How are extinction coefficients determined for Proteins?

Extinction coefficients for proteins are determined at absorbance maxima near 280 nm.

Protein analysis is needed to determine if a sample solution contains the desired protein. For example, measuring the absorbance of a protein sample at 280 nm with a spectrophotometer is a rapid and straightforward method. In many bio-analytical applications, it is important to estimate or accurately determine the concentration of sample solutions containing purified biomolecules such as oligonucleotides, peptides or proteins. Often this information is needed or used for the design of down-stream experiments in analytical chemistry, biology, biochemistry, biophysics, medicinal chemistry, and pharmacy.

• Absorption of UV light by side chains and peptide bonds of a protein.
• Chromogenic reactions involving complexes formed under alkaline conditions between protein and cuprous ions employing the biuret reaction. 
• Binding of a chromophore to the protein.
• Dot-blotting and staining.

Each method has advantages and limitations. Therefore amino acid analysis should also be considered for quantitative analysis of unknown proteins.

Amino acid analysis in combination with UV-absorbance measurements at 280 nm can be used to accurately determine protein concentrations as well as extinction coefficients in unknown protein samples. UV absorbance is the most popular method because it is fast, convenient, and reproducible. UV-absorbance measurements do not consume the protein and do not require additional reagents, standards or incubations. However, the measurement of protein solutions at 280 nm is not strictly quantitative for all proteins since the assay is based on the strong absorbance of tyrosine, tryptophan and phenylalanine residues. Protein concentrations can also be measured at 214 nm, and at 205 nm. 

No method of protein concentration determination is perfect because each method has different constrains. Interfering buffer components, contaminating proteins or reactivity of individual proteins and buffer components can influence the measurement and lead to false values. Therefore amino acid analysis is still considered to be the most accurate method for protein quantification, in particular when a highly purified protein sample is used. If accurate protein concentrations are critical, results from several methods or assays may need to be compared to trust the observed values. 

Proteins and peptides containing aromatic amino acid side chains exhibit strong UV-light absorption, and each protein has a distinct UV spectrum. Proteins and peptides absorb UV-light proportional to their amino acid content and total concentration. Different proteins may have widely varying extinction coefficients. If a protein does not contain any tyrosine, tryptophan, and phenylalanine residues, it will not be detected.

Optical spectroscopy is used in biochemistry for the observation and measurement of the absorption of oligonucleotide, peptide and protein solutions in the UV range. According to Planck’s law, E = hν, the absorbed energy must be related to the difference between energy levels and the linearity of absorbance is usually confined to dilute solutions governed by the Beer-Lambert law describing the absorption process:

A = log (I/I₀) = ϵlc    => Beer-Lambert equation.

where A is the absorbance, I and I0 are the intensities of the transmitted and incident light beams, respectively, ϵ is the proportionality constant or specific extinction coefficient, l is the optical path length, and c is the concentration of the absorbing species usually reported in mol/L.

When light of a specific wavelength λ is passed through a solution layer at a path length L of the solution, a certain portion of the light is absorbed by the solution if the solution has a specific absorbance at this wavelength. The fraction of light transmitted is known as transmittance T. For homogenous samples, each successive layer of the solution will receive fractionally less light. Beer-Lamberts law mathematically describes this phenomenon. Beer-Lamberts law describes the exponential decay of the transmitted light versus path length and concentration.

The transmittance T decreases exponentially with respect to the concentration C of the compound and to the length of the light path, L.

T = 10^-ϵcL  =>  -log₁₀T = log₁₀(1/T) = ϵcL =A    => Beer-Lambert equation.

Where ϵ is the absorption coefficient or absorptivity, characteristic for the compound measured at the particular wavelength of light under a defined set of conditions. The absorptivity is also known as extinction coefficient.

The absorbance A is defined as –log10T.  
Often absorbance is also called optical density (OD).

