal slope is k me. “Residual” slope is “K”.

November 2007 The Formation Rate Constant k fm and fraction of drug transformed into metabolite CLtot = CLr +CLmet CLmet = CLtot-CLr CLtot =Dose/AUC CLtot =Vd x K CLren = Vd x k e K = k e + k fm CLmet = Vd x k fm f met =CLmet/CLtot = k fm /K D M Urine ke kfm kme Note: Metabolic Clearance of Drug = Vd x k fm Clearance of Metabolite = Vm x Kmet

November 2007 Some drugs, e.g. Moxifloxacin, form more than one metabolite Moxifloxacin M1 M2 keke k mf1 k mf2 k nr Urine M2sec Some metabolites can be further biotransformed to produce secondary and tertiary metabolites. Metabolites can be excreted in urine, in bile, or… Bile k mf = k mf1 + k mf2 +…

November 2007 Mini Quiz Q1: Drug dose of 250 mg was given I.V. bolus. Mol.Wt. of the drug is 200 Da. The metabolite, conjugate, is formed in the body and its Mol.Wt. is 350 Da. (a) We would like to calculate Cm in the plasma in ng/mL. What will be the correction factor? b) We would like to calculate Cm in  M. What should we do?

November 2007 Answers (a) Drug M.Wt. = 200 Da Metabolite M.Wt =350 Da Correction= 350/200= 1.75 Dose 250 mg =  g, Vm = x L units  g/L=ng/mL (b) 200 mg = 1 mmol = 1000  mol 250 mg = 1250  mol Vm = x L units 

November 2007 Mini Quiz, Cont’d Q2: Drug t 1/2 is 4 h. M1 t 1/2 is 1.2 h, and M2 t 1/2 is 7h when given I.V. on a separate occasions. What will be t 1/2 of M1 and M2 when formed in the body from the parent drug?

November 2007 Mini Quiz, Cont’d Q3: “K” of the drug is /h. One metabolite is formed and k mf is /h. Another drug, the inducer of metabolism, was co-administered and k mf is /h. No change in “K” was observed. What fraction of the dose was metabolized before and following the co-administration of the inducer?