Loops are geometric catalysts for DNA integration.

The insertion of DNA elements within genomes underpins both genetic diversity and disease when unregulated. Most of DNA insertions are not random and the physical mechanisms underlying the integration site selection are poorly understood. Here, we perform Molecular Dynamics simulations to study the insertion of DNA elements, such as viral DNA or transposons, into naked DNA or chromatin substrates. More specifically, we explore the role of loops within the polymeric substrate and discover that they act as 'geometric catalysts' for DNA integration by reducing the energy barrier for substrate deformation. Additionally, we discover that the 1D pattern and 3D conformation of loops have a marked effect on the distribution of integration sites. Finally, we show that loops may compete with nucleosomes to attract DNA integrations. These results may be tested in vitro and they may help to understand patterns of DNA insertions with implications in genome evolution and engineering.

Effects of monovalent and divalent cations on the rheology of entangled DNA.

In this paper we investigate the effects of varying cation valency and concentration on the rheology of entangled λDNA solutions. We show that monovalent cations moderately increase the viscoelasticty of the solutions mainly by stabilising linear concatenation of λDNA "monomers" via hybridisation of their sticky ends. On the contrary, divalent cations have a far more complex and dramatic effect on the rheology of the solution and we observe evidence of inter-molecular DNA-DNA bridging by Mg2+. We argue that these results may be interesting in the context of dense solutions of single and double stranded DNA, e.g. in vivo or in biotechnology applications such as DNA origami and DNA hydrogels.

Restrictor synergizes with Symplekin and PNUTS to terminate extragenic transcription.

Transcription termination pathways mitigate the detrimental consequences of unscheduled promiscuous initiation occurring at hundreds of thousands of genomic cis-regulatory elements. The Restrictor complex, composed of the Pol II-interacting protein WDR82 and the RNA-binding protein ZC3H4, suppresses processive transcription at thousands of extragenic sites in mammalian genomes. Restrictor-driven termination does not involve nascent RNA cleavage, and its interplay with other termination machineries is unclear. Here we show that efficient termination at Restrictor-controlled extragenic transcription units involves the recruitment of the protein phosphatase 1 (PP1) regulatory subunit PNUTS, a negative regulator of the SPT5 elongation factor, and Symplekin, a protein associated with RNA cleavage complexes but also involved in cleavage-independent and phosphatase-dependent termination of noncoding RNAs in yeast. PNUTS and Symplekin act synergistically with, but independently from, Restrictor to dampen processive extragenic transcription. Moreover, the presence of limiting nuclear levels of Symplekin imposes a competition for its recruitment among multiple transcription termination machineries, resulting in mutual regulatory interactions. Hence, by synergizing with Restrictor, Symplekin and PNUTS enable efficient termination of processive, long-range extragenic transcription.

Geometric learning of knot topology.

Knots are deeply entangled with every branch of science. One of the biggest open challenges in knot theory is to formalise a knot invariant that can unambiguously and efficiently distinguish any two knotted curves. Additionally, the conjecture that the geometrical embedding of a curve encodes information on its underlying topology is, albeit physically intuitive, far from proven. Here we attempt to tackle both these outstanding challenges by proposing a neural network (NN) approach that takes as input a geometric representation of a knotted curve and tries to make predictions of the curve's topology. Intriguingly, we discover that NNs trained with a so-called geometrical "local writhe" representation of a knot can distinguish curves that share one or many topological invariants and knot polynomials, such as mutant and composite knots, and can thus classify knotted curves more precisely than some knot polynomials. Additionally, we also show that our approach can be scaled up to classify all prime knots up to 10-crossings with more than 95% accuracy. Finally, we show that our NNs can also be trained to solve knot localisation problems on open and closed curves. Our main discovery is that the pattern of "local writhe" is a potentially unique geometric signature of the underlying topology of a curve. We hope that our results will suggest new methods for quantifying generic entanglements in soft matter and even inform new topological invariants.

Dynamic ParB-DNA interactions initiate and maintain a partition condensate for bacterial chromosome segregation.

