Chromosome Compaction by Active Loop Extrusion

Abstract

During cell division, chromosomes are compacted in length by more than a 100-fold. A wide range of experiments demonstrated that in their compacted state, mammalian chromosomes form arrays of closely stacked consecutive ∼100 kb loops. The mechanism underlying the active process of chromosome compaction into a stack of loops is unknown. Here we test the hypothesis that chromosomes are compacted by enzymatic machines that actively extrude chromatin loops. When such loop-extruding factors (LEF) bind to chromosomes, they progressively bridge sites that are further away along the chromosome, thus extruding a loop. We demonstrate that collective action of LEFs leads to formation of a dynamic array of consecutive loops. Simulations and an analytically solved model identify two distinct steady states: a sparse state, where loops are highly dynamic but provide little compaction; and a dense state, where there are more stable loops and dramatic chromosome compaction. We find that human chromosomes operate at the border of the dense steady state. Our analysis also shows how the macroscopic characteristics of the loop array are determined by the microscopic properties of LEFs and their abundance. When the number of LEFs are used that match experimentally based estimates, the model can quantitatively reproduce the average loop length, the degree of compaction, and the general loop-array morphology of compact human chromosomes. Our study demonstrates that efficient chromosome compaction can be achieved solely by an active loop-extrusion process.

Figure 1

Simulations of chromosome compaction by loop extruding factors (LEFs). The action of LEFs can be simulated using a one-dimensional lattice model with four dynamic rules (a–d): (a) LEFs extrude loops by moving the two connected heads along the chromosome, (b) LEF heads block each other, (c) LEFs dissociate from chromatin, and (d) LEFs in the solution rebind to the chromosome. (e) Simulations show that LEFs can fold a chromosome into an array of consecutive loops. The diagram shows the loops formed by LEFs in a simulation with L = 2000, N = 200, τ = 450, and v = 1 after 45,000 time steps. (f and g) The system of LEFs on a long chromatin fiber converges to a steady state. The steady distribution of loop sizes and the degree of compaction depends on the control parameters, but is independent of initial state. Results are shown for different simulation parameters and starting conditions; data for each curve is averaged over 10 simulation replicas. To see this figure in color, go online.

Figure 2

Simulations of LEFs reveal two distinct steady states. (a and b) The properties of loop arrays formed by LEFs, such as the portion of the chromosome extruded into loops, the portion of branched loops, and the number of LEFs per loop, depend on the dimensionless ratio λ/d. This ratio defines the two steady states of the system: (c) the sparse state (λ/d ≪ 1), where the loops are supported by single LEFs and separated by big loop-free gaps; and (d) the dense state (λ/d ≫ 1), where the whole chromosome is extruded into an array of consecutive loops supported by multiple LEFs. In both steady states, the loops are not branched (a). The vertical dotted lines at λ/d = 0.5 and $20$ roughly show the transition region. To see this figure in color, go online.

Figure 3

The mechanism of loop reinforcement in the dense state. Upon binding to an existing loop, a LEF reextrudes it and stacks on top of the LEFs already supporting the loop. To see this figure in color, go online.

Figure 4

The model of loop death and division explains the origin of the dense steady state. (a) Loops occasionally disassemble when the number of reinforcing LEFs fluctuates to zero. The chromatin of the disassembled loop is immediately extruded into the adjacent loops. (b) A loop splits upon simultaneous landing of two reinforcing LEFs. The rates of loop death (c) and division (d) in the dense state can be estimated using simple analytical formulas (red dots) or more accurate computational models (blue dots). (e) In the dense state, the steady-state balance between loop death and division provides an approximate analytical expression for the average loop length (the red line). In the sparse state, the average loop length is predicted to be equal λ (the red line). Both predictions agree well with the simulations (the black line). The four horizontal overlapping gray bands show the available independent experimental estimates of $\overline{\ell }/d$ in mitotic human chromosomes: $\overline{\ell }$ = 42–70 kb (3), 54–112 kb (25), 80–90 kb (24), 80–120 kb (9), and d ≈ 30 kb (22). To see this figure in color, go online.