In [ ]:
import os
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
from cycler import cycler
import seaborn as sns
%matplotlib inline
%config InlineBackend.figure_format='retina' # for hi-dpi displays
In [ ]:
from mpl_toolkits.mplot3d import Axes3D
from numpy import pi, cos, sin
In [ ]:
figure_size = (5, 4)
default_figure = lambda: plt.subplots(figsize=figure_size)
save_figures = True
def savefig(filename, **kwargs):
if not save_figures:
return
import os
dir_ = 'figures/'
kwargs_ = dict(dpi=300, bbox_inches='tight')
#frameon=True, facecolor='white', transparent=False)
kwargs_.update(kwargs)
plt.savefig(dir_ + filename, **kwargs_)
print('Saved: %s' % (dir_ + filename))
In [ ]:
sns.set_style('whitegrid')
In [ ]:
r = 1 # (nm) dsDNA radius
δ = 0.34 # (nm) dsDNA base-pair pitch
n = 10.5 # number of bases per turn
Δφ = 132.4 # (degree) minor-grove angle between the two strands backbones
This function computes the dye position according to the passed parameters:
In [ ]:
def dye_position(i, l=1.6, λ=0.5, ψ=0):
# global structural params: r, δ, n, Δφ
Δφr = Δφ*pi/180
φ = 2*pi/n # (radiants) rotation for base-pair
Dx = r * cos(φ*i) + λ*( r*cos(φ*i + Δφr) - r*cos(φ*i) ) + l*cos(ψ)*cos(φ*i + 0.5*Δφr)
Dy = r * sin(φ*i) + λ*( r*sin(φ*i + Δφr) - r*sin(φ*i) ) + l*cos(ψ)*sin(φ*i + 0.5*Δφr)
Dz = i*δ + l*sin(ψ)
return np.array([Dx, Dy, Dz])
Function to plot the dye position:
In [ ]:
def plot_dye(P, axes=None, **kws):
kws_ = dict(marker='o', ls='-')
kws_.update(kws)
if axes is None:
fig = plt.figure(figsize=(9, 9))
ax_xy = plt.subplot2grid((2,2), (1,0))
ax_xz = plt.subplot2grid((2,2), (0,0))
ax_yz = plt.subplot2grid((2,2), (0,1))
ax_3d = fig.add_subplot(224, projection='3d')
else:
ax_xy, ax_xz, ax_yz, ax_3d = axes
ax_xy.plot(P[0], P[1], **kws_)
ax_xz.plot(P[0], P[2], **kws_)
ax_yz.plot(P[1], P[2], **kws_)
for ax in (ax_xy, ax_xz):
ax.set_xlabel('x (nm)')
ax_xy.set_ylabel('y (nm)')
ax_xz.set_xlabel('x (nm)')
ax_xz.set_ylabel('z (nm)')
ax_yz.set_xlabel('y (nm)')
ax_yz.set_ylabel('z (nm)')
lim = max(1.5, np.abs(P[0]).max(), np.abs(P[1]).max())*1.05
ax_xy.set_xlim(-lim, lim)
ax_xy.set_ylim(-lim, lim)
ax_xz.set_xlim(-lim, lim)
ax_yz.set_xlim(-lim, lim)
ax_3d.plot(P[0], P[1], P[2], **kws_)
return (ax_xy, ax_xz, ax_yz, ax_3d)
FRET as a function of $R$ and $R_0$:
In [ ]:
def fret(R, R0):
return 1 / (1 + (R/R0)**6)
In [ ]:
λ = 0.5
ψ = 0
i = 7 # number of bases from reference "base 0"
l = 1.6 # (nm) distance between S and dye position D
In [ ]:
dye_position(7)
In [ ]:
D_params = dict(l=1, λ=1, ψ=0)
A_params = dict(l=1, λ=0, ψ=-pi/2)
In [ ]:
bp = np.arange(0, 1)
PD = dye_position(bp, **D_params)
PA = dye_position(bp, **A_params)
In [ ]:
bp1 = np.arange(0, 10.1, 0.02)
PD1 = dye_position(bp1, **D_params)
PA1 = dye_position(bp1, **A_params)
In [ ]:
axes = plot_dye(PD, marker='s')
plot_dye(PA, axes, color='r', marker='s');
plot_dye(PA1, axes, marker='', ls='-', color='r');
plot_dye(PD1, axes, marker='', ls='-', color='b');
In [ ]:
bp = np.arange(0, 40, 0.1)
In [ ]:
PD = dye_position(bp, l=1.6, λ=0.2, ψ=0)
PA = dye_position(0, l=1.6, λ=0.8, ψ=-pi/2)
R = np.linalg.norm(PD.T - PA, axis=1)
#R
In [ ]:
plt.plot(bp, R);
plt.xlabel('Base-pair')
plt.ylabel('Distance (nm)')
plt.ylim(0);
In [ ]:
R0 = 6.7 # nm
In [ ]:
plt.plot(bp, fret(R, R0));
In [ ]:
E_mspot = pd.read_csv(
'results/Multi-spot - dsDNA - Corrected E - all_samples all_ch.csv', index_col=0)
E_mspot.columns.name = 'Channel'
E_mspot
In [ ]:
