(a) Simulation snapshots of chromosomes compacted (left) and spatially resolved (right) by two-sided extrusion. (b) Simulation snapshots showing deficient compaction (left) and resolution (right) of chromosomes with pure one-sided loop extrusion. (c) One-sided loop extrusion model, as compared to the two-sided model. (i) Linear fold compaction, FC, as a function of the dimensionless ratio, λ/d, of the processivity to the mean distance between LEFs. Pure one-sided extrusion (green) saturates at ≈10-fold compaction for large λ/d, as predicted by mean-field theory (green dashed line). FC by two-sided extrusion (black) surpasses the 1000-fold linear compaction expected for human chromosomes (black dashed line) for λ/d > 50. Insets: cartoons of extrusion of chromatin (gray) by active LEF subunits (yellow). Stationary passive subunit for one-sided LEF is purple. (ii) Number of gaps per parent loop, ng/nℓ, saturates at ≈0.25 (dashed line) as λ/d increases in the pure one-sided model (green), as expected from theory. For two-sided extrusion, ng/nℓ approaches 0 (black). Insets: mechanisms of gap formation and closure. (iii) Chromosome volume, V, decreases as λ/d increases. V achieves smaller values in the two-sided model (black) than in the one-sided model (green). Insets: Images of concave hulls of simulated chromosomes compacted by one- and two-sided extrusion (top and bottom, respectively). (iv) Scaled distance, ΔR/Rb, between sister chromatid backbones in one- or two-sided models. Insets: chromatid backbones in simulations of one- and two-sided extrusion (top and bottom, respectively). (d) Semi-diffusive model. (i) FC <1000 for λ/d < 1000. Color from blue to red indicates increasing scaled diffusive stepping speed, vdiff/v. Inset: a semi-diffusive LEF. (ii) Number of gaps per loop, ng/nℓ, versus λ/d. (iii) Compacted chromosome volume, V, versus λ/d. Inset: chromosome compacted by semi-diffusive LEFs with vdiff/v = 1. (iv) Scaled distance, ΔR/Rb, between chromatid backbones. Inset: image of spatial resolution with vdiff/v = 1. (e) Switching model. (i) FC can surpass 1000-fold linear compaction for rapid scaled switching rates, kswitch/kunbind > 10 (red). Simulations with large λ/d match mean-field theoretical predictions (colored dashed lines). Inset: illustration of the model. (ii) Number of gaps per loop, ng/nℓ, with mean-field theoretical predictions (dashed lines). (iii) Compacted chromosome volume, V. Inset: image of compacted chromosome with kswitch/kunbind = 30. (iv) Scaled distance, ΔR/Rb, between chromatid backbones. Inset: spatial resolution in simulations with kswitch/kunbind = 30. (f) Linear fold-compaction for a chromosome with LEFs that are able to traverse each other. Dashed line shows theoretical fold compaction, as quantified by loop coverage, FC = eλ/d. (g) Simulation snapshot of chromosome compacted by LEFs that may traverse each other. (h) Simulation snapshot of chromatids resolved by LEFs that may traverse each other. Each data point is a mean quantity (see Materials and methods). Standard deviation of the mean for each point is <15% of the mean, or else smaller than the size of a data point.