Consider a ribosome translating a codon to an amino acid. Compared to a perfect pairing, imagine that a codon-anticodon paring with one incorrect base pair is 10 kJ/mol higher in energy, two incorrect base pairs is 15 kJ/mol higher, and three incorrect base pairs is 20 kJ/mol higher. How many ways are there of making a one-, two-, or three-base-pair mis-match? What is the partition function of the codon-anticodon system at 300 K? If energy difference is the only consideration, what percent of decoding events occur with an error (no mismatches) at 300 K?

There are 9 ways to make a single base mismatch, 27 ways to make a two base pair mismatch and, again, 27 ways to make a three base pair mismatch (and only 1 way to do it correctly). Q = e − U i k b T i ∑ = e − U zeromismatches k b T + 9 × e − U onemismatche k b T + 27 × e − U twomismatches k b T + 27 × e − U threemismatches k b T = e 0 k b T + 9 × e − 10 kJ / mol k b T + 27 × e − 20 kJ / mol k b T 27 × e − 30 kJ / mol k b T = 1 + 9 × (0.018) + 27 × (0.00033) + 27 × (0.000006) = 1 + (0.163) + (0.0089) + (0.00016) =1.17 p 0 = e − U 0 k b T Q = e − 0 k b T 1.17 = 1 1.17 = 0.853 => 85.3% Therefore, approximately 85.3% of all amino acids are translated faithfully. The redundancy built into the genetic code and other energetic considerations raise this number considerably.

Explanation:

Check attachment for details

the number of valence electrons for each molecule or ion is shown beneath the structure. remember hydrogen will not have more than two electrons. this hydrogen is part of a covalent bond (sharing two electrons). a double bond here would cause hydrogen to share four electrons with phosphorus.