- [Professor] So in this video,
our goal is to take what we've learned about the acid-base
and speciation chemistry of amino acids
and apply it to peptides.
What I have drawn here is just an example peptide
that we're gonna use in this video.
Its sequence is alanine, glutamic acid, alanine, serine.
And I'm also showing you a table
that has some useful pKa values.
And I'll note here that in this table,
pKA1 always corresponds to the C-terminus.
PKa2 always corresponds to the N-terminus.
And then the third pKA, as the table says,
is always the side chain.
And not all of these amino acids have side chain pKas,
and that's because not all of them are functional groups
that can be protonated or deprotonated.
So if they're not acids or bases, they don't have pKas.
Okay, so I think what you'll find is that determining the,
like I said, going through the speciation
for peptides is really similar to doing it for amino acids.
The only big difference is
that you might have a couple more functional groups.
But at the end of the day, the approach is really similar.
So let's look at our representative peptide here.
And to save ourselves a little bit of time and effort,
what I'm gonna do is suggest that we redraw this
in an abbreviated, simplified form,
where we only worry about functional groups.
So I'm gonna abbreviate the backbone just as a solid line.
So when I do this, I have this solid line
where I have my N-terminus, alanine side chain,
glutamic acid side chain,
alanine side chain, serine side chain
and now we finish up with the C-terminus.
All right, this is an easier way of drawing the peptide.
And we ignore all the peptide backbone,
because as we mentioned before,
once the peptide bond forms, nothing is reactive.
So in terms of the chemistry of the peptide,
the only part of the peptide backbone
that matters is the N-terminus and the C-terminus.
So this is a nice way of writing out the peptide,
where we only focus in on functional groups.
And in fact, in this case,
I'm gonna even go even one step further
and erase some of the side chains.
The side chains that I'm going to erase are the ones
that don't have pKas.
So alanine does not have a side chain pKa.
Serine does not have a side chain pKa,
meaning that they are not gonna be important
in our acid-base speciation.
So I'm gonna go ahead and erase them
so that we're not confused and bothered by writing them out.
And what we see is we end up with a peptide
that has three functional groups
that participate in acid-base chemistry.
We have the amine group at the N-terminus.
We have the side chain of glutamic acid.
And we have the carboxylic acid
at the C-terminus of our peptide.
So we have an H3X situation.
And this is very manageable.
So the very first thing that we want to do is we want
to be able to predict what the charge of these things are
in the fully protonated form.
So remember amines when they're protonated are NH3,
and they have a positive charge.
And carboxylic acids when they're protonated
in their acid form, they're neutral.
So I need to redraw my amine here
so that I have an NH3 with a positive charge.
And what we see is the other two functional groups
are carboxylic acids, so they're neutral.
So in the fully protonated form, H3X,
this peptide has a plus-one charge,
meaning that as we start losing protons, right,
so we go from an H3X to the H2X.
When I've done this, I've lost a hydrogen atom,
and I've also lost a positive charge.
So H2X is neutral.
HX must be negative one.
And the fully deprotonated form is negative two.
So the next step is to write out
what these things look like in these different forms
and convince ourselves that we did it right.
So we need to figure out what the pKas are for each
of these individual functional groups.
Glutamic acid side chain is the easy one.
We find glutamic acid in our table.
The pKa of the side chain is 4.07.
So that functional group has a pKa of 4.07.
To figure out the pKa of the amino group at the N-terminus,
we need to specifically choose the N-terminus of alanine.
Alanine is our N-terminal amino acid,
so this amine is attached to alanine.
And alanine's N-terminus has a pKa of 9.87.
And finally, the C-terminus is on serine.
So serine's C-terminus has a pKa of 2.19.
So our three pKas are 2.19, 4.07 and 9.87.
The C-terminus has the most acidic pKa,
so when we convert from the H3X to the H2X,
we're gonna deprotonate the C-terminus,
'cause it's the most acidic.
So let's go ahead and redraw this peptide
in the H2X form.
