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Chromosome compaction is essential for reliable transmission of genetic information. Experiments suggest that ∼1000-fold compaction is driven by condensin complexes that extrude chromatin loops, by progressively collecting chromatin fiber from one or both sides of the complex to form a growing loop. Theory indicates that  symmetric  two-sided loop extrusion can achieve such compaction, but recent single-molecule studies (Golfier et al., 2020) observed diverse dynamics of condensins that perform one-sided, symmetric two-sided, and  asymmetric  two-sided extrusion. We use simulations and theory to determine how these molecular properties lead to chromosome compaction. High compaction can be achieved if even a small fraction of condensins have two essential properties: a long residence time and the ability to perform two-sided (not necessarily symmetric) extrusion. In mixtures of condensins I and II, coupling two-sided extrusion and stable chromatin binding by condensin II promotes compaction. These results provide missing connections between single-molecule observations and chromosome-scale organization.

The interplay between asymmetric and symmetric DNA loop extrusion