Shape and size tunability of sheets of interlocked ring copolymers.

Mechanically bonded membranes of interlocked ring polymers are a significant generalization of conventional elastic sheets, where connectivity is provided by covalent bonding, and represent a promising class of topological meta-materials. In this context, two open questions regard the large-scale reverberations of the heterogeneous composition of the rings and the inequivalent modes of interlocking neighboring rings. We address these questions with Langevin dynamics simulations of chainmails with honeycomb-lattice connectivity, where the rings are block copolymers with two segments of different rigidity. We considered various combinations of the relative lengths of the two segments and the patterns of the over- and under-passes linking neighboring rings. We find that varying ring composition and linking patterns have independent and complementary effects. While the former sets the overall size of the chainmail, the latter defines the shape, enabling the selection of starkly different conformation types. Notably, one of the considered linking patterns favors saddle-shaped membranes, providing a first example of spontaneous negative Gaussian curvature in mechanically bonded sheets. The results help establish the extent to which mechanically bonded membranes can differ from conventional elastic ones, particularly for the achievable shape and size tunability.

RNA folding pathways from all-atom simulations with a variationally improved history-dependent bias.

Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. As a step forward in tackling these issues, we extend to RNA an enhanced path-sampling method previously successfully applied to proteins. In this scheme, the information about the RNA's native structure is harnessed by a soft history-dependent biasing force promoting the generation of productive folding trajectories in an all-atom force field with explicit solvent. A rigorous variational principle is then applied to minimize the effect of the bias. Here, we report on an application of this method to RNA molecules from 20 to 47 nucleotides long and increasing topological complexity. By comparison with analog simulations performed on small proteins with similar size and architecture, we show that the RNA folding landscape is significantly more frustrated, even for relatively small chains with a simple topology. The predicted RNA folding mechanisms are found to be consistent with the available experiments and some of the existing coarse-grained models. Due to its computational performance, this scheme provides a promising platform to efficiently gather atomistic RNA folding trajectories, thus retain the information about the chemical composition of the sequence.

Nonequilibrium Thermodynamics of DNA Nanopore Unzipping.

Using theory and simulations, we carried out a first systematic characterization of DNA unzipping via nanopore translocation. Starting from partially unzipped states, we found three dynamical regimes depending on the applied force f: (i) heterogeneous DNA retraction and rezipping (f<17 pN), (ii) normal (17 pN60 pN) drift-diffusive behavior. We show that the normal drift-diffusion regime can be effectively modeled as a one-dimensional stochastic process in a tilted periodic potential. We use the theory of stochastic processes to recover the potential from nonequilibrium unzipping trajectories and show that it corresponds to the free-energy landscape for single-base-pair unzipping. Applying this general approach to other single-molecule systems with periodic potentials ought to yield detailed free-energy landscapes from out-of-equilibrium trajectories.

Structure and elasticity of model disordered, polydisperse, and defect-free polymer networks.

The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly cross-linked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carried out, but that systems with the same mean valence and same assembly density have the same structural properties. Moreover, we compute the long-time limit of the mean-squared displacement, also known as the (squared) localization length, of the cross-links and of the middle monomers of the strands, showing that the dynamics of long strands is well described by the tube model. Finally, we find a relation connecting these two localization lengths at high density and connect the cross-link localization length to the shear modulus of the system.

essHi-C: essential component analysis of Hi-C matrices.

MOTIVATION: Hi-C matrices are cornerstones for qualitative and quantitative studies of genome folding, from its territorial organization to compartments and topological domains. The high dynamic range of genomic distances probed in Hi-C assays reflects in an inherent stochastic background of the interactions matrices, which inevitably convolve the features of interest with largely non-specific ones. RESULTS: Here, we introduce and discuss essHi-C, a method to isolate the specific or essential component of Hi-C matrices from the non-specific portion of the spectrum compatible with random matrices. Systematic comparisons show that essHi-C improves the clarity of the interaction patterns, enhances the robustness against sequencing depth of topologically associating domains identification, allows the unsupervised clustering of experiments in different cell lines and recovers the cell-cycle phasing of single-cells based on Hi-C data. Thus, essHi-C provides means for isolating significant biological and physical features from Hi-C matrices. AVAILABILITY AND IMPLEMENTATION: The essHi-C software package is available at https://github.com/stefanofranzini/essHIC. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Density-tunable pathway complexity in a minimalistic self-assembly model.