What we see here is that side chain
of glutamic acid is still protonated,
because it is not deprotonated yet.
The amino group, at the N-terminus, is still protonated,
but the C-terminus has been deprotonated.
This now gives us a negative-one charge at the C-terminus,
a plus-one charge at the N-terminus,
and the side chain of glutamic acid is neutral,
so the overall charge of zero makes sense.
When we draw the HX form, the next proton
that gets removed is the side chain of glutamic acid,
because it has the next most acidic pKa.
So we draw this out.
The N-terminus is still protonated.
The C-terminus is still deprotonated.
And now the side chain
of glutamic acid is also deprotonated.
So I have a negative-one charge from the C-terminus,
a plus-one charge from the N-terminus,
and a negative-one charge on my side chain.
So a charge of negative one overall makes sense.
And finally, to redraw this for the fully deprotonated,
we now deprotonate the amine.
So now we have a negative-one charge on the C-terminus,
a negative-one charge on the side chain,
and the N-terminus is neutral.
So the charge of negative two is accurate.
All right, so our final step here is let's figure out
what the isoelectric point is?
Just like we saw with amino acids,
we want to figure out which of these is neutral,
and we've already done this.
So we know that it's the H2X form that is neutral,
so if we average the two pKas that surround this,
then that will give us the isoelectric point.
So in this case, our two pKas are 2.19,
the most acidic, right.
So this transition is 2.19,
and the next one is 4.07.
We always start most acidic and start working our way up.
From H3 to H2 is 2.19.
From H2 to HX is 4.07.
So then the last transition would be the 9.87
for the N-terminus, meaning that the pH
where this molecule exists in 100% abundance is the average
of 2.19 and 4.07.
And this ends up being 3.13.
Let's go ahead and try one more sample problem here.
Lysine, aspartic acid, alanine,
let's choose glutamic acid.
So we have four amino acid,
which means we have an N-terminus and a C-terminus.
And let's go ahead and draw this out using that shortcut
that we've talked about before.
We have an NH2.
Our lysine is L-Y-S-I-N-E.
Aspartic acid is the carboxylic acid.
Alanine is a single methyl group.
Glutamic acid is a carboxylic acid.
And then we have our C-terminus.
Okay, and I'm gonna go ahead and take this one step further
and draw everything protonated.
Amines are NH3 when protonated,
and they have a positive charge.
Carboxylic acids are neutral, so they're neutral.
So overall, we have one, two,
three, four, five functional groups
that contain ionizable protons.
And the overall charge is plus two,
two amines, three carboxylic acids.
So when we convert to H4X, we have plus one.
H3X is our neutral form.
H2X would be negative one.
HX is negative two.
So then X would be negative three.
Okay, and just to save time,
I'm not gonna bother going through
and drawing out the actual side chains
for all of these different forms.
But what we do want to do is to assign pKa values,
because we need to know what this pKa is
and what this pKa is so that we can average them.
So let's start with the C-terminus.
So we have glutamic acid at the C-terminus.
We want to get the C-terminal pKa
for glutamic acid, which is 2.10.
We also want the side chain pKa
for glutamic acid, which is 4.07.
We want the side chain pKa for aspartic acid, 3.9,
and the side chain pKa for lysine, 10.54.
And finally, we want to have the N-terminal pKa
for lysine, so 9.06.
So each of these pKas correspond to a transition
from one species to another.
And we start with the most acidic
and work our way to the most basic.
The most acidic is 2.1.
This corresponds to the C-terminus.
The next is 3.9, which corresponds
to the side chain of aspartic acid.
Next, we have 4.07, which corresponds
to the side chain of glutamic acid.
And then we have the N-terminus, 9.06,
and finally, the side chain of lysine, 10.54.
So these are our five pKas, and as we see here,
the neutral form is between 3.9 and 4.07.
So to figure out our pI, we average them.
3.9 plus 4.07 divided by two,
this ends up being 3.99.
So this is the strategy for determining the pI
for absolutely any peptide.
We are gonna consistently see amines and carboxylic acids,
so please be familiar with them.
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