Question

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

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

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 \(n_1 = n_2 = 2\).

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.

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)#

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).

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.

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