Transcription of genetic information in the framework of quantum information theory

It is now well known that DNA can be regarded as a physical elastic object in a viscous environment. Two strands of double helix are antiparallel and two polynucleotide chains are coiled about the same axis such that B-DNA (Z-DNA) has right-handed (left-handed) helical sense. The existence of supercoiled DNA has been confirmed in experiments long ago and it was found that in vivo chromosomal DNA molecules contain topological domains along which supercoiling can occur.1–3 DNA molecules from prokaryotes (cells without nuclear membranes) often adopt the interwound structures which are called “plectonemic” supercoils. In eukaryotes (cells with nuclei and other organelles with their own internal membranes) chromosomal DNA molecules are also known to be organized into topological independent loops.2–5 Statistical mechanics of supercoiled DNA has been studied by several authors.6 The experiments of Boles et al.7 suggest that thermal fluctuations determine the structure of supercoils. Experiments of Bednar et al.8 indicated that DNA-DNA attraction may compete with fluctuation entropy. In this note we shall study different statistical mechanical aspects of DNA supercoils by taking into consideration that a DNA supercoil can be viewed as a chain of spin system. In fact as two polynucleotide chains are coiled about the same axis with a specific helical sense in a DNA molecule, we may visualize it such that a spin with a specific orientation is inserted on the axis in the coil such that two adjacent coils have opposite orientations of the spin. This follows from the fact that with each turn two strands move in the opposite side of the axis and so the spin orientations assigned for two adjacent coils should be opposite to each other.