# Charge of an amino acid sequence

I have the following problem:

A polypeptide has the following sequence (amino end on the left) $$\mathbf{lysine - aspartic~acid-histidine-arginine-serine}$$

Using the $pK_a$ information that follows, what would be the approximate charge on this molecule at pH = 3.3?

$pK_a$ values for the various groups in the molecule are as follows:

\begin{array}{|cc|}\hline \rm Alpha~carboxyl & 2.2 \\ \rm Alpha~amino & 9.5 \\ \rm R-group~amino & 11.7 \\ \rm R-group~carboxyl & 4.5 \\\hline\end{array}

After my calculations I got +2 and my answer was wrong. How to solve it correctly?

My effort:

$\ce{NH3}$ has $+1$ when on and $0$ when off. $\ce{NH3}$ are Lysine, Histadine, and arginine. $\ce{COOH}$ has $0$ when on and $-1$ when off. $\ce{COOH}$ are Serine and aspartic acid. Based on the pH and $pK_a$ values the answer should be 2. Lysine=+1 Aps=0 His=+1 Arg=+1 Serine=-1

• This is a homework question. We ‎have a policy which states that you should show your thoughts and/or efforts into solving the ‎problem. It'll make us certain that we aren't doing your homework for you. Start by further explaining what you did. Just telling us that you got a 2 as an answer isn't helping us help you. – It's Over Jan 24 '16 at 19:08
• updated the post – Mr.SrJenea Jan 24 '16 at 19:13
• I find your current wording a bit confusing. What do you mean by "ammonia are lysine, histadine, and arginine". Do you mean they are the compounds with an amine group? – It's Over Jan 24 '16 at 19:26
• Serine isn't a carboxylic acid. – jerepierre Jan 24 '16 at 20:57

When the pH is lower than the pKa, the group will be protonated, and when the pH is higher than the pKa, the group will be deprotonated. Your explanation is correct that basic groups will be positively charged when protonated and neutral when deprotonated and that acidic groups will be neutral when protonated and negatively charged when deprotonated. Shown below is the compound in it's fully protonated state with the given pKa's.*

The given pH is 3.3 which means that:

• N-terminus: pH < pKa, protonated basic group, +1
• lys-sidechain: pH < pKa, protonated basic group, +1
• asp-sidechain: pH < pKa, protonated acidic group, 0
• his-sidechain: pH < pKa, protonated basic group, +1
• arg-sidechain: pH < pKa, protonated basic group, +1
• C-terminus: pH > pKa, deprotonated acidic group, -1

The overall charge is +3.

*An aside, the pKa's for the side chains are a gross approximation here. It turns out they are sufficient to answer the question, but given a higher pH, the answer wouldn't be correct.