Polymer Models (Theory)

Alongside the Analytical Flory Random Coil, the afrc package implements several other analytical polymer models. Each takes an amino acid sequence and returns an end-to-end distance distribution plus mean values through a common interface (get_end_to_end_distribution, get_mean_end_to_end_distance, …).

For each model, the pages below give (1) the formalism that is actually implemented, (2) the free parameters, what they mean and sensible values for a polypeptide, and (3) the primary references. For usage examples and the code reference, 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 parameterized by a persistence length.
Worm-like chain (O’Brien)	WormLikeChain2	Semiflexible chain; exact finite extensibility, 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.

Models

• Analytical Flory Random Coil
• Freely jointed chain
• Freely rotating chain
• Worm-like chain (Zhou)
• Worm-like chain (O’Brien)
• Self-avoiding walk
• nu-dependent self-avoiding walk

A note on conventions

Throughout, \(N\) is the number of residues, \(r\) is the end-to-end distance, \(R_e\) the end-to-end distance and \(R_g\) the radius of gyration. All distances are in Angstroms.

Distributions are returned as discrete, normalized probability mass functions (distances, probabilities) on a grid whose spacing is set by p_of_r_resolution (0.05 Å by default). This is a numerical discretization, not a model parameter.

get_mean_end_to_end_distance always returns the mean, \(\langle R_e \rangle\), and get_root_mean_squared_end_to_end_distance returns \(\sqrt{\langle R_e^2 \rangle}\). For the AFRC, get_mean_radius_of_gyration returns the true mean \(\langle R_g \rangle\). The other models have no \(R_g\) distribution, so their get_mean_radius_of_gyration returns the root-mean-square value \(\sqrt{\langle R_g^2 \rangle}\) from a closed-form ratio; for an ideal chain this is about 3% larger than \(\langle R_g \rangle\).