The Persistence Length of DNA Is Reached from the Persistence Length of Its Null Isomer through an Internal Electrostatic Stretching Force

To understand better the effect of electrostatics on the rigidity of the DNA double helix, we define DNA*, the null isomer of DNA, as the hypothetical structure that would result from DNA if its phosphate groups were not ionized. For the purposes of theoretical analysis, we model DNA* as identical to ordinary DNA but supplemented by a longitudinal compression force equal in magnitude but oppositely directed to the stretching (tension) force on DNA caused by phosphate-phosphate repulsions. The null isomer DNA* then becomes an elastically buckled form of fully ionized DNA. On this basis, we derive a nonadditive relationship between the persistence length P of DNA and the persistence length P* of its null isomer. From the formula obtained we can predict the value of P* if P is known, and we can predict the ionic strength dependence of P under the assumption that P* does not depend on ionic strength. We predict a value of P* for null DNA drastically lower than the value of P for DNA in its ordinary state of fully ionized phosphates. The predicted dependence of P on salt concentration is log-c over most of the concentration range, with no tendency toward a salt-independent value in the range of validity of the theory. The predictions are consistent with much of the persistence-length data available for DNA. Alternate theories of the Odijk-Skolnik-Fixman type, including one by the author, are considered skeptically on the grounds that the underlying model may not be realistic. Specifically, we doubt the accuracy for real polyelectrolytes of the Odijk-Skolnik-Fixman assumption that the polymer structure is invariant to changes in electrostatic forces.