Final answer:
Using the formula of 20^250, the number of unique molecules with a 250 amino acid long sequence is astronomically large. Three nucleotides, known as a codon, code for a single amino acid. If there were 200 amino acids, the shortest codon length would be four nucleotides to encode for them all.
Step-by-step explanation:
Assuming an amino acid sequence is 250 amino acids long, the number of different molecules, each with a unique sequence, could be formed by calculating using the formula 20^n, where n is the number of amino acids. In this case, 20^250 is the calculation required because there are 20 common amino acids and the sequence is 250 amino acids long. However, the actual number resulting from 20^250 is so large it is beyond the realm of comprehension, and computer systems often represent it in scientific notation.
It's important to note that three nucleotides make up a codon, which corresponds to one amino acid in the genetic code — meaning that the number of 'letters' of an RNA molecule, in sequence, it takes to provide the code for a single amino acid is three. This is relevant because the enormous variety of protein sequences comes from the combinations of these codons.
If there were 200 commonly occurring amino acids, the shortest possible codon length that could encode for all of these would need to be longer than our current three-nucleotide codon. To work this out, we find the smallest number x such that 4^x is greater than or equal to 200, which in this case, is x = 4 codons because 4^4 is 256.