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Chapter 22: Problem 89

Write the sequence of all possible tetrapeptides composed of the following amino acids. a. two phenylalanines and two glycines b. two phenylalanines, glycine, and alanine

Short Answer

Expert verified
The possible tetrapeptide sequences are: a. Two phenylalanines (F) and two glycines (G): 1. FFGG, 2. FGFG, 3. FGGF, 4. GFFG, 5. GFGF, 6. GGFF b. Two phenylalanines (F), one glycine (G), and one alanine (A): 1. FFGA, 2. FFAg, 3. FGFA, 4. FGAF, 5. FAGF, 6. FAFG, 7. GFFA, 8. GFAF, 9. GFAG, 10. AGFF, 11. AGFA, 12. AFGF

Step by step solution

01

Understand the formula for permutations with repetitions

Due to the repetitions of two phenylalanines and two glycines, we can use the formula for permutations with repetitions: \(P(n_1, n_2, ..., n_k) = \frac{n!}{n_1! n_2! ... n_k!}\), where n is the total number of items, and \(n_1, n_2, ..., n_k\) are the numbers of each item being repeated. In this case, n = 4 (since there are 4 amino acids), and there are two repetitions of phenylalanines (F) and glycines (G), so \(n_1 = n_2 = 2\).
02

Calculate the number of possible permutations

Using the formula, we can calculate the possible permutations as follows: \(P(2,2) = \frac{4!}{2!2!} = \frac{24}{2 \times 2} = 6\) This shows that there are 6 possible tetrapeptide sequences composed of two phenylalanines and two glycines.
03

Write out the sequences

Here are the six possible sequences for a tetrapeptide composed of two phenylalanines and two glycines: 1. FFGG 2. FGFG 3. FGGF 4. GFFG 5. GFGF 6. GGFF #b. Two phenylalanines (F), one glycine (G), and one alanine (A)#
04

Understand the formula for permutations without repetitions

Due to the use of distinct amino acids with no repetition, we can use the factorial formula for permutations without repetitions: \(n! = n \times (n-1) \times (n-2) \times ... \times 2 \times 1\) In this case, n = 4 (since there are 4 amino acids).
05

Calculate the number of possible permutations

Using the factorial formula, we can calculate the possible permutations as follows: \(4! = 4 \times 3 \times 2 \times 1 = 24\) However, we have two phenylalanines in our sequence. So, we need to divide the number of permutations by the number of times phenylalanines is repeated, which is 2. This will give us the number of possible tetrapeptides composed of two phenylalanines, one glycine, and one alanine. \(\frac{24}{2} = 12\) This shows that there are 12 possible tetrapeptide sequences composed of two phenylalanines, one glycine, and one alanine.
06

Write out the sequences

Here are the twelve possible sequences for a tetrapeptide composed of two phenylalanines (F), one glycine (G), and one alanine (A): 1. FFGA 2. FFAg 3. FGFA 4. FGAF 5. FAGF 6. FAFG 7. GFFA 8. GFAF 9. GFAG 10. AGFF 11. AGFA 12. AFGF

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Most popular questions from this chapter

Consider the following reactions. For parts \(\mathrm{b}-\mathrm{d}\), see Exercise \(62 .\) a. When \(\mathrm{C}_{5} \mathrm{H}_{12}\) is reacted with \(\mathrm{Cl}_{2}(g)\) in the presence of ultraviolet light, four different monochlorination products form. What is the structure of \(\mathrm{C}_{5} \mathrm{H}_{12}\) in this reaction? b. When \(\mathrm{C}_{4} \mathrm{H}_{8}\) is reacted with \(\mathrm{H}_{2} \mathrm{O}\), a tertiary alcohol is produced as the major product. What is the structure of \(\mathrm{C}_{4} \mathrm{H}_{8}\) in this reaction? c. When \(\mathrm{C}_{7} \mathrm{H}_{12}\) is reacted with \(\mathrm{HCl}\), 1 -chloro-1-methylcyclohexane is produced as the major product. What are the two possible structures for \(\mathrm{C}_{7} \mathrm{H}_{12}\) in this reaction? d. When a hydrocarbon is reacted with \(\mathrm{H}_{2} \mathrm{O}\) and the major product of this reaction is then oxidized, acetone (2-propanone) is produced. What is the structure of the hydrocarbon in this reaction? e. When \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}\) is oxidized, a carboxylic acid is produced. What are the possible structures for \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}\) in this reaction?

Polycarbonates are a class of thermoplastic polymers that are used in the plastic lenses of eyeglasses and in the shells of bicycle helmets. A polycarbonate is made from the reaction of bisphenol A (BPA) with phosgene \(\left(\mathrm{COCl}_{2}\right)\) : polycarbonate \(+2 n \mathrm{HCl}\) Phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\) is used to terminate the polymer (stop its growth). a. Draw the structure of the polycarbonate chain formed from the above reaction. b. Is this reaction a condensation or an addition polymerization?

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