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Particle Wrapping by Circular DNA

Motivated by the work on hydrogel filaments in IRG1 and their prospect as microactuators, three years ago we began a theoretical effort at understanding the effect of twist and writhe in the conformation and dynamics of filaments and twist-storing polymers such double strand DNA.  Recently, we have become interested in the interaction between such filaments and polymers with particles when topological constraints restrict the twist and writhe in the molecule.  The simplest topological constraint is to have a ring with a given linking number.  The following two sets of figures obtained using the length and charge of the polymer corresponding to a DNA of 600 bps, and a total charge of +40e for the sphere show the energy-minimum structures of the wrapping states as a function of increasing salt concentration on the left and decreasing salt concentration on the right.  Along each path, there are continuous shape evolutions (states within the same arrow) followed by discontinuous changes in the wrapping states.  That the salt-decreasing path follows a different progression in the wrapping states than the reverse of the salt-increasing path suggests strong hysteresis.