eli5: why do strong bases dissolve proteins but strong acids precipitate them?

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eli5: why do strong bases dissolve proteins but strong acids precipitate them?

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Well, that’s not quite true. Protein solubility is actually a complex phenomenon and still a subject of research.
Ultimately you could think of protein solubility as a function of their composition and structure, they’re not all the same.

I will try to simplify the matter as best as I can:

Proteins have 4 orders of structure. Primary structure is the sequence of amino acids that constitute one particular protein, that is it’s chemical composition. We can classify amino acids by their chemical interactions on their side chain as polar and non polar. Subsequently polar amino acids are classified as charged and non charged; charged amino acids will exhibit acid or base behavior.

When an amino acid has electrically-neutral charge (positive and negative charges cancel out), it has the least solubility in water, such thing extrapolates to proteins as well. Addition of acids or bases will change the charges in acid/basic amino acids and therefore affect their solubility, wich will depend mostly in how many of them are there.

In consequence: with more acidic amino acids, more solubility in basic solution a protein will have; and conversely, with more basic amino acids, a higher solubility in acidic solution…

But wait, there’s more! Remember we talked about non polar amino acids? They don’t contribute that much to protein solubility in water and sometimes they make it even harder to happen. To put it simple: when there are more amino acids like that, pH effect on protein solubility will be less significant; and the addition of solvents like ethanol or the addition of salts will cause them to either solubilize or precipitate respectively. In extreme cases, highly hydrophobic proteins are simply insoluble in water (think of it like oil in water).

And there’s even more! Remember we just mentioned before about the 4 orders of structure? While the first represents the chemical composition, the other three are about their spatial arrangement, that is the way they “fold”. Think of this like a folded blanket, there will be parts that remain hidden on the inside, and all the external surface will remain exposed. Innermost amino acids will interact more with each other, and outermost ones with the external medium. And that of course will affect solubility, adding another layer of complexity.