THEORY FOR THE EXTENSION OF A LINEAR POLYELECTROLYTE ATTACHED AT ONE END IN AN ELECTRIC-FIELD

A simple theory is developed for the extension of a uniformly charged linear polyion attached at one end in an electric field. For a polyion consisting of a very large number (N) of Kuhn lengths (b), the mean extension in the direction of the electric field (E) is given accurately by Rz = (b/A) In (sinh (NA)/NA), where A = EQb/kBT and Q is the effective charge associated with each Kuhn length. For any value of E, no matter how small, a polyion of sufficient length, such that NA ≫ 1.0, will be essentially fully extended. When A ≪ 1.0, as is the case for DNA in weak electric fields, the head end of the chain is only weakly oriented, even though the stem and tail may be completely aligned. In the linear regime, NA < 1.0, Rz is proportional to E, Q, and N2. The linear density of chain elements is calculated for a chain in the linear regime. This theory provides a basis to determine the product Qb from direct microscopic measurements of Rz vs. E for fluorescent‐labeled circular DNAs that are topologically snared near voids or surfaces of gels. Experimental realization of this suggestion is described in the following paper. Copyright © 1990 John Wiley & Sons, Inc.