In Chapter 1, we have DNA as a kind of nucleic acid consisting of two strands which
are made up of two Watson-Crick base pairs: adenine-thymine (AT) and guanine-cytosine
(GC). There are three components of the total energy. These are the inharmonic stacking
interaction, hydrogen bond interaction and kinetic energy. Morse potential is used to mimic
the hydrogen bond interaction between bases on the opposite strands for the overlapping π electrons, when two neighboring bases move out of the stack. The AT pair has 2 hydrogen
bonds and the GC pair has 3 of them. The π electrons obey Bose - Einstein (BE) statistics,
and the overlapping of them results in quantum fluctuation. It will be shown that this can be
simplified into < Δy(t)Δy(t) >= 2DqΔt type fluctuation between the base pairs. Thus, a
metropolis algorithm can be developed for the total potential energy by superposing two
potential energy terms as well as including the quantum fluctuation in terms of random
displacement of the π electrons. So, one can calculate the melting temperature of base pairs.
Keywords: Biological matter, Living systems, Stochastic analysis methods.
