Non-Equilibrium Living Polymers

Systems of "living" polymers are ubiquitous in industry and are traditionally realised using surfactants. Here I review the state-of-the-art of living polymers and discuss non-equilibrium extensions that may be realised with advanced synthetic chemistry or DNA functionalised by proteins. These systems are not only interesting in order to realise novel "living" soft matter but can also shed insight into how genomes are (topologically) regulated in vivo.Comment: 6 pages, 4 figure

Topological patterns in two-dimensional gel electrophoresis of DNA knots

Gel electrophoresis is a powerful experimental method to probe the topology of DNA and other biopolymers. While there is a large body of experimental work which allows us to accurately separate different topoisomers of a molecule, a full theoretical understanding of these experiments has not yet been achieved. Here we show that the mobility of DNA knots depends crucially and subtly on the physical properties of the gel, and in particular on the presence of dangling ends. The topological interactions between these and DNA molecules can be described in terms of an “entanglement number”, and yield a non-monotonic mobility at moderate fields. Consequently, in two-dimensional electrophoresis, gel bands display a characteristic arc pattern; this turns into a straight line when the density of dangling ends vanishes. We also provide a novel framework to accurately predict the shape of such arcs as a function of molecule length and topological complexity, which may be used to inform future experiments

Simplifying Topological Entanglements by Entropic Competition of Slip-Links

Topological entanglements are abundant, and often detrimental, in polymeric systems in biology and materials science. Here we theoretically investigate the topological simplification of knots by diffusing slip-links (SLs), which may represent biological or synthetic molecules, such as proteins on the genome or cyclodextrines in slide-ring gels. We find that SLs entropically compete with knots and can localise them, greatly facilitating their downstream simplification by transient strand-crossing. We further show that the efficiency of knot localisation strongly depends on the topology of the SL network and, informed by our findings, discuss potential strategies to control the topology of biological and synthetic materials

Competition between local erasure and long-range spreading of a single biochemical mark leads to epigenetic bistability

The mechanism through which cells determine their fate is intimately related to the spreading of certain biochemical (so-called epigenetic) marks along their genome. The mechanisms behind mark spreading and maintenance are not yet fully understood, and current models often assume a long-range infection-like process for the dynamics of marks, due to the polymeric nature of the chromatin fibre which allows looping between distant sites. While these existing models typically consider antagonising marks, here we propose a qualitatively different scenario which analyses the spreading of a single mark. We define a 1D stochastic model in which mark spreading/infection occurs as a long-range process whereas mark erasure/recovery is a local process, with an enhanced rate at boundaries of infected domains. In the limiting case where our model exhibits absorbing states, we find a first-order-like transition separating the marked/infected phase from the unmarked/recovered phase. This suggests that our model, in this limit, belongs to the long-range compact directed percolation universality class. The abrupt nature of the transition is retained in a more biophysically realistic situation when a basal infection/recovery rate is introduced (thereby removing absorbing states). Close to the transition there is a range of bistability where both the marked/infected and unmarked/recovered states are metastable and long lived, which provides a possible avenue for controlling fate decisions in cells. Increasing the basal infection/recovery rate, we find a second transition between a coherent (marked or unmarked) phase, and a mixed, or random, one.Comment: 11 pages, 7 figures, 2 appendice

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 its 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 absence of tethering and a third type of Z-loop, which has not yet been identified in experiments, to appear. Our model naturally explains road-block bypassing and the appearance of steps larger than the SMC size as a consequence of non-contiguous DNA grabbing. Finally, it 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.Comment: to appear in biophysical journa

Loops are Geometric Catalysts for DNA Integration

The insertion of HIV and other DNA elements within genomes underpins both genetic diversity and disease when unregulated. Most of these insertions are not random and occupy specific positions within the genome but 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 HIV viral DNA or transposons, into naked DNA or chromatin substrate. More specifically, we explore the role of loops in the DNA substrate and discover that they act as "geometric catalysts" for DNA integration. Additionally, we discover that the 1D and 3D clustering of loops affects the distribution of integration sites. Finally, we show that loops may compete with nucleosomes at attracting 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 gene therapy

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 lambda DNA solutions. We show that monovalent cations moderately increase the viscoelasticty of the solutions mainly by stabilising linear condensation of lambda DNA ``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.Comment: 8 pages, 5 figure