Non-equilibrium structural dynamics of supercoiled DNA plasmids exhibits asymmetrical relaxation.

Many cellular processes occur out of equilibrium. This includes site-specific unwinding in supercoiled DNA, which may play an important role in gene regulation. Here, we use the Convex Lens-induced Confinement (CLiC) single-molecule microscopy platform to study these processes with high-throughput and without artificial constraints on molecular structures or interactions. We use two model DNA plasmid systems, pFLIP-FUSE and pUC19, to study the dynamics of supercoiling-induced secondary structural transitions after perturbations away from equilibrium. We find that structural transitions can be slow, leading to long-lived structural states whose kinetics depend on the duration and direction of perturbation. Our findings highlight the importance of out-of-equilibrium studies when characterizing the complex structural dynamics of DNA and understanding the mechanisms of gene regulation.

Free energy of a knotted polymer confined to narrow cylindrical and conical channels.

Monte Carlo simulations are used to study the conformational behavior of a semiflexible polymer confined to cylindrical and conical channels. The channels are sufficiently narrow that the conditions for the Odijk regime are marginally satisfied. For cylindrical confinement, we examine polymers with a single knot of topology 3_{1}, 4_{1}, or 5_{1}, as well as unknotted polymers that are capable of forming S loops. We measure the variation of the free energy F with the end-to-end polymer extension length X and examine the effect of varying the polymer topology, persistence length P, and cylinder diameter D on the free-energy functions. Similarly, we characterize the behavior of the knot span along the channel. We find that increasing the knot complexity increases the typical size of the knot. In the regime of low X, where the knot/S-loop size is large, the conformational behavior is independent of polymer topology. In addition, the scaling properties of the free energy and knot span are in agreement with predictions from a theoretical model constructed using known properties of interacting polymers in the Odijk regime. We also examine the variation of F with the position of a knot in conical channels for various values of the cone angle α. The free energy decreases as the knot moves in a direction where the cone widens, and it also decreases with increasing α and with increasing knot complexity. The behavior is in agreement with predictions from a theoretical model in which the dominant contribution to the change in F is the change in the size of the hairpins as the knot moves to the wider region of the channel.