data_file = 'results/usALEX-5samples-E-corrected-all-ph.csv'
data_alex = pd.read_csv(data_file).set_index('sample')
E_alex = data_alex.E_gauss_w
E_alex.index.name = 'Sample'
E_alex
In [ ]:
%config InlineBackend.figure_format='retina' # for hi-dpi displays
In [ ]:
fig, ax = plt.subplots()
E_alex.plot(ax=ax)
E_mspot.plot(marker='+', mew=1, ls='none', ax=ax)
In [ ]:
E_alexi = E_alex.rename(lambda x: int(x[:-1])).to_frame()
E_alexi.columns = ['μs-ALEX']
E_alexi
In [ ]:
E_mspoti = E_mspot.rename(lambda x: int(x[:-1]))
#E_mspoti
In [ ]:
sns.set(style='ticks', font_scale=1.4)
In [ ]:
R0 = 7.3 # nm Forster Radius
PD = dye_position(bp, l=2, λ=0.6, ψ=0)
PA = dye_position(0, l=1.6, λ=0.4, ψ=-pi/2)
R = np.linalg.norm(PD.T - PA, axis=1)
In [ ]:
pitch = δ*n
min_groove_pitch = 1.2
min_groove_pitch/pitch * 360
In [ ]:
bp = np.arange(0, 30, 0.2)
bpm = np.array([7, 12, 17, 22, 27])
In [ ]:
D_params = dict(l=2.4, λ=0.5, ψ=pi)
A_params = dict(l=2, λ=0.5, ψ=-1.2*pi/2)
n = 10.5 # number of bases per turn
Δφ = 131 # (degree) minor-grove angle between the two strands backbones
R0 = 7.5 # nm Forster Radius
In [ ]:
D_params = dict(l=1.28, λ=0.61, ψ=0)
A_params = dict(l=1.28, λ=0.39, ψ=-pi/2)
n = 10.5 # number of bases per turn
Δφ = 132 # (degree) minor-grove angle between the two strands backbones
R0 = 6.7 # nm Forster Radius
In [ ]:
D_params = dict(l=1.246, λ=1-0.256, ψ=0)
A_params = dict(l=1.246, λ=0.256, ψ=-pi/2)
n = 10.5 # number of bases per turn
Δφ = 2.31 * (180/np.pi) # (degree) minor-grove angle between the two strands backbones
R0 = 6.7 # nm Forster Radius
In [ ]:
PD = dye_position(bp, **D_params)
PA = dye_position(0, **A_params)
R = np.linalg.norm(PD.T - PA, axis=1)
fig, ax = plt.subplots()
E_alexi.plot(ax=ax, marker='s', lw=0, label='usALEX')
#E_mspoti.plot(marker='+', mew=2, ms=10, ls='none', ax=ax)
ax.set_ylim(0)
ax.set_xlim(5, 30)
ax.set_xlabel('D-A Separation (base-pairs)')
ax.set_ylabel('FRET Efficiency')
plt.xticks(E_alexi.index)
sns.despine(trim=True, offset=10, ax=ax)
ax.plot(bp, fret(R, R0), color='gray', alpha=0.5);
#savefig('multi-spot E vs distance.png');
In [ ]:
PD = dye_position(bp, **D_params)
PA = dye_position(0, **A_params)
R = np.linalg.norm(PD.T - PA, axis=1)
fig, ax = plt.subplots()
E_alexi.plot(ax=ax, label='usALEX')
E_mspoti.plot(marker='+', mew=2, ms=10, ls='none', ax=ax)
ax.set_ylim(0)
ax.set_xlim(5, 30)
ax.set_xlabel('D-A Separation (base-pairs)')
ax.set_ylabel('FRET Efficiency')
plt.xticks(E_alexi.index)
sns.despine(trim=True, offset=10, ax=ax)
ax.plot(bp, fret(R, R0), color='gray', alpha=0.5);
savefig('multi-spot E vs distance.png');
In [ ]:
PD0 = dye_position(bp, l=0, λ=0, ψ=0)
PA0 = dye_position(bp, l=0, λ=1, ψ=0)
PDm = dye_position(bpm, **D_params)
axes = plot_dye(PDm, marker='s', ls='')
plot_dye(PDm[:, :1], axes, color='k', marker='s', ms=10);
plot_dye(PD[:, :1], axes, color='k', marker='o', ms=10);
plot_dye(PA[:, np.newaxis], axes, color='r', marker='s');
plot_dye(PD0, axes, color='g', marker='', ls='-');
plot_dye(PA0, axes, color='m', marker='', ls='-');
plot_dye(PD0[:, :1], axes, color='g', marker='o');
plot_dye(PA0[:, :1], axes, color='m', marker='o');
t = np.arange(361)
axes[0].plot(cos(t/180*pi), sin(t/180*pi), lw=1, color='gray');
plot_dye(PD, axes, marker='', ls='-', color='b');
In [ ]:
# leg = ax[1].get_legend()
# h, l = ax[1].get_legend_handles_labels()
# ax[1].legend(h[1:] + h[:1], l[1:] + l[:1], title='Sample', loc='lower right')