An open challenge in self-assembly is learning how to design systems that can be conditionally guided towards different target structures depending on externally-controlled conditions. Using a theoretical and numerical approach, here we discuss a minimalistic self-assembly model that can be steered towards different types of ordered constructs at the equilibrium by solely tuning a facile selection parameter, namely the density of building blocks. Metadynamics and Langevin dynamics simulations allow us to explore the behavior of the system in and out of equilibrium conditions. We show that the density-driven tunability is encoded in the pathway complexity of the system, and specifically in the competition between two different main self-assembly routes. A comprehensive set of simulations provides insight into key factors allowing to make one self-assembling pathway prevailing on the other (or vice versa), determining the selection of the final self-assembled products. We formulate and validate a practical criterion for checking whether a specific molecular design is predisposed for such density-driven tunability of the products, thus offering a new, broader perspective to realize and harness this facile extrinsic control of conditional self-assembly.

Polymer Physics by Quantum Computing.

Sampling equilibrium ensembles of dense polymer mixtures is a paradigmatically hard problem in computational physics, even in lattice-based models. Here, we develop a formalism based on interacting binary tensors that allows for tackling this problem using quantum annealing machines. Our approach is general in that properties such as self-avoidance, branching, and looping can all be specified in terms of quadratic interactions of the tensors. Microstates' realizations of different lattice polymer ensembles are then seamlessly generated by solving suitable discrete energy-minimization problems. This approach enables us to capitalize on the strengths of quantum annealing machines, as we demonstrate by sampling polymer mixtures from low to high densities, using the D-Wave quantum annealer. Our systematic approach offers a promising avenue to harness the rapid development of quantum machines for sampling discrete models of filamentous soft-matter systems.

Transcriptional supercoiling boosts topoisomerase II-mediated knotting of intracellular DNA.

Recent studies have revealed that the DNA cross-inversion mechanism of topoisomerase II (topo II) not only removes DNA supercoils and DNA replication intertwines, but also produces small amounts of DNA knots within the clusters of nucleosomes that conform to eukaryotic chromatin. Here, we examine how transcriptional supercoiling of intracellular DNA affects the occurrence of these knots. We show that although (-) supercoiling does not change the basal DNA knotting probability, (+) supercoiling of DNA generated in front of the transcribing complexes increases DNA knot formation over 25-fold. The increase of topo II-mediated DNA knotting occurs both upon accumulation of (+) supercoiling in topoisomerase-deficient cells and during normal transcriptional supercoiling of DNA in TOP1 TOP2 cells. We also show that the high knotting probability (Pkn ≥ 0.5) of (+) supercoiled DNA reflects a 5-fold volume compaction of the nucleosomal fibers in vivo. Our findings indicate that topo II-mediated DNA knotting could be inherent to transcriptional supercoiling of DNA and other chromatin condensation processes and establish, therefore, a new crucial role of topoisomerase II in resetting the knotting-unknotting homeostasis of DNA during chromatin dynamics.

Dynamics of supercoiled DNA with complex knots: large-scale rearrangements and persistent multi-strand interlocking.

Knots and supercoiling are both introduced in bacterial plasmids by catalytic processes involving DNA strand passages. While the effects on plasmid organization has been extensively studied for knotting and supercoiling taken separately, much less is known about their concurrent action. Here, we use molecular dynamics simulations and oxDNA, an accurate mesoscopic DNA model, to study the kinetic and metric changes introduced by complex (five-crossing) knots and supercoiling in 2 kbp-long DNA rings. We find several unexpected results. First, the conformational ensemble is dominated by two distinct states, differing in branchedness and knot size. Secondly, fluctuations between these states are as fast as the metric relaxation of unknotted rings. In spite of this, certain boundaries of knotted and plectonemically-wound regions can persist over much longer timescales. These pinned regions involve multiple strands that are interlocked by the cooperative action of topological and supercoiling constraints. Their long-lived character may be relevant for the simplifying action of topoisomerases.

Pore translocation of knotted DNA rings.

We use an accurate coarse-grained model for DNA and stochastic molecular dynamics simulations to study the pore translocation of 10-kbp-long DNA rings that are knotted. By monitoring various topological and physical observables we find that there is not one, as previously assumed, but rather two qualitatively different modes of knot translocation. For both modes the pore obstruction caused by knot passage has a brief duration and typically occurs at a late translocation stage. Both effects are well in agreement with experiments and can be rationalized with a transparent model based on the concurrent tensioning and sliding of the translocating knotted chains. We also observed that the duration of the pore obstruction event is more controlled by the knot translocation velocity than the knot size. These features should advance the interpretation and design of future experiments aimed at probing the spontaneous knotting of biopolymers.

