How do I calculate the overall charge of the peptide 'Asp-His-Arg' at various pHs?

[Joe]

I have been given the following table of the pKa associated with each ionizable group in the peptide 'Asp-His-Arg'

Asp: pKa NH3+: 9.9, pKa COOH: 2.0, pKa Side Chain: 3.9
His: pKa NH3+: 9.3, pKa COOH: 1.8, pKa Side Chain: 6.0
Arg: pKa NH3+: 9.0, pKa COOH: 1.8, pKa Side Chain: 12.5

I have worked out the overall charge to be +1 at pH 7 (though this could be incorrect), but have now been asked to calculate the overall charge at pHs: 1.8, 6, 7, 9.9

How do I do this?? Any help would be greatly appreciated, thanks.

[Kunal Pandya]

When pH is equal to pKa value then half of the carboxyl group get deprotonated result in -0.5 charge and when pH is greater then pKa value of COOH result in generation of -1 charge (COO- generate which have -1 charge)

When pH is equal to pKa value then half of the amino group get deprotonated result in + 0.5 charge and when pH is greater pKa value of NH3+ result in loss of +1 charge (NH2 generate which have zero charge)

Now your sequence is NH2-Asp-His-Arg-COOH

So Asp having one NH2 group while one caroxyl functionality in side chain
His having one imidazole group functionality in side chain
Arg having one COOH group while Guanidine functionality in side chain

So now you can easily calulate charge on peptide at various pH


At pH 1.8 = Asp amino group having +1 charge while carboxyl Zero
His side chain group posses +1 charge
Arg Side chain posses +1 charge while carboxyl group having -0.5 charge
Total charge = +1+0+1+1-0.5 = + 2.5

At pH 6 = Asp amino group having +1 charge while carboxyl having -1 charge
His side chain group posses + 0.5 charge (Half group get deprotonated)
Arg Side chain posses +1 charge while carboxyl group having -1 charge
Total charge = +1-1+0.5+1-1 = + 0.5


At pH 7 = Asp amino group having +1 charge while carboxyl having -1 charge
His side chain group posses 0 charge
Arg Side chain posses +1 charge while carboxyl group having -1 charge
Total charge = +1-1+0+1-1 = 0

At pH 9.9= Asp amino group having +0.5 charge while carboxyl having -1 charge
His side chain group posses 0 charge
Arg Side chain posses +1 charge while carboxyl group having -1 charge
Total charge = +0.5-1+0+1-1 = - 0.5