Dose-Response
Supported IC50 and EC50 dose-response fitting with unweighted 3PL, 4PL and 5PL models
The supported dose-response path converts a concentration series into a potency estimate, with a confidence interval when it can be estimated. IC₅₀ and EC₅₀ use the same relative half-response endpoint; 4PL is the default. Cytotoxicity and neutralization variants remain Preview.
Common variants and Preview workflows
- IC₅₀ (inhibition). Concentration at half-maximal inhibition. The signal goes down with dose.
- EC₅₀ (stimulation). Concentration at half-maximal response. The signal goes up with dose.
- CC₅₀ (cytotoxicity, Preview). IC₅₀ on a viability readout. Often reported alongside an EC₅₀ as a selectivity index (CC₅₀/EC₅₀).
- NT₅₀ (neutralization, Preview). Antibody or serum titer at 50% neutralization. Doses are dilution factors rather than concentrations and require a separately reviewed endpoint definition.
Choose the supported dose-response workflow in the new-run picker. Review the concentration and response columns and their units before starting. Automatic control normalization is outside the launch method. If your response values are already normalized, label their units and preserve the controls and calculation used to obtain them.
The model
4PL (the default)
The supported four-parameter logistic fits a sigmoid that is symmetric on a log-concentration axis. For positive concentrations, Gradiance uses this parameterization:
y = Bottom + (Top - Bottom) / (1 + (x / IC50)^Hill)- Top - upper plateau (e.g. 100% viability)
- Bottom - lower plateau (e.g. 0% viability)
- IC₅₀ / EC₅₀ - concentration at the midpoint between Top and Bottom
- Hill - direction and steepness: positive for decreasing responses and negative for increasing responses in this parameterization. Steepness alone does not establish a biological mechanism.
Zero-dose observations are retained using the model's limit at zero.
Constrained 3PL (LL.3)
Request 3PL to fix the lower plateau at zero and fit Top, midpoint and Hill slope. This is the three-parameter log-logistic model used in the published ryegrass example. Its midpoint is half the fitted Top. A decreasing three-parameter log-normal model (LN.3) is also available when explicitly requested; it is a different curve family.
y = Top / (1 + (x / C50)^Hill); Bottom = 05PL for asymmetric curves
Request 5PL to add a fitted asymmetry parameter. The primary result is the concentration at half the fitted asymptote span. The scale parameter is shown separately and is generally different from that midpoint.
y = Bottom + (Top - Bottom) / (1 + (x / Scale)^Hill)^s
C50 = Scale * (2^(1/s) - 1)^(1/Hill)The midpoint interval propagates the full fitted covariance through log(C50), uses Student-t with n − 5 residual degrees of freedom, and transforms the bounds back to concentration units. It is conditional on the model and supplied observations, not a measure of biological variability. The scale interval is never reused as the midpoint interval. Fits at numerical bounds or with poorly identified parameters can have no interval. Compare residuals and uncertainty as well as fit quality before accepting the extra asymmetry parameter.
Supported constraints
The 3PL lower plateau is fixed at zero by its model definition. Other user-fixed parameters, custom bounds and weighting are unavailable. 4PL and 5PL fit all their parameters within recorded numerical bounds. Unsupported settings must not silently produce a different model.
Concentrations and response units
Supply non-negative concentrations in one consistent unit. A logarithmic plot changes the display, not the concentration values passed to the fit. Review any blank handling or exclusions in the executed method. Changing a unit label does not convert the observations, and a percent label does not normalize a raw response.
Reviewing observations and exclusions
Review the fitted observations, residuals and calculator warnings. The supported path does not automatically identify or remove outliers. An exclusion must identify the source row and a reason in the reviewed calculation. A refinement starts a new attempt on the same run and preserves the previous result; the source record shows which rows were included or excluded.
QC checks specific to dose-response
See Quality Control for the full list. The ones that matter most here:
- IC₅₀ extrapolated. The fitted midpoint sits outside your tested range. Review whether the experiment brackets the response midpoint before relying on the estimate.
- Curve may not reach both plateaus. This calculator warning is a prompt to inspect the measured range and fitted curve; it does not identify a particular missing plateau.
- Unusual Hill slope. The calculator flags an absolute slope below 0.5 or above 4. The sign describes curve direction; this warning alone does not explain the biological cause.
- Uncertain or unavailable intervals. Too few observations or an unstable covariance estimate can prevent an interval. A covariance interval crossing zero concentration is explicitly flagged as unreliable. Missing intervals remain unavailable.
Before accepting the result
Check that the mapped rows belong to the intended experiment, the units and any prior normalization are correct, and the observed range supports the reported midpoint and plateaus. A high R² or a completed fit does not resolve missing controls, an unsuitable model or uncertain parameters.
What the result looks like
A successful fit reports the midpoint, Top, Bottom, Hill, R² and calculator warnings, with available 95% covariance intervals. Free accounts can export a PNG figure and basic CSV results. Entitled accounts may also export the figure in other formats and Figure replay (Python); that replay does not refit your raw data. See Understanding your results for how to read the parameter table.