Last updated: July 3, 2026
Protein Solubility Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The protein solubility calculator applies the Cohn salting-out equation, log10(S) = β − Ks × I, to estimate protein solubility during ammonium sulfate precipitation. It can compute S in g/L, the ionic strength required for a target solubility, or the salting-out constant Ks from measured data.
Protein solubility during ammonium sulfate salting-out can be estimated with the Cohn equation: log base ten of solubility equals beta minus Ks times ionic strength. Solubility is ten raised to beta minus Ks times ionic strength.
Key Takeaways
- The Cohn equation models salting-out as log10(S) = β − Ks × I.
- Solubility falls exponentially as ionic strength increases when Ks is positive.
- The same equation can solve for target ionic strength or fit Ks from measured solubility.
- Ammonium sulfate percent saturation tracks ionic strength but is not identical to it.
- Proteins are often least soluble near pI, so pH strongly affects precipitation behavior.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
log10(S) = beta - Ks × I; S = 10^(beta - Ks × I)
Where:
- S=Protein solubility(g/L)
- β=Cohn intercept, the log10 solubility extrapolated to zero ionic strength(log10(g/L))
- Ks=Salting-out constant for the protein-salt system(L/mol)
- I=Ionic strength of the salt solution(mol/L)
- log10(S)=Common logarithm of protein solubility(dimensionless)
Worked Examples
Intercept solubility at zero ionic strength
With β = 3 and Ks = 0.5, no added salt gives the Cohn intercept value.
- 1Start with log10(S) = β − Ks × I.
- 2Substitute β = 3, Ks = 0.5, and I = 0.
- 3log10(S) = 3 − 0.5 × 0 = 3.
- 4S = 10^3 = 1000 g/L.
Moderate ammonium sulfate ionic strength
At I = 2 mol/L, salting-out lowers solubility by one log unit.
- 1Use log10(S) = 3 − 0.5 × 2.
- 2The product Ks × I is 1.
- 3log10(S) = 2.
- 4S = 10^2 = 100 g/L.
Strong salting-out at I = 4 mol/L
A higher ionic strength reduces the predicted soluble protein to 10 g/L.
- 1Use log10(S) = 3 − 0.5 × 4.
- 2The product Ks × I is 2.
- 3log10(S) = 1.
- 4S = 10^1 = 10 g/L.
Ionic strength needed for 10 g/L
Solve the Cohn equation backward to find the ionic strength for a target solubility.
- 1Rearrange to I = (β − log10(S)) / Ks.
- 2For S = 10 g/L, log10(S) = 1.
- 3I = (3 − 1) / 0.5 = 4 mol/L.
Salting-out constant from measured data
Estimate Ks when β, I, and measured solubility are known.
- 1Rearrange to Ks = (β − log10(S)) / I.
- 2For S = 100 g/L, log10(S) = 2.
- 3Ks = (3 − 2) / 2 = 0.5 L/mol.
Introduction
Protein solubility during ammonium sulfate precipitation is often described in the salting-out region by the Cohn equation, log10(S) = β − Ks × I. This calculator predicts solubility in g/L from β, Ks, and ionic strength, or rearranges the same relationship to solve for a target ionic strength or fitted Ks. Use it with the isoelectric point calculator because proteins are least soluble near pI, and with the molarity calculator when preparing salt solutions. The model reflects classic salting-out chemistry summarized by IUPAC ionic strength terminology and practical ammonium sulfate guidance from Current Protocols.
Cohn equation for salting-out
The Cohn equation states that the common logarithm of protein solubility decreases linearly with ionic strength in the salting-out region: log10(S) = β − Ks × I. β is the intercept for a particular protein, pH, temperature, and solvent system. Ks is the salting-out constant, which captures how strongly ammonium sulfate reduces solubility. A larger Ks means a steeper drop in log solubility for each mol/L increase in ionic strength.
- Solve for solubility:
S = 10^(β − Ks × I).
- Solve for ionic strength:
I = (β − log10(S)) / Ks.
- Solve for the salting-out constant:
Ks = (β − log10(S)) / I.
Use common logarithms, not natural logarithms, unless β and Ks were fitted differently.
Salting-in versus salting-out
At low salt, some proteins become more soluble because ions shield surface charges and reduce attractive protein-protein interactions; this is called salting-in. At higher ammonium sulfate concentrations, water activity decreases and salt ions compete for hydration water, so hydrophobic patches interact and proteins precipitate. The Cohn equation is meant for this high-salt salting-out region, not for the initial salting-in rise.
If experimental data show solubility increasing with small additions of salt, fit the Cohn line only after the maximum solubility has passed.
