Self-organization of domain structures by DNA-loop-extruding enzymes

Abstract

The long chromosomal DNAs of cells are organized into loop domains much larger in size than individual DNA-binding enzymes, presenting the question of how formation of such structures is controlled. We present a model for generation of defined chromosomal loops, based on molecular machines consisting of two coupled and oppositely directed motile elements which extrude loops from the double helix along which they translocate, while excluding one another sterically. If these machines do not dissociate from DNA (infinite processivity), a disordered, exponential steady-state distribution of small loops is obtained. However, if dissociation and rebinding of the machines occurs at a finite rate (finite processivity), the steady state qualitatively changes to a highly ordered 'stacked' configuration with suppressed fluctuations, organizing a single large, stable loop domain anchored by several machines. The size of the resulting domain can be simply regulated by boundary elements, which halt the progress of the extrusion machines. Possible realizations of these types of molecular machines are discussed, with a major focus on structural maintenance of chromosome complexes and also with discussion of type I restriction enzymes. This mechanism could explain the geometrically uniform folding of eukaryote mitotic chromosomes, through extrusion of pre-programmed loops and concomitant chromosome compaction.

Figure 1.

Schematic drawing of machine positions on the lattice as time progresses; lattice model equivalent is sketched below each panel. Black dumbbell shapes (and arrows in the lattice sketch) depict enzymes and green lines show DNA. Panel (a) depicts the starting point and the progression of infinitely processive machines, while Panel (b) shows machines with lower processivity (disassociation rate is still relatively small, see text). Panel (c) depicts a single step, with ATP binding, hydrolysis and release associated with extrusion of a small amount of DNA.

Figure 2.

Loop-size distribution for M = 5 pairs of non-disassociating loop-extruding machines on a lattice of size L = 50. The probability distribution broadens as the bias () increases. Main figure shows results for 1.05 (dot-dashed line), 1.5 (dashed line) and 4.0 (solid line). Inset: comparison of steady-state loop-size distributions for exact statistical theory (solid black line) and kinetic simulation (gray bars); difference between them is negligibly small. The simulation was run times, each for a time of Standard errors for the histogram bars have a maximum value of and are invisible on this plot.

Figure 3.

Example time series of loop size for for a (a) non-disassociating and a (b) dissociating case (), for M = 5 machines on a substrate of length L = 50. The dark solid line shows the average of the sizes of the M loops, and the red and blue dashed lines indicate the width (one standard deviation) of the distribution of loop sizes subtended by the machines as a function of time. As in all cases mentioned in this article, time is in units of .

Figure 4.

Results for model with dissociation, for L = 50, M = 5 and for different motor biases (a), 1.50 (b) and 4.00 (c). Panels (a–c) show loop-size distributions for the simulation steady state: as bias is increased, a peak grows at as motor pairs begin to trap the entire domain. Each panel was computed using simulations each of total time The maximum size of the standard error bars for the histograms are and for panels (a)–(c), respectively. The insets show the motor position (labeled ‘head index’) index along the lattice: dashed lines show the average ( 1 SD for the simulations (standard error bars for the insets are invisible on this plot); solid curves show average obtained from approximate effective Boltzmann description of the steady state. As bias is increased, fluctuations are suppressed and the motors become ‘stacked’.

Figure 5.

Loop-size distribution and motor position index profile for larger lattice (L = 200) with bias , and M = 5 motor pairs. The simulation was run times, each for a time of The maximum size of the standard error bars is For the profile (inset, labeled ‘head index’), the solid line is the effective Boltzmann theory, dashed lines show average ± 1 SD of the simulation distribution; standard errors of the simulation results are negligibly small. Dissociation rate is .

Figure 6.

Condensation of multiple loop domains. (a) Initially condensins (black dumbbell shapes) bind along a long stretch of chromatin (green), between condensation boundary elements (red octagons). (b) As condensation proceeds, condensins organize into a ‘stacked’ configuration at the bases of chromatin loops defined by the boundary elements. The resultant crowding of chromatin at the bases of the loops generates inter-chromatid tension that will drive topo II to remove inter-chromatid entanglements.

Figure 7.

Treadmilling as an alternative to individual machine translocation. Binding of machines with ATP bound (black machines) leads to multiple-machine cluster [(a–d)]; ATP hydrolysis [gray machine in (d)] followed by machine release (e) leads to effective translocation of a machine cluster and formation of a loop domain, following a mechanism similar to treadmilling of monomers of cytoskeletal filaments. Numbers indicate binding order of machines in a cluster.