Extinction Coefficient

According to Merriam-Webster, the extinction coefficient refers to “a measure of the rate of transmitted light via scattering and absorption for a medium.” However, in analytical chemistry, the quantity ϵ (epsilon) is called the molar absorptivity (ϵmolar) or extinction coefficient. ϵ has the units M-1 cm-1. Molar absorptivity refers to the characteristics of a substance that tells how much light is absorbed at a particular wavelength.  Whereas the “specific absorption coefficient (a)” refers to the absorbance of light per unit path length, usually expressed in cm, and per unit of mass concentration. 

The “molar absorption coefficient (ϵ_molar)” refers to the absorbance of light per unit path length and per unit of concentration expressed in “moles per liter.”

For proteins, an absorbance maximum near 280 nm (A₂₈₀) in the UV spectra of a protein solution is mostly due to the presence of aromatic tryptophan and tyrosine residues, and to a minor portion phenylalanine. For a given protein, the A₂₈₀ is proportional to its concentration of amino acids. However, corrections may be needed to calculate the accurate absorbance value, the type, and the environment the amino acids are in. Using the known amino acid sequence of a protein allows estimation of a sufficiently accurate extinction coefficient.

In general, a 1 mg/ml solution of most proteins has an A₂₈₀ of ~ 1 ± 0.6. 

Since the introduction of the NanoDrop 1000 and the NanoDrop 8000 A280 instruments, these spectrophotometers are now often used for routine measurements of protein absorbance at 280 nm.  

Using a spectrophotometer such as the nanodrop instrument the concentration of a purified protein samples is determined according the Beer-Lambert equation [A = E * b * c ] which is used for all protein calculations to correlate absorbance with concentration. Where A = absorbance value (A), E = wavelength-dependent molar absorptivity coefficient (or extinction coefficient) with units of liter/mol-cm, b = the path length in centimeters, c = analyte concentration in moles/liter or molarity (M).

The equation for the Beer-Lambert law can also be written as [ A_λ = ϵ_λbc ] because A and ϵ depend on the wavelength of light. The greater the molar absorptivity, the greater the absorbance, and A and ϵ vary with the wavelength. Furthermore, the part of a molecule that is responsible for light absorption is called a chromophore. 

Each protein has a distinct UV spectrum as well as an extinction coefficient at 280 nm (ϵ₂₈₀). The specific UV spectrum is based on its amino acid composition. Major contributions to the spectra stem from aromatic tryptophan (W) and tyrosine (Y) residues with high extinction coefficients of 5500 and 1490 M-1cm-1. Phenylalanine (F) absorbs maximally at 260 nm but little at 280 nm. Cystine (C) in disulfide bonds has a relatively low extinction coefficient of 125 M-1cm-1. The absorbance of reduced cysteine is negligible at wavelength above 260 nm.

If the number of absorbing side chains in the amino acid sequence of a protein is known the specific extinction coefficient at 280 nm can be estimated using the following formula:

ϵ₂₈₀ = nW x 5,500 + nY x 1,490 + nC x 125

where ϵ₂₈₀ is the molar extinction coefficient at 280 nm, and n is the number of corresponding residues present in the protein.

Molar concentration can be calculated as follows:

Molar concentrations = A₂₈₀ x (dilution factor) / ϵ₂₈₀

Concentrations [mg/ml] =  A₂₈₀ x (dilution factor) x (moluclar weight in daltons  / ϵ₂₈₀

When nucleic acids are present, the following correction can be used:

Protein concentration (mg/ml) = 1.55A₂₈₀ – 0.75A₂₆₀

where A₂₈₀ and A₂₆₀ are the absorbance values of the protein solution at 280 nm and 260 nm.

A table of extinction coefficient values for selected proteins is shown in Table 1.

Table 1:  Absorbance and Extinction Coefficient Values for selected Proteins

Measuring Absorbance

Measurements of protein samples can be performed in a standard spectrophotometer with quartz or methacrylate cuvettes or, in the case of a Nanodrop instrument, by directly using a small aliquot of the solution, ~1.5 μl. To monitor the quality of the spectrum, a scan over a range of wavelengths should be performed to determine the maximum absorbance of the protein solution. For a protein solution, the maximum absorbance should occur near 280 nm. 

