A. Draw the predominant structure of the following peptide at ...

Question

A. Draw the predominant structure of the following peptide at pH 9: Asn-Arg-Cys. What is its net charge?

(Asn pK_a1 = 8.8, Arg pK_R = 12.48, Cys pK_a2 = 1.96, Cys pK_R = 8.18).

B. What is the net charge of the same peptide if the pH is lowered to pH = 2? Draw the newly ionized peptide.

C. Within what pH range would the net charge on the peptide above be approximately +1?

pH: ______________

Accepted Answer

Alright. So here's a 3 part practice problem broken up into parts a, b, and c down below. And part a asks us to draw the predominant structure of the following peptides, specifically at pH 9, and the peptide is asparagine, arginine, and cysteine. And then it asks, what is its net charge? And it gives us the pKas for all of the relevant ionizable groups. And so first, we're gonna start off by drawing the peptide. And the first step in drawing a peptide is to draw the peptide backbone and identify alpha carbons. So we know that we're gonna draw a nitrogen carbon carbon set for each of the amino acid residues. And because we have 3 amino acid residues, we draw 3 nitrogen carbon carbon sets. So let's go ahead and do that first. So here's a nitrogen carbon carbon set, here's another nitrogen carbon carbon set, and then here's another nitrogen carbon carbon set. Perfect. So now to identify the alpha carbons, we know that it's going to be the middle carbon in each n c c set. So it'll be this carbon here, it'll be this carbon here, and it'll be this carbon over here. Alright. Great. So in the next step, what we're gonna do is draw in all of the carbonyl groups and consider amino acid chirality, and the carbonyl groups are gonna be on the carbons that are not labeled with alpha carbon. So there'll be one right here, one over here, and one over here. And then when we're considering amino acid chirality, that's just remembering that life predominantly uses L amino acids, and the way to ensure that we're drawing L amino acids is that when the r group is going down, it should be on a dash. And when the r group is going up, it should be on a wedge. And so notice that this alpha carbon is pointing in an upwards fashion, so its r group is going to be going up, and it should be on a wedge. This alpha carbon is pointing downward, so it should be down and on a dash. This one's pointing up, so it should be up and on a wedge. Alright. So in our next step, we need to draw in all of the hydrogens on our nitrogen atoms, so we have one here and one over here. And this nitrogen over here is the free amino group that is potentially ionizable. So before we actually draw in the hydrogens, we first need to compare its pKa to the pH. So we'll hold off on drawing the hydrogens on this nitrogen for now. And so now what we need to do is draw in the r groups. And, recall that asparagine's one letter amino acid code is an n, arginine's one letter amino acid code is an r, and cysteine's one letter amino acid code is a c. And the mnemonic that helps us memorize the 7 amino acids with ionizable R groups is Yucky Crazy Dragons Eat Nights Riding Horses. And because we want to make sure that we're drawing our R groups in the appropriate ionization state, it's going to be important to know which ones, which amino acids have ionizable R groups. And so notice that asparagine does not fall into this mnemonic over here, so it does not have an ionizable R group. But arginine and cysteine both fall into this mnemonic, so they do have ionizable R groups. And so we're gonna need to hold off on drawing the ionization of those R groups until we compare the pKas with the pH. And so first, let's draw a spargene's r group, which we know is literally just alanine with an amide group. So it's literally just CH 2, the carbon double bonded to an oxygen with an NH 2 coming off. And again, it does not have an ionizable R group, so, essentially, we can just leave it as is. And this asparagine p k a that we're given, the only ionizable group that asparagine has in this residue is its amino group. So we can label this, p k a up here as the amino group p k a. Alright. So now we can move on to arginine's r group. And because arginine has has features of a sword, we count up how many pointy ends it has on its one letter code, and there are 3 pointy ends, which reminds us that it has a 3 carbon start. So c h 2 c h 2 c h 2. And then that also reminds us that there's a nitrogen, triangular nitrogen structure at the bottom. So the way that works is there's a nitrogen, there's a carbon, there's a nitrogen, and then the carbons double bonded to a nitrogen. And we know that this nitrogen has 1 hydrogen, this one has 2, and then this one is the one that's potentially ionizable, so we actually need to hold off and compare its p k r to the pH before we can determine how many hydrogens it has here. So we'll hold off on that. And then last but not least, what we have is cysteine, and cysteine spends time in the cysteine chapel, so he's always like, So it's literally just alanine, so CH 2, with a SH group, a SH group. But again, cysteine is ionizable, so we're not sure if this, sulfur here has a hydrogen on it or not, so we need to compare its p k r here to the pH to determine that. And then of course, this last group over here is the c terminal end, which we know is gonna have an oxygen, and we need to compare its pka to the pH to determine if it is ionized or not. And so that's exactly what we're gonna do next is, start to determine what is the net charge here. And so in order to do that, we need to compare the p k, the pH's to, the pH of the solution to the p k a's of all the ionizable groups. So down here, what we have is a reminder for you guys on how that works. And so we're gonna go ahead and compare, the first group here, the amino group p k a. And so a p k a of 8.8 is smaller than a pH of 9. And so that means that the pH is greater. And when the pH is greater than