Mechanisms for destabilisation of RNA viruses at air-water and liquid-liquid interfaces.

Understanding the interactions between viruses and surfaces or interfaces is important, as they provide the principles underpinning the cleaning and disinfection of contaminated surfaces. Yet, the physics of such interactions is currently poorly understood. For instance, there are longstanding experimental observations suggesting that the presence of air-water interfaces can generically inactivate and kill viruses, yet the mechanism underlying this phenomenon remains unknown. Here we use theory and simulations to show that electrostatics may provide one such mechanism, and that this is very general. Thus, we predict that the electrostatic free energy of an RNA virus should increase by several thousands of kBT as the virion breaches an air-water interface. We also show that the fate of a virus approaching a generic liquid-liquid interface depends strongly on the detailed balance between interfacial and electrostatic forces, which can be tuned, for instance, by choosing different media to contact a virus-laden respiratory droplet. Tunability arises because both the electrostatic and interfacial forces scale similarly with viral size. We propose that these results can be used to design effective strategies for surface disinfection.

Complex small-world regulatory networks emerge from the 3D organisation of the human genome.

The discovery that overexpressing one or a few critical transcription factors can switch cell state suggests that gene regulatory networks are relatively simple. In contrast, genome-wide association studies (GWAS) point to complex phenotypes being determined by hundreds of loci that rarely encode transcription factors and which individually have small effects. Here, we use computer simulations and a simple fitting-free polymer model of chromosomes to show that spatial correlations arising from 3D genome organisation naturally lead to stochastic and bursty transcription as well as complex small-world regulatory networks (where the transcriptional activity of each genomic region subtly affects almost all others). These effects require factors to be present at sub-saturating levels; increasing levels dramatically simplifies networks as more transcription units are pressed into use. Consequently, results from GWAS can be reconciled with those involving overexpression. We apply this pan-genomic model to predict patterns of transcriptional activity in whole human chromosomes, and, as an example, the effects of the deletion causing the diGeorge syndrome.

Polymer compaction and bridging-induced clustering of protein-inspired patchy particles.

There are many proteins or protein complexes which have multiple DNA binding domains. This allows them to bind to multiple points on a DNA molecule (or chromatin fibre) at the same time. There are also many proteins which have been found to be able to compact DNA in vitro, and many others have been observed in foci or puncta when fluorescently labelled and imaged in vivo. In this work we study, using coarse-grained Langevin dynamics simulations, the compaction of polymers by simple model proteins and a phenomenon known as the 'bridging-induced attraction'. The latter is a mechanism observed in previous simulations [Brackley et al 2013 Proc. Natl Acad. Sci. USA 110 E3605], where proteins modelled as spheres form clusters via their multivalent interactions with a polymer, even in the absence of any explicit protein-protein attractive interactions. Here we extend this concept to consider more detailed model proteins, represented as simple 'patchy particles' interacting with a semi-flexible bead-and-spring polymer. We find that both the compacting ability and the effect of the bridging-induced attraction depend on the valence of the model proteins. These effects also depend on the shape of the protein, which determines its ability to form bridges.

Chromosome compaction and chromatin stiffness enhance diffusive loop extrusion by slip-link proteins.

We use Brownian dynamics simulations to study the formation of chromatin loops through diffusive sliding of slip-link-like proteins, mimicking the behaviour of cohesin molecules. We recently proposed that diffusive sliding is sufficient to explain the extrusion of chromatin loops of hundreds of kilo-base-pairs (kbp), which may then be stabilised by interactions between cohesin and CTCF proteins. Here we show that the flexibility of the chromatin fibre strongly affects this dynamical process, and find that diffusive loop extrusion is more efficient on stiffer chromatin regions. We also show that the dynamics of loop formation are faster in confined and collapsed chromatin conformations but that this enhancement is counteracted by the increased crowding. We provide a simple theoretical argument explaining why stiffness and collapsed conformations favour diffusive extrusion. In light of the heterogeneous physical and conformational properties of eukaryotic chromatin, we suggest that our results are relevant to understand the looping and organisation of interphase chromosomes in vivo.

Bridging-induced microphase separation: photobleaching experiments, chromatin domains and the need for active reactions.

