Neuropharmacology — NIH NIDA / NIMH / NINDS mechanistic grain; study of drug action on the nervous system, including neurotransmitter-receptor interactions, synaptic modulation, and clinical therapeutics. Foundations: (1)…
neuropharmacology
Cheng-Prusoff: IC50 = Ki·(1 + [S]/Km); Ki from competitive IC50
Cheng & Prusoff (1973) derived the closed-form relation between the experimentally-measured IC50 of a competitive enzyme inhibitor (the…
Therapeutic index: TI = TD50 / ED50; clinical safety-margin metric
The therapeutic index (TI) is the canonical quantitative measure of drug safety margin: the ratio of the dose producing toxicity in 50% of…
First-order elimination: C(t)=C₀·e^(−kt); t½ = ln(2)/k
First-order elimination is the foundational pharmacokinetic model for most therapeutic drugs at therapeutic concentrations: the plasma…
Cheng-Prusoff pins: IC50(S=0)=Ki; IC50(S=Km)=2·Ki
Sympy-exact witness of the Cheng-Prusoff limiting-case identities. Setup: IC50 = Ki · (1 + [S]/Km) as a three-symbol function. Identity 1…
Therapeutic-index anchor: TI(TD50=10·ED50) = 10
Sympy-exact witness of the therapeutic-index arithmetic. Setup: TI = TD50 / ED50, as a two-symbol ratio. Anchor: at TD50 = 10·ED50…
First-order half-life: C(t½)/C₀ = 1/2; t½ = log(2)/k_e
Sympy-exact witness of the first-order half-life identity. Setup: C(t) = C₀ · exp(−k_e · t), half-life t½ defined by C(t½) = C₀/2. …