Synergy of topoisomerase and structural-maintenance-of-chromosomes proteins creates a universal pathway to simplify genome topology

Abstract

Topological entanglements severely interfere with important biological processes. For this reason, genomes must be kept unknotted and unlinked during most of a cell cycle. Type II topoisomerase (TopoII) enzymes play an important role in this process but the precise mechanisms yielding systematic disentanglement of DNA in vivo are not clear. Here we report computational evidence that structural-maintenance-of-chromosomes (SMC) proteins-such as cohesins and condensins-can cooperate with TopoII to establish a synergistic mechanism to resolve topological entanglements. SMC-driven loop extrusion (or diffusion) induces the spatial localization of essential crossings, in turn catalyzing the simplification of knots and links by TopoII enzymes even in crowded and confined conditions. The mechanism we uncover is universal in that it does not qualitatively depend on the specific substrate, whether DNA or chromatin, or on SMC processivity; we thus argue that this synergy may be at work across organisms and throughout the cell cycle.

Keywords: Brownian dynamics; SMC proteins; entanglements; genome topology; topoisomerase.

Fig. 1.

Sliding of SMC proteins localizes topological entanglements. (A) Schematics of knot localization starting from a fully delocalized trefoil via loop extrusion/diffusion. (B) Corresponding Brownian dynamics simulations. (C) Kymograph showing the shortest knotted arc along the chain as a function of time. The blue curves show the position of the SMC heads ($h_1\left(t\right),h_2\left(t\right)$) and demonstrate that the knot localizes over time. (D) Schematics of link localization starting from a delocalized Hopf link. (E) Corresponding Brownian dynamics simulations. (F) Kymograph showing the shortest linked segments for the two polymers. As the SMC protein is loaded on the gray polymer, the linked region in the sister strand is free to slide and this gives rise to a localized but fluctuating orange-shaded area (Movies S1 and S2).

Fig. 2.

SMC-recruited TopoII. (A) Motivated by experimental findings (24, 50), we assume that TopoII is colocalized with SMC and it is found on the outside of the SMC-mediated loop (dark-colored segments). (B) Implementation of A in a bead-spring polymer model: The SMC slip link is enforced by a FENE bond between blue beads which are updated in time. TopoII beads (green) are set to display a soft repulsive potential with all other beads thus allowing thermally activated strand crossing. Dark green and light green beads have different energy barriers against overlapping ($5k_{B}T$ and $20k_{B}T$, respectively). (C and D) Kymographs showing synergistic knot simplification. In C, SMC-driven loop extrusion localizes the shortest knotted arc while in D, two SMCs localize only the knot’s essential crossings (Insets). We find that D is predominant for diffusive SMC (SI Appendix and Movies S3 and S7).

Fig. 3.

Efficient unknotting under confinement. The synergistic action of SMC and TopoII proteins can systematically simplify knotted substrates even under confinement. Here we show the case of torus ($7_1$) and twist ($7_2$) knots confined within a sphere with radius $R_c/⟨R_g⟩\simeq 1/3$. In the snapshots, light gray beads are the ones that have been extruded by, hence behind, the SMC. Dark gray beads are the ones outside the extruded loop. Blue beads mark the location of the SMC heads. Green and dark green beads mark the location of TopoII, as described in the text. (A) Unknotting of a $7_1$ knot through the “cascade” of torus knots $5_1$ and $3_1$. (B) Unknotting of a $7_2$ knot through $5_2$ and $3_1$ knots. Direct simplification $7_2\hspace{0.17em}\to \hspace{0.17em}{0}_1$ is also observed in more than half of the simulations (Table 1, SI Appendix, and Movies S4 and S5).

Fig. 4.

Localized vs. random TopoII under confinement. We perform simulations on a trefoil under confinement $R/⟨R_g⟩=1/3$ and measure (A) the knotting probability $P_{\mathcal{K}}$ and (B) the fraction of completed loops $f_e$ as a function of time. Our results show that while models of randomly bound TopoII can lead to substrate unknotting, they entail a return to equilibrium values of $P_{\mathcal{K}}$ once SMCs stop extruding.