Michaelis-Menten Enzyme Kinetics

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(654)

# Enzyme kinetics
substrate = np.linspace(0.1, 50, 55)
vmax = 100
km = 8
velocity = (vmax * substrate) / (km + substrate) + np.random.normal(0, 3, 55)

# Theoretical curve
s_smooth = np.linspace(0.1, 50, 200)
v_smooth = (vmax * s_smooth) / (km + s_smooth)

fig, ax = plt.subplots(figsize=(10, 7), facecolor='#0a0a0f')
ax.set_facecolor('#0a0a0f')

# Asymptote and Km markers
ax.axhline(y=vmax, color='#F5B027', linestyle='--', linewidth=1.5, alpha=0.5)
ax.axhline(y=vmax/2, color='#666666', linestyle=':', linewidth=1, alpha=0.5)
ax.axvline(x=km, color='#666666', linestyle=':', linewidth=1, alpha=0.5)

# Confidence band
ax.fill_between(s_smooth, v_smooth - 5, v_smooth + 5, color='#276CF5', alpha=0.12, linewidth=0)

ax.plot(s_smooth, v_smooth, color='#276CF5', linewidth=2.5, zorder=3)
ax.scatter(substrate, velocity, c='#6CF527', s=60, alpha=0.85, edgecolors='white', linewidths=0.4, zorder=4)

# Annotations
ax.text(48, vmax + 3, f'Vmax = {vmax}', fontsize=10, color='#F5B027', ha='right')
ax.text(km + 1, vmax/2 - 5, f'Km = {km} μM', fontsize=10, color='#888888')

for spine in ['top', 'right']:
    ax.spines[spine].set_visible(False)
for spine in ['bottom', 'left']:
    ax.spines[spine].set_color('#333333')

ax.set_xlabel('[Substrate] (μM)', fontsize=12, color='white', fontweight='500', labelpad=10)
ax.set_ylabel('Reaction Velocity (μmol/min)', fontsize=12, color='white', fontweight='500', labelpad=10)
ax.set_title('Enzyme Saturation Kinetics', fontsize=15, color='white', fontweight='bold', pad=20, loc='left')
ax.tick_params(colors='#666666', labelsize=10, length=0)
ax.set_xlim(0, 52)
ax.set_ylim(0, 115)

plt.tight_layout()
plt.show()