The Beer–Lambert Law and Protein Concentration Formula
Protein concentration is calculated by rearranging the Beer–Lambert law, which describes how light absorption relates to the concentration of an absorbing species. The standard form relates absorbance to the extinction coefficient, pathlength, and molar concentration. Since proteins are typically quantified by mass rather than molarity, we incorporate the molecular weight to convert between these units.
C = (A ÷ (ε × b)) × m × n
C— Protein concentration (mg/mL or µg/mL depending on units chosen)A— Absorbance measured at λmax (typically 280 nm for proteins)ε— Extinction coefficient in M⁻¹ cm⁻¹ (specific to the protein and wavelength)b— Pathlength of the cuvette in cm (usually 1 cm for standard spectrophotometry)m— Molecular weight of the protein in g/moln— Dilution factor (1 for undiluted stock; higher values for diluted samples)
Understanding the Key Parameters
Absorbance at 280 nm: Proteins absorb ultraviolet light most strongly at 280 nm due to the aromatic amino acids tryptophan and tyrosine. A spectrophotometer measures how much light the sample absorbs at this wavelength, expressed as a dimensionless absorbance value (optical density). Higher absorbance indicates higher protein concentration, but only within the linear range of the instrument.
Extinction Coefficient: This wavelength-specific constant quantifies how strongly a particular protein absorbs light. It varies based on amino acid composition—proteins rich in tryptophan and tyrosine have higher extinction coefficients. You can obtain this value from literature, supplier documentation, or by calculation if you know the protein sequence.
Pathlength and Dilution: Standard cuvettes have a 1 cm pathlength. If you dilute your sample before measurement (e.g., a 1:5 dilution), enter the dilution factor (5 in this example) so the calculator accounts for the dilution and reports the concentration of the original stock solution.
Measurement Techniques Beyond Absorbance at 280 nm
While UV absorbance at 280 nm is the most straightforward and rapid method, alternative colorimetric assays exist for specialized applications:
- Bradford assay: The Coomassie Brilliant Blue G-250 dye shifts from red to blue when bound to denatured proteins, with peak absorbance shifting from 465 to 595 nm. This method is sensitive and works well for denatured samples but requires a calibration curve.
- BCA assay: Bicinchoninic acid produces a purple complex with Cu⁺ ions released during protein reduction. It is more compatible with detergents and reducing agents than Bradford but is slower and requires incubation.
- Lowry assay: An older method combining Folin–Ciocalteu reagent with the BCA reaction, offering high sensitivity but susceptibility to interference from common lab reagents.
Each method has trade-offs in speed, sensitivity, and compatibility with sample buffers. For purified proteins without interfering substances, direct 280 nm measurement remains the gold standard.
Common Pitfalls and Best Practices
Accurate protein quantification requires attention to several practical details.
- Ensure spectrophotometer calibration — Spectrophotometers drift over time and with temperature changes. Calibrate with a blank cuvette (usually your buffer or solvent) before measuring samples. Use matched cuvettes and ensure the optical surfaces are clean and dry to avoid systematic errors that inflate or deflate readings.
- Account for interfering substances — Nucleic acids, phenol, and some reducing agents also absorb at 280 nm, causing overestimation of protein concentration. If your sample contains significant DNA or RNA, consider removing it via RNase/DNase treatment or use an alternative method like Bradford assay that is less affected by nucleic acids.
- Work within the linear absorbance range — Most spectrophotometers are accurate between absorbance values of 0.1 and 1.0. If your sample is too concentrated (A > 2), dilute it proportionally and adjust the dilution factor in the calculator. If it is too dilute (A < 0.05), concentrate the sample or increase the pathlength if your instrument allows it.
- Verify extinction coefficient and molecular weight — Using incorrect values for extinction coefficient or molecular weight will produce misleading results. Confirm these parameters from the protein supplier, UniProt database, or literature before entering them. For custom proteins, calculate the extinction coefficient from the amino acid sequence using Sauer's algorithm or similar tools.