The Duplexing of the Genetic Code and Sequence-Dependent DNA Geometry

It is well known that sequences of bases in DNA are translated into sequences of amino acids in cells via the genetic code. More recently, it has been discovered that the sequence of DNA bases also influences the geometry and deformability of the DNA. These two correspondences represent a naturally arising example of duplexed codes, providing two different ways of interpreting the same DNA sequence. This paper will set up the notation and basic results necessary to mathematically investigate the relationship between these two natural DNA codes. It then undertakes two very different such investigations: one graphical approach based only on expected values and another analytic approach incorporating the deformability of the DNA molecule and approximating the mutual information of the two codes. Special emphasis is paid to whether there is evidence that pressure to maximize the duplexing efficiency influenced the evolution of the genetic code. Disappointingly, the results fail to support the hypothesis that the genetic code was influenced in this way. In fact, applying both methods to samples of realistic alternative genetic codes shows that the duplexing of the genetic code found in nature is just slightly less efficient than average. The implications of this negative result are considered in the final section of the paper.