Braiding DNA: Experiments, Simulations, and Models

Abstract

DNA encounters topological problems in vivo because of its extended double-helical structure. As a consequence, the semiconservative mechanism of DNA replication leads to the formation of DNA braids or catenanes, which have to be removed for the completion of cell division. To get a better understanding of these structures, we have studied the elastic behavior of two braided nicked DNA molecules using a magnetic trap apparatus. The experimental data let us identify and characterize three regimes of braiding: a slightly twisted regime before the formation of the first crossing, followed by genuine braids which, at large braiding number, buckle to form plectonemes. Two different approaches support and quantify this characterization of the data. First, Monte Carlo (MC) simulations of braided DNAs yield a full description of the molecules' behavior and their buckling transition. Second, modeling the braids as a twisted swing provides a good approximation of the elastic response of the molecules as they are intertwined. Comparisons of the experiments and the MC simulations with this analytical model allow for a measurement of the diameter of the braids and its dependence upon entropic and electrostatic repulsive interactions. The MC simulations allow for an estimate of the effective torsional constant of the braids (at a stretching force F = 2 pN): C(b) approximately 48 nm (as compared with C approximately 100 nm for a single unnicked DNA). Finally, at low salt concentrations and for sufficiently large number of braids, the diameter of the braided molecules is observed to collapse to that of double-stranded DNA. We suggest that this collapse is due to the partial melting and fraying of the two nicked molecules and the subsequent right- or left-handed intertwining of the stretched single strands.

Self-consistent treatment of electrostatics in molecular DNA braiding through external forces

“…In second part, we compare the self-consistent theory with experimental data of Ref. [16] and find good agreement with the model. In the last section, our discussion and outlook, we discuss extensions to the work, as well as the possibility that weak chiral interactions may account for the slight asymmetry between left and right handed braids seen in some of the experimental data.…”

“…However, only recently, has there also been an interest in performing dual braiding experiments [14,15,16], which may provide insights into braiding in DNA catenane like structures. The experiments, reported in Refs.…”

“…The experiments, reported in Refs. [14] and [16], involve the two DNA molecules being attached by antibodies to a substrate and a magnetic bead. The magnetic field that is applied to the bead provides a pulling force that stretches out the DNA molecules, supressing the undulations of the molecular centrelines, and a moment that produces a fixed number of turns of the bead, and so a braid.…”

“…However, in two recent publications [33,34], we have developed a new model that describing braiding experiments of the form of those done in Ref. [16]. These models allow for the two ends of the two DNA molecules to be apart a distance much larger than diameter of the braid which they form, which is relevant for the experiments of Ref.…”

“…These models allow for the two ends of the two DNA molecules to be apart a distance much larger than diameter of the braid which they form, which is relevant for the experiments of Ref. [16], as the DNA are attached to the bead with an end to end separation between the two molecules of the order of one micron. Also, one important improvement over the work of Ref.…”