1. Our genetic material, DNA, is formed from a 4 letter\"alphabet\" of bases: A,
ID: 2916355 • Letter: 1
Question
1. Our genetic material, DNA, is formed from a 4 letter"alphabet" of bases: A, T, G, C (adenine, thymine, guanine, andcytosine). The order in which the letters are arranged isimportant, but because a molecule can move, there is no differencebetween a sequence and the same sequence reversed. For example, thesequence (A, A, T, A, G, A, T) is the same as the sequence (T, A,G, A, T, A, A).How many distinct DNA sequences of 6 bases are there?
I tried 4^6, and it's wrong because i forgot the reverse ofsequences is not distinct.
46/2 is also not the correct answer.
I also tried 4*4*4*3*3*3, trying to avoid the mistake I made thefirst time. But that's also not the correct answer.
Right now, I'm thinking it's some form of
4*4*4*3*4*4 + 4*4*4*4*3*4 + 4*4*4*4*4*3 , since one of the lastbases can only have 3 choices to avoid being the reverse. I don'tknow if it's (45 * 3)*6 or (45 * 3)*3. Or ifit's something completely different, since with this approach iwould get a number way bigger than 46, which I thoughtwas the total number of strings of six bases (with four choices foreach base). I can only submit the answer one more time, so it hasto be right :(
Explanation / Answer
I think the only reversed sequences you need to worry about arepalindromes since for DNA, the combinations of nucleotides are likewords and the reverse of a word is distinct from the original word;that is the word "apple" is not the same as it's reverse"elppa". Anyways, first calculate the number of combinations of bases youcan get, that's 4^6. Since palindromes don't count you cansubtract the number of palindromes from 4^6. The number ofpalindromes is just the number of distinct sequences of 3 baseswhich is 4^3. So I guess the # of distinct non palindromicsequences is 4^6-4^3 which is 4032. I suppose if youignore the directionality of DNA then the reverse sequence is thesame as the original sequence in which case you need to divide 4032by 2. You then add the number of palindromes, 4^3 or 64 to thatnumber to get 2080 distinct 6 nucleotide sequences.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.