Standard Curves

Standard curve analysis allows you to quantify unknown sample concentrations by interpolating from a calibration curve built with known standards.

When to Use Standard Curves

• ELISA: Quantify cytokines, antibodies, antigens
• Protein quantification: BCA, Bradford, Lowry assays
• Metabolite assays: Glucose, lactate, ATP quantification
• Nucleic acid quantification: DNA/RNA concentration

Curve Fitting Models

Linear Regression

The simplest model: y = mx + b

Best for: Narrow concentration ranges and simple assays like Bradford protein assays.

4-Parameter Logistic (4PL)

The gold standard for ELISA and other immunoassays with wide dynamic ranges.

Parameters: Top, Bottom, EC₅₀, Hill Slope

Best for: Sandwich ELISA, competitive binding assays, most immunoassays.

Polynomial Regression

2nd or 3rd order polynomial fits: y = a + bx + cx² (+ dx³)

Best for: Non-linear assays that don't fit sigmoidal curves (some metabolic kits).

Log-Log Linear

Linear fit on log-transformed data: log(y) = m × log(x) + b

Best for: Power-law relationships and certain colorimetric assays.

Model Selection

Gradiance will automatically suggest the best model based on your data:

• Default: Starts with linear regression
• If non-linear: Suggests polynomial or 4PL
• Wide dynamic range: Recommends 4PL (especially for ELISA)

Configuration Options

Weighting

Weighting adjusts the importance of different points in the fit:

• None: All points weighted equally (default)
• 1/Y: Lower concentrations have higher precision
• 1/Y²: Stronger weighting for low concentrations

Limits of Quantification

Define the valid quantification range:

• LLOQ (Lower Limit of Quantification): Lowest reliable concentration
• ULOQ (Upper Limit of Quantification): Highest reliable concentration

Unknown samples outside this range will be flagged as below/above quantification limits.

Quantifying Unknowns

After fitting the standard curve, Gradiance can interpolate unknown sample concentrations:

Data Format

Include unknowns in your data file with identifier labels:

Sample,Concentration,Absorbance,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,NA,0.687,unknown
Sample_B,NA,1.456,unknown

Interpolation

Gradiance will:

1. Fit the curve using standards
2. Interpolate unknown concentrations from their measured responses
3. Calculate confidence intervals
4. Flag values outside LLOQ/ULOQ

Quality Control

Standard Recovery Check

Coming soon: Back-calculate standard concentrations and compare to known values. Recovery should be 80-120% for high-quality fits.

R² Threshold

For publication-quality standard curves:

• Linear fits: R² > 0.99
• 4PL fits: R² > 0.98

Curve Inspection

Always visually inspect your standard curve to check for:

• Outliers (standards that don't fit the trend)
• Hook effect (signal decrease at high concentrations in sandwich ELISA)
• Poor dynamic range (limited signal change across standards)

Example Analysis

Best Practices