We review the mechanism and consequences of the 'bridging-induced attraction', a generic biophysical principle that underpins some existing models for chromosome organization in 3D. This attraction, which was revealed in polymer physics-inspired computer simulations, is a generic clustering tendency arising in multivalent chromatin-binding proteins, and it provides an explanation for the biogenesis of nuclear bodies and transcription factories via microphase separation. Including post-translational modification reactions involving these multivalent proteins can account for the fast dynamics of the ensuing clusters, as is observed via microscopy and photobleaching experiments. The clusters found in simulations also give rise to chromatin domains that conform well with the observation of A/B compartments in HiC experiments.

Non-equilibrium effects of molecular motors on polymers.

We present a generic coarse-grained model to describe molecular motors acting on polymer substrates, mimicking, for example, RNA polymerase on DNA or kinesin on microtubules. The polymer is modeled as a connected chain of beads; motors are represented as freely diffusing beads which, upon encountering the substrate, bind to it through a short-ranged attractive potential. When bound, motors and polymer beads experience an equal and opposite active force, directed tangential to the polymer; this leads to motion of the motors along the polymer contour. The inclusion of explicit motors differentiates our model from other recent active polymer models. We study, by means of Langevin dynamics simulations, the effect of the motor activity on both the conformational and dynamical properties of the substrate. We find that activity leads, in addition to the expected enhancement of polymer diffusion, to an effective reduction of its persistence length. We discover that this effective "softening" is a consequence of the emergence of double-folded branches, or hairpins, and that it can be tuned by changing the number of motors or the force they generate. Finally, we investigate the effect of the motors on the probability of knot formation. Counter-intuitively our simulations reveal that, even though at equilibrium a more flexible substrate would show an increased knotting probability, motor activity leads to a marked decrease in the occurrence of knotted conformations with respect to equilibrium.

Non-equilibrium phase transition in a model for supercoiling-dependent DNA transcription.

We study a variant of a recently proposed non-equilibrium stochastic model for supercoiling-dependent transcription in DNA. In the case of a circular DNA molecule with overall positive supercoiling, we find a non-equilibrium phase transition between an absorbing phase, where all genes are switched off due to the supercoiling, and an active phase with a non-zero transcription rate. Mean field theory predicts that the transition should be continuous at a critical value of the background supercoiling, and we focus our analysis on this case. Our simulations suggest that the switch between the transcribed and silent phases may actually be a fluctuation-induced discontinuous transition, where the jump in the transcription rate decreases with the number of genes in the system.

Extrusion without a motor: a new take on the loop extrusion model of genome organization.

Chromatin loop extrusion is a popular model for the formation of CTCF loops and topological domains. Recent HiC data have revealed a strong bias in favour of a particular arrangement of the CTCF binding motifs that stabilize loops, and extrusion is the only model to date which can explain this. However, the model requires a motor to generate the loops, and although cohesin is a strong candidate for the extruding factor, a suitable motor protein (or a motor activity in cohesin itself) has yet to be found. Here we explore a new hypothesis: that there is no motor, and thermal motion within the nucleus drives extrusion. Using theoretical modelling and computer simulations we ask whether such diffusive extrusion could feasibly generate loops. Our simulations uncover an interesting ratchet effect (where an osmotic pressure promotes loop growth), and suggest, by comparison to recent in vitro and in vivo measurements, that diffusive extrusion can in principle generate loops of the size observed in the data. Extra View on : C. A. Brackley, J. Johnson, D. Michieletto, A. N. Morozov, M. Nicodemi, P. R. Cook, and D. Marenduzzo "Non-equilibrium chromosome looping via molecular slip-links", Physical Review Letters 119 138101 (2017).

Entropic elasticity and dynamics of the bacterial chromosome: A simulation study.

We study the compression and extension dynamics of a DNA-like polymer interacting with non-DNA binding and DNA-binding proteins, by means of computer simulations. The geometry we consider is inspired by recent experiments probing the compressional elasticity of the bacterial nucleoid (DNA plus associated proteins), where DNA is confined into a cylindrical container and subjected to the action of a "piston"-a spherical bead to which an external force is applied. We quantify the effect of steric interactions (excluded volume) on the force-extension curves as the polymer is compressed. We find that non-DNA-binding proteins, even at low densities, exert an osmotic force which can be a lot larger than the entropic force exerted by the compressed DNA. The trends we observe are qualitatively robust with respect to changes in protein sizes and are similar for neutral and charged proteins (and DNA). We also quantify the dynamics of DNA expansion following removal of the "piston": while the expansion is well fitted by power laws, the apparent exponent depends on protein concentration and protein-DNA interaction in a significant way. We further highlight an interesting kinetic process which we observe during the expansion of DNA interacting with DNA-binding proteins when the interaction strength is intermediate: the proteins bind while the DNA is packaged by the compression force, but they "pop-off" one-by-one as the force is removed, leading to a slow unzipping kinetics. Finally, we quantify the importance of supercoiling, which is an important feature of bacterial DNA in vivo.

