Finding Epsilon For A Protein Calculator

This calculator estimates the molar extinction coefficient (ε) of a protein at 280 nm, assuming all Cysteine residues form disulfide bonds (Cystine).

Parameter	Value	Unit
Number of Trp		residues
Number of Tyr		residues
Number of Cys		residues
Molecular Weight		Da
Assumed Cystine Bonds		bonds
Epsilon (Molar)		M⁻¹cm⁻¹
Epsilon (0.1%)		(mg/ml)⁻¹cm⁻¹

Summary of inputs and calculated extinction coefficients.

What is a Protein Extinction Coefficient?

The protein extinction coefficient, often denoted as epsilon (ε), is a measure of how much light a protein absorbs at a particular wavelength, typically 280 nm. It's a crucial parameter used in the Beer-Lambert law (A = εbc) to determine the concentration of a protein solution from its absorbance reading. The absorbance at 280 nm is primarily due to the presence of Tryptophan (Trp) and Tyrosine (Tyr) residues, and to a lesser extent, Cystine (disulfide bonds formed by Cysteine residues).

Knowing the extinction coefficient is essential for biochemists, molecular biologists, and anyone working with purified proteins who needs to accurately determine protein concentration. This protein extinction coefficient calculator helps estimate this value based on the amino acid composition.

Common misconceptions include thinking all proteins have the same extinction coefficient or that it's solely based on protein size. In reality, it's highly dependent on the number of Trp, Tyr, and Cys residues.

Protein Extinction Coefficient Formula and Mathematical Explanation

The molar extinction coefficient (ε) at 280 nm for a protein can be estimated based on the contributions of Tryptophan (Trp), Tyrosine (Tyr), and Cystine residues. The widely used formula, based on the work of Gill and von Hippel (1989) and Pace et al. (1995), is:

ε (M⁻¹cm⁻¹) = (Number of Trp × 5500) + (Number of Tyr × 1490) + (Number of Cystine × 125)

Where:

• Number of Trp is the count of Tryptophan residues in the protein.
• Number of Tyr is the count of Tyrosine residues in the protein.
• Number of Cystine is the count of disulfide bonds (each formed by two Cysteine residues). Our protein extinction coefficient calculator assumes all Cys residues form disulfide bonds, so Number of Cystine = Number of Cys / 2.
• 5500, 1490, and 125 are the molar extinction coefficients (in M⁻¹cm⁻¹) for Trp, Tyr, and Cystine at 280 nm, respectively, under specific conditions (e.g., 6 M guanidinium hydrochloride).

To express the extinction coefficient in terms more practical for concentration determination in mg/ml (or 0.1%), we use the protein's molecular weight (MW):

ε (0.1% or 1 mg/ml) = ε (M⁻¹cm⁻¹) / MW (in Daltons)

The protein extinction coefficient calculator provides both values.

Variables in Extinction Coefficient Calculation

Variable	Meaning	Unit	Typical Range/Value
#Trp	Number of Tryptophan residues	Count	0 – 50+
#Tyr	Number of Tyrosine residues	Count	0 – 100+
#Cys	Number of Cysteine residues	Count	0 – 50+
#Cystine	Number of disulfide bonds (#Cys/2)	Count	0 – 25+
ε(Trp)	Molar extinction coefficient of Trp	M⁻¹cm⁻¹	5500 or 5690
ε(Tyr)	Molar extinction coefficient of Tyr	M⁻¹cm⁻¹	1490 or 1280
ε(Cystine)	Molar extinction coefficient of Cystine	M⁻¹cm⁻¹	125
MW	Molecular Weight	Da (g/mol)	1,000 – 1,000,000+
ε (Molar)	Molar Extinction Coefficient	M⁻¹cm⁻¹	0 – 300,000+
ε (0.1%)	Extinction Coefficient for 0.1% (1 mg/ml) solution	(mg/ml)⁻¹cm⁻¹ or cm⁻¹ for 0.1%	0 – 3.0+

Practical Examples (Real-World Use Cases)

Let's see how our protein extinction coefficient calculator works with some examples.

Example 1: Bovine Serum Albumin (BSA)

Bovine Serum Albumin (BSA) has a molecular weight of approximately 66,463 Da. Its sequence contains about 2 Trp, 20 Tyr, and 35 Cys residues. Assuming all 35 Cys form 17.5 (so 17 complete) disulfide bonds:

• Number of Trp = 2
• Number of Tyr = 20
• Number of Cys = 35 (17 cystine bonds)
• Molecular Weight = 66463 Da

Using the formula: ε = (2 * 5500) + (20 * 1490) + (17 * 125) = 11000 + 29800 + 2125 = 42925 M⁻¹cm⁻¹. The ε (0.1%) = 42925 / 66463 ≈ 0.646 (mg/ml)⁻¹cm⁻¹. Published values for BSA are around 0.667 (mg/ml)⁻¹cm⁻¹, showing our calculator provides a good estimate.

Example 2: Lysozyme (Chicken Egg White)

Lysozyme has a MW of about 14,300 Da, with 6 Trp, 3 Tyr, and 8 Cys residues (forming 4 disulfide bonds).

