Pharmacology
Dose-Response Curve Generator
Plots the sigmoid Emax (Hill) equation for one or more drugs on linear and log-dose axes, so potency and efficacy can be compared side by side.
Drug A · EC₅₀
10nM
Emax 100%, Hill n = 1, baseline 0%
Scale
Log-dose scale
Effect against log₁₀ concentration. Black dots mark each curve's EC₅₀.
Black dots mark each curve's true EC₅₀ point (baseline + Emax/2) — not a fixed y = 50, since baseline and Emax vary per drug.
Curves
Each drug is one set of Hill parameters. Add a second to compare potency against efficacy.
Maximum effect above baseline — efficacy.
Concentration giving half of Emax — potency.
Steepness. n = 1 is a simple single-site curve.
Effect present with no drug at all.
Plot settings
Sets the right-hand end of the linear axis only.
Working
Key points read off this curve.
Every curve is the sigmoid Emax (Hill) equation:
E = E₀ + (Emax × C ⁿ) / (EC₅₀ ⁿ + C ⁿ)
E₀ is the baseline effect with no drug, Emax the maximum effect above that baseline, C the concentration, EC₅₀ the concentration producing half of Emax, and n the Hill coefficient.
At C = EC₅₀ the two powered terms are equal, so the fraction is exactly ½ and the effect is E₀ + Emax/2 — which is where the markers sit. The concentration needed for 90% of Emax is EC₅₀ × 9^(1/n), so a steeper curve (larger n) reaches saturation over a narrower range.
Each axis is drawn from 151 points. An EC₅₀ of zero or below is substituted with 0.001 nM to keep the logarithm defined.
Keep learning
References
- Rowland and Tozer's Clinical Pharmacokinetics and Pharmacodynamics: Concepts and Applications. 5th ed. Philadelphia: Wolters Kluwer; 2019.
Common questions
They are the same equation. On a linear axis the curve is a rectangular hyperbola that rises steeply and flattens; taking logs of the concentration stretches the low end and compresses the high end, which straightens the middle into the familiar S-shape and makes EC₅₀ easy to read off.
Steepness. n = 1 gives a simple single-site curve spanning about two log units from 10% to 90% effect. n above 1 (positive cooperativity, like haemoglobin binding oxygen) makes the curve steeper; n below 1 makes it shallower.
No. A low EC₅₀ means high potency — less drug is needed — but says nothing about how large an effect is achievable. A partial agonist can be very potent and still have a low Emax, which is why both numbers are plotted here.
Because EC₅₀ is half of that curve's own maximum, measured from its baseline. With a baseline of 20% and an Emax of 60%, the half-maximal point is at 50% — but with a baseline of 0 and an Emax of 80%, it is at 40%.
Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy