In [1]:

    

%matplotlib inline
%config InlineBackend.figure_format='retina'  # for hi-dpi displays
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import seaborn as sns
from numpy import pi, cos, sin


    

In [2]:

    

sns.set_style('whitegrid')


    

In [58]:

    

r = 1        # (nm) dsDNA radius
δ = 0.34     # (nm) dsDNA base-pair pitch
n = 10.5     # number of bases per turn
Δφ = 2.31    # (radiants) minor-grove angle between the two strands backbones


    

In [50]:

    

φ = 2*pi/n  # (radiants) rotation for base-pair


    

In [51]:

    

def dye_position(i, l=1.6, λ=0.5, ψ=0):
    # global structural params: r, δ, n, Δφ
    
    φ = 2*pi/n  # (radiants) rotation for base-pair
    Dx = r * cos(φ*i) + λ*( r*cos(φ*i + Δφ) - r*cos(φ*i) ) + l*cos(ψ)*cos(φ*i + 0.5*Δφ)
    Dy = r * sin(φ*i) + λ*( r*sin(φ*i + Δφ) - r*sin(φ*i) ) + l*cos(ψ)*sin(φ*i + 0.5*Δφ)
    Dz = i*δ + l*sin(ψ)
    return np.array([Dx, Dy, Dz])


    

In [52]:

    

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), (0,0))
        ax_xz = plt.subplot2grid((2,2), (1,0))
        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)')

    ax_3d.plot(P[0], P[1], P[2], **kws_)
    return (ax_xy, ax_xz, ax_yz, ax_3d)


    

In [53]:

    

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 [54]:

    

dye_position(7)


    

    
Out[54]:





array([ 1.38564065, -0.8       ,  2.338     ])

In [55]:

    

bp = np.arange(0, 40)


    

In [56]:

    

PD = dye_position(bp)
PA = dye_position(bp, l=1.6, λ=0.5, ψ=pi)


    

In [57]:

    

axes = plot_dye(PD)
plot_dye(PA, axes, color='r');


    

In [109]:

    

bp = np.arange(0, 40, 0.1)


    

In [119]:

    

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)


    

In [126]:

    

R = np.array([np.linalg.norm(px - PA) for px in PD.T])
#R


    

In [127]:

    

plt.plot(bp, R);
plt.xlabel('Base-pair')
plt.ylabel('Distance (nm)')
plt.ylim(0);


    

In [128]:

    

R0 = 6.7  # nm


    

In [129]:

    

def fret(R, R0):
    return 1 / (1 + (R/R0)**6)


    

In [131]:

    

plt.plot(bp, fret(R, R0));


    

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