In most bacteria, chromosome segregation is driven by the ParABS system where the CTPase protein ParB loads at the parS site to trigger the formation of a large partition complex. Here, we present in vitro studies of the partition complex for Bacillus subtilis ParB, using single-molecule fluorescence microscopy and AFM imaging to show that transient ParB-ParB bridges are essential for forming DNA condensates. Molecular Dynamics simulations confirm that condensation occurs abruptly at a critical concentration of ParB and show that multimerization is a prerequisite for forming the partition complex. Magnetic tweezer force spectroscopy on mutant ParB proteins demonstrates that CTP hydrolysis at the N-terminal domain is essential for DNA condensation. Finally, we show that transcribing RNA polymerases can steadily traverse the ParB-DNA partition complex. These findings uncover how ParB forms a stable yet dynamic partition complex for chromosome segregation that induces DNA condensation and segregation while enabling replication and transcription.

Fluidification of Entanglements by a DNA Bending Protein.

In spite of the nanoscale and single-molecule insights into nucleoid associated proteins (NAPs), their role in modulating the mesoscale viscoelasticity of entangled DNA has been overlooked so far. By combining microrheology and molecular dynamics simulation, we find that the abundant NAP "integration host factor" (IHF) lowers the viscosity of entangled λDNA 20-fold at physiological concentrations and stoichiometries. Our results suggest that IHF may play a previously unappreciated role in resolving DNA entanglements and in turn may be acting as a "genomic fluidizer" for bacterial genomes.

Topological gelation of reconnecting polymers.

DNA recombination is a ubiquitous process that ensures genetic diversity. Contrary to textbook pictures, DNA recombination, as well as generic DNA translocations, occurs in a confined and highly entangled environment. Inspired by this observation, here, we investigate a solution of semiflexible polymer rings undergoing generic cutting and reconnection operations under spherical confinement. Our setup may be realized using engineered DNA in the presence of recombinase proteins or by considering micelle-like components able to form living (or reversibly breakable) polymer rings. We find that in such systems, there is a topological gelation transition, which can be triggered by increasing either the stiffness or the concentration of the rings. Flexible or dilute polymers break into an ensemble of short, unlinked, and segregated rings, whereas sufficiently stiff or dense polymers self-assemble into a network of long, linked, and mixed loops, many of which are knotted. We predict that the two phases should behave qualitatively differently in elution experiments monitoring the escape dynamics from a permeabilized container. Besides shedding some light on the biophysics and topology of genomes undergoing DNA reconnection in vivo, our findings could be leveraged in vitro to design polymeric complex fluids-e.g., DNA-based complex fluids or living polymer networks-with desired topologies.

Geometric Predictors of Knotted and Linked Arcs.

Inspired by how certain proteins "sense" knots and entanglements in DNA molecules, here, we ask if local geometric features that may be used as a readout of the underlying topology of generic polymers exist. We perform molecular simulations of knotted and linked semiflexible polymers and study four geometric measures to predict topological entanglements: local curvature, local density, local 1D writhe, and nonlocal 3D writhe. We discover that local curvature is a poor predictor of entanglements. In contrast, segments with maximum local density or writhe correlate as much as 90% of the time with the shortest knotted and linked arcs. We find that this accuracy is preserved across different knot types and also under significant spherical confinement, which is known to delocalize essential crossings in knotted polymers. We further discover that nonlocal 3D writhe is the best geometric readout of the knot location. Finally, we discuss how these geometric features may be used to computationally analyze entanglements in generic polymer melts and gels.

Rheology and Viscoelasticity of Proteins and Nucleic Acids Condensates.

Phase separation is as familiar as watching vinegar separating from oil in vinaigrette. The observation that phase separation of proteins and nucleic acids is widespread in living cells has opened an entire field of research into the biological significance and the biophysical mechanisms of phase separation and protein condensation in biology. Recent evidence indicates that certain proteins and nucleic acids condensates are not simple liquids and instead display both viscous and elastic behaviors, which in turn may have biological significance. The aim of this Perspective is to review the state-of-the-art of this quickly emerging field focusing on the material and rheological properties of protein condensates. Finally, we discuss the different techniques that can be employed to quantify the viscoelasticity of condensates and highlight potential future directions and opportunities for interdisciplinary cross-talk between chemists, physicists, and biologists.

ParB proteins can bypass DNA-bound roadblocks via dimer-dimer recruitment.

The ParABS system is essential for prokaryotic chromosome segregation. After loading at parS on the genome, ParB (partition protein B) proteins rapidly redistribute to distances of ~15 kilobases from the loading site. It has remained puzzling how this large-distance spreading can occur along DNA loaded with hundreds of proteins. Using in vitro single-molecule fluorescence imaging, we show that ParB from Bacillus subtilis can load onto DNA distantly of parS, as loaded ParB molecules themselves are found to be able to recruit additional ParB proteins from bulk. Notably, this recruitment can occur in cis but also in trans, where, at low tensions within the DNA, newly recruited ParB can bypass roadblocks as it gets loaded to spatially proximal but genomically distant DNA regions. The data are supported by molecular dynamics simulations, which show that cooperative ParB-ParB recruitment can enhance spreading. ParS-independent recruitment explains how ParB can cover substantial genomic distance during chromosome segregation, which is vital for the bacterial cell cycle.

