So this practice problem wants us to calculate cysteine's PI or its isoelectric point, and recall that cysteine's one letter code is just a c. And again, the mnemonic for memorizing those 7 amino acids with ionizable R groups is just yucky crazy dragons eat knights riding horses. And so you can see that cysteine indeed is one of those 7 ionizable amino acid R groups. And so because the c here stands for crazy and crazy in this context is negative, then, that means that cysteine's r group is gonna have a negative charge when it's ionized. And so, recall that the first step in calculating the p I is just to know the ionizations for the r group. And so knowing that cysteine's r group is going to have a negative charge when it's ionized is completing the first step. So we can check that off and move to the second step. And the second step is to order the p k a values from smallest to largest. And so we've got 3 pKA values. We've got pKA 1 for the amino group. We've got pka 2 for the carboxyl group, and we've got pkr or the pka for the r group. And so, all we need do is order these from smallest to largest. And so the first one is, pKa 2, which is the lowest one, 1.8, and so we can put that one here, and this corresponds with the carboxyl group pKa. The next one is going to be the pkr, so it's, p k 8.3. And this is referring to the R group pKa. And then our last one, which is the highest one, is 10.8, which is the PKA one for the amino group. And so all we need to do at this point, this is an 8 by the way, all we need to do at this point is, realize that we're going to use the middle pKa here as a guide for our next step. And in our next step, we're just going to determine the net charges for the predominant structures at any pH between the, adjacent pKa values using the middle one as a guide. So basically, what we're saying is we need to determine the net charge of the predominant structures in this range right here between these 2 pKas, as well as in this range over here between these 2 pKas. And what we've been doing is just using the first one as our starting point, and so all we need to do is pick any pH, as long as the pH falls between the pKa values, these 2 pKa values. So let's just choose any pH, let's just choose, I don't know, pH 5. Let's do pH 5. And so, all we need to do at this point is say, alright, well, we just need to determine the net charge of the predominant structure at pH 5. And the way to do that is to compare the pH of the solution here, pH 5, individually to each of the pKas. And so let's first compare the pH to the amino group p k a. And so the pH 5 is less than the amino group p k a of 10.8. And so what that means is that the conjugate acid form of the amino group is going to predominate at pH 5. And the conjugate acid form of the amino group is just an NH 3 with a protonated, amino group, so it's gonna have a positive charge. So next, what we can do is check the carboxyl group. And so, notice that the pH of 5 is actually greater than the carboxyl group pKa of 1.8. And so, what that means is that the conjugate base is going to predominate at pH 5 for the carboxyl group and the conjugate base of a carboxyl group is just the carboxylate anion, which has a negative charge. And then we can, look at the r group, and And the R group here is given to us for cysteine. It's just going to be a CH2 with a sulfhydryl group. So it'll be CH2 with a sulfhydryl group. And the goal is to determine if this sulfhydryl group here is going to be protonated or deprotonated. And so to figure that out, we need to compare the pH of the solution to the p k r or the p k a of the r group. And so notice the pH of 5 is less than the p k of the r group, which means that the conjugate acid form of the r group is gonna predominate at pH 5, and the acid form is gonna be protonated, so that means SH or the sulfhydryl group will be protonated. And the protonated sulfhydryl group is neutral. And so at this point, what we've done is we've said that pretty much at any pH that you choose in this yellow region here, the predominant, amino acid structure is going to have a neutral net charge and so that's because the amino group, positive charge and the carboxylate anion negative charge cancel each other out, and the r group has no charge at all. So we've determined that the net charge here is going to be 0. And so that's exactly what we were looking for. We're looking for the neutral net charge because again, the pI is all about the pH where the structure is gonna have a neutral net charge, and so what we can say is that in this region over here, the yellow region, that the the predominant amino acid structure is gonna have a neutral net charge. And so, if we had, chosen the blue region to start first for whatever reason, if we decided to do that, we would have realized that the predominant structure has a negative one charge, and then we would have realized that the yellow region would have been the region that we wanna check. And so, here, this identifies the 2 pKas that we really want to average to get our p I or our isoelectric point. And those 2 pKas are sandwiching the neutral net charge, so it's gonna be the p kr or the pKa of the r group and the pKa of the carboxyl group. And so, all we need to do for our PI calculation is to take the middle pKa, which is the R group, 8.3, and add that to the other pKa that's sandwiching the neutral net charge, 1.8 divided by 2. And so what we end up getting is that the p I comes out to 10.1 over 2, which is equal to 5.05. And so what this means is that our answer is actually gonna be option c. So we can go ahead and give option c a check mark to indicate that c here is the correct answer and all the other ones here are incorrect. So this concludes this practice problem and I'll see you guys in our next one.

Table of contents

1. Introduction to Biochemistry4h 34m
2. Water3h 23m
3. Amino Acids8h 10m
4. Protein Structure10h 4m
5. Protein Techniques14h 5m
6. Enzymes and Enzyme Kinetics13h 38m
7. Enzyme Inhibition and Regulation 8h 42m
8. Protein Function 9h 41m
9. Carbohydrates7h 49m
10. Lipids5h 49m
11. Biological Membranes and Transport 6h 37m
12. Biosignaling9h 45m
Review 1: Nucleic Acids, Lipids, & Membranes2h 47m
Review 2: Biosignaling, Glycolysis, Gluconeogenesis, & PP-Pathway3h 12m
Review 3: Pyruvate & Fatty Acid Oxidation, Citric Acid Cycle, & Glycogen Metabolism2h 26m
Review 4: Amino Acid Oxidation, Oxidative Phosphorylation, & Photophosphorylation1h 48m

3. Amino Acids

Isoelectric Point of Amino Acids with Ionizable R-Groups

Biochemistry

3. Amino Acids

Isoelectric Point of Amino Acids with Ionizable R-Groups

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Multiple Choice

Calculate Cys's pI.

2.3

3.14

5.05

6.05

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Verified step by step guidance

Identify the ionizable groups in cysteine: the amino group (pKa1 = 10.8), the carboxyl group (pKa2 = 1.8), and the thiol side chain (pKR = 8.3).

Understand that the isoelectric point (pI) is the pH at which the molecule carries no net electric charge. For amino acids with ionizable side chains, the pI is calculated using the pKa values of the groups that are closest in value.

For cysteine, the relevant pKa values for calculating the pI are pKa2 (1.8) and pKR (8.3), as these are the pKa values between which the molecule will be neutral.

Calculate the pI by taking the average of the two closest pKa values: pI = (pKa2 + pKR) / 2.

Substitute the values into the formula: pI = (1.8 + 8.3) / 2, and solve for the pI.