E = E0 + (Emax − E0) · [A]ⁿ / (EC50ⁿ + [A]ⁿ) (four-parameter logistic Hill equation)
pioneer
Archibald V. Hill (1910 concentration-response formulation) and Alfred J. Clark (receptor occupancy theory)
Core Principles & Analysis
On a graded concentration-response curve, EC50 is the molar concentration of an agonist that elicits 50% of its own maximal physiological or cellular response (Emax), whereas on a quantal curve (ED50) it is the dose producing a specified all-or-none response in 50% of tested subjects.
Because tissues with high receptor reserve ("spare receptors") and strong downstream signal amplification can reach maximal response when only a small fraction of receptors are occupied, a full agonist's functional EC50 is often substantially lower (more potent) than its equilibrium binding constant (Kd).
Fitting concentration-response data to a four-parameter logistic (4PL) sigmoidal curve estimates four independent parameters: basal response (Bottom), maximal efficacy (Top / Emax), potency (log EC50), and steepness (Hill slope nH).