TADs do not stay in the loop.

In a recent issue of Science, Gabriele et al. have, for the first time, quantified the dynamics of a topologically associating domain (TAD) in live cells by coupling super-resolution imaging and computational modelling, concluding that a TAD spends most of its life in a "partially extruded state" and that CTCF-CTCF loops are rare.

Dynamic and facilitated binding of topoisomerase accelerates topological relaxation.

How type 2 Topoisomerase (TopoII) proteins relax and simplify the topology of DNA molecules is one of the most intriguing open questions in genome and DNA biophysics. Most of the existing models neglect the dynamics of TopoII which is expected of proteins searching their targets via facilitated diffusion. Here, we show that dynamic binding of TopoII speeds up the topological relaxation of knotted substrates by enhancing the search of the knotted arc. Intriguingly, this in turn implies that the timescale of topological relaxation is virtually independent of the substrate length. We then discover that considering binding biases due to facilitated diffusion on looped substrates steers the sampling of the topological space closer to the boundaries between different topoisomers yielding an optimally fast topological relaxation. We discuss our findings in the context of topological simplification in vitro and in vivo.

Condensin extrudes DNA loops in steps up to hundreds of base pairs that are generated by ATP binding events.

The condensin SMC protein complex organizes chromosomal structure by extruding loops of DNA. Its ATP-dependent motor mechanism remains unclear but likely involves steps associated with large conformational changes within the ∼50 nm protein complex. Here, using high-resolution magnetic tweezers, we resolve single steps in the loop extrusion process by individual yeast condensins. The measured median step sizes range between 20-40 nm at forces of 1.0-0.2 pN, respectively, comparable with the holocomplex size. These large steps show that, strikingly, condensin typically reels in DNA in very sizeable amounts with ∼200 bp on average per single extrusion step at low force, and occasionally even much larger, exceeding 500 bp per step. Using Molecular Dynamics simulations, we demonstrate that this is due to the structural flexibility of the DNA polymer at these low forces. Using ATP-binding-impaired and ATP-hydrolysis-deficient mutants, we find that ATP binding is the primary step-generating stage underlying DNA loop extrusion. We discuss our findings in terms of a scrunching model where a stepwise DNA loop extrusion is generated by an ATP-binding-induced engagement of the hinge and the globular domain of the SMC complex.

Three-dimensional loop extrusion.

Loop extrusion convincingly describes how certain structural maintenance of chromosome (SMC) proteins mediate the formation of large DNA loops. Yet most of the existing computational models cannot reconcile recent in vitro observations showing that condensins can traverse each other, bypass large roadblocks, and perform steps longer than their own size. To fill this gap, we propose a three-dimensional (3D) "trans-grabbing" model for loop extrusion, which not only reproduces the experimental features of loop extrusion by one SMC complex but also predicts the formation of so-called Z-loops via the interaction of two or more SMCs extruding along the same DNA substrate. By performing molecular dynamics simulations of this model, we discover that the experimentally observed asymmetry in the different types of Z-loops is a natural consequence of the DNA tethering in vitro. Intriguingly, our model predicts this bias to disappear in the absence of tethering and a third type of Z-loop, which has not yet been identified in experiments, to appear. Our model naturally explains roadblock bypassing and the appearance of steps larger than the SMC size as a consequence of non-contiguous DNA grabbing. Finally, this study is the first, to our knowledge, to address how Z-loops and bypassing might occur in a way that is broadly consistent with existing cis-only 1D loop extrusion models.

Polycomb condensates can promote epigenetic marks but are not required for sustained chromatin compaction.

Organization of the genome into transcriptionally active euchromatin and silenced heterochromatin is essential for eukaryotic cell function. Phase-separation has been implicated in heterochromatin formation, but it is unclear how phase-separated condensates can contribute to stable repression, particularly for heritable epigenetic changes. Polycomb complex PRC1 is key for heterochromatin formation, but the multitude of Polycomb proteins has hindered our understanding of their collective contribution to chromatin repression. Here, we show that PRC1 forms multicomponent condensates through hetero-oligomerization. They preferentially seed at H3K27me3 marks, and subsequently write H2AK119Ub marks. We show that inducing Polycomb phase-separation can cause chromatin compaction, but polycomb condensates are dispensable for maintenance of the compacted state. Our data and simulations are consistent with a model in which the time integral of Polycomb phase-separation is progressively recorded in repressive histone marks, which subsequently drive compaction. These findings link the equilibrium thermodynamics of phase-separation with the fundamentally non-equilibrium concept of epigenetic memory.

