Protein Molar Ratio Calculation: 10 kDa vs 20 kDa Solutions Mixed Equally

Core Calculation

Mixing 20 μl of 10 mg/ml protein A (MW 10 kDa) with 20 μl of 10 mg/ml protein B (MW 20 kDa) yields a distinct molar ratio (A:B). Although each solution contributes 0.2 mg of protein, the number of moles differs due to their molecular weights:

• Protein A: 0.2 mg / 10,000 g/mol = 0.00002 mol = 20 nmol
• Protein B: 0.2 mg / 20,000 g/mol = 0.00001 mol = 10 nmol

Thus, the molar ratio A:B = 20 nmol : 10 nmol, which simplifies to 2:1. Protein A, which has half the molecular weight, has twice the number of moles for equal mass.

Step-by-Step Molar Ratio Math

1. Calculate mass of protein A:
   20 μl × 10 mg/ml = 0.2 mg = 0.0002 g
2. Calculate moles of protein A:
   \( \frac{0.0002 \text{ g}}{10,000 \text{ g/mol}} = 2 \times 10^{-8} \text{ mol} = 20 \text{ nmol} \)
3. Calculate moles of protein B:
   \( \frac{0.0002 \text{ g}}{20,000 \text{ g/mol}} = 1 \times 10^{-8} \text{ mol} = 10 \text{ nmol} \)
4. Compute molar ratio: A : B = 20 nmol : 10 nmol = 2:1

The total solution volume (40 μl) is ignored for ratio calculation because molar ratio depends on absolute moles, not concentration.

Why Not Other Options?

• 1:1 — Incorrect, assumes equal moles for equal mass/concentration, ignoring molecular weight difference.
• 2:1 — Correct; reflects the inverse proportionality of moles to molecular weight.
• 1:2 — Incorrect; reverses the protein order (would be B:A, not A:B).
• 2:2 — Incorrect; simplifies to 1:1 and ignores mole differences.

Biochemistry Applications

This molar ratio calculation is essential in:

• Protein-protein binding studies
• Determining stoichiometry in protein complexes
• Enzyme-substrate or antibody-antigen assays like ELISA where molar equivalence matters

Always convert mass concentration (mg/ml) to molarity using the molecular weight (kDa) before mixing:

M (μmol/ml) = (mg/ml × 10) / kDa