  The genetic code is the function from the set of codons to the set of amino
acids by which a DNA sequence encodes proteins. Since the codons also influence
the shape of the DNA molecule itself, the same sequence that encodes a protein
also has a separate geometric interpretation. A question then arises: How
well-duplexed are these two "codes"? In other words, in choosing a genetic
sequence to encode a particular protein, how much freedom does one still have
to vary the geometry (or vice versa). A recent paper by the first author
addressed this question using two different methods. After reviewing those
results, this paper addresses the same question with a third method: the use of
Monte Carlo and Gaussian sampling methods to approximate a multi-integral
representing the mutual information of a variety of possible genetic codes.
Once again, it is found that the genetic code used in nuclear DNA has a
slightly lower than average duplexing efficiency as compared with other
hypothetical genetic codes. A concluding section discusses the significance of
these surprising results.
