(a) Arch diagram schematically showing two-sided LEFs (orange) and one-sided LEFs (purple) with different unbinding rates (and residence times), and , respectively. (b) Top: Example trajectories for mixtures of one- and two-sided LEFs illustrating the theoretical limits of very long-lived two-sided LEFs (left) and very short-lived two-sided LEFs (right). In both scenarios, a two-sided LEF (orange) extrudes at speed until encountering a one-sided LEF (blue or purple), which acts as a barrier. Encounters with barriers reduce the effective mean speed, , indicated by black dashed lines. Bottom: Arch diagrams from simulation snapshots for the two scenarios. Two-sided LEFs are orange and one-sided LEFs are purple. (c) Fold-compaction, , as a function of the ratio, , for 50/50 mixes of one- and two-sided LEFs in which each species has a different residence time. Color from blue to gray to red indicates increasing ratio, , of residence times. Green box on the color bar indicates estimated range of residence time ratios for condensin II as compared to condensin I (Gerlich et al., 2006a; Gibcus et al., 2018; Walther et al., 2018). Gray points are data for . Black dashed line indicates 1000-fold compaction. (d) Maximum fold compaction, , as a function of the ratio of residence times, . Colors from blue to gray to red indicate increasing fractions, , of one-sided LEFs. Dotted lines indicate theory, with results for shown for , results for shown for , and the mean-field () result shown with straight lines interpolating to other theoretical results. Yellow region indicates estimated range of residence time ratios for condensin II as compared to condensin I. Green box indicates approximate range of observed in experiments with metazoan condensins (Golfier et al., 2020; Kong et al., 2020). (e) Phase diagram colored by fold linear compaction, , for various fractions, , of one-sided LEFs and ratios, of residence times (red: high compaction, blue: low compaction, gray: ). Yellow region indicates range of residence time ratios for condensin II as compared to condensin I and experimentally observed fractions of one-sided extruders. Black dotted line is the theoretically predicted boundary () between high and low compaction regimes. Standard error for all displayed data points is .