Internal condensation of a single DNA molecule

We report a theoretical description of the collapse of a single chain molecule, such as DNA, from a voluminous random coil to a condensed state. With the polymer lattice theory developed by Flory as a starting point, the configurational free energy of a single polymer molecule in solution is expressed as a virial expansion in the polymer segment volume fraction. We have extended the series by one term beyond Flory's analysis and have evaluated the third virial coefficient. Whenever the potential of interaction between two chain segments is attractive, the addition of this new term causes a new minimum to appear in the free energy. The new minimum represents a polymer configuration in which the chain occupies a very small solution volume; we identify this minimum with the collapsed state. There is a critical point for the transition to the collapsed state; above a certain value of the rms end‐to‐end distance, the change in the polymer solution volume is a sudden one, whereas below this value the transition is gradual. An example of the results of the free energy calculation using parameters from T2 DNA is presented. DNA should show a sudden collapse, but synthetic polymers such as polystyrene should show a gradual collapse.

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