MACS Matchmaker

4PL Equilibrium (Dose-Response)

The four-parameter logistic curve is the standard model for steady-state dose-response data: ELISA, IC50/EC50 assays, and equilibrium binding titrations. Use this simulator to see how the bottom, top, EC50, and Hill slope shape the sigmoid.

Equation
log[concentration]responseEC₅₀bottomtop
R(C)=bottom+top−bottom1+(EC50/C)hR(C) = \text{bottom} + \frac{\text{top} - \text{bottom}}{1 + (EC_{50} / C)^{h}}

R(C): response at concentration C · bottom: minimum plateau · top: maximum plateau · EC50: concentration giving half-maximal response · h: Hill slope (steepness of the transition).

Assumptions
  • System is at equilibrium at every concentration.
  • Response is monotonic in concentration.
  • Hill slope h captures cooperativity (h> 1) or negative cooperativity (h < 1); h = 1 reduces to the Langmuir isotherm.
  • No assumption about kinetic mechanism.
Parameters

EC50 (M)

Hill slope (h)

Sampled concentrations (nM)

Noise σ (pg/mm²)

Derived

EC50 = 10 nM

Dynamic range = 100

Midpoint response = 50

Diagnostic cues
  • Top plateau not reached → highest concentration too low.
  • Bottom plateau not reached → blank or low control missing.
  • Hill slope far from 1 → cooperativity, multiple sites, or assay artefact (aggregation, depletion).
Download curve (CSV)