2.3 Drug Metabolism

Drug metabolism (biotransformation) converts lipophilic drugs into more polar, water-soluble metabolites for excretion. The liver is the primary site of metabolism, with cytochrome P450 (CYP) enzymes playing a central role. Understanding metabolism is critical for predicting drug interactions, toxicity, and individual variation.

Historical Context

R.T. Williams (1947) classified drug metabolism into Phase I (functionalization) and Phase II (conjugation). Omura and Sato (1962) isolated cytochrome P450 from liver microsomes. The discovery that CYP450 exists as a superfamily of enzymes with genetic polymorphisms (Gonzalez, 1980s) revolutionized our understanding of interindividual variability in drug response.

Derivation 1: CYP450 Michaelis-Menten Kinetics

CYP450 enzymes catalyze drug oxidation following Michaelis-Menten kinetics, identical in form to enzyme kinetics.

Step 1: Enzyme-Substrate Binding

Drug (S) binds CYP enzyme (E) to form enzyme-substrate complex (ES), which yields product (P):

\( E + S \underset{k_{-1}}{\overset{k_1}{\rightleftharpoons}} ES \overset{k_{cat}}{\rightarrow} E + P \)

Step 2: Steady-State Assumption

At steady state, d[ES]/dt = 0. Solving:

\( k_1[E][S] = (k_{-1} + k_{cat})[ES] \)

Define K_m = (k_-1 + k_cat)/k_1 and V_max = k_cat * [E_T]:

\( v = \frac{V_{max}[S]}{K_m + [S]} \)

Step 3: Intrinsic Clearance

At low substrate concentrations ([S] is much less than K_m), the rate is approximately first-order:

\( v \approx \frac{V_{max}}{K_m} \cdot [S] = CL_{int} \cdot [S] \)

The intrinsic clearance CL_int = V_max/K_m represents the inherent ability of the liver to metabolize drug in the absence of flow limitations.

Derivation 2: Well-Stirred Model of Hepatic Clearance

The well-stirred model relates hepatic clearance to liver blood flow, protein binding, and intrinsic clearance.

Step 1: Mass Balance Across the Liver

At steady state, the rate of drug entering the liver equals the rate leaving plus the rate of metabolism:

\( Q_H \cdot C_{in} = Q_H \cdot C_{out} + CL_{int} \cdot f_u \cdot C_{out} \)

where Q_H = hepatic blood flow (approximately 1.5 L/min), f_u = fraction unbound in blood, and C_out is assumed equal to the intrahepatic concentration (well-stirred assumption).

Step 2: Derive Hepatic Extraction Ratio

The extraction ratio E_H = (C_in - C_out)/C_in. From the mass balance:

\( C_{out} = \frac{Q_H \cdot C_{in}}{Q_H + f_u \cdot CL_{int}} \)

\( E_H = \frac{f_u \cdot CL_{int}}{Q_H + f_u \cdot CL_{int}} \)

Well-Stirred Model

\( CL_H = Q_H \cdot E_H = \frac{Q_H \cdot f_u \cdot CL_{int}}{Q_H + f_u \cdot CL_{int}} \)

Step 3: Limiting Cases

High Extraction (E_H > 0.7)

f_u * CL_int is much greater than Q_H:

CL_H approaches Q_H (flow-limited)

Lidocaine, propranolol, morphine

Low Extraction (E_H < 0.3)

Q_H is much greater than f_u * CL_int:

CL_H approaches f_u * CL_int (capacity-limited)

Warfarin, diazepam, phenytoin

Derivation 3: Enzyme Inhibition Kinetics

Drug interactions frequently involve CYP450 inhibition. Three types of reversible inhibition alter Michaelis-Menten parameters differently.

Competitive Inhibition

Inhibitor (I) competes with substrate for the active site. The apparent K_m increases while V_max is unchanged:

\( v = \frac{V_{max}[S]}{K_m\left(1 + \frac{[I]}{K_i}\right) + [S]} \)

Examples: ketoconazole (CYP3A4), fluoxetine (CYP2D6)

Noncompetitive Inhibition

Inhibitor binds a site other than the active site. V_max decreases while K_m is unchanged:

\( v = \frac{\frac{V_{max}}{1 + [I]/K_i} \cdot [S]}{K_m + [S]} \)

Uncompetitive Inhibition

Inhibitor binds only to ES complex. Both K_m and V_max decrease proportionally:

\( v = \frac{\frac{V_{max}}{1 + [I]/K_i} \cdot [S]}{\frac{K_m}{1 + [I]/K_i} + [S]} \)

Fold-Change in AUC (Clinical Prediction)

For a competitive inhibitor, the expected fold-increase in substrate AUC is:

\( \frac{AUC_{inhibited}}{AUC_{control}} = 1 + \frac{[I]}{K_i} \)

This is the basis of FDA guidance for predicting clinical DDIs from in vitro K_i data.

