The free enrgy for unfolding (H2O), against pH has the max point near pI. In this pH average of charges is zero. But what the axact relationship is between the stability and pI,. We know all chargeable residues in proteins do not contribute in the salt bridges. In this case some time burreid uncharged residues may gain charge and induce folding pertubation with ethalpic effects.
I don't think it is true that the stability of a protein is related to its pI. This might be a coincidence if it was seen for one protein. The authors of this paper concluded that stability was not correlated with pI for a sample of 310 proteins.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2911520/
Thank you so much for the answers, the article is very useful. At work I have found similar results, But in the preformulation and formulation processes for proteins, in many times, proteins are more stable in their pI and far from natural pH like that in attached file. Some say that chemical potential in this pH is in the lowest level.
Most proteins are more stable, less prone to aggregate and easier to purify if you avoid working at the pI. A charged protein behaves better than an uncharged protein. If you have a protein with a pI of 7, work at pH 8. This is based on working with many proteins, not calculations.
A clarifying point: a protein at its pI has zero net charge. It still has charge, just an equal number of positive and negative charges. Concentrated solutions of purified proteins are more likely to aggregate/precipitate at the pI because of reduced electrostatic repulsive force between molecules, but this does not mean the tertiary structure of the protein is less stable at the pI.