IC50 Calculator — 4PL Dose-Response & EC50 Curve Fitting
Calculate half-maximal inhibitory concentration (IC50), EC50, and Hill slope from biological dose-response data using four-parameter logistic non-linear regression. Includes Cheng-Prusoff Ki affinity conversion and interactive curve plotting.
Dose-Response (IC50 / EC50) Regression
| Conc. (nM) | Response (%) | |
|---|---|---|
IC50 Calculator Formulas: 4PL Model & Cheng-Prusoff Equation
1. Four-Parameter Logistic (4PL) Hill Equation
The gold standard mathematical model for sigmoidal bioassay dose-response relationships:
Where X is log₁₀(Concentration), Bottom and Top represent the lower and upper asymptotic plateaus, and HillSlope indicates the steepness of the curve.
2. Converting IC50 to Ki: The Cheng-Prusoff Equation
While IC₅₀ depends on experimental substrate concentration, the inhibition constant (Ki) represents the true thermodynamic binding affinity:
Applicable for classical competitive enzyme inhibitors where [S] is substrate concentration and Km is the Michaelis constant.
3. Significance of the Hill Slope (n)
IC50 Calculator Assay Design & Serial Dilution Quality Controls
Establish Complete Plateaus
Ensure at least 2 concentration points define the upper baseline (0% inhibition) and 2 points define the maximal effect plateau (100% inhibition) to prevent unbounded regression errors.
Even Logarithmic Spacing
Use 3-fold or half-log (3.16-fold) serial dilutions across a 3–4 order of magnitude dynamic range (e.g., 10 nM to 100 µM) for balanced curve fitting.
Solvent / DMSO Vehicle Control
Maintain a constant DMSO concentration (≤ 0.5% v/v) across all wells, including untreated negative controls, to eliminate vehicle-induced cytotoxicity artifacts.
Frequently Asked Questions
What is the difference between IC50 and EC50?
IC50 (half-maximal inhibitory concentration) measures the potency of an antagonist or inhibitor in reducing a biological response by 50%. EC50 (half-maximal effective concentration) measures the concentration of an agonist or drug that produces 50% of its maximal stimulatory effect.
Why is Cheng-Prusoff Ki conversion necessary instead of relying solely on IC50?
IC50 is an operational measurement that varies directly with experimental substrate concentration [S]. Higher substrate concentrations competitively displace the inhibitor, making the observed IC50 appear higher. The Cheng-Prusoff equation converts IC50 into Ki, which is an intrinsic thermodynamic affinity constant independent of substrate concentration.
What does a Hill slope (nH) significantly greater or less than 1.0 indicate?
A Hill slope of 1.0 reflects standard mass-action binding to a single independent site. Slopes > 1.5 suggest positive cooperativity or threshold mechanism, while slopes < 0.8 suggest negative cooperativity, multiple receptor subtypes, or solubility limitations.
How many concentration points should be included in an IC50 dose-response curve?
A minimum of 7 to 10 serial concentration points spanning at least 3 to 4 orders of magnitude is recommended, with multiple points defining both the lower and upper asymptotic plateaus.
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