  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 localisation of essential crossings in turn
catalysing 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.
