pI of Amino Acids - Average of pKa of Side Chains

[sxld_cu]

I am assuming that when you calculate the pI of an amino acid, you average the pKa of all the side groups (R group, carboxyl group and amino group) - Why is it that in this question, it is only taking the average of two?

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[Teleologist]

The pI of an amino acid is the pH at which the amino acid has no net charge. You ignore the amino group because that won't have any effect at the pI point.

 

[The Brown Knight]

net charge on cysteine from lowest to highest pH:
+1 ---pKa(carboxyl)---> 0 ---pKa(side chain)---> -1 ---pKa(amino)---> -2
0 net charge occurs between carboxyl and side chain pKas; hence average those

if you averaged all 3, the number you get will create a solution with slight net negative charge on amino acid

 

[sxld_cu]

The pI of an amino acid is the pH at which the amino acid has no net charge. You ignore the amino group because that won't have any effect at the pI point.

Can you clarify what you mean by the amino group won't having any effect on the pI point?

 

[sxld_cu]

net charge on cysteine from lowest to highest pH:
+1 ---pKa(carboxyl)---> 0 ---pKa(side chain)---> -1 ---pKa(amino)---> -2
0 net charge occurs between carboxyl and side chain pKas; hence average those

if you averaged all 3, the number you get will create a solution with slight net negative charge on amino acid

I think I understand what you're trying to say, but can't you say that 0 net charge occurs between the side chain and amino pKas too?

 

[sxld_cu]

Also, if the pH (or pI) is ~ 5, wouldn't both the amino and R group be protonated, leading to a positive charge?

 

[The Brown Knight]

I think I understand what you're trying to say, but can't you say that 0 net charge occurs between the side chain and amino pKas too?

What net charge do you see on my continuum above between the pKas for amino group and side chain?
Here's a bit more intuitive explanation:
If the solution had a pH between the pKa values of carboxyl and side chain groups, the overall net charge of all amino acids together will be 0; if you are closer to the side chain pKa, the net charge on the amino acids is closer to -1 and if you are closer to carboxyl pKa, the net charge is closer to +1
Here's a better representation:
primarily +1 ---pKa(carboxyl)---> -1 < X < +1 ---pKa(side chain)---> -2 < X < 0 ---pKa(amino)---> primarily -2

Point here is that between the pKas mentioned, the net overall charge of all the amino acids in solution is between these ranges. For a pI you want the net overall charge of all the amino acids in solution to be 0. If you go beyond the side chain pKa, it's true you will have a very tiny number of zwitterions floating around in solution but the net overall charge of all the amino acids in solution will be between 0 and -2 and hence no pI reached in that range.

 

[The Brown Knight]

Also, if the pH (or pI) is ~ 5, wouldn't both the amino and R group be protonated, leading to a positive charge?

For your second question, at pH 5 here are the charges on each group:
carboxyl = -1
side group = 0
amino group = +1
net charge = 0
I think your misconception here is that the side group will also be charged +1, which is not the case; the side chain goes from neutral (CH2SH) to anionic (CH2S-) from protonation to deprotonation

 

[sxld_cu]

Thanks - I think you're right
Can you explain why if your pH is closer to the side chain pKa you would get closer to -1 charge for the solution?
My understanding is that at the side chain pKa, the COOH chain would be negatively charged and the NH3 chain would be positively charged

 

[The Brown Knight]

say if you are at pH 3 or pH 6; in both cases you will have some amino acid molecules with +1, some with 0, and some with -1 charges. For pH 3, you have a lot more of the +1 types, so your net overall charge of all the amino acids in solution will be something like +0.8 (just a hypothetical #). For pH 6, you have a lot more of the -1 types, so your net overall charge of all the amino acids in solution will be something like -0.3

 

[Hadi7183]

Read the TBR O-Chem book if you have it. It gives you a simple and straightforward approach for these types of questions. This is one of those questions that is most likely to appear on the MCAT. Let me know if you don't have the book and I'll write a summary for you.

 

[sxld_cu]

Thanks for your patience @The Brown Knight - Really appreciate it
@Hadi7183 - I have actually just used Kaplan and some EK and Kaplan surprisingly never really addressed this in their review books and I haven't taken bchem yet; if you get a chance, a summary of this material would be really really helpful! Thank you so much!

 

[Hadi7183]

Sorry for my delay in getting back to you, @sxld_cu.

So, as other members have mentioned, PI is determined by averaging the two pKa values surrounding the pH at which the zwitterion has the highest concentration. TBR offers a protocol to find these two pKa values. First of all, make sure you know the three basic amino acids, i.e. histdine, lysine, and arginine (or, as TBR says His Lies Are Basic 🙂). Now, if you are given a polypeptide chain of multiple amino acids and asked for its PI:

1) sort pKa values (from the lowest to the highest) for all groups in that polypeptide, i.e. those of the side groups on acidic and basic amino acids, as well as terminal carboxylate and amino groups (the terminal carboxylate group is always #1, b/c it has the lowest pKa in almost any polypeptide chain),
2) find the number of basic amino acids in that polypeptide chain (let's say you have "nb" basic amino acids - you could also have no basic amino acids in your chain, in which case nb=0),
3) now, the PI is found by averaging the pKa #nb+1 and pKa #nb+2 from the list you made in the first step. You see that it's critical to sort pKa values correctly (again, from the lowest to the greatest).

This may sound a lengthy approach at the beginning, but the good thing is it applies to any situation and so you don't get confused no matter how long the polypeptide chain is. Also, keep in mind that normally in a typical MCAT question, your polypeptide chain doesn't have more that 3-4 amino acids....

Hope this helps!