  The standard genetic code is known to be robust to translation errors and
point mutations. We studied how small modifications of the standard code affect
its robustness. The robustness was assessed in terms of a proper stability
function, the negative variations of which correspond to a more robust code.
The fraction of more robust codes obtained under small modifications appeared
to be unexpectedly high, ranged from 0.1 to 0.4 depending on the choice of
stability function and code modifications, yet significantly lower than the
corresponding fraction in the random codes (about a half). In this sense the
standard code ought to be considered distinctly non-random in accordance with
previous observations. The distribution of the negative variations of stability
function revealed very abrupt drop beyond one standard deviation, much sharper
than for Gaussian distribution or for the random codes with the same number of
codons in the sets coding for amino acids or stop-codons. This behavior holds
for both the standard code as a whole and its binary NRN-NYN, NWN-NSN, and
NMN-NKN blocks. Previously, it has been proved that such binary block structure
is necessary for the robustness of a code and is inherent to the standard
genetic code. The modifications of the standard code corresponding to more
robust coding may be related to the different variants of the code. These
effects may also contribute to the rates of replacements of amino acids. The
observed features demonstrate the joint impact of random factors and natural
selection during evolution of the genetic code.

Quantitative Methods;Genomics