Topological tuning of DNA mobility in entangled solutions of supercoiled plasmids.

Ring polymers in dense solutions are among the most intriguing problems in polymer physics. Because of its natural occurrence in circular form, DNA has been extensively used as a proxy to study the fundamental physics of ring polymers in different topological states. Yet, torsionally constrained-such as supercoiled-topologies have been largely neglected so far. The applicability of existing theoretical models to dense supercoiled DNA is thus unknown. Here, we address this gap by coupling large-scale molecular dynamics simulations with differential dynamic microscopy of entangled supercoiled DNA plasmids. We find that, unexpectedly, larger supercoiling increases the size of entangled plasmids and concomitantly induces an enhancement in DNA mobility. These findings are reconciled as due to supercoiling-driven asymmetric and double-folded plasmid conformations that reduce interplasmid entanglements and threadings. Our results suggest a way to topologically tune DNA mobility via supercoiling, thus enabling topological control over the (micro)rheology of DNA-based complex fluids.

Parameter-free molecular super-structures quantification in single-molecule localization microscopy.

Understanding biological function requires the identification and characterization of complex patterns of molecules. Single-molecule localization microscopy (SMLM) can quantitatively measure molecular components and interactions at resolutions far beyond the diffraction limit, but this information is only useful if these patterns can be quantified and interpreted. We provide a new approach for the analysis of SMLM data that develops the concept of structures and super-structures formed by interconnected elements, such as smaller protein clusters. Using a formal framework and a parameter-free algorithm, (super-)structures formed from smaller components are found to be abundant in classes of nuclear proteins, such as heterogeneous nuclear ribonucleoprotein particles (hnRNPs), but are absent from ceramides located in the plasma membrane. We suggest that mesoscopic structures formed by interconnected protein clusters are common within the nucleus and have an important role in the organization and function of the genome. Our algorithm, SuperStructure, can be used to analyze and explore complex SMLM data and extract functionally relevant information.

Nonequilibrium dynamics and action at a distance in transcriptionally driven DNA supercoiling.

We study the effect of transcription on the kinetics of DNA supercoiling in three dimensions by means of Brownian dynamics simulations of a single-nucleotide-resolution coarse-grained model for double-stranded DNA. By explicitly accounting for the action of a transcribing RNA polymerase (RNAP), we characterize the geometry and nonequilibrium dynamics of the ensuing twin supercoiling domains. Contrary to the typical textbook picture, we find that the generation of twist by RNAP results in the formation of plectonemes (writhed DNA) some distance away. We further demonstrate that this translates into an "action at a distance" on DNA-binding proteins; for instance, positive supercoils downstream of an elongating RNAP destabilize nucleosomes long before the transcriptional machinery reaches the histone octamer. We also analyze the relaxation dynamics of supercoiled double-stranded DNA, and characterize the widely different timescales of twist diffusion, which is a simple and fast process, and writhe relaxation, which is much slower and entails multiple steps.

Bridging-induced phase separation induced by cohesin SMC protein complexes.

Structural maintenance of chromosome (SMC) protein complexes are able to extrude DNA loops. While loop extrusion constitutes a fundamental building block of chromosomes, other factors may be equally important. Here, we show that yeast cohesin exhibits pronounced clustering on DNA, with all the hallmarks of biomolecular condensation. DNA-cohesin clusters exhibit liquid-like behavior, showing fusion of clusters, rapid fluorescence recovery after photobleaching and exchange of cohesin with the environment. Strikingly, the in vitro clustering is DNA length dependent, as cohesin forms clusters only on DNA exceeding 3 kilo-base pairs. We discuss how bridging-induced phase separation, a previously unobserved type of biological condensation, can explain the DNA-cohesin clustering through DNA-cohesin-DNA bridges. We confirm that, in yeast cells in vivo, a fraction of cohesin associates with chromatin in a manner consistent with bridging-induced phase separation. Biomolecular condensation by SMC proteins constitutes a new basic principle by which SMC complexes direct genome organization.