---
id: wiki-2026-0508-enzyme-inhibition-kinetics
title: Enzyme Inhibition Kinetics
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Inhibitor Kinetics, Michaelis-Menten Inhibition]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [biochemistry, kinetics, enzymes, pharmacology]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: python
  framework: scipy
---

# Enzyme Inhibition Kinetics

## 매 한 줄
> **"매 inhibitor 의 binding mode 가 Vmax/Km 의 어떻게 shift 의 결정"**. 매 1913 Michaelis-Menten + 1934 Lineweaver-Burk extension. 매 2026 의 cryo-EM + MD simulation + AlphaFold-Multimer 가 mechanism elucidation 의 정밀.

## 매 핵심

### 매 4 inhibitor types
- **Competitive**: 매 active site binding — Km ↑, Vmax 불변. 매 substrate 증가 시 reversible.
- **Uncompetitive**: 매 ES complex binding — Km ↓, Vmax ↓ (same fold). 매 high [S] 의 deeper inhibition.
- **Non-competitive (mixed)**: 매 enzyme + ES 모두 binding — Vmax ↓, Km 의 shift (α, α').
- **Irreversible (covalent)**: 매 covalent bond (suicide inhibitor) — 매 time-dependent IC50.

### 매 핵심 equation
- **Michaelis-Menten**: v = Vmax·[S] / (Km + [S]).
- **Competitive**: v = Vmax·[S] / (αKm + [S]), α = 1 + [I]/Ki.
- **Ki** (inhibition constant): 매 lower Ki = stronger binding.
- **IC50**: 매 50% inhibition concentration — 매 [S]-dependent.
- **Cheng-Prusoff**: Ki = IC50 / (1 + [S]/Km) for competitive.

### 매 응용
1. Statins (HMG-CoA reductase competitive).
2. Methotrexate (DHFR competitive).
3. Aspirin (COX irreversible acetylation).
4. Drug-drug interaction (CYP450 inhibition).

## 💻 패턴

### Michaelis-Menten fitting
```python
import numpy as np
from scipy.optimize import curve_fit

def mm(S, Vmax, Km):
    return Vmax * S / (Km + S)

S = np.array([0.1, 0.3, 1.0, 3.0, 10.0, 30.0])
v = np.array([0.91, 2.31, 5.00, 7.50, 9.09, 9.68])
(Vmax, Km), _ = curve_fit(mm, S, v, p0=[10, 1])
print(f"Vmax={Vmax:.2f}, Km={Km:.2f}")
```

### Competitive inhibition fit (global fit over [I])
```python
def competitive(S_I, Vmax, Km, Ki):
    S, I = S_I
    alpha = 1 + I / Ki
    return Vmax * S / (alpha * Km + S)

S_grid, I_grid = np.meshgrid([0.1, 1, 10], [0, 0.5, 2.0])
xdata = np.vstack([S_grid.ravel(), I_grid.ravel()])
# ydata = experimental velocities at each (S, I)
(Vmax, Km, Ki), _ = curve_fit(competitive, xdata, ydata, p0=[10, 1, 1])
```

### IC50 fit (Hill equation)
```python
def hill(I, IC50, n, top=1.0, bottom=0.0):
    return bottom + (top - bottom) / (1 + (I / IC50) ** n)

(IC50, n), _ = curve_fit(lambda I, IC50, n: hill(I, IC50, n),
                         I_data, response_data, p0=[1.0, 1.0])
```

### Cheng-Prusoff conversion
```python
def cheng_prusoff_ki(IC50: float, S: float, Km: float, mode: str = "competitive") -> float:
    if mode == "competitive":
        return IC50 / (1 + S / Km)
    if mode == "uncompetitive":
        return IC50 / (1 + Km / S)
    if mode == "non-competitive":
        return IC50  # mixed: independent of [S] in pure non-competitive
    raise ValueError(mode)
```

### Time-dependent (irreversible) kinetics
```python
def kobs_vs_inhibitor(t: np.ndarray, kinact: float, KI: float, I: float) -> np.ndarray:
    """Fractional active enzyme over time."""
    kobs = kinact * I / (KI + I)
    return np.exp(-kobs * t)
```

### Lineweaver-Burk diagnostic
```python
import matplotlib.pyplot as plt
inv_S = 1 / S
inv_v = 1 / v
plt.plot(inv_S, inv_v, "o")
# Slope = Km/Vmax, y-intercept = 1/Vmax.
# Competitive: lines intersect at y-axis. Non-competitive: at x-axis.
```

## 매 결정 기준
| 상황 | Diagnostic |
|---|---|
| Km↑, Vmax 동일 | competitive |
| Km↓, Vmax↓ (same factor) | uncompetitive |
| Vmax↓, Km variable | mixed/non-competitive |
| time-dependent kobs | irreversible/slow-binding |
| High [S] 의 inhibition deepening | uncompetitive |

**기본값**: 매 global non-linear fit over (S, I) grid > Lineweaver-Burk linearization (매 error 의 distort).

## 🔗 Graph

## 🤖 LLM 활용
**언제**: 매 mechanism classification 의 plot interpretation, 매 fitting code 의 생성, 매 literature Ki 의 aggregation.
**언제 X**: 매 raw fluorescence/absorbance 의 직접 fit — 매 background subtraction, inner-filter correction 의 manual review 필요.

## ❌ 안티패턴
- **Lineweaver-Burk 의 fitting**: 매 error 의 1/v transformation 시 distort — 매 non-linear fit 사용.
- **IC50 의 Ki 의 동일시**: 매 [S]-dependent — 매 Cheng-Prusoff 변환 필수.
- **Single [I] 의 mechanism 결정**: 매 ambiguous — 매 multiple [I] 의 (S, v) curve 비교.
- **Ignoring substrate depletion**: 매 initial-rate assumption violation.

## 🧪 검증 / 중복
- Verified (Cornish-Bowden "Fundamentals of Enzyme Kinetics" 4th ed, Copeland "Evaluation of Enzyme Inhibitors" 2nd ed).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — 4 inhibitor types, scipy fitting, Cheng-Prusoff 추가 |
