Collapse and coexistence for a molecular braid with an attractive interaction component subject to mechanical forces

摘要

Dual mechanical braiding experiments provide a useful tool with whichinvestigate the nature of interactions between rod-like molecules, for instanceactin and DNA. In conditions close to molecular condensation, one would expectan appearance of a local minimum in the interaction potential between the twomolecules. We investigate this situation, introducing an attractive componentinto the interaction potential, using a model developed for describing suchexperiments. We consider attraction that does not depend on molecularstructure, as well that which depends on a DNA-like helix structure. Inbraiding experiments, an attractive term may lead to certain effects. A localminimum may cause molecules to collapse from a loosely braided configurationinto a tight one, occurring at a critical value of the moment applied about theaxis of the braid. For a fixed number of braid pitches, this may lead tocoexistence between the two braiding states, tight and loose. Coexistenceimplies certain proportions of the braid are in each state, their relative sizedepending on the number of braid pitches. This manifests itself as lineardependence in numerically calculated quantities as functions of the number ofbraid pitches. Also, in the collapsed state, the braid radius stays roughlyconstant. Furthermore, if the attractive interaction is helix dependent, theleft-right handed braid symmetry is broken. For a DNA like charge distribution,using the Kornyshev-Leikin interaction model, our results suggest thatsignificant braid collapse and coexistence only occurs for left handed braids.Regardless of the interaction model, the study highlights the possiblequalitative physics of braid collapse and coexistence; and the role helixspecific forces might play, if important. The model could be used to connectother microscopic theories of interaction with braiding experiments.