Genetic information in DNA can be represented by strings consisting of the lette

Question

Genetic information in DNA can be represented by strings consisting of the letters A, T, C, and G, which represent the four nucleotide bases: adenine, thymine, cytosine, and guanine. The natural process of evolution depends on random mutation of the genetic code, which can occur in a variety of different ways. To simplify our discussion, we will focus on three types of mutation. Substitution. One or more base is replaced with another. For example, ACTCGTTG AG becomes AQTCGTTGAG Deletion. One or more base is deleted, but not replaced. For example. ACICGTTGAG becomes ACCGTTGAG Reversal. A consecutive portion of the string is put in reversed order. For example, ACTCGTTGAG becomes ATGCTCTGAG. (The portion that is reversed must haw length greater than or equal to 2.) In each example, the modified portion b underlined. a. For a string of length ten. how many different ways are there to substitute one, two. or three letters? b. For the string ACTCGTTGAG. how many different ways are there to delete one or two letters? c. For the string ACTCGTTGAG, how many different ways are there to reverse a single consecutive portion of the string? d. Count a single replacement as one move, a single deletion as one move, and a reversal (of any length) as one move. What is the minimal number of moves to get from the string ACTCGTTGAG to the string CTACGAGTC?

Explanation / Answer

(a) for one letter substitution there are 10*3=30 ways.

for two letter substitution there are (3*3)(9+8+7+6+5+4+3+2+1)=405 ways.

for three letter substitution there are (3*3*3)(8+7+6+5+4+3+2+1)=972 ways

(b) for one letter deletion there are 9 ways.

for two letter deletion there are (8+7+6+5+4+3+2+1)=36 ways.

(c) for letter reversel (8+7+6+6+5+4+3+2+1)=42ways

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