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Synergy of Topoisomerase and Structural-Maintenance

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Synergy of Topoisomerase and Structural-Maintenance Synergy of topoisomerase and structural-maintenance- of-chromosomes proteins creates a universal pathway to simplify genome topology Enzo Orlandinia, Davide Marenduzzob, and Davide Michielettob,1 aDipartimento di Fisica e Astronomia “Galileo Galilei,” Sezione Istituto Nazionale di Fisica Nucleare, Universita` degli Studi di Padova, I-35131 Padova, Italy; and bSchool of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom Edited by Michael L. Klein, Institute of Computational Molecular Science, Temple University, Philadelphia, PA, and approved March 14, 2019 (received for review September 6, 2018) Topological entanglements severely interfere with important bio- cal simplification. Our simulations reveal that this mechanism is logical processes. For this reason, genomes must be kept unknot- independent of either substrate condensation or crowding and is ted and unlinked during most of a cell cycle. Type II topoisomerase therefore likely to lead to unknotting and unlinking even under (TopoII) enzymes play an important role in this process but the extreme conditions such as those in the cell nucleus. Finally, we precise mechanisms yielding systematic disentanglement of DNA discuss our model in the context of recent experiments report- in vivo are not clear. Here we report computational evidence that ing that SMC proteins are essential to achieve correct sister structural-maintenance-of-chromosomes (SMC) proteins—such as chromatid decatenation in metaphase (23), that DNA damage cohesins and condensins—can cooperate with TopoII to establish is frequently found in front of cohesin motion (24), and that a synergistic mechanism to resolve topological entanglements. there is a remarkable low frequency of knots in intracellular SMC-driven loop extrusion (or diffusion) induces the spatial local- chromatin (17). ization of essential crossings, in turn catalyzing the simplification of knots and links by TopoII enzymes even in crowded and con- Results and Discussion fined conditions. The mechanism we uncover is universal in that it Model and System Setup. We perform Brownian dynamics (BD) BIOPHYSICS AND does not qualitatively depend on the specific substrate, whether simulations of a generic polymer substrate modeled as a semi- DNA or chromatin, or on SMC processivity; we thus argue that this flexible bead-spring circular chain of 500 beads of size σ, taken COMPUTATIONAL BIOLOGY synergy may be at work across organisms and throughout the cell to be 2.5 nm for DNA (25) and 10 nm for chromatin (26). We cycle. consider circular chains as representative of DNA plasmids or stably looped genomic regions such as the so-called “topolog- genome topology j SMC proteins j topoisomerase j Brownian dynamics j ically associated domains” (TADs) bound by CTCF proteins entanglements (27) and knotted and linked topologies as capturing topologi- cal entanglements that typically occur in genetic materials (8, enomes are long polymers stored in extremely crowded 17, 28–30) (Fig. 1). Unlike in previous works (31, 32), here we Gand confined environments; the ensuing inevitable entan- explicitly forbid spontaneous strand-crossing events by imposing glements are thought to cause DNA damage, interfere with gene transcription and DNA replication, and interrupt anaphase, Significance eventually leading to cell death (1–3). In vitro and under dilute conditions, type II topoisomerase (TopoII) proteins efficiently Vital biological processes such as gene transcription and cell resolve topological entanglements and stabilize a population of division may be severely impaired by inevitable entangle- knotted DNA below the expected value in thermodynamic equi- ments ensuing from the extreme length and confinement of librium (4). These findings can be partially explained by a model the genome. The family of topoisomerase proteins has inde- where TopoII enzymes recognize specific DNA–DNA juxtapo- pendently evolved in different organisms to resolve these sitions (5–7). However, how this model can lead to efficient topological problems, yet no existing model can explain how unknotting and unlinking in crowded environments and crum- topoisomerase alone can reduce the topological complexity pled DNA or chromatin substrates is unclear (2, 8, 9). Even more of DNA in vivo. We propose that a synergistic mechanism intriguing is the in vitro experimental finding that, in the pres- between topoisomerase and a family of slip-link–like pro- ence of polycations (10) or with superstochiometric abundance teins called structural maintenance of chromosomes (SMC) of TopoII (11), the action of these proteins may increase the can provide a pathway to systematically resolve topological topological complexity of DNA substrates (10, 12, 13). entanglements even under physiological crowding and con- While it has been suggested that DNA supercoiling may pro- finement. Given the ubiquity of topoisomerase and SMC, we vide a solution for this problem by promoting hooked DNA argue that the uncovered mechanism is at