Nucleation of Multiple Buckled Structures in Intertwined DNA Double Helices

Investigating site-selection mechanisms of retroviral integration in supercoiled DNA braids

We theoretically study the integration of short viral DNA in a DNA braid made up by two entwined double-stranded DNA molecules. We show that the statistics of single integration events substantially differ in the straight and buckled, or plectonemic, phase of the braid and are more likely in the latter. We further discover that integration is most likely close to plectoneme tips, where the larger bending energy helps overcome the associated energy barrier and that successive integration events are spatio-temporally correlated, suggesting a potential mechanistic explanation of clustered integration sites in host genomes. The braid geometry we consider provides a novel experimental set-up to quantify integration in a supercoiled substrate in vitro, and to better understand the role of double-stranded DNA topology during this process.

DNA Mechanics and Topology

We review the current understanding of the mechanics of DNA and DNA-protein complexes, from scales of base pairs up to whole chromosomes. Mechanics of the double helix as revealed by single-molecule experiments will be described, with an emphasis on the role of polymer statistical mechanics. We will then discuss how topological constraints- entanglement and supercoiling-impact physical and mechanical responses. Models for protein-DNA interactions, including effects on polymer properties of DNA of DNA-bending proteins will be described, relevant to behavior of protein-DNA complexes in vivo. We also discuss control of DNA entanglement topology by DNA-lengthwise-compaction machinery acting in concert with topoisomerases. Finally, the chapter will conclude with a discussion of relevance of several aspects of physical properties of DNA and chromatin to oncology.

Plectoneme dynamics and statistics in braided polymers

Braids composed of two interwoven polymer chains exhibit a "buckling" transition whose origin has been explained through the onset of plectonemic structures. Here we study, by a combination of simulation and analytics, the dynamics of plectoneme formation and their statistics in steady state. The introduction of an order parameter-the plectonemic fraction-allows us to map out the phase boundary between the straight-braid phase and the plectonemic one. We then monitor the formation and the growth of plectonemes, observing events typical of phase separation kinetics for liquid-gas systems (fusion, fission, and one-dimensional Ostwald ripening) but also of DNA supercoiling dynamics (plectonemic hopping). Finally, we propose a stochastic field theory for the coupled dynamics of twist and local writhe which explains the phenomenology found with Brownian dynamics simulations as well as the power laws underlying the coarsening of plectonemes.

Defect-facilitated buckling in supercoiled double-helix DNA

We present a statistical-mechanical model for stretched twisted double-helix DNA, where thermal fluctuations are treated explicitly from a Hamiltonian without using any scaling hypotheses. Our model applied to defect-free supercoiled DNA describes the coexistence of multiple plectoneme domains in long DNA molecules at physiological salt concentrations (≈0.1M Na^{+}) and stretching forces (≈1pN). We find a higher (lower) number of domains at lower (higher) ionic strengths and stretching forces, in accord with experimental observations. We use our model to study the effect of an immobile point defect on the DNA contour that allows a localized kink. The degree of the kink is controlled by the defect size, such that a larger defect further reduces the bending energy of the defect-facilitated kinked end loop. We find that a defect can spatially pin a plectoneme domain via nucleation of a kinked end loop, in accord with experiments and simulations. Our model explains previously reported magnetic tweezer experiments [A. Dittmore et al., Phys. Rev. Lett. 119, 147801 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.147801] showing two buckling signatures: buckling and "rebuckling" in supercoiled DNA with a base-unpaired region. Comparing with experiments, we find that under 1 pN force, a kinked end loop nucleated at a base-mismatched site reduces the bending energy by ≈0.7 k_{B}T per unpaired base. Our model predicts the coexistence of three states at the buckling and rebuckling transitions, which warrants new experiments.