Two-phase dynamics of DNA supercoiling based on DNA polymer physics

Abstract

DNA supercoils are generated in genome regulation processes such as transcription and replication and provide mechanical feedback to such processes. Under tension, a DNA supercoil can present a coexistence state of plectonemic and stretched phases. Experiments have revealed the dynamic behaviors of plectonemes, e.g., diffusion, nucleation, and hopping. To represent these dynamics with conformational changes, we demonstrated first the fast dynamics on the DNA to reach torque equilibrium within the plectonemic and stretched phases, and then identified the two-phase boundaries as collective slow variables to describe the essential dynamics. According to the timescale separation demonstrated here, we developed a two-phase model on the dynamics of DNA supercoiling, which can capture physiologically relevant events across timescales of several orders of magnitudes. In this model, we systematically characterized the slow dynamics between the two phases and compared the numerical results with those from the DNA polymer physics-based worm-like chain model. The supercoiling dynamics, including the nucleation, diffusion, and hopping of plectonemes, have been well represented and reproduced, using the twophase dynamic model, at trivial computational costs. Our current developments, therefore, can be implemented to explore multiscale physical mechanisms of the DNA supercoiling-dependent physiological processes.

A spatially resolved stochastic model reveals the role of supercoiling in transcription regulation

“…We cannot simulate a higher diffusion coefficient with the explicit random walk model due to computational limitations. We found no major difference between the two models in the response of mean mRNA production to promoter strength (S15A We also need to point out that our model neglected the complex dynamics of supercoiling, i.e., the different diffusion behavior of the twist and the writhe [63] and the hopping of plectonemes [29]. According to a recent two-phage dynamic model of supercoiling [63], twist diffusion reaches fast equilibrium, compared to the RNAP translocation, while writhe diffusion is slow.…”

“…We found no major difference between the two models in the response of mean mRNA production to promoter strength (S15A We also need to point out that our model neglected the complex dynamics of supercoiling, i.e., the different diffusion behavior of the twist and the writhe [63] and the hopping of plectonemes [29]. According to a recent two-phage dynamic model of supercoiling [63], twist diffusion reaches fast equilibrium, compared to the RNAP translocation, while writhe diffusion is slow. Meanwhile, the transition from the twisted to the writhed state could happen dynamically during the translocation process [63].…”

“…According to a recent two-phage dynamic model of supercoiling [63], twist diffusion reaches fast equilibrium, compared to the RNAP translocation, while writhe diffusion is slow. Meanwhile, the transition from the twisted to the writhed state could happen dynamically during the translocation process [63]. However, our model did not differentiate the twisted or writhed states and used a single diffusion coefficient to describe the transport of the linking number.…”

DNA supercoiling in bacteria: state of play and challenges from a modeling viewpoint

“…This hypothesis appears to be reasonable, for example, in the case of transcription, whose initiation step requires the formation of a DNA denaturation bubble [30]. Namely, the twist and writhe relaxation times (below 1 ms) for a 10 kb long molecule are typically 5 orders of magnitude smaller than the time for synthesizing a 1 kb long messenger RNA (100 s) [31][32][33] and 2 orders of magnitude with respect to the time for synthesizing a single base pair. Thus, questions concerning the energy required to denature DNA have been systematically addressed in the context of the equilibrium statistical mechanics of one-dimensional systems [29,34,35].…”

“…Finally, hypothesis (iv) was made by considering the relaxation speed of the linking number as given by the diffusion speed of plectonemes. However, both single-molecule experiments [45,106] and polymer simulations [31][32][33]51] have shown that the former, which is responsible for the formation of plectonemes, is much higher than the latter. In other words, supercoiling establishment during transcription can be regarded as a quasi-static process [33].…”