D. Michieletto, M. Chiang, D. Coli, A. Papantonis, E. Orlandini, P. R. Cook, D. Marenduzzo
Shaping Epigenetic Memory via Genomic Bookmarking
bioRxiv, 2017 Supplementary Movies

Reconciling the stability of epigenetic landscapes with the rapid turnover of histone modifications and their adaptability to external stimuli is an outstanding challenge. Here, we propose a new biophysical mechanism that can establish and maintain robust yet plastic epigenetic domains via genomic bookmarking (GBM). We model chromatin as a polymer whose segments bear non-permanent histone marks (or “colours”) which can be modified by “writer” proteins. The three-dimensional chromatin organisation is mediated by protein bridges, or “readers”, such as Polycomb-Repressive-Complexes and Transcription-Factors. The coupling between readers and writers drives spread- ing of biochemical marks and sustains the memory of local chromatin states across replication and mitosis. On the contrary, GBM-targeted perturbations destabilise the epigenetic landscape. Strikingly, we show that GBM can explain the full distribution of Polycomb marks in a whole Drosophila chromosome. Our model provides a starting point for an understanding of the biophysics of cellular differentiation and reprogramming.

Y.A.G. Fosado, D. Michieletto, D. Marenduzzo
Dynamical Scaling and Phase Coexistence in Topologically Constrained DNA Melting
Phys. Rev. Lett., 119 2017

There is a long-standing experimental observation that the melting of topologically constrained DNA, such as circular closed plasmids, is less abrupt than that of linear molecules. This finding points to an important role of topology in the physics of DNA denaturation, which is, however, poorly understood. Here, we shed light on this issue by combining large-scale Brownian dynamics simulations with an analytically solvable phenomenological Landau mean field theory. We find that the competition between melting and supercoiling leads to phase coexistence of denatured and intact phases at the single-molecule level. This coexistence occurs in a wide temperature range, thereby accounting for the broadening of the transition. Finally, our simulations show an intriguing topology-dependent scaling law governing the growth of denaturation bubbles in supercoiled plasmids, which can be understood within the proposed mean field theory.

D. Michieletto, D. Marenduzzo, E. Orlandini, M. S. Turner
Ring Polymers: Threadings, Knot Electrophoresis and Topological Glasses
Polymers, 9(8) 2017

Elucidating the physics of a concentrated suspension of ring polymers, or of an ensemble of ring polymers in a complex environment, is an important outstanding question in polymer physics. Many of the characteristic features of these systems arise due to topological interactions between polymers, or between the polymers and the environment, and it is often challenging to describe this quantitatively. Here we review recent research which suggests that a key role is played by inter-ring threadings (or penetrations), which become more abundant as the ring size increases. As we discuss, the physical consequences of such threadings are far-reaching: for instance, they lead to a topologically-driven glassy behaviour of ring polymer melts under pinning perturbations, while they can also account for the shape of experimentally observed patterns in two-dimensional gel electrophoresis of DNA knots.

D. Michieletto, E. Orlandini, D. Marenduzzo
Epigenetic Transitions and Knotted Solitons in Stretched Chromatin
arXiv:1705.03226, 2017
Supplementary Movies

The spreading and regulation of epigenetic marks on chromosomes is crucial to establish and maintain cellular identity. Nonetheless, the dynamical mechanism leading to the establishment and maintenance of a given, cell-line specific, epigenetic pattern is still poorly understood. In this work we propose, and investigate in silico, a possible experimental strategy to illuminate the interplay between 3D chromatin structure and epigenetic dynamics. We consider a set-up where a reconstituted chromatin fibre is stretched at its two ends (e.g., by laser tweezers), while epigenetic enzymes (writers) and chromatin-binding proteins (readers) are flooded into the system. We show that,by tuning the stretching force and the binding affinity of the readers for chromatin, the fibre undergoes a sharp transition between a stretched, epigenetically disordered, state and a crumpled, epigenetically coherent, one. We further investigate the case in which a knot is tied along the chromatin fibre, and find that the knotted segment enhances local epigenetic order, giving rise to "epigenetic solitons" which travel and diffuse along chromatin. Our results point to an intriguing coupling between 3D chromatin topology and epigenetic dynamics, which may be investigated via single molecule experiments

