Polymer physics-based mathematical models for the correlation of DNA and mRNA in a eukaryotic cell

DNA and mRNA are essential aspects of cells. They are responsible for much of the genomic activity that takes place in a cell, and are significant macromolecules for research in cell and molecular biology. DNA and mRNA are polymers, molecules that are composed of repeating subunits known as monomers. In the past, a number of theoretical models that elucidate the physical properties of polymers have been proposed to the scientific community. These models include the Freely-Jointed Chain, Freely-Rotating Chain, Worm-Like Chain, and Gaussian Chain Models. In this paper, I make use of such theoretical models in polymer physics, and derive a number of theoretical models that correlate DNA, its respective pre-mRNA strand, and the corresponding post-mRNA strand in a eukaryotic cell. Furthermore, graphical representations of some of the mathematical models derived in the paper are also rendered. Based on this, the theoretical models formulated in this paper can be applied to research in the fields of mathematical biology, biophysics, biochemistry, and cell/molecular biology.