Histidine has pka of 6. What will be the net charge in Histidine in a solution of (a) pH 8.0 (b) pH 5.0

Answer 1

There is an easy answer to this question -- histidine is protonated when the pH is lower than its pKa, and not protonated when the pH is above the pKa. As such, it is +1 below pH=6 (so, at pH=5), and neutral at pH=8.

But there's a lot more detail to understand than that. First of all, at both of these pH values, the protonation state is not truly 100% protonated or 100% un-protonated -- it's an equilibrium mixture of those protonation states. The Henderson-Hasselbalch equation is used to calculate the concentrations of [HA] and [A-] (or, in this case, [B:] and [BH+]) in a situation like this. If you need a more specific answer than "positive at pH=5, neutral at pH=8" you'll need to use the HH equation -- look it up. Approximating the results, it would be about +0.9 at pH=5 (it's about 90% protonated and positive, and 10% un-protonated and neutral), and about +0.01 at pH=8 (about 99% un-protonated and neutral, and 1% protonated and positive).

With even another level of detail, it is worth remembering that histidine has THREE acidic/basic functional groups, and the overall charge is a function of the pH compared to the pKa of all THREE of these FGs (or, at least, any which are pertinent). The easy assumption, which holds fairly consistently true for all amino acids, is that between the pH of ~2 and ~9-10, the charge on the AA is determined solely by the protonation state of the side chain. That's because, above the pKa of the carboxylic acid (usually ~2), it will be deprotonated and anionic, but below the pKa of the conjugate acid of the alpha-amine group (usually ~9-10), it will be protonated and positive. That is, between 2 and 9-10, most amino acids are "zwitterions" which means they are overall neutral in charge, but have regions of both positive (protonated alpha-amine -NH3+) and negative (deprotonated acid carboxylate -CO2-) charge. The positive of the -NH3 and negative of the -CO2- cancel each other, so the overall charge of the molecule depends only on the charge of any side chain FG.

All of that is implicit in the question -- the pKa they are giving you is for the amine in the imidazole ring of the histidine side chain. That is the only pertinent pKa for this problem, since both pH values are in the "zwitterion" pH range of 2-10.

That said, if the more precise (fractional) charge is desired, you would need to consider protonation of the alpha-amine group of histidine as well, as it will not be 100.00000% protonated at pH=8. Looking up the pKa of the alpha amine group, it is 9.33 for histidine. (The pKa of the acid FG is 1.80, so it IS essentially 100.00000% deprotonated an anionic -- so we can ignore the insignificant concentration of protonated neutral acid FG.)

Using the HH equation, the side-chain amine is only about 1% protonated at pH=8 -- which is how I approximated the charge to be +0.01. But that ignores the concentration of the species where the alpha-amine FG is NOT protonated. While the pH (8) is lower than the pKa of the alpha amine (9.33), and this means that it is MOSTLY protonated, it is not 100.00000% protonated.... Since the pH is 1.33 pH units below the pKa, there is between 1% and 10% of the alpha amine which is NOT protonated. You could theoretically use the HH equation to calculate exactly how much -- but I'm too lazy to do that, since that's almost certainly NOT what you're being asked. But if it's, say, around 5% not protonated, at the same time as the side chain is about 1% protonated (and the carboxylate is always deprotonated and anionic), the actual overall charge could be slightly negative -- something like -0.04.

Questions about pH and pKa for amino acids are usually straightforward, and can be answered algorithmically -- that is, based on some recipe or formula, without you needing to actually think it through. But getting into the habit of answering questions that way comes with risk! Any time you are presented with a question which can NOT be answered algorithmically, you can't figure it out -- and even if you are presented with an algorithmic question, if you mis-remember something and screw up your answer, you can't self correct! Unless you UNDERSTAND WHY the answers are what they are, you won't recognize a wrong answer if it bites you. It is ALWAYS to your benefit to strive for understanding, even of simple algorithmic questions.