Theory of acoustic mode vibrations of DNA fibers

A previous model for acoustic mode vibrations of a DNA molecule in water is extended to the case of an array of many DNA molecules, as occurs in the fibers studied in most experimental work on DNA. The acoustic modes of this system are found to consist of coupled modes of water sound vibrations and DNA acoustic modes. This model is used to study the electrostatic coupling of acoustic vibrations to the relaxational modes of the orientational degrees of freedom of the water molecules. It is found that the long-range or macroscopic electric field generated by the acoustic mode vibrations of the water-DNA system gives too small a damping and frequency shift of the acoustic modes to account for the observations on DNA fibers. Therefore, the observed damping and frequency shifts are most likely due to either friction between the surrounding water and the vibrating DNA, or coupling to the water orientation degrees of freedom resulting from the short range (i.e., screened) Coulomb interaction. The latter explanation (which is most likely the correct one) implies that the relaxation time of the hydration shell water is longer than the observed relaxation time by a factor of the static dielectric constant of the hydration water.