Nonequilibrium Chromosome Looping via Molecular Slip Links.

We propose a model for the formation of chromatin loops based on the diffusive sliding of molecular slip links. These mimic the behavior of molecules like cohesin, which, along with the CTCF protein, stabilize loops which contribute to organizing the genome. By combining 3D Brownian dynamics simulations and 1D exactly solvable nonequilibrium models, we show that diffusive sliding is sufficient to account for the strong bias in favor of convergent CTCF-mediated chromosome loops observed experimentally. We also find that the diffusive motion of multiple slip links along chromatin is rectified by an intriguing ratchet effect that arises if slip links bind to the chromatin at a preferred "loading site." This emergent collective behavior favors the extrusion of loops which are much larger than the ones formed by single slip links.

A single nucleotide resolution model for large-scale simulations of double stranded DNA.

The computational modelling of DNA is becoming crucial in light of new advances in DNA nano-technology, single-molecule experiments and in vivo DNA tampering. Here we present a mesoscopic model for double stranded DNA (dsDNA) at the single nucleotide level which retains the characteristic helical structure, while being able to simulate large molecules - up to a million base pairs - for time-scales which are relevant to physiological processes. This is made possible by an efficient and highly-parallelised implementation of the model which we discuss here. The model captures the main characteristics of DNA, such as the different persistence lengths for double and single strands, pitch, torsional rigidity and the presence of major and minor grooves. The model constitutes a starting point for the future implementation of further features, such as sequence specificity and electrostatic repulsion. We show that the behaviour of the presented model compares favourably with single molecule experiments where dsDNA is manipulated by external forces or torques. We finally present some results on the kinetics of denaturation of linear DNA and supercoiling of closed dsDNA molecules.

Simulating topological domains in human chromosomes with a fitting-free model.

We discuss a polymer model for the 3D organization of human chromosomes. A chromosome is represented by a string of beads, with each bead being "colored" according to 1D bioinformatic data (e.g., chromatin state, histone modification, GC content). Individual spheres (representing bi- and multi-valent transcription factors) can bind reversibly and selectively to beads with the appropriate color. During molecular dynamics simulations, the factors bind, and the string spontaneously folds into loops, rosettes, and topologically-associating domains (TADs). This organization occurs in the absence of any specified interactions between distant DNA segments, or between transcription factors. A comparison with Hi-C data shows that simulations predict the location of most boundaries between TADs correctly. The model is "fitting-free" in the sense that it does not use Hi-C data as an input; consequently, one of its strengths is that it can - in principle - be used to predict the 3D organization of any region of interest, or whole chromosome, in a given organism, or cell line, in the absence of existing Hi-C data. We discuss how this simple model might be refined to include more transcription factors and binding sites, and to correctly predict contacts between convergent CTCF binding sites.

Stochastic Model of Supercoiling-Dependent Transcription.

We propose a stochastic model for gene transcription coupled to DNA supercoiling, where we incorporate the experimental observation that polymerases create supercoiling as they unwind the DNA helix and that these enzymes bind more favorably to regions where the genome is unwound. Within this model, we show that when the transcriptionally induced flux of supercoiling increases, there is a sharp crossover from a regime where torsional stresses relax quickly and gene transcription is random, to one where gene expression is highly correlated and tightly regulated by supercoiling. In the latter regime, the model displays transcriptional bursts, waves of supercoiling, and up regulation of divergent or bidirectional genes. It also predicts that topological enzymes which relax twist and writhe should provide a pathway to down regulate transcription.

A simple model for DNA bridging proteins and bacterial or human genomes: bridging-induced attraction and genome compaction.

