 codex/past-exam-of-the-biological-physics-course-of-the-university-of-oxford/2015-dna-search-and-tweezers.py

"""Original conceptual tweezers diagram and exact dimensionless search scaling."""
from pathlib import Path
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from matplotlib.patches import Circle, Rectangle
fig, (ax, bx) = plt.subplots(1, 2, figsize=(12, 5), layout='constrained', facecolor='white')
ax.set(xlim=(-2, 2), ylim=(-.4, 6.4), aspect='equal', title='Magnetic tweezers: conceptual geometry')
ax.add_patch(Rectangle((-1.7, 5.5), 1.2, .5, color='#c05229'))
ax.add_patch(Rectangle((.5, 5.5), 1.2, .5, color='#176b87'))
ax.text(0, 6.2, 'Rotating magnets impose turns', ha='center', fontsize=10)
ax.add_patch(Circle((0, 4.5), .45, facecolor='#b9d9e5', edgecolor='black'))
ax.annotate('Magnetic bead', xy=(.4, 4.6), xytext=(.8, 4.8), fontsize=10)
ax.annotate('', xy=(0, 5.4), xytext=(0, 4.95), arrowprops={'arrowstyle': '->', 'lw': 1.5})
ax.text(-.3, 5.2, 'pull', ha='right', fontsize=10)
y = np.linspace(.3, 4.05, 500)
x = .13 * np.sin(8 * y)
ax.plot(x, y, color='#176b87', lw=2)
ax.plot(-x, y, color='#c05229', lw=1.5)
ax.add_patch(Circle((0, 2.1), .35, facecolor='#e6c877', edgecolor='black', zorder=5))
ax.text(.5, 2.15, 'RNAP: local\nDNA opening', va='center', fontsize=10)
ax.plot([-1.5, 1.5], [.2, .2], color='.3', lw=5)
ax.text(0, -.15, 'Torsionally fixed attachment', ha='center', fontsize=10)
ax.annotate('', xy=(-.9, 4.5), xytext=(-.9, .3), arrowprops={'arrowstyle': '<->'})
ax.text(-1.15, 2.7, 'Bead height', rotation=90, va='center', fontsize=10)
ax.axis('off')
u = np.logspace(-1, 1, 400)
bx.plot(u, .5 * u, '--', label='Sliding: u / 2')
bx.plot(u, .5 / u, '--', label='Bulk relocation: 1 / (2u)')
bx.plot(u, .5 * (u + 1 / u), color='#176b87', lw=2.3, label='Total')
bx.plot([1], [1], 'o', color='#c05229')
bx.axvline(1, color='.6', ls=':', lw=1)
bx.set(xscale='log', xlim=(.1, 10), ylim=(0, 5.5), xlabel=r'$u=\lambda/\lambda_*$', ylabel=r'$\tau/\tau_{\min}$', title='Balance of local scanning and relocation')
bx.legend(frameon=False)
fig.savefig(Path.cwd() / Path(__file__).with_suffix('.png').name, dpi=120, facecolor='white', metadata={'Software': 'matplotlib'})