[fighter127]

A professor was preparing a manuscript for publication in which she reported that the pI of the tripeptide Lys-Lys-Lys was 10.6. One of her students pointed out that there must be an error in her calculations because the pka of the ε-amino group of lysine is 10.8 and the pI of the tripeptide has to be greater than any of its individual pka values. Was the student correct?

Ok so I understand that the pI is where the amount of positive charge is equal to the amount of negative charge, but i am confused on how to apply that to this problem. Why would the pI of the tripeptide have to be greater than the individual pka values? I can think of a number of cases in which amino acids have individual pka values that are lower than the pI of the amino acid itself. Can anyone explain this to me? The solutions manual said that the student was in fact correct.

[Babcock_Hall]

This is a more complicated question than it first appears to be.  In the absence of additional information I think we might have to make the assumption that the pK_a values within the tripeptide are unchanged from what they are in the free amino acid, which is dubious.  At the pI of the tripeptide the carboxylate group has a full negative charge.  The sum of the positive charges on the three side chains and the amino terminus must be equal to +1 at the pI.  That is as far as I feel comfortable going with this problem.