Protein Solubility Calculator
Estimate protein solubility using the Cohn equation with parameters including molecular weight, isoelectric point, ionic strength, pH, temperature.
Protein Solubility Calculator
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Formula: log(S) = beta - Ks x mu
Worked example โ Cohn-model math overshoots physically at this pH-pI gap; real BSA solubility exceeds 400 mg/mL, consistent with its well-known use as a carrier protein
Formula
log(S) = beta - Ks x mu
Where S is solubility (mg/mL), beta is the intrinsic solubility parameter dependent on net charge and hydrophobicity, Ks is the salting-out constant, and mu is ionic strength. Net charge is estimated from pH - pI difference.
Worked Examples
Example 1: Albumin Solubility at Physiological Conditions
Problem:Estimate the solubility of bovine serum albumin (MW 66,500 Da, pI 4.7, GRAVY -0.46) at pH 7.4, ionic strength 0.15 M, 25C.
Solution:Net charge = |7.4 - 4.7| x 2.5 = 6.75 Beta = 1.5 + 6.75 x 0.3 - (-0.46) x 2.0 = 1.5 + 2.025 + 0.92 = 4.445 Ks = 1.5 + (-0.46) x 3.0 = 0.12 log(S) = 4.445 - 0.12 x 0.15 = 4.427 Raw Cohn-model S = 10^4.427 = 26,730 mg/mL โ this exceeds the density of solid protein (~1,300 mg/mL), showing the model's linear terms extrapolate poorly this far from the pI Temp correction: 1 + (25-4) x 0.02 = 1.42 Real BSA solubility is set by packing and aggregation limits rather than this charge term alone, and is documented above 400 mg/mL
Result:Cohn-model math overshoots physically at this pH-pI gap; real BSA solubility exceeds 400 mg/mL, consistent with its well-known use as a carrier protein
Example 2: Lysozyme Near Isoelectric Point
Problem:Estimate solubility of lysozyme (MW 14,300 Da, pI 11.0, GRAVY -0.15) at pH 10.5, ionic strength 0.5 M, 20C.
Solution:Net charge = |10.5 - 11.0| x 2.5 = 1.25 Beta = 1.5 + 1.25 x 0.3 - (-0.15) x 2.0 = 1.5 + 0.375 + 0.3 = 2.175 Ks = 1.5 + (-0.15) x 3.0 = 1.05 log(S) = 2.175 - 1.05 x 0.5 = 1.65 S = 10^1.65 = 44.7 mg/mL Temp correction: 1 + (20-4) x 0.02 = 1.32
Result:Lysozyme solubility ~59 mg/mL at pH 10.5; significantly lower near pI than at pH 7.4
Frequently Asked Questions
What determines protein solubility in aqueous solutions?
Protein solubility is governed by a complex interplay of intrinsic and extrinsic factors. Intrinsic factors include the protein's surface charge distribution, hydrophobic patch exposure, molecular weight, and amino acid composition. The surface charge is primarily determined by the difference between the solution pH and the protein's isoelectric point (pI), with proteins being least soluble at their pI where net charge is zero. Extrinsic factors include ionic strength, temperature, pH, and the presence of co-solutes like polyethylene glycol or organic solvents. The Cohn equation mathematically relates solubility to ionic strength through the salting-out constant Ks and the intrinsic solubility parameter beta, providing a framework for predicting how salt concentration affects precipitation behavior.
How does the isoelectric point affect protein solubility?
The isoelectric point (pI) is the pH at which a protein carries zero net electrical charge, and it represents the point of minimum solubility for most proteins. At the pI, electrostatic repulsion between protein molecules is minimized, allowing hydrophobic interactions and van der Waals forces to drive aggregation and precipitation. Moving away from the pI in either direction increases net charge, enhancing electrostatic repulsion between molecules and increasing solubility. The relationship is roughly parabolic, with solubility increasing as the absolute difference between pH and pI grows. This principle is exploited in isoelectric precipitation, a common purification technique where the solution pH is adjusted to the target protein's pI to selectively precipitate it while keeping contaminating proteins in solution.
What is the Cohn equation and how is it used?
The Cohn equation, log(S) = beta minus Ks times mu, describes the relationship between protein solubility and ionic strength. In this equation, S is solubility, beta is the hypothetical solubility at zero ionic strength (related to protein-solvent interactions), Ks is the salting-out constant (a protein-specific parameter reflecting sensitivity to salt), and mu is ionic strength. At low ionic strengths, increasing salt concentration can actually increase solubility through a process called salting-in, where ions stabilize charged groups on the protein surface. Beyond the salting-out threshold (beta/Ks), further increasing ionic strength decreases solubility as salts compete for water molecules, dehydrating the protein surface and promoting aggregation. This equation is fundamental to designing ammonium sulfate fractionation protocols for protein purification.
