Compaction and Segregation of Sister Chromatids Via Active Loop Extrusion

1 Compaction and segregation of sister chromatids 2 via active loop extrusion 3 4 5 Anton Goloborodko1, Maxim V. Imakaev1, John F. Marko2, and Leonid Mirny1,3,* 6 7 Short title: Compaction and segregation of sister chromatids 8 9 10 1 Department of Physics, Massachusetts Institute of Technology, Cambridge MA 02139 11 2 Department of Molecular Biosciences and Department of Physics and Astronomy, 12 Northwestern University, Evanston IL 60208 13 3 Institute for Medical Engineering & Science, Massachusetts Institute of Technology, 14 Cambridge MA 02139 15 16 * Corresponding author: Leonid Mirny, Institute for Medical Engineering & Science, 17 Massachusetts Institute of Technology, 77 Mass Ave, Cambridge MA 02139, [email protected], 18 +16174524862 19 Keywords: prophase, polymers, condensin, structural maintenance of chromosomes 20 1 21 22 Abstract 23 24 The mechanism by which chromatids and chromosomes are segregated during mitosis 25 and meiosis is a major puzzle of biology and biophysics. Using polymer simulations of 26 chromosome dynamics, we show that a single mechanism of loop extrusion by 27 condensins can robustly compact, segregate and disentangle chromosomes, arriving at 28 individualized chromatids with morphology observed in vivo. Our model resolves the 29 paradox of topological simplification concomitant with chromosome “condensation”, and 30 explains how enzymes a few nanometers in size are able to control chromosome 31 geometry and topology at micron length scales. We suggest that loop extrusion is a 32 universal mechanism of genome folding that mediates functional interactions during 33 interphase and compacts chromosomes during mitosis. 34 2 35 Introduction 36 The mechanism whereby eukaryote chromosomes are compacted and concomitantly 37 segregated from one another remains poorly understood. A number of aspects of this 38 process are remarkable. First, the chromosomes are condensed into elongated 39 structures that maintain the linear order, i.e. the order of genomic elements in the 40 elongated chromosome resembles their order along the genome 1. Second, the 41 compaction machinery is able to distinguish different chromosomes and chromatids, 42 preferentially forming intra-chromatid cross-links: if this were not the case, segregation 43 would not occur 2. Third, the process of compaction is coincident with segregation of 44 sister chromatids, i.e. formation of two separate chromosomal bodies. Finally, originally 45 intertwined sister chromatids become topologically disentangled, which is surprising, 46 given the general tendency of polymers to become more intertwined as they are 47 concentrated 3. 48 49 None of these features cannot be produced by indiscriminate cross-linking of 50 chromosomes 4, which suggests that a novel mechanism of polymer compaction must 51 occur, namely “lengthwise compaction” 3,5,6, which permits each chromatid to be 52 compacted while avoiding sticking of separate chromatids together. Cell-biological 53 studies suggest that topoisomerase II and condensin are essential for metaphase 54 chromosome compaction 7–10, leading to the hypothesis that mitotic compaction- 55 segregation relies on the interplay between the activities of these two protein 56 complexes. Final structures of mitotic chromosomes were shown to consist arrays of 57 consecutive loops 11–13. Formation of such arrays would naturally results in lengthwise 58 chromosome compaction. 59 3 60 One hypothesis of how condensins can generate compaction without crosslinking of 61 topologically distinct chromosomes is that they bind to two nearby points and then slide 62 to generate a progressively larger loop 2. This “loop extrusion” process creates an 63 array of consecutive loops in individual chromosomes 2. When loop-extruding 64 condensins exchange with the solvent, the process eventually settles at a dynamical 65 steady state with a well-defined average loop size14. Simulations of this system at larger 66 scales 14 have established that there are two regimes of the steady-state dynamics: (i) a 67 sparse regime where little compaction is achieved and, (ii) a dense regime where a 68 dense array of stabilized loops efficiently compacts a chromosome. Importantly, loop 69 extrusion in the dense regime generates chromatin loops that are stabilized by multiple 70 “stacked” condensins 15, making loops robust against the known dynamic binding- 71 unbinding of individual condensin complexes 16., These two quantitative studies of loop 72 extrusion kinetics14,15 focused on the hierarchy of extruded loops and did not consider 73 the 3D conformation and topology of the chromatin fiber in the formed loop arrays. The 74 question of whether loop-extruding factors can act on a chromatin fiber so as to form an 75 array of loops, driving chromosome compaction and chromatid segregation, as originally 76 hypothesized for condensin in 2, is salient and unanswered. The main objective of this 77 paper is to test this hypothesis and to understand how formation of extruded loop arrays 78 ultimately leads to compaction, segregation and disentanglement (topology 79 simplification) of originally intertwined sister chromatids. 