6.7.1 The Four-Parameter Logistic (4PL) Model

Dose-response relationships in pharmacology are almost universally sigmoidal when plotted against the logarithm of concentration, and are conventionally...

Dose-response relationships in pharmacology are almost universally sigmoidal when plotted against the logarithm of concentration, and are conventionally fitted using a four-parameter logistic model: Y = Bottom + (Top − Bottom) / (1 + 10^((LogIC50 − X) × HillSlope)), where X represents the logarithm of concentration and Y represents the percentage inhibition or percentage response. The 'Bottom' parameter represents the minimum response (typically constrained to 0%), the 'Top' parameter represents the maximum response (typically constrained to 100%), 'LogIC50' represents the log-concentration at which the response equals 50% of maximum, and the 'Hill slope' describes the steepness of the curve — a Hill slope near 1 is consistent with simple, non-cooperative receptor occupancy, while steeper or shallower slopes suggest cooperative binding or a heterogeneous population of binding sites. In GraphPad Prism, this analysis is performed via Analyze → Nonlinear regression → Dose-response → log(inhibitor) vs. normalised response (variable slope), and results are conventionally reported as IC50 = X.XX µM (with its 95% confidence interval), the goodness-of-fit statistic R², and the number of independent experiments (n), each performed in technical triplicate, contributing to the analysis.