Before measuring the absorbance of the protein sample, a matching buffer or a water reference is scanned as a blank of baseline to correct for background absorbance. For accurate measurements, it is important to adjust the protein concentration to an absorbance value within the linear dynamic range of the spectrophotometer.

Dilute samples may need to be concentrated, and more concentrated samples must be diluted prior to measurements. Also,  accurate UV spectra of protein solutions depend on the absence of interfering substances that absorb at 280 nm or close to 280 nm. These include nucleic acids (DNA, RNA) or nucleotides (ATP, GTP, etc.), many small molecules (imidazole, nicotinamide adenine dinucleotide [NADH], and others), certain detergents (for example Triton X-100, Nonidet P-40), or proteins with prosthetic groups, such as heme, that absorb in the near-UV range.   

Conversions

The relationship between molar extinction coefficient (ϵ_molar) and percent extinction coefficient (ϵ^1%) is:

  (ϵ_molar)*10 = (ϵ^1%) x (molecular weight of protein)

Example 1:  Determination of ϵ^1% for a protein.

Molar extinction coefficient = 43,824 M^-1cm^-1.

Molecular weight (Mw) = 66,400 daltons.

   ϵ^1% = 6.6

Example 2:  Determination of ϵ^1% for an IgG protein.

Molar extinction coefficient = 210,000 M-1cm-1.

Molecular weight (Mw) = 150,000 daltons.

  ϵ^1% = 14

Example 3:  Bovine serum albumin (BSA). NIST based solution at 2 mg/ml in 0.9% NaCl.

The product (BSA standard Nos. 23209 or 23210 from Pierce) is calibrated by absorbance at 280 nm to a BSA Fraction V standard from the National Institute of Standards and Technology (NIST) for which the reported percent solution absorbance (= ϵpercent ) is equal to 6.67.

The predicted absorbance at 280 nm for this standard solution at 2 mg/ml is:

   {(6.67)(2.00)(1)} / 10 = 1.334

If an absorbance reading of 1.346 is obtained relative to a water reference, the calculated concentration is:

(1.346 / 6.67) 10 = 2.018 mg/ml 

Immunoglobulins

Most mammalian antibodies (i.e., immunoglobulins) have protein extinction coefficients (ε percent) in the range of 12 to 15. Therefore, for typical antibody solutions, the following numbers are assumed:

For a typical IgG with MW = 150,000, this value corresponds to a molar extinction coefficient (ε) equal to 210,000 M-1cm-1. 

The typical ϵ_percent or A_percent280nm used for the nanodrop for IgGs is A_{^1%280 nm} = 13.7  or A^0.1%_280nm = 1.37.

For unknown IgG samples the reference option is used to calculate protein concentrations using the mass extinction coefficient of 13.7 at 280 nm for a 1% (10 mg/ml) IgG solution.

Another useful conversion is a conversion from DNA units to protein units and vice versa:

   10,000 Mw protein ~ 270 bp DNA

Reference

Bollag, Daniel M. and Edelstein, Stuart J.; Protein Methods. Wiley-Liss. 1991. 

Green, Michael R. and Sambrook, Joseph; Molecular Cloning – A Laboratory Manual. 4th Edition. Cold Spring Habor Laboratory Press. 2012.

Harris, Daniel C.; Quantitative Chemical Analysis. 5th edition. W.H. Freeman and Company, NY. 1998.

NanoDrop 1000 & 8000 T010-Technical Bulletin. Thermo Fisher Scientific.

Ninfa, Alexander and Ballou, David P.; Fundamental Laboratory Approaches for Biochemistry and Biotechnology. Fitzgerald Science Press, Inc. Bethesda, Maryland.  1998.

Simpson, Richard J., Adams, Peter D. , and Golemis, Erica A.; Basic Methods in Protein Purification and Analysis – A laboratory manual. CSH Press. 2009.

TECH TIP #6 Extinction Coefficients Thermo Scientific