C. A. Brackley, B. Liebchen, D. Michieletto, F. Mouvet, P. R. Cook, D. Marenduzzo
Ephemeral Protein Binding to DNA Shapes Stable Nuclear Bodies and Chromatin Domains

Biophys. J., 112, pp 1085-1093, 2017

Fluorescence microscopy reveals that the contents of many (membrane-free) nuclear bodies exchange rapidly with the soluble pool
while the underlying structure persists; such observations await a satisfactory biophysical explanation. To shed light on this, we perform large-scale Brownian dynamics simulations of a chromatin
fiber interacting with an ensemble of (multivalent) DNA-binding proteins able to switch between an "on" (binding) and an "off" (nonbinding) state. This system provides a model for any DNA-binding protein
that can be posttranslationally modified to change its affinity for DNA (e.g., through phosphorylation).
Protein switching is a nonequilibrium process, and it leads to the formation of clusters of self-limiting size,
where individual proteins in a cluster exchange with the soluble pool with kinetics similar to those seen in photobleaching experiments
This behavior contrasts sharply with that exhibited by nonswitching proteins, which are permanently in the on-state; when these bind to DNA nonspecifically, they form clusters that grow indefinitely in size.
To explain these findings, we propose a mean-field theory from which we obtain a scaling relation between the typical cluster size and the protein switching rate. Protein switching also reshapes intrachromatin contacts to give networks resembling those seen in topologically associating domains, as switching markedly favors local (short-range) contacts over distant ones.
Our results point to posttranslational modification of chromatin-bridging proteins as a generic mechanism driving the self-assembly of highly dynamic, nonequilibrium, protein clusters with the properties of nuclear bodies


D. Michieletto
On the Tree-Like Structure of Rings in Dense Solutions
Soft Matter, 12, pp 9485-9500, 2016
Suppl. Movie M1

One of the most challenging problems in polymer physics is providing a theoretical description for the behaviour of rings in dense solutions and melts. Although it is nowadays well established that the overall size of a ring in these conditions scales like that of a collapsed globule, there is compelling evidence that rings may exhibit ramified and tree-like conformations. In this work I show how to characterise these local tree-like structures by measuring the local writhing of the rings’ segments and by identifying the patterns of intra-chain contacts.
These quantities reveal two major topological structures: loops and terminal branches which strongly suggest that the strictly double-folded "lattice animal" picture for rings in the melt may be replaced by a more relaxed tree-like structure accommodating loops.

D. Michieletto, E. Orlandini, D. Marenduzzo
Polymer Model with Epigenetic Recolouring Reveals a Pathway for
the de novo Establishment and 3D Organisation of Chromatin Domains

Phys. Rev. X, 6, pp 041047, 2016 APS Focus "How Cells Remember Who They Are"
Movies: M1 M2 M3 M4 M5 M6 M7 M8 M9

The establishment and maintenance of epigenetic domains during development is a poorly understood subject in Biology. To address this question, we propose a framework which couples 3D chromatin folding dynamics, to a "recolouring" process modeling the writing of epigenetic marks.
This "recolourable polymer model" with two equivalently strong epigenetic marks displays a first-order-like transition between a swollen, epigenetically disordered, phase, and a compact, epigenetically coherent, chromatin globule. If the self-attraction strength exceeds a threshold, the chromatin dynamics becomes glassy, and the corresponding interaction network freezes. By modifying the epigenetic read-write process according to more biologically-inspired assumptions, our polymer model with recolouring recapitulates the ultrasensitive response of epigenetic switches to perturbations, and accounts for long-lived multi-domain conformations, strikingly similar to the topologically-associating-domains observed in eukaryotic chromosomes.

