Worm Like Chain Simulator

Description

Simulates a bundle of n Worm-Like-Chains in 2D with a defined Persistence Length p and a contour length L. Units can be plugged in arbitrarily since the result does not change if 1.0 stands for 1.0 meter or 1.0 nanometer.

Dependencies

python (2.7 or 3.5), numpy, scipy, matplotlib

Usage

Simulate Bundle of Chains

from WLC import ChainBundle
bundle = ChainBundle()
bundle.compute(n_chains=10, persistence_length=1, contour_length=10, n_segments=100) 
# n_segments: How smooth chain should be approximated by linear segments.
# Should be at least 50 for meaningful results

Output Data

bundle.data.shape
>>>(10, 100, 2) # 10 chains, containing 100 points, (x,y) coordinates

bundle.data
>>>array([[[ 0.        ,  0.        ],
        [ 0.1       ,  0.        ],
        [ 0.19048374, -0.04257573],
        ..., 
        [ 3.98511392,  5.23248311],
        [ 3.92634524,  5.31339197],
        [ 3.90761667,  5.41162252]],
       ...,        
       [[ 0.        ,  0.        ],
        [ 0.1       ,  0.        ],
        [ 0.19048374,  0.04257573],
        ..., 
        [-1.33431195,  1.46191013],
        [-1.30943588,  1.55876663],
        [-1.24568973,  1.63581485]]])

Compute persistence length

This algorithm computes the mean correlation of chain segments over distance and returns lambda of a fitted exponential of the decay of correlation values. In verbose mode, lambda is returned along with the exponential curve.

bundle.compute_persistence_length()
>>>1.0849898854583857

l, xvals, yvals = bundle.compute_persistence_length(verbose=True)
plt.plot(xvals, yvals)
plt.xlabel('Distance on the chain')
plt.ylabel('Correlation of segments')

Plotting

import matplotlib.pyplot as plt
bundle1 = ChainBundle()
bundle1.compute(n_chains=10, persistence_length=1, contour_length=10, n_segments=100)
bundle10 = ChainBundle()
bundle10.compute(n_chains=10, persistence_length=10, contour_length=10, n_segments=100)
bundle100 = ChainBundle()
bundle100.compute(n_chains=10, persistence_length=100, contour_length=10, n_segments=100)

bundle1.plot(color='red', label='Pers.Length 1 nm') 
bundle10.plot(color='green', label='Pers.Length 10 nm')
bundle100.plot(color='blue', label='Pers.Length 100 nm')

plt.legend()
plt.xlabel('x [nm]')
plt.ylabel('y [nm]')

plt.show()

References

Simulation procedure is explained in appendix of this paper:

• Castro, C. E., Su, H.-J., Marras, A. E., Zhou, L., & Johnson, J. (2015). Mechanical design of DNA nanostructures. Nanoscale, 7(14), 5913–5921. https://doi.org/10.1039/C4NR07153K_

Computation of persistence length of a bundle is adapted from:

• https://pythonhosted.org/MDAnalysis/_modules/MDAnalysis/analysis/polymer.html"""

I am not author of/affiliated to either of above references.