Dose-Response & IC50

Dose-response curves require non-linear regression. Licklider fits the 4-parameter logistic model (4PL), reports IC50/EC50 with 95% CI, discloses asymptote constraints, and flags when the Hill slope deviates from 1 in ways that affect biological interpretation.

STEP 1 — The Scenario

Researcher Profile

A pharmacologist testing the cytotoxicity of a novel kinase inhibitor in a cancer cell line (MCF-7). Cells are treated with 8 concentrations (0.001–100 µM) in triplicate, and cell viability is measured by MTT assay at 72 hours.

Research Question

"What is the IC50 of the compound in MCF-7 cells, and is the dose-response curve sigmoidal? What is the Hill slope and the confidence interval around IC50?"

Dataset

• 8 dose levels: 0.001, 0.01, 0.1, 1, 10, 30, 100 µM (plus vehicle control)
• 3 technical replicates per dose; 3 independent biological experiments
• Outcome: Cell viability (% of DMSO control)

STEP 2 — Licklider Analysis Path

1. Data Upload & Replicate Structure

Licklider detects three replicate columns and an Experiment column (3 biological replicates). It confirms: "Should technical replicates be averaged per dose per experiment before fitting, or should all individual measurements be used as raw data?" The Biological vs. Technical Replicate guard (4.5.2) clarifies this step.

2. Data Contract Declaration

Observation unit: one technical replicate measurement. Biological replicates: 3 independent experiments. Outcome type: continuous proportion (% viability), constrained between 0 and 100.

3. Log-Transformation of Dose Axis

Licklider automatically log10-transforms the concentration axis for 4PL fitting (required for sigmoidal dose-response). The transformation is disclosed in the Methods text and the x-axis label includes the log10 scale notation.

4. 4PL Curve Fitting

The 4-parameter logistic model is fitted: y = Bottom + (Top − Bottom) / (1 + (IC50/x)^HillSlope). Parameters reported: Bottom (minimum response), Top (maximum response), IC50 (µM), HillSlope. 95% CI for each parameter via asymptotic approximation or bootstrap (n=1000).

5. Goodness of Fit

R² and Root Mean Square Error (RMSE) are reported. Residual plot checks that errors are random across the dose range (no systematic deviation at low or high doses).

6. Figure Generation

Sigmoid dose-response curve with log10 concentration on x-axis, % viability on y-axis. Individual data points from all replicates overlaid. IC50 point marked with vertical and horizontal reference lines. 95% CI band shaded around the fitted curve.

STEP 3 — Guards & Disclosures Activated

Biological vs. Technical Replicate Guard (4.5.2)

Technical replicates within a well or plate must be averaged before treating measurements as independent observations for IC50 confidence interval estimation. Licklider enforces this averaging and reports both the number of technical replicates and the number of biological replicates used for the fit.

Compositional Data Warning (4.7.2)

% viability data are bounded [0, 100]. If the raw data include values outside this range (e.g., >100% due to assay noise), Licklider flags this and allows the researcher to clip, cap, or keep as-is with a disclosure note.

Asymptote Constraint Disclosure

If the Top parameter is constrained to 100% (assuming full viability at vehicle) or the Bottom is constrained to 0% (assuming complete cytotoxicity at infinite dose), these constraints are disclosed. Unconstrained fits that produce biologically implausible asymptotes (Top > 130% or Bottom < -10%) trigger a warning.

Hill Slope Interpretation Guard

Hill slopes significantly greater than 1 (cooperativity) or less than 0.5 (shallow slope, possible multi-mechanism action) are flagged with a note recommending biological interpretation. The Hill slope and its 95% CI are always reported.

N Disclosure (1.2.1)

The number of biological replicates (3 experiments) and technical replicates (3 per dose per experiment) are both reported in the figure legend. "n=3 independent experiments, each with 3 technical replicates per dose."

STEP 4 — Export Package

• Figure: Sigmoidal 4PL dose-response curve with IC50 marker and 95% CI band — 300 dpi TIFF/PDF
• Statistical Report: IC50 (µM) with 95% CI; Hill slope with 95% CI; Top, Bottom parameters with CIs; R², RMSE; goodness-of-fit summary
• Methods Text: "Dose-response data were fitted to a 4-parameter logistic (4PL) model using non-linear regression. IC50 and 95% CI were calculated by [bootstrap/asymptotic approximation]. The Hill slope was unconstrained. Data are mean ± SEM of n=3 independent experiments (3 technical replicates per dose, averaged prior to fitting)."
• Figure Legend: IC50 value with CI, Hill slope, R², n (biological and technical), constraint disclosures
• Preprocessing Audit Log: Log-transformation applied; technical replicate averaging applied; any out-of-range viability values clipped/retained