Patterns of coevolving amino acids unveil structural and dynamical domains.

Patterns of interacting amino acids are so preserved within protein families that the sole analysis of evolutionary comutations can identify pairs of contacting residues. It is also known that evolution conserves functional dynamics, i.e., the concerted motion or displacement of large protein regions or domains. Is it, therefore, possible to use a pure sequence-based analysis to identify these dynamical domains? To address this question, we introduce here a general coevolutionary coupling analysis strategy and apply it to a curated sequence database of hundreds of protein families. For most families, the sequence-based method partitions amino acids into a few clusters. When viewed in the context of the native structure, these clusters have the signature characteristics of viable protein domains: They are spatially separated but individually compact. They have a direct functional bearing too, as shown for various reference cases. We conclude that even large-scale structural and functionally related properties can be recovered from inference methods applied to evolutionary-related sequences. The method introduced here is available as a software package and web server (spectrus.sissa.it/spectrus-evo_webserver).

TacoxDNA: A user-friendly web server for simulations of complex DNA structures, from single strands to origami.

Simulations of nucleic acids at different levels of structural details are increasingly used to complement and interpret experiments in different fields, from biophysics to medicine and materials science. However, the various structural models currently available for DNA and RNA and their accompanying suites of computational tools can be very rarely used in a synergistic fashion. The tacoxDNA webserver and standalone software package presented here are a step toward a long-sought interoperability of nucleic acids models. The webserver offers a simple interface for converting various common input formats of DNA structures and setting up molecular dynamics (MD) simulations. Users can, for instance, design DNA rings with different topologies, such as knots, with and without supercoiling, by simply providing an XYZ coordinate file of the DNA centre-line. More complex DNA geometries, as designable in the cadnano, CanDo and Tiamat tools, can also be converted to all-atom or oxDNA representations, which can then be used to run MD simulations. Though the latter are currently geared toward the native and LAMMPS oxDNA representations, the open-source package is designed to be further expandable. TacoxDNA is available at http://tacoxdna.sissa.it. © 2019 Wiley Periodicals, Inc.

Spatial confinement induces hairpins in nicked circular DNA.

In living cells, DNA is highly confined in space with the help of condensing agents, DNA binding proteins and high levels of supercoiling. Due to challenges associated with experimentally studying DNA under confinement, little is known about the impact of spatial confinement on the local structure of the DNA. Here, we have used well characterized slits of different sizes to collect high resolution atomic force microscopy images of confined circular DNA with the aim of assessing the impact of the spatial confinement on global and local conformational properties of DNA. Our findings, supported by numerical simulations, indicate that confinement imposes a large mechanical stress on the DNA as evidenced by a pronounced anisotropy and tangent-tangent correlation function with respect to non-constrained DNA. For the strongest confinement we observed nanometer sized hairpins and interwound structures associated with the nicked sites in the DNA sequence. Based on these findings, we propose that spatial DNA confinement in vivo can promote the formation of localized defects at mechanically weak sites that could be co-opted for biological regulatory functions.

Unifying view of mechanical and functional hotspots across class A GPCRs.

G protein-coupled receptors (GPCRs) are the largest superfamily of signaling proteins. Their activation process is accompanied by conformational changes that have not yet been fully uncovered. Here, we carry out a novel comparative analysis of internal structural fluctuations across a variety of receptors from class A GPCRs, which currently has the richest structural coverage. We infer the local mechanical couplings underpinning the receptors' functional dynamics and finally identify those amino acids whose virtual deletion causes a significant softening of the mechanical network. The relevance of these amino acids is demonstrated by their overlap with those known to be crucial for GPCR function, based on static structural criteria. The differences with the latter set allow us to identify those sites whose functional role is more clearly detected by considering dynamical and mechanical properties. Of these sites with a genuine mechanical/dynamical character, the top ranking is amino acid 7x52, a previously unexplored, and experimentally verifiable key site for GPCR conformational response to ligand binding.

KymoKnot: A web server and software package to identify and locate knots in trajectories of linear or circular polymers.