We present computer simulations of the phase behaviour of an ensemble of proteins interacting with a polymer, mimicking non-specific binding to a piece of bacterial DNA or eukaryotic chromatin. The proteins can simultaneously bind to the polymer in two or more places to create protein bridges. Despite the lack of any explicit interaction between the proteins or between DNA segments, our simulations confirm previous results showing that when the protein-polymer interaction is sufficiently strong, the proteins come together to form clusters. Furthermore, a sufficiently large concentration of bridging proteins leads to the compaction of the swollen polymer into a globular phase. Here we characterise both the formation of protein clusters and the polymer collapse as a function of protein concentration, protein-polymer affinity and fibre flexibility.

Topological constraints strongly affect chromatin reconstitution in silico.

The fundamental building block of chromatin, and of chromosomes, is the nucleosome, a composite material made up from DNA wrapped around a histone octamer. In this study we provide the first computer simulations of chromatin self-assembly, starting from DNA and histone proteins, and use these to understand the constraints which are imposed by the topology of DNA molecules on the creation of a polynucleosome chain. We take inspiration from the in vitro chromatin reconstitution protocols which are used in many experimental studies. Our simulations indicate that during self-assembly, nucleosomes can fall into a number of topological traps (or local folding defects), and this may eventually lead to the formation of disordered structures, characterised by nucleosome clustering. Remarkably though, by introducing the action of topological enzymes such as type I and II topoisomerase, most of these defects can be avoided and the result is an ordered 10-nm chromatin fibre. These findings provide new insight into the biophysics of chromatin formation, both in the context of reconstitution in vitro and in terms of the topological constraints which must be overcome during de novo nucleosome formation in vivo, e.g. following DNA replication or repair.

Models for twistable elastic polymers in Brownian dynamics, and their implementation for LAMMPS.

An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions relating to both bending and twisting of the rod are derived for both continuous and discrete cases, and results are compared with numerical simulations. Finally, two possible implementations of the discretised model in the multi-purpose molecular dynamics software package LAMMPS are described.

Intracellular facilitated diffusion: searchers, crowders, and blockers.

In bacteria, regulatory proteins search for a specific DNA-binding target via "facilitated diffusion": a series of rounds of three-dimensional diffusion in the cytoplasm, and one-dimensional (1D) linear diffusion along the DNA contour. Using large scale Brownian dynamics simulations we find that each of these steps is affected differently by crowding proteins, which can either be bound to the DNA acting as a road block to the 1D diffusion, or freely diffusing in the cytoplasm. Macromolecular crowding can strongly affect mechanistic features such as the balance between three-dimensional and 1D diffusion, but leads to surprising robustness of the total search time.

Facilitated diffusion on mobile DNA: configurational traps and sequence heterogeneity.

We present Brownian dynamics simulations of the facilitated diffusion of a protein, modeled as a sphere with a binding site on its surface, along DNA, modeled as a semiflexible polymer. We consider both the effect of DNA organization in three dimensions and of sequence heterogeneity. We find that in a network of DNA loops, which are thought to be present in bacterial DNA, the search process is very sensitive to the spatial location of the target within such loops. Therefore, specific genes might be repressed or promoted by changing the local topology of the genome. On the other hand, sequence heterogeneity creates traps which normally slow down facilitated diffusion. When suitably positioned, though, these traps can, surprisingly, render the search process much more efficient.

Two-point heterogeneous connections in a continuum neural field model.

We examine a novel heterogeneous connection scheme in a 1D continuum neural field model. Multiple two-point connections are added to a local connection function in order to model the "patchy" connections seen in, for example visual cortex. We use a numerical approach to solve the equations, choosing the locations of the two-point connections stochastically. We observe self-sustained persistent fluctuations of activity which can be classified into two types (one of which is similar to that seen in network models of discrete excitable neurons, the other being particular to this model). We study the effect of parameters such as system size and the range, number and strength of connections, on the probability that a particular realisation of the connections is able to exhibit persistent fluctuations.

Persistent fluctuations of activity in undriven continuum neural field models with power-law connections.

We study the effect of random inhomogeneous connections on a continuous field description of neural tissue. We focus on a regime in which persistent random fluctuations in activity arise spontaneously in the absence of either time-varying or spatially inhomogeneous input. While present in real tissue and network models of discrete neurons, such behavior has not been reported in continuum models of this type. The activity contains frequencies similar to those seen experimentally. We consider a power-law envelope r(-alpha) for the inhomogeneity and present evidence that the statistical coherence (a measure of two-point correlation) rapidly percolates across the system as alpha is reduced below alphac approximately 1,2 in one and two dimensions, respectively.