D. Michieletto, M. S. Turner
A Topologically Driven Glass in Ring Polymers [Highlighted in Nature Physics !!]
Proc. Natl. Acad. Sci. USA, 113(19), pp 5195-5200, 2016
Suppl. Movies: Movie1 Movie 2

The glass transition is commonly associated with a reduction in the temperature of liquids or by an increase in density of granular materials. In this work, we propose a radically different approach to study dynamical arrest that relies on the topology of the components.
We find that a concentrated solution of ring polymers can be driven to a kinetically arrested state by randomly pinning a small fraction of rings,
a transition that cannot be observed in linear polymers.
We attribute this jamming to topological interactions, called "threadings", that populate solutions of rings. Our work provides the first evidence for these threadings and suggests that very long rings
may be expected to be kinetically arrested even as the fraction of pinned rings approaches zero. Finally, our findings strongly encourage the experimental realisation of a novel class of systems where the glass transition can be induced by non-trivial topological interactions among the constituents and, ultimately, lead to the design of novel materials.

D. Michieletto, D. Marenduzzo, Ajazul H. Wani Chromosome-wide simulations uncover folding pathway
and 3D organization of interphase chromosomes
, arXiv:1604.03041, 2016
Movies: M1 M2 M3 M4 M5 M6 M7

The principles governing the three-dimensional (3D) interphase genome architecture and its faithful transmission through disruptive events of cell-cycle, like mitosis,
are not fully understood. Here, we use Brownian Dynamics simulations guided by chromatin immunoprecipitation (ChIP-seq) data to investigate whether the 1D
arrangement of chromatin-associated proteins along the genome can be used to predict the 3D organization and simulate the kinetics of chromosome relaxation
from its mitotic-like state to the typical interphase structure in a time scale of minutes.
Our simulations show that chromosome 3R attains interphase organization from mitotic state by a two-step process in which formation of local TADs is followed
by the establishment of long-range interactions. The final predicted topology of chr3R is validated by comparison with Hi-C and 4C-seq data.
Our model also explains statistical features and tracks the assembly kinetics of polycomb subnuclear clusters.
In conclusion, our approach can be used to predict structural and kinetic features of 3D chromosome folding and
its associated proteins in biologically relevant genomic and time scales.

Y. A. G. Fosado, D. Michieletto, J. Allan, C. A. Brackley, O. Henrich, D. Marenduzzo
A single nucleotide resolution model for large-scale simulations of double stranded DNA
Soft Matter, 12, pp 9458 (2016)
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.


D. Michieletto, D. Marenduzzo, E. Orlandini
Topological Patterns in two-dimensional gel electrophoresis of DNA knots,
Proc. Natl. Acad. Sci. USA, 112(40), pp E5471-E5477, 2015

Gel electrophoresis is a ubiquitous biophysical technique.
It consists of dragging charged biopolymers through a porous gel, by applying an electric field.
Because the migration speed depends on topology, this method can be used to classify DNA knots.
Currently, electrophoresis relies on empirical observations, and its theoretical understanding is limited.
No theory can explain why knot mobility under strong fields depends non-monotonically on complexity.
Our study reveals a possible reason: Although complex knots have a smaller size, and hence move faster through the gel,
they can become severely entangled with the gel, causing longer pauses.
This creates a competition between the shrinking of the knot's overall size and the enhancing in entanglement with the gel
due to its increasing complexity. Such trade-off results in a non-monotonic response of the knots' migration speed when dragged with strong
external electric fields. Ultimately, our results can improve the design of future electrophoresis experiments

D. Michieletto, M. Baiesi, E. Orlandini and M. S. Turner
Rings in Random Environments: Sensing Disorder Through Topology
Soft Matter, 11, pp 1100-1106, 2015