• Number of Trp = 6
• Number of Tyr = 3
• Number of Cys = 8 (4 cystine bonds)
• Molecular Weight = 14300 Da

ε = (6 * 5500) + (3 * 1490) + (4 * 125) = 33000 + 4470 + 500 = 37970 M⁻¹cm⁻¹. The ε (0.1%) = 37970 / 14300 ≈ 2.655 (mg/ml)⁻¹cm⁻¹. Published values are around 2.64-2.65.

How to Use This Protein Extinction Coefficient Calculator

1. Enter Amino Acid Counts: Input the total number of Tryptophan (Trp), Tyrosine (Tyr), and Cysteine (Cys) residues found in your protein sequence. If you don't know these, you can obtain them from the protein sequence using online tools by inputting the FASTA sequence. Our protein molecular weight calculator might also provide this.
2. Enter Molecular Weight: Input the molecular weight of your protein in Daltons (Da) or g/mol.
3. Calculate: The calculator automatically updates, or click "Calculate". It assumes all Cys form disulfide bonds (#Cystine = #Cys / 2, rounded down if odd #Cys).
4. Read Results: The calculator displays the Molar Extinction Coefficient (ε) in M⁻¹cm⁻¹ and the extinction coefficient for a 1 mg/ml (0.1%) solution. Intermediate contributions from Trp, Tyr, and Cystine are also shown.
5. Use for Concentration: Once you have ε (1 mg/ml), you can measure the absorbance (A) of your protein solution at 280 nm in a 1 cm cuvette and calculate concentration (C) in mg/ml using: C (mg/ml) = A / ε (1 mg/ml). Explore our protein concentration calculator for this step.

Key Factors That Affect Protein Extinction Coefficient Results

• Amino Acid Composition: The number of Trp, Tyr, and Cys residues are the primary determinants of ε at 280 nm. Proteins rich in Trp will have a much higher ε.
• Disulfide Bonds (Cystine): The formation of disulfide bonds (Cystine) contributes to absorbance at 280 nm, though less significantly than Trp or Tyr. Our protein extinction coefficient calculator assumes full disulfide bonding for Cys. Reduced Cys do not contribute via the 125 M⁻¹cm⁻¹ factor.
• Wavelength: The extinction coefficient is wavelength-dependent. This calculator is specifically for 280 nm. Other wavelengths (e.g., 205 nm) are more sensitive but also more prone to interference.
• Solvent Conditions: pH, ionic strength, and denaturants (like 6M Guanidine HCl) can slightly alter the ε values of Trp and Tyr, and affect protein conformation which might expose or bury these residues. The values 5500, 1490, and 125 are often cited for denatured proteins in 6M GdnHCl.
• Protein Conformation/Folding: The local environment of Trp and Tyr residues within the folded protein can slightly shift their absorbance maxima and ε values compared to denatured state values.
• Presence of Other Chromophores: If the protein contains non-amino acid components (e.g., heme groups, cofactors) that absorb at 280 nm, the calculated ε based on amino acids alone will be an underestimate.
• Light Scattering: Particulate matter or protein aggregation in the solution can cause light scattering, leading to an artificially high absorbance reading and incorrect concentration if not accounted for. Read more about protein quantification methods.

Frequently Asked Questions (FAQ)

Why is 280 nm used for protein concentration?

280 nm is used because Tryptophan and Tyrosine residues have strong absorbance maxima near this wavelength, and most other biological molecules (except nucleic acids) absorb weakly at 280 nm, reducing interference.

What if my protein has no Tryptophan or Tyrosine?

If a protein lacks Trp and Tyr, its absorbance at 280 nm will be very low, mainly due to Cystine, making concentration determination at 280 nm inaccurate. Other methods (e.g., BCA, Bradford, or absorbance at 205 nm) would be better. See protein quantification methods.

How accurate is the calculated extinction coefficient?

The calculated value is an estimate. It's generally accurate to within ±5-10% for many proteins, especially if the 5500/1490/125 values are appropriate for the conditions. For highly accurate work, experimental determination is recommended.

What if not all Cysteine residues form disulfide bonds?

Our protein extinction coefficient calculator assumes all Cys form disulfide bonds. If you know the exact number of disulfide bonds, you can manually calculate using #Cystine = number of bonds. If some Cys are free, their contribution at 280 nm is negligible compared to Cystine.

Can I use this for peptides?

Yes, the principle is the same, but for very small peptides, the contribution of the peptide bond itself (absorbing around 205-220 nm) might become relatively more significant if measuring at lower wavelengths.

What does ε (0.1%) mean?

It refers to the absorbance of a 0.1% (which is 1 mg/ml) solution of the protein in a 1 cm path length cuvette. It's a convenient unit for direct concentration calculation in mg/ml from absorbance readings.

How do I get the number of Trp, Tyr, and Cys from a sequence?

You can use sequence analysis tools (like ExPASy's ProtParam or our protein molecular weight calculator by inputting the FASTA sequence) to get the amino acid composition.

What if my protein has prosthetic groups that absorb at 280 nm?

If your protein contains non-protein components (like heme or NAD) that absorb significantly at 280 nm, the calculated ε based only on amino acids will be lower than the true ε of the holo-protein.