Theory of the toroidal compact form of DNA in polymer solution

The diagram of states of a single long rigid DNA macromolecule in a solution of a short flexible polymer has been constructed. It is shown that the compacting action of the polymer solvent on DNA may be interpreted as the hydrostatic pressure of the gas of polymer coils on the "walls" of the DNA globule impermeable for them. The conditions for the existence of compact (globular) states in the form of a sphere (stable for very long DNA) and torus (for relatively short) have been found. The possibility of intramolecular liquid crystalline ordering of the DNA segments in the globules is analysed. The regions of application of both regimes have been studied-when compression by the added polymer is equilibrated by the forces of steric repulsion of the DNA segments and when it is equilibrated by the entropic flexibility of the flexures of the DNA chain.