Reference no: EM132463824

The human genome is a double helix containing some 3 billion nucleotide base pairs. For purposes of discussion we can imagine DNA as a long string of four letters (A,T,G,C) corresponding to the four nucleotides (Adenine, Thymine, Guanine, and Cytosine).

1. A sequence of three nucleotides (for example ATC, CCG, TCT, etc.) form a codon. These codons get translated into one of twenty amino acids. These amino acids, in turn, are strung together into a polymer chain to form a protein. (The translation or mapping from codon to amino acid is virtually the same for all oranisms on Earth.) Three of the codons (TAA, TGA, TAG) have a special meaning: STOP - to signal the end of the gene. Nevertheless, explain why it must be the case that there are four codons that all translate to some particular amino acid. Hint: what mathematical principle are you invoking?
2. How many DNA sequences of length 12 are possible? Note: DNA sequences have a definite direction or orientation, so reversing the sequence produces a different DNA sequence.
3. Suppose we were to distinguish the 12-base sequences only by the total number of A's, T's, G's, and C's. For example, (6A, 6G), (1A, 3T, 2G, 6C), etc. Now how many sequences are there?
4. Sometimes when we scan along a genomic sequence, we see repeats such as AT AT AT AT AT AT (a length-2 repeat) or GCT GCT GCT GCT (a length-3 repeat). Longer repeating motifs are also possible. How many DNA sequences of length 12 are there if we exclude sequences consisting only of repeating motifs of length 1, 2, or 3?