Ammonium Sulfate Precipitation Calculator: Solid Amount for Protein Fractionation

Salting-out and ammonium sulfate fractionation

High salt concentrations compete for the solvation water around protein surfaces, reducing protein solubility and causing aggregation and precipitation. Different proteins begin to precipitate at different salt concentrations; exploiting this difference for crude separation is called fractionation. Ammonium sulfate has extremely high solubility, is inexpensive, and largely preserves activity—making it the reagent of choice.

Amounts are conventionally expressed as percent saturation rather than mol/L: at a given temperature the two can be interconverted precisely, and historical literature and textbook tables are indexed by saturation.

Formula

Solid grams to add per liter of solution: A = Gsat × (s₂ − s₁) ÷ (1 − P × s₂)

s₁, s₂  are saturation as **fractions** (50% entered as 0.5)
Gsat = grams of ammonium sulfate per liter of saturated solution
P    = specific volume × Gsat ÷ 1000     (specific volume = volume occupied by 1 g solid, mL/g)

The (1 − P·s₂) term in the denominator corrects for the volume occupied by the added solid itself. Omitting it systematically under-estimates: 13.6% short at a 50% target, 21.8% short at 80%.

Four-temperature constants (Wingfield 2001, Appendix 3F, Table A.3F.1; original table adapted from Dawson et al. 1986):

P is not looked up separately; it is calculated from the specific volume and Gsat in the same table—the resulting 0.27216 and 0.29447 match the 0.2722 and 0.2945 given elsewhere in the reference.

Higher temperature requires more salt, not less. The 25 °C saturated solution contains more salt than the 0 °C solution (541.80 vs. 515.35 g/L), so reaching the same target saturation requires weighing out more: 5.9% more at a 30% target, 7.6% more at 80%. A cold-room recipe used at room temperature will be short.

Verification

Table A.3F.2 in the reference is an empirical table for 0 °C that accounts for the change in specific volume with concentration. Spot-checking saturations that fall on table columns shows the formula over-estimates by 0.1%–1.9% compared to the empirical values:

This 1–2% gap is a method difference, not a calculation error: the formula uses a fixed specific volume, while the table uses the true concentration-dependent value. If higher accuracy is needed, consult the table directly; the formula’s advantage is that it works for any starting and ending saturation.

Applicable range

• s₁ from 0%–80%; s₂ greater than s₁ and no more than 100%.
• Choose the temperature closest to your actual working condition. The 0 °C set covers cold rooms (0–4 °C); the difference between adjacent steps is about 2%.
• The background salt concentration of the starting buffer should be negligible (≤ 0.2 M); otherwise the actual required amount will be under-estimated.
• Not applicable when adding liquid saturated solution—that case uses a different formula (dilution effects differ). Wingfield (2001) Table A.3F.3 covers that situation.

Common mistakes

1. Confusing the discard and collect directions in two-step fractionation. The typical protocol is to spin at low saturation, discard the pellet (contaminants), and keep the supernatant, then raise saturation and collect the pellet (target protein). Getting this backwards wastes the entire preparation.
2. Adding all the solid at once. Add slowly in small portions with continuous stirring, then let equilibrate for 30 minutes before centrifuging. Pouring in the full amount at once creates local supersaturation and non-specific co-precipitation.
3. Dropping the volume-correction term from the denominator. Simplifying to Gsat × (s₂−s₁) under-estimates by 21.8% at an 80% target—the weighed-out amount will never reach that saturation.
4. Applying a cold-room recipe at room temperature. Higher temperature requires more salt (see above); the direction is easy to remember incorrectly.