Peptides

Transcript

0:00Introduction

Hello everyone! Let us start with a small puzzle. Glycine has a molar mass of seventy five grams per mole, and alanine has eighty nine. Join one glycine to one alanine to make a dipeptide, and its molar mass should be seventy five plus eighty nine, which gives one hundred and sixty four, right? But the real value is one hundred and forty six. So where did eighteen grams go? Today, with peptides, we find out. Peptide bonds, molar masses and sequences come up often in JEE questions, so let's begin.

0:36The peptide bond

So, look at the figure, with glycine on the left and alanine on the right. The carboxyl group of glycine, COOH, reacts with the amino group of alanine, N H two; the small two means two hydrogen atoms. This amino group sits on the alpha carbon, the carbon carrying the carboxyl group, marked by the Greek letter alpha on screen. Okay? Now look at the box in the figure. It holds an O H from glycine and an H from alanine. So tell me, O H plus H, which small molecule is that? Yes, exactly, it is water. One molecule of water, H two O, is lost; the minus sign in front of it means it leaves. Remember this for our puzzle. Right? What remains between the two units is the shaded C O, N H group, and each small dash on screen is a bond. This amide bond, joining two amino acids, is called the peptide bond, or peptide linkage. Clear? Each amino acid unit in a chain is called a residue. Now look at the two ends. The glycine end still has a free N H two group, so glycine is the N-terminal residue, and we always write it on the left. Got it? The alanine end still has a free COOH group, so alanine is the C-terminal residue, written on the right. So this dipeptide is glycyl-alanine, Gly-Ala for short. With me? So here is my question. Glycyl-alanine and alanyl-glycine contain the same two amino acids. Are they the same compound? No, they are different compounds, and many students miss this. In glycyl-alanine the free N H two belongs to glycine, but in alanyl-glycine it belongs to alanine. Order matters, hence the not-equal sign on screen. Okay?

2:32Counting peptide bonds, and the molar mass

Now, let us count bonds. Think of the residues as beads on a string, and each peptide bond as the link between two beads. If n residues sit in a line, how many links join them? That is right, it is n minus one. Two residues need one bond, and three residues need two. So a linear chain of n residues has n minus one peptide bonds. Right? But careful, here comes a trap. If the chain closes into a ring, the last residue also bonds back to the first one. So a cyclic peptide of n residues has n peptide bonds, not n minus one. Clear? And every peptide bond releases one water molecule, of mass eighteen. So the molar mass of a linear peptide, capital M, is the sum of the molar masses of its amino acids, shown by the big Greek letter sigma, minus eighteen times the bracket n minus one. Got it?

3:27How many peptides? Order matters

Since order matters, we can also count peptides. From n different amino acids, each used once, we get n factorial peptides of n residues; the exclamation mark on screen is the factorial sign. Okay? And if any of k amino acids may be used at each of the n positions, with repeats allowed, the count is k to the power n; the small raised n is the power. With me? Quick check from the course. With glycine and alanine, how many dipeptides can you make, first with each used once, and then with repetition allowed? Each used once, two factorial gives two, glycyl-alanine and alanyl-glycine. With repetition, two to the power two gives four, because glycyl-glycine and alanyl-alanine join in. Right?

4:16Names by size, and a flat peptide group

Now the names, by size. Two residues make a dipeptide, three a tripeptide, and four a tetrapeptide. Clear? With more than ten residues, we call it a polypeptide. Okay? And with more than about a hundred residues, a molar mass above ten thousand, it is a protein; note the word about, because the boundary is not sharp. Got it? One last fact. The peptide group is flat, which we call planar, because its C N bond, the dash between C and N on screen, has partial double-bond character. Right?

4:49Example 1: structure and molar mass of the dipeptide Gly-Ala

Now, remember our puzzle from the start? Let's finish it. Write the structure of the dipeptide glycyl-alanine, and find its molar mass. Pause the video and try it first. Done? Okay, let's check. Glycine comes first, so the chain starts with its free amino group and its C H two, then the peptide bond. Then alanine's alpha carbon, carrying a methyl group, the C H three in brackets, and the free carboxyl group at the right end. Clear? Now the mass. Glycine is seventy five and alanine eighty nine grams per mole, from the amino acids lesson; the minus one on mol in the unit means per mole. The sum is one hundred and sixty four. So is that the molar mass of the dipeptide? No, and now you know why. One peptide bond formed, so one water molecule of mass eighteen left. Seventy five plus eighty nine minus eighteen gives one hundred and forty six grams per mole. So our eighteen grams went into the water, and the puzzle is solved. Okay?

5:57Example 2: glycine count in a tetrapeptide of mass 274

Now a harder one. Read it with me. Here is a tetrapeptide made only of glycine and alanine, and its molar mass is two hundred and seventy four. How many glycine residues does it contain? Pause the video and try it. Here is a hint: let the letter a stand for the number of glycine residues, and write one equation. Done? Okay, let's check. Let the number of glycine residues be a, okay? There are four residues in all, so there are four minus a alanine residues. Right? Now, how much water do we subtract? Only one eighteen, like the dipeptide? If you said only one, careful, that is the trap. Four residues in a line have three peptide bonds, so three water molecules leave. Three times eighteen gives fifty four. Got it? So the equation is seventy five times a, plus eighty nine times the bracket four minus a, minus fifty four, equals two hundred and seventy four. With me? Open the bracket and collect the terms: the plain numbers give three hundred and two, and the a terms give minus fourteen times a. The double arrow on screen means this gives. So fourteen times a is twenty eight, and a is two, which means there are two glycine residues. Clear? Now a topper's trick. If all four residues were alanine, the mass would be three hundred and two. Each swap of an alanine for a glycine drops the mass by fourteen, the difference between eighty nine and seventy five. We need a drop of twenty eight, and twenty eight over fourteen gives two swaps. Okay? Let us check. Two glycines give one hundred and fifty, two alanines give one hundred and seventy eight, and minus fifty four for the water gives two hundred and seventy four. Perfect, it matches!

7:50Quick revision: peptide bond, n minus 1 bonds, molar mass

So, quick revision. Each peptide bond, C O, N H, costs one water molecule. Linear chains of n residues have n minus one bonds, and their molar mass is the sum minus eighteen times the bracket n minus one; cyclic peptides have n bonds. And the N-terminal residue goes on the left, the C-terminal on the right. Now go and try the practice problems on this page. All the best!