Diffusion of nanochannel-confined knot along a tensioned polymer*

Abstract The knots frequently occur in biopolymer and their diffusion plays an active role in the gene regulation. In this work, Langevin dynamics simulations were carried out to detect the diffusion behaviours of a knot along a tensioned polymer in different spatial constraints. The polymer accommodating a knot was tethered to two macrospheres to block the unravelling of the knot. As a result, the curves for the diffusion coefficients of the knot with different bending stiffness as a function of the tension in different spatial constraints were obtained. In the space without constraints or with weak constraints, the corresponding curves for the knot with relatively large bending stiffness exhibited two turnover behaviours. On the contrary, for the knot with relatively small bending stiffness, the diffusion coefficients were monotonically reduced with increasing tension. However, in a space with strong constraints, all the curves showed one turnover behaviour regardless of the bending stiffness. The turnover behaviours divided the curves into different regimes, and the dominant diffusion mechanisms in the regimes, namely, knot-region breathing, self-reptation, and internal friction, were clearly identified. The effective friction coefficients ξ of the knots with 31, 41, 51 and 52 types as a function of the knot size N at a fixed tension were well fitted by the relation ξ ∝ N. The effective friction coefficients of the knots at relatively large tension f > 3 sharply increased with the knot complexity, which is not dependent on the spatial constraints. By contrast, the values of these coefficients at relatively small tension f ≤ 3 were remarkably dependent on the spatial constraints. Our work not only provides valuable simulation results to assist the understanding of the diffusion of DNA knot, but also highlights the single-molecule design for the manipulation of DNA knots in future.