The Analytical Flory Random Coil — a sequence-specific reference model for unfolded and intrinsically disordered proteins.
afrc implements the Analytical Flory Random Coil (AFRC): a closed-form, sequence-specific
polymer model that reports the dimensions a polypeptide would adopt if it behaved as an ideal
chain in a theta solvent (apparent scaling exponent of 0.5, no finite-size effects). Given only
an amino acid sequence, it returns a wide range of polymeric properties — instantly and
without running any simulations.
The AFRC is intended as a reference (null) model, not a predictor of real dimensions. Real unfolded-state dimensions depend on sequence-encoded chain–chain and chain–solvent interactions that the AFRC deliberately omits. Its value is as a fixed, sequence-matched touchstone: deviations of a simulation or experiment from the AFRC directly report sequence-specific intramolecular interactions, and normalising to the AFRC lets chains of different length and composition be compared on a common footing.
Alongside the AFRC, the package ships a family of classic analytical polymer models that share a common interface, so the same sequence can be compared against several reference frames.
afrc requires Python 3.10 or later (tested through Python 3.14) and depends only on
NumPy and SciPy.
pip install afrcfrom afrc import AnalyticalFRC
# create an AnalyticalFRC object from a sequence
P = AnalyticalFRC('MEEPQSDPSVEPPLSQETFSDLWKLLPENNVLSPLPSQAMDDLMLSPDDI')
# ensemble-average dimensions (Angstroms)
mean_rg = P.get_mean_radius_of_gyration()
mean_e2e = P.get_mean_end_to_end_distance()
mean_rh = P.get_mean_hydrodynamic_radius()
# full probability distributions, returned as (distances, probabilities)
rg_r, rg_p = P.get_radius_of_gyration_distribution()
re_r, re_p = P.get_end_to_end_distribution()
# distribution of the distance between two specific residues
d_r, d_p = P.get_interresidue_distance_distribution(4, 20)
# whole-chain maps
distance_map = P.get_distance_map()
contact_map = P.get_contact_map(15.0) # contact fractions at a 15 A thresholdEvery model takes an amino acid sequence and exposes a common interface
(get_end_to_end_distribution, get_mean_end_to_end_distance, ...), so they can be swapped in
and compared directly.
| Model | Import | Description |
|---|---|---|
| Analytical Flory Random Coil | from afrc import AnalyticalFRC |
Sequence-specific ideal (theta-state) chain; the reference null model. |
| Freely jointed chain | from afrc.polymer_models.fjc import FreelyJointedChain |
Ideal chain with finite extensibility (non-Gaussian Kuhn–Grun). |
| Freely rotating chain | from afrc.polymer_models.frc import FreelyRotatingChain |
Ideal chain with a tunable characteristic ratio (stiffness). |
| Worm-like chain (Zhou) | from afrc.polymer_models.wlc import WormLikeChain |
Semiflexible chain parameterised by a persistence length. |
| Worm-like chain (O'Brien) | from afrc.polymer_models.wlc2 import WormLikeChain2 |
Semiflexible chain; better large-chain stability, also gives Rg. |
| Self-avoiding walk | from afrc.polymer_models.saw import SAW |
Good-solvent (excluded-volume) chain at a fixed scaling exponent. |
| nu-dependent SAW | from afrc.polymer_models.nudep_saw import NuDepSAW |
Excluded-volume chain with a tunable Flory scaling exponent. |
The full mathematical formalism, parameters, and usage examples for each model are in the documentation.
Use the AFRC (and the other polymer models) directly in a Google Colab notebook.
Full documentation — including a theory section (formalism, parameters, references) and an
application section (usage examples and code reference) for every model — is hosted at
afrc.readthedocs.io. Worked, plotted examples for each model are
in the demo/ directory.
If you use the AFRC in your work, please cite:
Alston, J. J., Ginell, G. M., Soranno, A., & Holehouse, A. S. (2023). The Analytical Flory Random Coil is a simple-to-use reference model for unfolded and disordered proteins. The Journal of Physical Chemistry B, 127(21), 4746–4760. https://doi.org/10.1021/acs.jpcb.3c01619
If you find a bug or have a feature request, please open an issue on GitHub.
The AFRC was developed by Garrett Ginell, Jhullian Alston, and Alex Holehouse in the Holehouse Lab.
Distributed by the Holehouse Lab under the GNU Lesser General Public License (LGPL v3).
- Alston, J. J., Ginell, G. M., Soranno, A., & Holehouse, A. S. (2023). The Analytical Flory Random Coil is a simple-to-use reference model for unfolded and disordered proteins. J. Phys. Chem. B, 127(21), 4746–4760.
- Flory, P. J. (1969). Statistical Mechanics of Chain Molecules. Wiley-Interscience.
- Mao, A. H., Lyle, N., & Pappu, R. V. (2013). Describing sequence–ensemble relationships for intrinsically disordered proteins. Biochemical Journal, 449(2), 307–318.