Polymer Models (Theory)
Alongside the headline Analytical Flory Random Coil, the afrc package implements
several additional analytical polymer models. Each one takes an amino acid sequence and
returns an end-to-end distance distribution together with associated mean values, exposing
a common interface (get_end_to_end_distribution, get_mean_end_to_end_distance, …).
The pages below describe, for each model: (1) the mathematical formalism that is actually implemented, (2) the free parameters, what they mean physically, and sensible values for a polypeptide, and (3) the primary references. For runnable usage examples and the full code reference for each class, see Polymer Models (Application).
Model |
Class |
In one line |
|---|---|---|
|
Sequence-specific ideal (theta-state) chain; the reference null model. |
|
|
Ideal chain with finite extensibility (non-Gaussian Kuhn-Grün). |
|
|
Ideal chain with a tunable characteristic ratio (stiffness). |
|
|
Semiflexible chain parameterised by a persistence length. |
|
|
Semiflexible chain; better large-chain stability, also gives Rg. |
|
|
Good-solvent (excluded-volume) chain at fixed scaling exponent. |
|
|
Excluded-volume chain with a tunable Flory scaling exponent. |
Models
A note on conventions
Throughout, \(N\) is the number of residues in the sequence, \(r\) is the
end-to-end distance, \(R_e\) the mean end-to-end distance, and \(R_g\) the radius
of gyration. All distances are in Angstroms. Distributions are returned as discrete,
normalised probability mass functions (distances, probabilities) evaluated on a grid
whose spacing is set by p_of_r_resolution (0.05 Å by default); this is a numerical
discretisation parameter, not a model parameter.