Hill: θ = Lⁿ/(Kⁿ+Lⁿ); θ(L=K) = 1/2; slope dθ/d(log L)|_K = n/4

Layer 2 — Chemistryin the bioorganic-chemistry subtree

Sympy-exact witness of the Hill cooperative-binding θ(L) and its two canonical anchors. Setup: L, K positive symbols; n positive; θ(L) = L^n/(K^n + L^n). Three pins: (i) theta_sym = sp.simplify(θ) = 'L**n/(K**n + L**n)' — the canonical…

Related concepts

Hill full framework: θ(L) = Lⁿ/(Kⁿ + Lⁿ); half-saturation at L = K; Hill slope n/4 at L = K
Single-molecule biophysics

Explore Hill: θ = Lⁿ/(Kⁿ+Lⁿ); θ(L=K) = 1/2; slope dθ/d(log L)|_K = n/4 on the interactive knowledge graph →