The KymoKnot software package and web server identifies and locates physical knots or proper knots in a series of polymer conformations. It is mainly intended as an analysis tool for trajectories of linear or circular polymers, but it can be used on single instances too, e.g. protein structures in PDB format. A key element of the software package is the so-called minimally interfering chain closure algorithm that is used to detect physical knots in open chains and to locate the knotted region in both open and closed chains. The web server offers a user-friendly graphical interface that identifies the knot type and highlights the knotted region on each frame of the trajectory, which the user can visualize interactively from various viewpoints. The dynamical evolution of the knotted region along the chain contour is presented as a kymograph. All data can be downloaded in text format. The KymoKnot package is licensed under the BSD 3-Clause licence. The server is publicly available at http://kymoknot.sissa.it/kymoknot/interactive.php .

Absence of knots in known RNA structures.

The ongoing effort to detect and characterize physical entanglement in biopolymers has so far established that knots are present in many globular proteins and also, abound in viral DNA packaged inside bacteriophages. RNA molecules, however, have not yet been systematically screened for the occurrence of physical knots. We have accordingly undertaken the systematic profiling of the several thousand RNA structures present in the Protein Data Bank (PDB). The search identified no more than three deeply knotted RNA molecules. These entries are rRNAs of about 3,000 nt solved by cryo-EM. Their genuine knotted state is, however, doubtful based on the detailed structural comparison with homologs of higher resolution, which are all unknotted. Compared with the case of proteins and viral DNA, the observed incidence of knots in available RNA structures is, therefore, practically negligible. This fact suggests that either evolutionary selection or thermodynamic and kinetic folding mechanisms act toward minimizing the entanglement of RNA to an extent that is unparalleled by other types of biomolecules. A possible general strategy for designing synthetic RNA sequences capable of self-tying in a twist-knot fold is finally proposed.

Non-monotonic knotting probability and knot length of semiflexible rings: the competing roles of entropy and bending energy.

We consider self-avoiding rings of up to 1000 beads and study, by Monte Carlo techniques, how their equilibrium knotting properties depend on the bending rigidity. When the rings are taken from the rigid to fully-flexible limit, their average compactness increases, as expected. However, this progressive compactification is not parallelled by a steady increase of the abundance of knots. In fact the knotting probability, Pk, has a prominent maximum when the persistence length is a few times larger than the bead size. At similar bending rigidities, the knot length has, instead, a minimum. We show that the observed non-monotonicity of Pk arises from the competition between two effects. The first one is the entropic cost of introducing a knot. The second one is the gain in bending energy due to the presence of essential crossings. These, in fact, constrain the knotted region and keep it less bent than average. The two competing effects make knots maximally abundant when the persistence length is 5-10 times larger than the bead size. At such intermediate bending rigidities, knots in the chains of 500 and 1000 beads are 40 times more likely than in the fully-flexible limit.

Sorting ring polymers by knot type with modulated nanochannels.

In this theoretical study we discuss a novel method for sorting ring polymers according to their topological, knotted state. The proposed approach harnesses the rich dynamical behaviour of polymers confined inside spatially-modulated nanochannels. The longitudinal mobility of the rings is shown to have two key properties that are ideally suited for knot sorting. First, at fixed topology, the mobility has an intriguing oscillatory dependence on chain length. Second, the mobility ranking of different knot types is inverted upon increasing the chain length. We show that this complex interplay of channel geometry, chain length and topology can be rationalised within a simple theoretical framework based on Fick-Jacobs's diffusive theory. The results and the interpretative scheme ought to be useful for designing microfluidic devices with optimal topological sorting capabilities.

Elastic network models for RNA: a comparative assessment with molecular dynamics and SHAPE experiments.

Elastic network models (ENMs) are valuable and efficient tools for characterizing the collective internal dynamics of proteins based on the knowledge of their native structures. The increasing evidence that the biological functionality of RNAs is often linked to their innate internal motions poses the question of whether ENM approaches can be successfully extended to this class of biomolecules. This issue is tackled here by considering various families of elastic networks of increasing complexity applied to a representative set of RNAs. The fluctuations predicted by the alternative ENMs are stringently validated by comparison against extensive molecular dynamics simulations and SHAPE experiments. We find that simulations and experimental data are systematically best reproduced by either an all-atom or a three-beads-per-nucleotide representation (sugar-base-phosphate), with the latter arguably providing the best balance of accuracy and computational complexity.