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

Analytical Flory Random Coil

AnalyticalFRC

Sequence-specific ideal (theta-state) chain; the reference null model.

Freely jointed chain

FreelyJointedChain

Ideal chain with finite extensibility (non-Gaussian Kuhn-Grün).

Freely rotating chain

FreelyRotatingChain

Ideal chain with a tunable characteristic ratio (stiffness).

Worm-like chain (Zhou)

WormLikeChain

Semiflexible chain parameterised by a persistence length.

Worm-like chain (O’Brien)

WormLikeChain2

Semiflexible chain; better large-chain stability, also gives Rg.

Self-avoiding walk

SAW

Good-solvent (excluded-volume) chain at fixed scaling exponent.

nu-dependent SAW

NuDepSAW

Excluded-volume chain with a tunable Flory scaling exponent.

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.