Thermodynamical Description of the Thermochemical Mechanisms of DNA Deformation

The purpose of this paper is to establish the thermodynamical description of thermochemical mechanisms of DNA deformation at packing it into a cell. The problem of packing of a DNA molecule in a cell is very actual because its length is much more then the diameter of a typical cell. For example, the total length of the DNA molecule from a human cell is about 2m and the cell diameter is 10−5m. For this end we will use the model of a DNA molecule in the form of the elastic rod with liquid crystal inner structure [1] and will adopt the previously developed theory of orientational deformation of liquid crystals [2]. Let us introduce three unit vectors e1, e2 and e3 imbedded in the plane for each base pair. These vectors form a local orthonormal coordinate system. Vectors e1 and e2 span a base pair plane in a way that the vector e1 is parallel to the short axis of the base pair, vector e2 is orthogonal to e1 and parallel to the long axis of the base plane and vector e3 is perpendicular to the base plane and directs along the axis of DNA double helix. This vector coincides with the tangent to the axis of the elastic rod. If we denote the vector of a small mutual rotation of the two neighboring local coordinate systems by Ψ then the deformation of a rod is described by the pseudovector [3] Ω = dΨ/ds where ds is the distance measured along the rod axis between the above mentioned systems. Vector Ω may be expanded on the orthogonal basis e1, e2 and e3