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. …
Schild regression: log(r−1) = log[B] − log K_B; slope = 1 defines competitive antagonism (pA_2)
Schild regression framework — the canonical competitive-antagonism quantification method in pharmacology (Schild 1947, 1949; Arunlakshana &…
Black-Leff operational model: E = τ·A/(K_A + A(1+τ)); τ-parameter captures receptor-reserve
Black-Leff operational model — the canonical receptor-theory framework separating affinity (K_A) from efficacy (τ) for agonist…
Schild: log(r−1) canonical log(B/K_B); r(B=K_B)=2, r(B=3K_B)=4, r(B=7K_B)=8; slope/log[B]=1
Sympy-exact symbolic witness of the Schild regression canonical form and three integer-dose-ratio anchors. Setup: r (dose-ratio), B…
Black-Leff: E_max=τ/(τ+1); EC_50=K_A/(τ+1); E(EC_50)=τ/[2(τ+1)]; low-A series E≈τA/K_A
Sympy-exact symbolic witness of the Black-Leff operational model canonical asymptotes and EC_50 expressions. Setup: τ, A, K_A, E — all…
Hill equation: E = E_max·C^n/(EC_50^n + C^n); cooperative-binding sigmoid (1910)
Hill equation framework — the canonical sigmoidal dose-response / cooperative-binding model spanning all of quantitative pharmacology (Hill…
Hill equation: E(EC_50)=E_max/2; E/(E_max−E)=(C/EC_50)^n; C_x=EC_50·(x/(1−x))^{1/n}
Sympy-exact symbolic witness of the Hill sigmoidal dose-response canonical form and three canonical identity anchors. Setup: C (dose,…
SSRIs (Wong 1987)
D Wong 1987 fluoxetine; modern Citalopram + Escitalopram + Sertraline; SSRI dominant antidepressant class.
Antipsychotics (Snyder 1976)
S Snyder 1976 D2-receptor; modern atypicals + clozapine + LAI; modern target serotonin-2a + D3-partial-agonism.
AEDs (Rogawski 2016)
M Rogawski 2016 mechanisms-AED review; modern levetiracetam + lacosamide + cannabidiol Epidiolex 2018 FDA.
Opioid receptors (Pert-Snyder 1973)
Pert-Snyder 1973 opiate-receptor; modern mu/delta/kappa + biased-agonism + oliceridine FDA 2020.
Psychedelics (Griffiths 2006)
R Griffiths 2006 psilocybin mystical-experience; modern MDMA-PTSD + psilocybin-depression Phase-3 2024.
Amyloid cascade (Hardy-Selkoe 1991)
Hardy-Selkoe 1991 amyloid-cascade hypothesis; modern lecanemab + donanemab anti-Abeta clinical mild-AD slowing.
Clark occupancy (1933)
A J Clark 1933 receptor-occupancy; modern modern foundational text + Stephenson 1956 efficacy + 2024 GPCR functional-selectivity bias.
Cheng-Prusoff (1973)
Y Cheng-W H Prusoff 1973 IC50/Ki conversion; modern modern foundational text + 2024 thermodynamic-corrections + 2024 ML drug-screen.
Schild plot (1947)
H Schild 1947 + Arunlakshana 1959 pA2; modern modern foundational text + 2024 functional-antagonism + Schild-allosteric.
Operational (Black-Leff 1983)
J Black-P Leff 1983 (Black Nobel 1988) operational-model τ; modern modern foundational + functional-selectivity + 2024 ligand-bias…
Opioid receptor (Pert-Snyder 1973)
C Pert-S Snyder 1973 opioid-receptor-binding; modern modern foundational + μ/κ/δ + 2024 G-protein-biased oliceridine pain biased-ligand.
Monoamine reuptake (Axelrod 1971)
J Axelrod 1971 (Nobel 1970) catecholamine-reuptake; modern modern foundational + SSRIs + SNRIs + 2024 GLYT1 schizophrenia + glutamate…