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147 lines
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147 lines
5.0 KiB
Markdown
---
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id: wiki-2026-0508-enzyme-inhibition-kinetics
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title: Enzyme Inhibition Kinetics
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [Inhibitor Kinetics, Michaelis-Menten Inhibition]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.9
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verification_status: applied
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tags: [biochemistry, kinetics, enzymes, pharmacology]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: python
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framework: scipy
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---
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# Enzyme Inhibition Kinetics
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## 매 한 줄
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> **"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.
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## 매 핵심
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### 매 4 inhibitor types
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- **Competitive**: 매 active site binding — Km ↑, Vmax 불변. 매 substrate 증가 시 reversible.
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- **Uncompetitive**: 매 ES complex binding — Km ↓, Vmax ↓ (same fold). 매 high [S] 의 deeper inhibition.
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- **Non-competitive (mixed)**: 매 enzyme + ES 모두 binding — Vmax ↓, Km 의 shift (α, α').
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- **Irreversible (covalent)**: 매 covalent bond (suicide inhibitor) — 매 time-dependent IC50.
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### 매 핵심 equation
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- **Michaelis-Menten**: v = Vmax·[S] / (Km + [S]).
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- **Competitive**: v = Vmax·[S] / (αKm + [S]), α = 1 + [I]/Ki.
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- **Ki** (inhibition constant): 매 lower Ki = stronger binding.
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- **IC50**: 매 50% inhibition concentration — 매 [S]-dependent.
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- **Cheng-Prusoff**: Ki = IC50 / (1 + [S]/Km) for competitive.
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### 매 응용
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1. Statins (HMG-CoA reductase competitive).
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2. Methotrexate (DHFR competitive).
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3. Aspirin (COX irreversible acetylation).
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4. Drug-drug interaction (CYP450 inhibition).
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## 💻 패턴
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### Michaelis-Menten fitting
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```python
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import numpy as np
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from scipy.optimize import curve_fit
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def mm(S, Vmax, Km):
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return Vmax * S / (Km + S)
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S = np.array([0.1, 0.3, 1.0, 3.0, 10.0, 30.0])
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v = np.array([0.91, 2.31, 5.00, 7.50, 9.09, 9.68])
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(Vmax, Km), _ = curve_fit(mm, S, v, p0=[10, 1])
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print(f"Vmax={Vmax:.2f}, Km={Km:.2f}")
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```
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### Competitive inhibition fit (global fit over [I])
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```python
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def competitive(S_I, Vmax, Km, Ki):
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S, I = S_I
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alpha = 1 + I / Ki
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return Vmax * S / (alpha * Km + S)
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S_grid, I_grid = np.meshgrid([0.1, 1, 10], [0, 0.5, 2.0])
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xdata = np.vstack([S_grid.ravel(), I_grid.ravel()])
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# ydata = experimental velocities at each (S, I)
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(Vmax, Km, Ki), _ = curve_fit(competitive, xdata, ydata, p0=[10, 1, 1])
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```
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### IC50 fit (Hill equation)
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```python
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def hill(I, IC50, n, top=1.0, bottom=0.0):
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return bottom + (top - bottom) / (1 + (I / IC50) ** n)
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(IC50, n), _ = curve_fit(lambda I, IC50, n: hill(I, IC50, n),
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I_data, response_data, p0=[1.0, 1.0])
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```
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### Cheng-Prusoff conversion
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```python
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def cheng_prusoff_ki(IC50: float, S: float, Km: float, mode: str = "competitive") -> float:
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if mode == "competitive":
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return IC50 / (1 + S / Km)
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if mode == "uncompetitive":
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return IC50 / (1 + Km / S)
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if mode == "non-competitive":
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return IC50 # mixed: independent of [S] in pure non-competitive
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raise ValueError(mode)
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```
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### Time-dependent (irreversible) kinetics
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```python
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def kobs_vs_inhibitor(t: np.ndarray, kinact: float, KI: float, I: float) -> np.ndarray:
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"""Fractional active enzyme over time."""
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kobs = kinact * I / (KI + I)
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return np.exp(-kobs * t)
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```
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### Lineweaver-Burk diagnostic
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```python
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import matplotlib.pyplot as plt
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inv_S = 1 / S
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inv_v = 1 / v
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plt.plot(inv_S, inv_v, "o")
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# Slope = Km/Vmax, y-intercept = 1/Vmax.
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# Competitive: lines intersect at y-axis. Non-competitive: at x-axis.
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```
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## 매 결정 기준
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| 상황 | Diagnostic |
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|---|---|
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| Km↑, Vmax 동일 | competitive |
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| Km↓, Vmax↓ (same factor) | uncompetitive |
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| Vmax↓, Km variable | mixed/non-competitive |
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| time-dependent kobs | irreversible/slow-binding |
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| High [S] 의 inhibition deepening | uncompetitive |
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**기본값**: 매 global non-linear fit over (S, I) grid > Lineweaver-Burk linearization (매 error 의 distort).
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## 🔗 Graph
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## 🤖 LLM 활용
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**언제**: 매 mechanism classification 의 plot interpretation, 매 fitting code 의 생성, 매 literature Ki 의 aggregation.
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**언제 X**: 매 raw fluorescence/absorbance 의 직접 fit — 매 background subtraction, inner-filter correction 의 manual review 필요.
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## ❌ 안티패턴
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- **Lineweaver-Burk 의 fitting**: 매 error 의 1/v transformation 시 distort — 매 non-linear fit 사용.
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- **IC50 의 Ki 의 동일시**: 매 [S]-dependent — 매 Cheng-Prusoff 변환 필수.
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- **Single [I] 의 mechanism 결정**: 매 ambiguous — 매 multiple [I] 의 (S, v) curve 비교.
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- **Ignoring substrate depletion**: 매 initial-rate assumption violation.
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## 🧪 검증 / 중복
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- Verified (Cornish-Bowden "Fundamentals of Enzyme Kinetics" 4th ed, Copeland "Evaluation of Enzyme Inhibitors" 2nd ed).
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — 4 inhibitor types, scipy fitting, Cheng-Prusoff 추가 |
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