Code for: The Hill Coefficient as Fisher Information: An Information-Theoretic Identity for Allosteric Cooperativity
Description
This repository contains the Python code that generates Figure 1 of the article "The Hill Coefficient as Fisher Information: An Information-Theoretic Identity for Allosteric Cooperativity" (BioSystems, Elsevier, 2026). The study is analytical and generated no experimental datasets; this script is the sole computational artifact and is provided so that the figure can be reproduced exactly. The script (make_figure1.py) produces a four-panel figure: (a) the Fisher information I(theta) = n_H^2 p(1-p) of a Hill-type dose-response curve for a range of Hill coefficients; (b) the midpoint identity I_mid = n_H^2/4, with hemoglobin (n_H = 2.8) and the bacterial flagellar motor (n_H = 10.3) marked against the no-cooperativity baseline; (c) the symmetry of the identity under n_H -> -n_H; and (d) the Fisher information on the binary manifold in the visibility coordinate, I(V) = 1/(1-V^2) with V = 2p-1. Requirements: Python 3.8+, numpy, matplotlib. Run "python make_figure1.py" to produce fig_hill.pdf. See README.md for details.