RNA polymer of 25% C & 75%A is used as a template in in vitro translation.Whats expected frequency of Lys,Gln?

among the amino acids incorporated into the polypeptides that form,what is the expected frequency of LYS?Pro?Gln? explain please

RNA polymer of 25% C %26amp; 75%A is used as a template in in vitro translation.Whats expected frequency of Lys,Gln?
This is a statistical problem and you have to ignore the fact that you won't have an ATG (Met) inititator codon with which to start translation, but I digress. Anyway, if the template is all C's and A's, then there are 8 possible combinations (actually permutations, n^r) of codons:





CCC


CCA


CAA


AAA


AAC


ACC


CAC


ACA





The codons for Lys, Pro and Gln are listed here (as well as other websites):





http://www.cbs.dtu.dk/courses/27619/codo...





Since there is only one codon for Lysine that has only C's and A's (AAA) and since there are two codons for Proline with only C's and A's (CCC, CCA) and since there is only one codon for Glutamine with only C's and A's (CAA), then with equal amounts of C's and A's in the mRNA:





1/8 (12.5%) of the amino acids would be Lys


2/8 (1/4, 25%) would be Pro


1/8 (12.5%) would be Gln





However, since there are 25% C and 75% A in the mRNA templates this will sway the probabilities a bit towards the codons containing more A's. So, since the codons that matter are:





AAA


CCC


CCA


CAA





Then, the probabilities are:





AAA (0.75 * 0.75 * 0.75 = 0.421875)


CCC (0.25 * 0.25 * 0.25 = 0.015625)


CCA (0.25 * 0.25 0.75 = 0.046875)


CAA (0.25 * 0.75 * 0.75 = 0.140625)





So, the probability (frequency) of Lys in the peptides is 42.1875%, Pro is 1.5625% + 4.6875% = 6.25% and Gln is 14.0625%