On the Role of Stop Codons in the Genetic Code

John Cole

A preliminary set of calculations:

                 As a preliminary step and a proof of concept, the steady state eigenvectors were calculated for 1000 random genetic codes.  In each case the genetic code considered had the same overall codon frequencies (ie. 6 leucine codons, 3 stop codons, etc.) as the wild type code.  These eigenvectors were used to calculate the respective expectation values for the number of heavy atoms, N,  mollecular mass, M, and ratios  H_f / N and  H_f / M.  As well, a measure of the afore mentioned polar requirement conservation,  ΔP—defined as the sum over all amino acids of the absolute values of the changes in polar requirement of a given amino acid converting to another amino acid under a SNS—was also calculated for each random code.  The means and standard deviations of each of these five values were calculated and compared to the values for the wild type code:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                 We see that the results are encouraging.  As expected, the wild type genetic code does appear incredibly effective in minimizing ΔP—with a value more than 12 sigma better than that of a random code.  Albeit not as striking, all four of the proposed measures of mollecular cost also appear unlikely to occur randomly.  M and N appear to be the strongest in this regard, both of which have expectation values lower than more than an estimated 99% of random codes (assuming a normal distribution).  M appears to be the best optimized by the wild type code of all four measures considered.

Data comparing a set of 1000 random genetic codes with the wild type code with respect to our four molecular cost measures: