Nonequilibrium Chromosome Looping via Molecular Slip Links

Abstract

We propose a model for the formation of chromatin loops based on the diffusive sliding of a DNA-bound factor which can dimerise to form a molecular slip-link. Our slip-links mimic the behaviour of cohesin-like molecules, which, along with the CTCF protein, stabilize loops which organize the genome. By combining 3D Brownian dynamics simulations and 1D exactly solvable non-equilibrium models, we show that diffusive sliding is sufficient to account for the strong bias in favour of convergent CTCF-mediated chromosome loops observed experimentally. Importantly, our model does not require any underlying, and energetically costly, motor activity of cohesin. We also find that the diffusive motion of multiple slip-links along chromatin may be rectified by an intriguing ratchet effect that arises if slip-links bind to the chromatin at a preferred "loading site". This emergent collective behaviour is driven by a 1D osmotic pressure which is set up near the loading point, and favours the extrusion of loops which are much larger than the ones formed by single slip-links.1 arXiv:1612.07256v1 [physics.bio-ph] Dec 2016The formation of long-range contacts, or loops, within DNA and chromosomes is a process which critically affects gene expression [1, 2]. For instance, looping between specific regulatory elements, such as enhancers and promoters, can dramatically increase transcription rates in eukaryotes [1]. The formation of these loops can often be successfully predicted by equilibrium polymer physics models, which balance the energetic gain of protein-mediated interactions with the entropic loss associated with loop formation [3][4][5].However, recent high-throughput chromosome conformation capture ("Hi-C") experiments [6, 7] have fundamentally challenged the view that equilibrium physics is sufficient to model chromosome looping. Hi-C experiments showed that the genomes of most eukaryotic organisms are partitioned into domains -called "topologically associated domains", or TADs. In several cases, these domains were found to be enclosed within a chromosome loop, 100 − 1000 kilo-basepairs (kpb) in size, and the bases of the loops are statistically enriched in binding sites for the CCCTC-binding factor (CTCF) [7, 8]. CTCF is a DNA-binding protein with an important role in gene regulation, and CTCF-mediated loops preferentially enclose inducible genes, which are normally silent and are pressed into action in response to a stimulus (e.g., an inflammation or an increased concentration of a morphogen during development) [8]. The DNA-binding motif of CTCF is not palindromic, meaning that it has a specific direction on the DNA. Surprisingly, Hi-C analyses have recently revealed that most of the CTCF binding sequences only form a loop when they are in a "convergent" orientation ( Fig. 1a) [7, 10]. Very few contacting CTCFs have a "parallel" orientation, and virtually none have a "divergent" one. This strong bias is puzzling, because, if we imagine drawing arrows on the chromatin fiber (corresponding to the CTCF binding site...

Models of polymer physics for the architecture of the cell nucleus

“…The LE model (Fudenberg et al, 2016;Goloborodko et al, 2016;Sanborn et al, 2015) quantifies another interesting scenario of chromatin folding, where an active motor (e.g., Cohesin) binds to DNA and actively extrude a DNA loop up to encountering oppositely oriented CTCF anchoring sites. A variant of the LE, the Slip-Link model proposes a similar scenario based on random sliding of the loop bridging sites, without requiring an active, energy burning mechanism (Brackley et al, 2017). Importantly, both the LE and the SL models describe well folding at loci where CTCF is the main driving force and are consistent with the CTCF convergence bias (Brackley et al, 2017;Sanborn et al, 2015).…”

“…Albeit diffusion is the origin of loop formation within the SL, technically the model describes an off-equilibrium system, because of the envisaged adsorbing boundary anchors. Computer simulations have shown that the SL model not only explains the CTCF convergence bias, but also well accounts for the size distribution of CTCF-based loops, as derived by ChIA-PET data (Brackley et al, 2017).…”

“…The other key hypothesis of the LE model is that the extruding factor producing the loops is an active motor, hence burning energy at each single step along the DNA sequence. The idea has been controversial because of the large amount of energy (and very high progression speed) required to organize chromatin at a genomic-scale (Brackley et al, 2017). Additionally, while it has been recently shown that the Condensin complex can undergo an adenosine triphosphate (ATP)-based unidirectional active motion along a DNA template (Terakawa et al, 2017), no similar evidences exist to date about Cohesin.…”

“…To try to overcome some of the problems inherent to the LE model, an interesting variant, the Slip-Link model (SL, Figure 1c), considers a scenario without active motors (Brackley et al, 2017). As in the LE, the SL model poses that the Cohesin complex becomes loaded at adjacent pairs of sites on the DNA chain and hand-cuffs the two together.…”

“…A class of models has considered the classical scenario of molecular biology where contacts between distal DNA sites and loops are established by diffusing molecules such as transcription factors (TFs) or some effective interaction potential, via mechanisms of equilibrium polymer thermodynamics (Barbieri, Chotalia, Fraser, et al, 2012;Bianco, Lupiáñez, Chiariello, et al, 2018;Bohn & Heermann, 2010;Brackley, Johnson, Kelly, Cook, & Marenduzzo, 2016;Brackley, Taylor, Papantonis, Cook, & Marenduzzo, 2013;Chiariello, Annunziatella, Bianco, Esposito, & Nicodemi, 2016;Di Pierro et al, 2016;Di Stefano, Paulsen, Lien, Hovig, & Micheletti, 2016;Jost, Carrivain, Cavalli, & Vaillant, 2014;Kreth, Finsterle, von Hase, Cremer, & Cremer, 2004;Nicodemi & Prisco, 2009). A different class of polymer models have focused on off-equilibrium folding mechanisms (Brackley, Johnson, Michieletto, et al, 2017;Fudenberg, Imakaev, Lu, et al, 2016;Goloborodko, Marko, & Mirny, 2016;Lieberman-Aiden et al, 2009;Sanborn, Rao, Huang, et al, 2015), in particular, on another classical scenario where loops are formed by molecules that bind to a site along DNA and extrude a loop. Those models are shedding light on the origin of contact patterns emerging from Hi-C data, as well as on the specific molecular mechanisms that fold different loci.…”