Derivation 4: Enzyme Induction Kinetics

Enzyme inducers increase CYP450 expression by activating nuclear receptors (PXR, CAR, AhR), leading to increased transcription of CYP genes.

Step 1: Enzyme Turnover Model

Enzyme levels are governed by synthesis (k_synth) and degradation (k_deg):

\( \frac{d[E]}{dt} = k_{synth} - k_{deg}[E] \)

At baseline steady state: [E]_0 = k_synth / k_deg

Step 2: Effect of Inducer

An inducer increases k_synth by a factor alpha (where alpha > 1):

\( \frac{d[E]}{dt} = \alpha \cdot k_{synth} - k_{deg}[E] \)

New steady state:

\( [E]_{induced} = \frac{\alpha \cdot k_{synth}}{k_{deg}} = \alpha \cdot [E]_0 \)

Step 3: Time Course

The approach to the new steady state follows:

\( [E](t) = [E]_{induced} - ([E]_{induced} - [E]_0) \cdot e^{-k_{deg} t} \)

The time to reach the new steady state depends on k_deg (enzyme half-life): t_1/2,enzyme = 0.693/k_deg. CYP3A4 has t_1/2 approximately 36 h, so full induction takes approximately 1 week. This is why induction is delayed (unlike inhibition, which is immediate).

Derivation 5: Phase I & Phase II Clearance

Total hepatic intrinsic clearance is the sum of all metabolic pathways:

\( CL_{int,total} = \sum_{i} \frac{V_{max,i}}{K_{m,i}} \)

where each i represents a different metabolic pathway (CYP3A4 oxidation, UGT glucuronidation, etc.).

Phase I Reactions

Oxidation (CYP450): Most common. CYP3A4 metabolizes approximately 50% of drugs, CYP2D6 approximately 25%, CYP2C9 approximately 15%.

Reduction: Ketone to alcohol, nitro to amine. Less common.

Hydrolysis: Esterases cleave ester bonds. Important for prodrugs (enalapril to enalaprilat).

Phase II Reactions

Glucuronidation (UGT): Most common conjugation. Morphine to M3G and M6G.

Sulfation (SULT): Limited capacity, saturates at high doses.

GSH conjugation: Detoxifies reactive metabolites (NAPQI from acetaminophen).

Acetylation (NAT): Isoniazid. Slow vs fast acetylator polymorphism.

Drug Metabolism Pathway

Python Simulation: Drug Metabolism

Drug Metabolism — CYP450 Kinetics, Well-Stirred Model, Inhibition & Induction

Python

script.py84 lines

import numpy as np

# ── Panel 1: Michaelis-Menten Enzyme Kinetics ──
S = np.linspace(0, 50, 200)
Vmax = 100  # nmol/min/mg protein
Km = 5      # uM
v = Vmax * S / (Km + S)

print("CHART1_TITLE: CYP450 Michaelis-Menten Kinetics")
print("CHART1_XLABEL: [Substrate] (uM)")
print("CHART1_YLABEL: Velocity (nmol/min/mg)")
for i in range(0, len(S), 5):
    print(f"S={S[i]:.2f} v={v[i]:.2f}")

# ── Panel 2: Well-Stirred Model — CL_H vs CL_int ──
QH = 1.5  # L/min (hepatic blood flow)
fu = 0.1  # fraction unbound
CLint_range = np.logspace(-2, 3, 200)
CLH = QH * fu * CLint_range / (QH + fu * CLint_range)
EH = fu * CLint_range / (QH + fu * CLint_range)

print("\nCHART2_TITLE: Well-Stirred Model: CL_H vs CL_int (f_u={:.2f})".format(fu))
print("CHART2_XLABEL: CL_int (L/min)")
print("CHART2_YLABEL: CL_H (L/min)")
for i in range(0, len(CLint_range), 5):
    print(f"CLint={CLint_range[i]:.4f} CLH={CLH[i]:.4f} EH={EH[i]:.4f}")

# ── Panel 3: Effect of fu on hepatic clearance ──
print("\nCHART3_TITLE: Effect of Protein Binding on CL_H")
print("CHART3_XLABEL: CL_int (L/min)")
print("CHART3_YLABEL: CL_H (L/min)")
fu_values = [0.01, 0.05, 0.1, 0.5, 1.0]
for i in range(0, len(CLint_range), 5):
    vals = []
    for f in fu_values:
        clh = QH * f * CLint_range[i] / (QH + f * CLint_range[i])
        vals.append(f"fu_{f:.2f}={clh:.4f}")
    print(f"CLint={CLint_range[i]:.4f} " + " ".join(vals))