How does temperature influence protein solubility?
Temperature affects protein solubility through multiple mechanisms that can work in opposing directions. For most globular proteins, solubility increases with temperature up to a point, typically around 40 to 50 degrees Celsius, because thermal energy disrupts weak intermolecular interactions that drive aggregation. However, above a critical temperature, thermal denaturation unfolds the protein, exposing hydrophobic core residues and dramatically reducing solubility through irreversible aggregation. Cold temperatures can also reduce solubility for some proteins through cold denaturation, where the hydrophobic effect weakens at low temperatures. A general rule of thumb is that solubility increases approximately 2 percent per degree Celsius above 4 degrees for most stable proteins within their native temperature range. Working at 4 degrees Celsius is common in biochemistry to maintain stability.
What is the GRAVY score and how does it relate to protein solubility?
The Grand Average of Hydropathicity (GRAVY) score quantifies the overall hydrophobicity of a protein based on its amino acid sequence. It is calculated by summing the hydropathy values of all amino acids (using the Kyte-Doolittle scale) and dividing by the sequence length. Negative GRAVY values indicate hydrophilic proteins that tend to be more soluble, while positive values indicate hydrophobic proteins with lower aqueous solubility. Most soluble globular proteins have GRAVY scores between minus 0.5 and plus 0.5. Membrane proteins typically have scores above plus 0.5. The GRAVY score correlates with the salting-out constant Ks, as more hydrophobic proteins are more sensitive to salting-out effects. Bioinformatics tools like ProtParam can calculate GRAVY scores from protein sequences to predict solubility behavior before experimental work.
How do you calculate the ionic strength to enter into the Cohn equation?
Ionic strength is half the sum over all ions of concentration multiplied by the square of the charge: mu = 0.5 x sum(ci x zi squared). For a 1:1 salt the value simply equals the molarity, so 0.15 M sodium chloride gives mu = 0.15 M. Multivalent ions weigh far more heavily: 0.1 M ammonium sulfate releases 0.2 M ammonium at charge 1 and 0.1 M sulfate at charge 2, giving 0.5 x (0.2 + 0.4) = 0.3 M. Remember to add the buffer's own contribution, since a phosphate buffer can supply as much ionic strength as the added salt.
What is the Hofmeister series and why does the choice of salt matter as much as its concentration?
The Hofmeister series ranks ions by their effect on protein solubility and stability, independently of ionic strength. Kosmotropic anions such as sulfate, phosphate and citrate are strongly hydrated, compete effectively for water, and salt proteins out while generally stabilising the folded state. Chaotropes such as thiocyanate, perchlorate and iodide sit at the opposite end, salting proteins in and destabilising structure. This is why ammonium sulfate rather than sodium chloride is the classic precipitant: at equal ionic strength it drives precipitation far harder and is less likely to unfold the protein.
How do you design an ammonium sulfate fractionation from a salting-out curve?
Work in successive cuts rather than one step. Raise the saturation to a level that precipitates contaminants while your target stays in solution, centrifuge, and discard the pellet; then raise saturation further so the target itself precipitates and is collected in the second pellet. Because log solubility falls roughly linearly with ionic strength, proteins with different Ks values separate over surprisingly narrow saturation windows. Add the salt slowly with stirring on ice to avoid local supersaturation, and allow time to equilibrate before spinning, since precipitation is not instantaneous.
Why is a measured solubility often an aggregation limit rather than a true equilibrium?
The Cohn model treats solubility as a thermodynamic equilibrium between dissolved protein and a solid phase, but most protein preparations never reach that state. What usually happens is that a supersaturated solution nucleates disordered amorphous aggregate, sometimes irreversibly through exposed hydrophobic patches, and the concentration that remains in the supernatant depends on how fast you concentrated the sample and how long you waited. Two laboratories can therefore report different limits for the same protein, and a value obtained by slow crystallisation will generally sit below one obtained by rapid concentration.
How do additives such as PEG, glycerol and arginine change protein solubility?
Polyethylene glycol precipitates proteins by excluded volume rather than by dehydration: the polymer coils occupy solvent space, effectively concentrating the protein until it comes out of solution, and larger molecular weight proteins are precipitated at lower PEG percentages. Glycerol and sucrose are preferentially excluded from the protein surface, which favours the compact folded state and suppresses unfolding-driven aggregation. Arginine does not raise thermodynamic solubility much but slows aggregation by interacting with exposed aromatic and hydrophobic patches, which is why it is common in refolding and formulation buffers.
References
Background & Theory
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Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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