BCA and Bradford protein assay standard curve calculator

$$\text{Net }A=A-\mathrm{mean}(A_{\mathrm{blank}})$$$$\begin{array}{rl}& \text{Quadratic:}\\ \text{net }A& =a+b\cdot c+q\cdot c^2\\ \Rightarrow c& =\frac{-b+\sqrt{b^2-4q(a-\text{net }A)}}{2q}\end{array}$$$$\begin{array}{rl}& \text{Linear:}\\ \text{net }A& =a+b\cdot c\\ \Rightarrow c& =(\text{net }A-a)/b\end{array}$$$$\begin{array}{rl}& \text{Protein in the sample}\\ & =c\times \text{dilution factor}\end{array}$$

The mean absorbance of the 0 µg/mL standard (the blank: diluent plus reagent) is subtracted from every standard and sample reading, as both kit protocols instruct. The curve is fitted by ordinary least squares to every replicate of every standard, including the blank as the 0 point. For the quadratic, the root on the rising part of the curve is taken; if the fitted parabola peaks inside the standard range, the top standards are saturated and the calculator says so. The mean net absorbance of each sample is converted to a concentration in the well and multiplied by its dilution factor. Samples above the top standard or below the lowest non-zero standard are flagged: dilute them, or concentrate them, and repeat.

BCA (A562). $\mathrm{Cu}{\phantom{A}}^{2+}$ is reduced to $\mathrm{Cu}{\phantom{A}}^{+}$ by protein in alkaline solution and bicinchoninic acid chelates $\mathrm{Cu}{\phantom{A}}^{+}$, forming a purple complex absorbing at 562 nm (Smith et al. 1985). The Pierce kit gives a working range of 20–2000 µg/mL and a standard series of 2000, 1500, 1000, 750, 500, 250, 125, 25 and 0 µg/mL BSA; its user guide notes that the response is “nearly linear” and that a quadratic or other best-fit curve gives more accurate results than a straight line.

Bradford (A595). Coomassie Brilliant Blue G-250 binds protein and shifts from its red cationic form (470 nm) to the blue anionic form (595 nm) (Bradford 1976). The response is not linear over the usual range: the free dye also absorbs at 595 nm and is used up as protein is added, so the curve flattens at high concentration (Zor and Selinger 1996). Bio-Rad’s Quick Start Bradford assay supplies BSA standards from 125 to 2000 µg/mL but gives a linear range for BSA of only 125–1000 µg/mL (1.25–10 µg/mL in the micro assay). Over the full series, fit a quadratic; for a straight line, keep to the linear range.

Assumptions. Standards and samples are in the same buffer and read at the same time; the protein responds like BSA (the colour yield varies between proteins, so report concentrations as “BSA equivalents”); and interfering substances (reducing agents and chelators for BCA, detergents for Bradford) are below the kit limits.

Sources: Smith PK, Krohn RI, Hermanson GT, et al. Measurement of protein using bicinchoninic acid. Anal Biochem 1985;150:76–85, doi:10.1016/0003-2697(85)90442-7. Bradford MM. A rapid and sensitive method for the quantitation of microgram quantities of protein utilizing the principle of protein-dye binding. Anal Biochem 1976;72:248–254, doi:10.1016/0003-2697(76)90527-3. Zor T, Selinger Z. Linearization of the Bradford protein assay increases its sensitivity: theoretical and experimental studies. Anal Biochem 1996;236:302–308, doi:10.1006/abio.1996.0171. Thermo Scientific Pierce BCA Protein Assay Kit user guide (MAN0011430); Bio-Rad Quick Start Bradford Protein Assay instruction manual (4110065A).

Both built-in examples are synthetic duplicates shaped like the BSA curves in the kit inserts.

BCA assay, test-tube protocol (A562)

1. Blank. The 0 µg/mL standard reads 0.115 and 0.103; the mean, 0.109, is subtracted from every reading.
2. Fit. A quadratic through the 18 standard readings gives

   $$\begin{array}{rl}\text{net }{A}_{562}=& 0.0000838+0.0014079\cdot c\\ & -1.3280\times {10}^{-7}\cdot c^2\end{array}$$

   ($c$ in µg/mL), $R^2=0.99986$. A straight line gives $R^2=0.9957$, which looks good but misreads the standards (table below).

3. Read the samples. Lysate A reads 0.952 and 0.968, a net A562 of 0.851. Solving the quadratic gives 643.5 µg/mL in the well; it was diluted 5-fold, so the lysate contains 3217 µg/mL (3.2 mg/mL). Lysate B (net 0.501, diluted 10-fold) reads 368.6 µg/mL in the well, or 3686 µg/mL.
4. Check the flags. Lysate C (net 2.541) reads 2307 µg/mL, above the 2000 µg/mL standard: dilute it and repeat. The flow-through (net 0.0105) reads 7.4 µg/mL, below the 25 µg/mL standard, so it is reported as below the range rather than as a number.

The straight line reads the middle standards about 5% high and the low ones far too low; for Lysate A it gives 3455 µg/mL instead of 3217 µg/mL, a 7% error.

Bradford assay (A595)

Standards 125–2000 µg/mL with a blank of 0.378. The curve bends clearly: a straight line has $R^2=0.969$ and recovers the 125 µg/mL standard at 47%, while the quadratic

$$\begin{array}{rl}\text{net }{A}_{595}=& 0.00241+0.0011249\cdot c\\ & -2.172\times {10}^{-7}\cdot c^2\end{array}$$

has $R^2=0.9997$ and recovers every standard within 99–105%. Sample 1 (net A595 0.6195, diluted 2-fold) reads 623.7 µg/mL in the well, so 1247 µg/mL in the sample; the straight line would give 1465 µg/mL, 17% too high.