Worm-like chain (O’Brien)

Usage examples and full code reference for WormLikeChain2. For the underlying theory, see Worm-like chain (O’Brien).

Quick start

from afrc.polymer_models.wlc2 import WormLikeChain2

# defaults: persistence length lp = 3.0 A, segment size aa_size = 3.8 A
model = WormLikeChain2('MASNDYTQQATQSYGAYPTQPGQGYSQQSSQPYG')

model.get_mean_end_to_end_distance()
model.get_root_mean_squared_end_to_end_distance()
model.get_mean_radius_of_gyration()       # closed-form Rg (unique to this model)

r, p = model.get_end_to_end_distribution()

Vary the persistence length:

for lp in (2.0, 3.0, 4.0):
    wlc = WormLikeChain2('MASNDYTQQATQSYG', lp=lp)
    print(lp, wlc.get_mean_radius_of_gyration())

Note

WormLikeChain2 requires the sequence to be at least as long as the persistence length, otherwise a WLC2Exception is raised.

See also the demo/demo_WormLikeChain2.ipynb notebook for a worked, plotted example.

Code reference

class afrc.polymer_models.wlc2.WormLikeChain2(seq, p_of_r_resolution=0.05, lp=3.0, aa_size=3.8)

This class generates an object that returns polymer statistics consistent with the Worm-like chain model as implemented by O’Brien. Provides mean Re, mean Rg, and Re distribution.

[1] O’Brien, E. P., Morrison, G., Brooks, B. R., & Thirumalai, D. (2009). How accurate are polymer models in the analysis of Forster resonance energy transfer experiments on proteins? The Journal of Chemical Physics, 130(12), 124903.

__init__(seq, p_of_r_resolution=0.05, lp=3.0, aa_size=3.8)

Method to create Polymer Object. Seq should be a valid upper-case amino acid sequence and p_of_r_resolution defines the resolution (in angstroms) to be used for distributions.

By default p_of_r_resolution is taken from the config.py file in the afrc package which defines the resolution at 0.05 A.

Parameters:

seq (str) – Amino acid sequence (used only to calculate number of residues)
p_of_r_resolution (float) – Bin width for bulding probability distributions. In Angstroms.
lp (float) – Persistence length. We use a default of 3 but 4 is also used a lot in the literature.
aa_size (float) – Size of one amino acid (called ‘b’ in the literature). 3.8 is the generally acceptable value used.

get_end_to_end_distribution()

Defines the end-to-end distribution based on the Worm-like chain (WLC) as defined by O’Brien et al.

This is a composition independent model for which the end-to-end distance depends solely on the number of amino acids. It is included here as an additional reference model.

Returns:: A 2-pair tuple of numpy arrays where the first is the distance (in Angstroms) and the second array is the probability of that distance.
Return type:: tuple of arrays

References

[1] O’Brien, E. P., Morrison, G., Brooks, B. R., & Thirumalai, D. (2009). How accurate are polymer models in the analysis of Forster resonance energy transfer experiments on proteins? The Journal of Chemical Physics, 130(12), 124903.

get_mean_end_to_end_distance()

Returns the mean end-to-end distance (\(R_e\)). As calculated from the Worm-like chain (WLC) model as defined by O’brien et al.

Note, the mean here is calculated by integrating over P(r) vs r.

Returns:: Value equal to the mean end-to-end distance distribution
Return type:: float

get_mean_radius_of_gyration()

Returns the mean radius of gyration (\(R_g\)) as defined by O’Brien et al in [1]. NOTE it doesn’t explicitly say it in the paper, but we’re assuming this is actually Rg^{2} so this returns the square root of the Rg defined in table 1 (WLC row).

[1] O’Brien, E. P., Morrison, G., Brooks, B. R., & Thirumalai, D. (2009). How accurate are polymer models in the analysis of Forster resonance energy transfer experiments on proteins? The Journal of Chemical Physics, 130(12), 124903.

Returns:: Value equal to the mean radius of gyration.
Return type:: float

get_root_mean_squared_end_to_end_distance()

Returns the mean end-to-end distance (\(R_e\)). As calculated from the Worm-like chain (WLC) model as defined by O’brien et al.

Note mean here is calculated by taking the square root after integrating over P(r) vs r^2.

Returns:: Value equal to the root-mean-squared end-to-end distance
Return type:: float