Ionic strength and percent ammonium sulfate saturation
Biochemists often describe ammonium sulfate precipitation by percent saturation rather than ionic strength. Percent saturation is convenient at the bench, but ionic strength is what appears in the Cohn equation. At a fixed temperature, higher percent saturation means higher ammonium sulfate concentration and higher ionic strength, so the model predicts lower S. Exact conversion depends on temperature, density, and activity corrections; use empirical tables for protocols rather than assuming a universal linear conversion.
For fractionation, increase ammonium sulfate stepwise and collect the precipitate in the saturation window where your target protein drops out while contaminants remain soluble.
Why pI and pH matter
Solubility is usually lowest near a protein's isoelectric point because net charge and electrostatic repulsion are minimized. Moving the buffer pH away from pI often keeps proteins soluble at lower salt, whereas operating near pI makes ammonium sulfate precipitation more efficient but can increase aggregation risk. Pair the calculator with the pH calculator when adjusting buffers and the concentration calculator for mass-volume conversions.
Near pI: low net charge, lower solubility, easier precipitation.
Far from pI: stronger charge repulsion, higher solubility.
Temperature, cofactors, ligands, and reducing agents can shift apparent solubility.
Always validate precipitation windows experimentally for each protein.
Worked benchmarks embedded in the tests
For β = 3 and Ks = 0.5, the predicted solubility is 1000 g/L at I = 0, 100 g/L at I = 2 mol/L, and 10 g/L at I = 4 mol/L. Rearranging for a target S = 10 g/L gives I = (3 − 1) / 0.5 = 4 mol/L. Rearranging for Ks from β = 3, I = 2, and S = 100 g/L gives Ks = (3 − 2) / 2 = 0.5 L/mol.
| β | Ks (L/mol) | I (mol/L) | S (g/L) |
|---|---|---|---|
| 3 | 0.5 | 0 | 1000 |
| 3 | 0.5 | 2 | 100 |
| 3 | 0.5 | 4 | 10 |
Model limitations and experimental use
The Cohn equation is an empirical log-linear model. It works best over a limited ionic-strength interval for one protein under fixed pH, temperature, buffer, and salt identity. It does not predict native stability, activity recovery, coprecipitation, or resolubilization after centrifugation. For enzymatic proteins, measure retained activity with an enzyme activity calculator after redissolving the pellet, and compare kinetic behavior with the Michaelis-Menten calculator. Practical protocols are detailed in Methods in Enzymology and LibreTexts biochemistry.
Quick Reference Card
Protein Salting-Out — Quick Reference
Quick reference • Protein Solubility Calculator
log10(S) = β − Ks × I; S = 10^(β − Ks × I)Valid range: Use only over the fitted salting-out range for one protein, salt, pH, and temperature; typical ammonium sulfate protocols span about 20–80% saturation.
Common Values
⚠ Watch Out
- •Do not extrapolate far outside the ionic-strength range used to fit β and Ks.
- •Do not confuse ammonium sulfate percent saturation with ionic strength without a conversion table.
- •The model does not predict irreversible aggregation, denaturation, or activity recovery.
- •Fit data at the same pH and temperature used for the intended precipitation.
- •Use log10 for S unless your fitted constants were built with natural logarithms.
Pro Tips
- →Plot log10(S) versus ionic strength; the slope is −Ks and the intercept is β.
- →Work near but not exactly at pI when you need precipitation without excessive aggregation.
- →Increase ammonium sulfate slowly with stirring to avoid local high-salt zones.
- →Check the supernatant and pellet by SDS-PAGE or activity assay after each cut.
- →Keep temperature constant because ammonium sulfate solubility and protein stability are temperature-sensitive.
FAQs
What does the Cohn equation calculate?
It estimates protein solubility in the salting-out region using log10(S) = β − Ks × I, where S is solubility in g/L, β is an empirical intercept, Ks is a salting-out constant, and I is ionic strength.
Is ionic strength the same as ammonium sulfate percent saturation?
No. Percent saturation is a practical formulation scale for ammonium sulfate, while ionic strength is a thermodynamic concentration measure. They rise together at a fixed temperature, but conversion requires empirical tables or activity corrections.
Why does ammonium sulfate precipitate proteins?
At high salt, ammonium sulfate lowers water activity and competes for hydration water. Protein-protein interactions become more favorable, so solubility decreases and proteins precipitate.
What is β in the Cohn equation?
β is the intercept of a plot of log10 protein solubility versus ionic strength. It depends on the protein, pH, temperature, salt, buffer composition, and how the experimental data were fitted.
What is Ks?
Ks is the salting-out constant. A larger Ks means solubility falls more sharply as ionic strength increases. It is empirical and should be fitted from data for the exact protein and salt system.
How does pI affect protein solubility?
Proteins are often least soluble near their isoelectric point because net charge is near zero and electrostatic repulsion is weak. Salting-out is usually easier near pI but may increase aggregation or activity loss.