In this paper we study the role of topology in DNA gel electrophoresis experiments via molecular dynamics simulations. The gel is modelled as a 3D array of obstacles from which half edges are removed at random with probability p, thereby generating a disordered environment. Changes in the microscopic structure of the gel are captured by measuring the electrophoretic mobility of ring polymers moving through the medium, while their linear counterparts provide a control system as we show they are insensitive to these changes. We show that ring polymers provide a novel, non-invasive way of exploiting topology to sense microscopic disorder. Finally, we compare the results from the simulations with an analytical model for the non-equilibrium differential mobility, and find a striking agreement between simulation and theory.

Experimental realisation of topological trapping:
Intermittent "stop-and-go" motion of E. Coli plasmids through a network of nanowires was filmed by Prof. Yasui in Nagoya U.
One can appreciate the existence of a critical field above which the rings start to display a lower average velocity and finally become permanently entangled and immobile.

D. Michieletto, D. Marenduzzo, E. Orlandini
Is the Kinetoplast DNA a Percolating Network of Linked Rings at its Critical Point?
Phys. Biol., 12, 036001, 2015

In this work we present a computational study of the kinetoplast genome, modelled as a large number of semiflexible unknotted loops allowed to link with each other. As the DNA density increases, the systems shows a percolation transition between a gas of unlinked rings and a network of linked loops which spans the whole system. Close to the percolation transition, we find that the mean valency of the network, i.e. the average number of loops which are linked to any one loop, is around three, as found experimentally for the kinetoplast DNA (kDNA). Even more importantly, by simulating the digestion of the network by a restriction enzyme, we show that the distribution of oligomers, i.e. structures formed by a few loops which remain linked after digestion, quantitatively matches experimental data provided that the density is, once again, close to the percolation transition. Finally, our findings spport the conjecture that the kDNA can be viewed as a network of linked loops positioned very close to the percolation transition, and we discuss the possible biological implications of this remarkable fact.


D. Michieletto, D. Marenduzzo, E. Orlandini, G. P. Alexander, M. S. Turner
Dynamics of Self-Threading Ring Polymers in a Gel
Soft Matter, 3, pp 255-259, 2014
We study the dynamics of ring polymers confined to diffuse in a background gel at low concentrations. We do this in order to probe the inter-play between topology and dynamics in ring polymers. We develop an algorithm that takes into account the possibility that the rings hinder their own motion by passing through themselves, i.e. "self-threading".
Our results suggest that the number of self-threadings scales extensively with the length of the rings and that this is substantially independent of the details of the model. The slowing down of the rings' dynamics is found to be related to the fraction of segments that can contribute to the motion. Our results give a novel perspective on the motion of ring polymers in a gel, for which a complete theory is still lacking, and may help us to understand the irreversible trapping of ring polymers in gel electrophoresis experiments.

D. Michieletto, D. Marenduzzo, E. Orlandini, G. P. Alexander, M. S. Turner
Threading Dynamics of Ring Polymers in a Gel
ACS Macro Lett., 2014, 3, pp 255-259
We perform large scale three-dimensional molecular dynamics simulations of unlinked and unknotted ring polymers diffusing through a background gel, here a three- dimensional cubic lattice. Taking advantage of this architecture, we propose a new method to unambiguously identify and quantify inter-ring threadings and to relate these to the dynamics of the ring polymers. We find that both the number and the persistence time of the threadings increase with the length of the chains, ultimately leading to a percolating network of inter-ring penetrations. We finally discuss the implications of these findings for the possible emergence of a topological jammed state of very long rings.
Awarded the Ian MacMillan Ward prize from the IOP Polymer Physics Group as best PhD student publication in 2015
See my Polymers & Pasta web page!


Y. Timofeeva, S. Coombes, DM, Gap junctions, dendrites and resonances: a recipe for tuning network dynamics, The Journal of Mathematical Neuroscience, 2013, 3(1), 15