work throughout juxtapositions (14–16), this argument is valid only for naked, the cell cycle and across different organisms. highly supercoiled DNA, such as bacterial plasmids. The under- standing of how efficient topological simplification is achieved Author contributions: E.O. and D. Michieletto designed research; E.O. and D. Michieletto in eukaryotes where the genome is packaged into chromatin performed research; E.O. and D. Michieletto analyzed data; and E.O., D. Marenduzzo, remains, on the other hand, an outstanding and unresolved and D. Michieletto wrote the paper.y problem (1, 17). The authors declare no conflict of interest.y Here we propose a mechanism for efficient topological simpli- This article is a PNAS Direct Submission.y fication in DNA and chromatin in vivo that is based on the syner- This open access article is distributed under Creative Commons Attribution License 4.0 gistic action of structural-maintenance-of-chromosomes (SMC)- (CC BY). y driven loop extrusion (18–21) [or diffusion (22)] and TopoII. We 1 To whom correspondence should be addressed. Email: [email protected] show that the sliding of slip-link–like proteins along DNA and This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. chromatin is sufficient to localize any knotted and linked regions 1073/pnas.1815394116/-/DCSupplemental.y or their essential crossings, in turn catalyzing their topologi- www.pnas.org/cgi/doi/10.1073/pnas.1815394116 PNAS Latest Articles j 1 of 6 Downloaded by guest on September 26, 2021 Fig. 1. Sliding of SMC proteins localizes topological entanglements. (A) Schematics of knot localization starting from a fully delocalized trefoil via loop extrusion/diffusion. (B) Corresponding Brownian dynamics simulations. (C) Kymograph showing the shortest knotted arc along the chain as a function of time. The blue curves show the position of the SMC heads (h1(t), h2(t)) and demonstrate that the knot localizes over time. (D) Schematics of link localization starting from a delocalized Hopf link. (E) Corresponding Brownian dynamics simulations. (F) Kymograph showing the shortest linked segments for the two polymers. As the SMC protein is loaded on the gray polymer, the linked region in the sister strand is free to slide and this gives rise to a localized but fluctuating orange-shaded area (Movies S1 and S2). that any pair of consecutive beads are connected by finitely exten- beads is shorter than 1:3σ. This rule ensures that no third bead sible (FENE) springs (33) while nonconsecutive ones are subject can pass through the segments bonded by the SMC protein dur- to a purely repulsive (Weeks–Chandler–Andersen) potential. A ing the update step and it effectively slows down the processivity Kratky–Porod term is used to set up the persistence length at of the complex, depending on the instantaneous substrate con- lp = 20σ. Note, however, that the results are not qualitatively formation. We highlight that the speed of the extrusion process affected by this choice (SI Appendix). does not qualitatively affect the synergistic mechanism found here, only its overall completion time. A Slip-Link Model for SMC. SMC proteins, including condensin and cohesin, are thought to regulate genome architecture across SMC Sliding Localizes Topological Entanglements. Thermally equili- organisms by topologically embracing DNA or chromatin in a brated knotted or linked polymers in good solvent display weakly slip-link–like fashion (18, 21, 34–36). Recent experiments in localized topological entanglements (41, 42); i.e., the shortest arc vitro suggest that condensin can move directionally at a speed that can be defined as knotted or linked, lK , grows sublinearly 0:75 v ' 0:6−1:5 kb=s (37) and that cohesin performs diffusive sliding with the overall contour length L, as lK ∼ L (Fig. 1A) (43, with diffusion constant D ' 0:1−1 µm2=s (38, 39). Previous work 44). Further topological delocalization is achieved by isotropic has crudely modeled SMC proteins as harmonic springs between confinement (45) and crowding (46), both conditions that are nonconsecutive chromosome segments which were dynamically typically found in vivo. Since delocalization of essential crossings updated (irrespective of local constraints) to extrude loops (20, is likely to hinder TopoII-mediated topological simplification, it 32, 40). In contrast, here we account for both the steric hin- is natural to ask whether there exists a physiological mechanism drance and the slip-link nature of the SMC complex by modeling that counteracts topological delocalization in vivo. the SMC bond with a FENE spring so that it is energetically To address this question we performed BD simulations of very unfavorable for a third segment to cross through the gap directed loop extrusion on thermalized polymers which display in between the bonded beads. The two chromosome segments delocalized entanglements (Fig. 1A). The ensuing extrusion, or bound by the SMC protein at time t, or SMC “heads,” are growth, of the subtended loop can be monitored by tracking the denoted as h1(t) and h2(t) and updated at rate κ (SI Appendix). location of the SMC heads h1(t) and h2(t) (blue curves in Fig.
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