Standard Curves & Quantification

A standard curve fits known concentrations against measured signal, then interpolates that curve to give concentrations for your unknowns. Three workflows in Gradiance share this machinery: sandwich ELISA, BCA/Bradford protein quant, and endpoint titer ELISA.

The three workflows

• Standard Curve / Sandwich ELISA. Linear or 4PL calibration to quantify cytokines, antibodies, antigens, or any other analyte with a sandwich-format readout.
• BCA / Bradford Protein. Total protein from a BSA or albumin standard. Linear or quadratic; account for sample dilution factor on output.
• Endpoint Titer ELISA. The dilution at which each sample crosses a cutoff (typically blank mean + 3 SD). Different shape, same idea: standards on one axis, signal on the other.

Choosing a model

Linear

y = mx + b. Fast and interpretable. Right for narrow ranges where the curve genuinely is linear (most BCA/Bradford experiments, the linear portion of an ELISA).

4PL

The standard for sandwich ELISA across a wide dynamic range. Fits Top, Bottom, EC₅₀, and Hill slope. Use it whenever your standards span enough orders of magnitude that the curve flattens at one or both ends.

Polynomial (2nd or 3rd order)

For metabolic kits and colorimetric assays that follow a smooth non-sigmoidal shape. Use only when linear is clearly insufficient and the data don't fit a sigmoid.

Log-log linear

Linear fit on log-transformed inputs and outputs. Right for power-law relationships and the rare colorimetric assay that produces a straight line on a log-log scale.

Gradiance suggests a model based on data shape. You can override: “use a 4PL for this curve” or “refit with a quadratic.”

Weighting

ELISA data is heteroscedastic — variance grows with signal. An unweighted fit lets the high standards dominate, which makes the curve accurate at the top and inaccurate at the bottom (where you often care most).

• None — equal weight on every point. Default for tight, low-noise standards.
• 1/Y — gives lower-signal points more leverage. Sensible when measuring low-abundance analytes.
• 1/Y² — stronger version of 1/Y. The right default for most clinical-style ELISAs.

Limits of quantification

LLOQ (lower) and ULOQ (upper) bound the range over which the curve is reliable. Gradiance derives them from the standards by default (±20% recovery on the low end, signal saturation on the high). Set them explicitly if your assay has validated values.

Unknowns falling below LLOQ are flagged <LLOQ; above ULOQ, >ULOQ. Either dilute the sample and re-measure, or report the limit, not a forced extrapolated value.

Marking standards vs unknowns

Two ways to identify which rows are standards and which are unknowns:

• Plate painter. If your data came from a 96-well layout, paint the standards (with concentrations) and unknowns on the plate. The agent picks them up automatically.
• Type column. Add a column to your CSV labelled type, role, or kind with values like standard and unknown. Standards must include a known concentration; unknowns can have any non-numeric placeholder.

Sample,Concentration,OD450,Type
Std1,0.1,0.245,standard
Std2,0.5,0.512,standard
Std3,2.0,1.123,standard
Std4,10.0,1.892,standard
Sample_A,,0.687,unknown
Sample_B,,1.456,unknown

Endpoint titer specifically

Endpoint titer is structurally a standard curve, but the question flips: instead of asking “what concentration produces this signal,” you ask “what dilution does this sample stop producing signal.”

• Each sample is a separate dilution series (typically 1:2 or 1:3).
• The cutoff is usually blank mean + 3 SD. Gradiance computes this automatically from the blank wells; you can override.
• Output is the dilution factor at which signal crosses the cutoff, per sample. Reported with 95% CI from the same 4PL machinery used for IC₅₀.

QC for standard curves

See Quality Control for the full list. The ones that matter here:

• R² threshold — > 0.99 for linear standards, > 0.98 for 4PL. Below those, refit with a different model rather than reporting a poor fit.
• Standard recovery. Each known standard is back-calculated from the fitted curve; recovery should land 80–120% of the nominal value.
• Hook effect. Sandwich ELISA can dip at very high concentrations. Watch for the highest standard sitting below the second-highest — that's the hook, and the fix is to drop that point or dilute samples below the hook region.

Designing a quantification run that fits well

• 6–8 standards spanning the expected unknown range, plus one standard well below and one well above where you expect samples to fall.
• Standards in duplicate or triplicate (recovery is more informative than extra concentrations).
• Plate the blanks consistently — a row, a column, or four replicates. The agent uses them to subtract background and compute LOD.
• Re-prep standards each run. Frozen reconstituted standards drift, and a drifted standard curve invalidates every unknown on the plate.