Is this the same Hill equation as hemoglobin saturation?

Same algebraic family, different meaning. Oxygen–hemoglobin uses n and P50 for binding saturation versus pO2. Here C is a drug dose and E is a graded response (or inhibition), with optional antagonist shifts and a therapeutic-window overlay.

What does a Hill slope nH > 1 mean?

The curve is steeper around EC50: a small change in log-dose produces a large change in effect. nH < 1 is shallower (negative cooperativity or mixed populations). The model is phenomenological, not a full receptor-occupancy mechanism.

Why plot dose on a log scale?

Potency ratios and parallel antagonist shifts are visually linear on log10 C. On a linear axis the rise is crushed near zero and the plateau is hard to compare.

Dose-Response & Hill Curves

Q: Why plot dose on a log scale?

Potency ratios and parallel antagonist shifts are visually linear on log10 C. On a linear axis the rise is crushed near zero and the plateau is hard to compare.

Pharmacologic Hill E(C): EC50/IC50, Hill slope nH, agonist vs antagonist shifts, and therapeutic-window sketch (ED50 vs TD50).

This is a pharmacologic dose–response page, not hemoglobin saturation. Concentration C is a drug dose; E is a graded tissue effect. A competitive antagonist shifts EC50 to the right (Schild); a noncompetitive antagonist lowers Emax. The therapeutic-window sketch overlays efficacy (ED50) and toxicity (TD50).

About this model

A four-parameter Hill (sigmoidal) dose–response curve maps concentration C to effect E = E0 + (Emax−E0) C^{nH}/(EC50^{nH}+C^{nH}). The same family describes inhibition when the plateau falls with C (IC50). A competitive antagonist produces a parallel rightward shift of EC50 (Schild-style), while a noncompetitive antagonist lowers Emax. A therapeutic-window sketch compares an efficacy curve (ED50) with a toxicity curve (TD50); their ratio is a simple therapeutic index.

Who it's for: Pharmacology, toxicology, pharmacy, and biomedical engineering courses introducing potency, efficacy, and Hill slope.

Key terms

Hill equation
EC50
IC50
Hill slope
Agonist
Antagonist
Therapeutic window
ED50
TD50

How it works

Pharmacologic Hill E(C): EC50/IC50, Hill slope, competitive vs noncompetitive antagonist, and a therapeutic-window sketch (ED50 vs TD50).

Key equations

E(C) = E0 + (Emax − E0) · C^{nH} / (EC50^{nH} + C^{nH})

Competitive: EC50_app = EC50 (1+[A]/Ki) · Noncompetitive: Emax_app = Emax / (1+[A]/Ki)

I(C) = Imax · C^{nH} / (IC50^{nH} + C^{nH}) · TI = TD50 / ED50

Frequently asked questions

Is this the same Hill equation as hemoglobin saturation?: Same algebraic family, different meaning. Oxygen–hemoglobin uses n and P50 for binding saturation versus pO2. Here C is a drug dose and E is a graded response (or inhibition), with optional antagonist shifts and a therapeutic-window overlay.
What does a Hill slope nH > 1 mean?: The curve is steeper around EC50: a small change in log-dose produces a large change in effect. nH < 1 is shallower (negative cooperativity or mixed populations). The model is phenomenological, not a full receptor-occupancy mechanism.
Why plot dose on a log scale?: Potency ratios and parallel antagonist shifts are visually linear on log10 C. On a linear axis the rise is crushed near zero and the plateau is hard to compare.

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