the pKa, this means that the concentration of conjugate base, abbreviated as cb here, is greater than the concentration of conjugate acid. And so, the conjugate base form of the amino group is just an NH 2, and it is not ionized. So it's just like that. So now we move on to the next, group here, and it is the R group of arginine. So arginine's p k r is 12.48, which is greater than the pH of 9. And so the pH is smaller, and if the pH is smaller than the p k a, the conjugate acid predominates, and the conjugate acid form of lysine's r group is gonna be protonated, so it's gonna have extra hydrogens, and it's gonna be charged positively. And so, we can move on to the next ionizable group in our peptide, which is cysteine's R group over here. And so cysteine's R group has a p k r of 8.18, which is smaller than the pH. The pH is greater. So if the pH is greater, the conjugate base predominates. The conjugate base of this is actually gonna be ionized, and it's gonna have a negative charge on it. And then last but not least, what we have is cysteine's p k a over here, which is the the pKa of the, c terminal, carboxyl group. And so, pKa of 1.96 is smaller than the pH, so the pH is greater. If the pH is greater, again, the conjugate base predominates, and the conjugate base of the carboxyl group is gonna be charged. It's gonna have a negative charge on it. And so when we're determining the net charge of our peptide here, essentially all we need to do is sum up all of the charges on these groups. So notice that we have 2 negative charges and one positive charge, so that comes out to a total net charge of negative one, and this is essentially the answer for part a, negative one charge. So now moving on to part b, it asks, what is the net charge of the same peptide if the pH is lowered to a pH of 2? And then it wants us, of course, to draw this newly ionized peptide. So essentially, just to save some time here, what we can do is we can take the same peptide right here, and we can essentially bring it right down to the bottom down below. And so, what we'll see here is that this peptide is gonna be exactly the same. The only thing that's gonna be different is its ionizable groups. So we need to determine its ionizable groups all over again, so we can get rid of them. Alright. And so, essentially what we're going to do is just do the same exact thing that we did, earlier, just comparing the pKas that are given to this new pH over here. So we'll start with the amino group and the pKa of 8.8 for the amino group is greater than the pH, and so the pH is smaller. And when the pH is smaller than the pKa, the conjugate acid predominates, and the conjugate acid of the amino group this time is gonna be positively charged. It's gonna be an NH 3 plus. Alright. So now moving on to our next group, what we have is, the arginine's p k r, which is 12.48, which is greater than the pH. So the pH is smaller again. If the pH is smaller than the p k a, that means that the conjugate acid predominates. And so, essentially down here, we can say that the conjugate acid is predominating again, so it's going to be NH 2 plus again. And then, moving on to the next group, which is cysteine's PKR here, 8.18, is greater than the pH of 2, and so the pH is smaller. When the pH is smaller, the conjugate acid predominates, and the conjugate acid of, cysteine's R group is gonna be protonated. It's gonna have the extra hydrogen, and it's gonna be neutral. And so there's gonna be no charge on it. And then last but not least, what we have is the p k a for the carboxyl group, 1.96, which is smaller than a pH of 2. So the pH is actually greater. And when the pH is greater than the p k a, the conjugate base predominates, and the conjugate base of the carboxyl group is going to have a charge on it. It's gonna be a carboxylate anion. So we'll put a negative charge here. And so when determining the net charge here, all we gotta do is sum up all of these charges. So the net charge is literally just gonna be the sum of all of these charges. So notice that we have one negative charge over here, and then we have 2 positive charges over here. So that means that the net charge is going to be plus 1. And this is essentially the answer for part b. And so moving on to part c down below, it asks, within what pH range would the net charge on the peptide above be approximately plus 1? And so all we need to do is essentially arrange all of those pKas that we have up above and arrange them in order from smallest to greatest. So we wanna arrange all of these pKas here, down below from smallest to greatest. So, what we'll see is that 1.96 is our smallest pka, and this is the pka of the carboxyl group. Then what we have next is, a pKa of 8.18, which was for cysteine's, r group. And then what we have is a pKa of 8.8, and this was the p k a of the amino group. And then last but not least, our largest p k a was 12.48, and that was the p k a of arginine's r group. And so essentially, what we did by checking a pH of 2 in our previous problem So in our previous problem, we checked a pH of 2, and we determined the net charge of the predominant structure was plus 1. So essentially what we see here is at this range, if we selected a pH of 2, which falls into this range, a pH equal to 2, essentially, what we said is our predominant structure has a plus one net charge. And so pretty much at any pH between these 2 pKas, essentially between the pKa of the carboxyl group and the pKa of cysteine's r group, our predominant structure is gonna have a net charge of plus plus 1. So, for the pH range, all we need to do is indicate 1.96 to 8.18. And essentially, any pH between 8 point I'm sorry. 1.96 and 8.18 will give our predominant structure on our peptide an approximately plus one charge. And so that here concludes this practice problem, and I'll see you guys in our next video.

Struggling with Biochemistry?

Watch next

Determining Net Charge of a Peptide practice set