80 81 Here we use large-scale polymer simulations to show that active loop extrusion in 82 presence of topo II is sufficient to reproduce robust lengthwise compaction of chromatin 83 into dense, elongated, prophase chromatids with morphology in quantitatively accord 84 with experimental observations. Condensin-driven lengthwise compaction, combined 85 with the strand passing activity of topo II drives disentanglement and segregation of 4 86 sister chromatids in agreement with theoretical prediction that linearly compacted 87 chromatids must spontaneously disentangle 3. 88 89 90 Model 91 We consider a chromosome as a flexible polymer, coarse-graining to monomers of 10 92 nm diameter, each corresponding to three nucleosomes (600bp). As earlier 13,17, the 93 polymer has a persistence length of ~5 monomers (3Kb), is subject to excluded volume 94 interactions and to the activity of loop-extruding condensin molecules and topo II (see 95 below, and in 17). We simulate chains of 50000 monomers, which corresponds to 30 Mb, 96 close to the size of the smallest human chromosomal arm. 97 98 Each condensin complex is modeled as a dynamic bond between a pair of monomers 99 that is changed as a function of time (Figure 1, Video 1). Upon binding, each 100 condensin forms a bond between two adjacent monomers; subsequently both bond 101 ends of a condensin move along the chromosome in opposite directions, progressively 102 bridging more distant sites and effectively extruding a loop. As in prior lattice models of 103 condensins 14,15, when two condensins collide on the chromatin, their translocation is 104 blocked; equivalently, only one condensin is permitted to bind to each monomer, 105 modeling their steric exclusion. Exchange of condensins between chromatin and 106 solution is modeled by allowing each condensin molecule to stochastically unbind from 107 the polymer. To maintain a constant number of bound condensins, when one 108 condensin molecule dissociates, another molecule associates at a randomly chosen 109 location, including chromatin within loops extruded by other condensins. This can 110 potentially lead to formation of reinforced loops (Video 2, see below) 14,15. 5 111 112 To simulate the strand-passing activity of topo II enzymes, we permit crossings of 113 chromosomal fiber by setting a finite energy cost of fiber overlaps. By adjusting the 114 overlap energy cost we can control the rate at which topology changes occur. 115 116 This model has seven parameters. Three describe the properties of the chromatin fiber 117 (linear density, fiber diameter, and persistence length); two control condensin kinetics 118 (the mean linear separation between condensins, and their processivity, i.e. the average 119 size of a loop formed by an isolated condensin before it dissociates, and defined as two 120 times the velocity of bond translocation times the mean residence time); one parameter 121 controls the length of the monomer-monomer bond mediated by a condensin (effectively 122 the size of a condensin complex), and finally we have the energy barrier to topological 123 change. 124 125 The effects of two of these parameters, linear separation of condensins and their 126 processivity, have been considered earlier in the context of a 1D model 14. These 127 parameters control the fraction of a chromosome extruded into loops and the average 128 loop length. In our simulations, we use the separation of 30kb (1000 condensins per 30 129 Mb chromosome, as measured in 18) and the processivity of 830 kb such that 130 condensins form a dense array of gapless loops with the average loop length of 100kb, 131 which agrees with available experimental observations 11–13,19. The effects of the other 132 five parameters are considered below. 133 134 Initially, chromosomes are compacted to the density of chromatin inside the human 135 nucleus and topologically equilibrated, thus assuming an equilibrium globular 136 conformation, corresponding to a chromosomal territory. In the simulations of sister 6 137 chromatid segregation, the initial conformation of one chromatid is generated as above, 138 while the second chromatid traces the same path at a distance of 50nm and winds one 139 full turn per 100 monomers (60 kb). In this state, two chromatids run parallel to each 140 other and are highly entangled, while residing in the same chromosome territory. This 141 represents

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