# ── Panel 4: Competitive Inhibition ──
S2 = np.linspace(0, 50, 200)
Ki = 2.0  # uM
inhibitor_concs = [0, 2, 5, 10, 20]
print("\nCHART4_TITLE: Competitive CYP Inhibition (Ki = {:.0f} uM)".format(Ki))
print("CHART4_XLABEL: [Substrate] (uM)")
print("CHART4_YLABEL: Velocity (nmol/min/mg)")
for i in range(0, len(S2), 5):
    vals = []
    for Ic in inhibitor_concs:
        apparent_Km = Km * (1 + Ic / Ki)
        vi = Vmax * S2[i] / (apparent_Km + S2[i])
        label = f"I_{Ic}" if Ic > 0 else "control"
        vals.append(f"{label}={vi:.2f}")
    print(f"S={S2[i]:.2f} " + " ".join(vals))

# ── Panel 5: Enzyme Induction Time Course ──
t_days = np.linspace(0, 14, 200)
kdeg_values = [
    ("CYP3A4", 0.693 / 1.5),   # t1/2 = 36h = 1.5 days
    ("CYP1A2", 0.693 / 1.7),
    ("CYP2D6", 0.693 / 2.5),
]
alpha_induction = 3.0  # 3-fold induction

print("\nCHART5_TITLE: Enzyme Induction Time Course (3-fold)")
print("CHART5_XLABEL: Time (days)")
print("CHART5_YLABEL: Fold Enzyme Level")
for i in range(0, len(t_days), 5):
    vals = []
    for name, kdeg in kdeg_values:
        E_ratio = alpha_induction - (alpha_induction - 1.0) * np.exp(-kdeg * t_days[i])
        vals.append(f"{name}={E_ratio:.3f}")
    print(f"t={t_days[i]:.2f} " + " ".join(vals))

# ── Panel 6: AUC Fold-Change with Inhibitor ──
print("\nCHART6_TITLE: Predicted AUC Fold-Change vs Inhibitor Concentration")
print("CHART6_XLABEL: [Inhibitor] / Ki")
print("CHART6_YLABEL: AUC Fold-Change")
I_ratio = np.linspace(0, 20, 100)
AUC_fold = 1 + I_ratio
for i in range(0, len(I_ratio), 3):
    print(f"I_Ki={I_ratio[i]:.2f} AUC_fold={AUC_fold[i]:.2f}")

print("\nSimulation complete: 6 panels generated")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Major CYP450 Enzymes & Clinical Interactions

Enzyme	% Drugs	Key Substrates	Inhibitors	Inducers
CYP3A4	~50%	Statins, cyclosporine, midazolam	Ketoconazole, ritonavir, grapefruit	Rifampin, carbamazepine
CYP2D6	~25%	Codeine, tamoxifen, metoprolol	Fluoxetine, paroxetine, quinidine	Not significantly inducible
CYP2C9	~15%	Warfarin, phenytoin, NSAIDs	Fluconazole, amiodarone	Rifampin
CYP2C19	~10%	Clopidogrel, omeprazole, diazepam	Omeprazole, fluvoxamine	Rifampin
CYP1A2	~5%	Theophylline, caffeine, clozapine	Ciprofloxacin, fluvoxamine	Smoking, charbroiled food

Clinical Applications

Acetaminophen Toxicity

At therapeutic doses, acetaminophen is conjugated (Phase II). At overdose, Phase II pathways saturate (zero-order kinetics), shifting metabolism to CYP2E1, producing hepatotoxic NAPQI. GSH depletion leads to liver necrosis. N-acetylcysteine replenishes GSH.

Ritonavir Boosting

Ritonavir potently inhibits CYP3A4 (K_i approximately 20 nM). Co-administered with HIV protease inhibitors, it increases their AUC 10-100 fold by blocking hepatic metabolism. This pharmacokinetic "boosting" allows lower doses and less frequent administration.

CYP2D6 Polymorphism

5-10% of Caucasians are poor metabolizers (PM) of CYP2D6. Codeine (prodrug) requires CYP2D6 to form morphine, so PMs get no analgesia. Ultra-rapid metabolizers may produce toxic morphine levels, especially dangerous in children.

Smoking & Clozapine

Polycyclic aromatic hydrocarbons in cigarette smoke induce CYP1A2, increasing clozapine clearance. When patients quit smoking, clozapine levels can double within days, risking seizures and sedation. Dose reduction is mandatory.

Key Takeaways

1.
CYP450 enzymes follow Michaelis-Menten kinetics: v = V_max[S]/(K_m + [S]). Intrinsic clearance CL_int = V_max/K_m.
2.
The well-stirred model: CL_H = Q_H * f_u * CL_int / (Q_H + f_u * CL_int). High extraction drugs are flow-limited; low extraction drugs are capacity-limited.
3.
Competitive inhibition increases apparent K_m; AUC fold-change = 1 + [I]/K_i for clinical DDI prediction.
4.
Enzyme induction increases V_max (more enzyme protein); time course depends on enzyme degradation half-life (days to weeks).
5.
Phase I (CYP450 oxidation) introduces functional groups; Phase II (conjugation) adds polar moieties for renal/biliary excretion.

← 2.2 Distribution 2.4 Excretion →

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