# Calculating a simple pI

Shane Albright insomnia at mendel.berkeley.edu
Tue Sep 6 14:01:38 EST 1994

```In article <34a3ok\$cgi at agate.berkeley.edu>, lhom at OCF.Berkeley.EDU (Louis
Hom) wrote:

> It's simple enough to calculate the pI for a molecule with one acidic group
> and one basic group -- you just take the arithmetic mean of the two pKa's
> (as in Lehninger).
> But what about systems with, say, two acidic groups and one basic group?
> Do you still just take the arithmetic mean?
> --

Lou -

You still take the arithmetic mean of _two_ pKa's.  The trick is to decide
which two.

As the pH is titrated from 0 to 14,  the protein accumulates more and more
negative charge due to deprotonation.  The pI is, by definition, the pH at
which the protein has no net charge and is therefore the mean of the two
pKa's on either side of this neutral state.  In the example you state--two
acidic and one basic group--a fully protonated protein will have a charge
of +1 (the -NH3+ basic group).  When the pH is at the lowest pKa, the
charge is +0.5; at the second lowest pKa (the other acidic group), the
charge is -0.5.  The pI is the pt halfway in-between.

Hope this helps.

Shane Albright
insomnia at mendel.berkeley.edu

```