scholarly journals Magnetic Polymer Models for Epigenetics-Driven Chromosome Folding

2019 ◽  
Author(s):  
Davide Coli ◽  
Davide Michieletto ◽  
Davide Marenduzzo ◽  
Enzo Orlandini
Keyword(s):  
Brownian Dynamics ◽  
Regulatory Networks ◽  
Mean Field ◽  
Thermal Fluctuations ◽  
First Order Phase Transition ◽  
Polymer Models ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations ◽  
First Order Phase

Epigenetics is a driving force of important and ubiquitous phenomena in nature such as cell differentiation or even metamorphosis. Oppositely to its widespread role, understanding the biophysical principles that allow epigenetics to control and rewire gene regulatory networks remains an open challenge. In this work we study the effects of epigenetic modifications on the spatial folding of chromosomes -- and hence on the expression of the underlying genes -- by mapping the problem to a class of models known as magnetic polymers. In this work we show that a first order phase transition underlies the simultaneous spreading of certain epigenetic marks and the conformational collapse of a chromosome. Further, we describe Brownian Dynamics simulations of the model in which the topology of the polymer and thermal fluctuations are fully taken into account and that confirm our mean field predictions. Extending our models to allow for non-equilibrium terms yields new stable phases which qualitatively agrees with observations in vivo. Our results show that statistical mechanics techniques applied to models of magnetic polymers can be successfully exploited to rationalize the outcomes of experiments designed to probe the interplay between a dynamic epigenetic landscape and chromatin organization.

scholarly journals Structure evolution of suspensions under time-dependent electric or magnetic field

2021 ◽  
Author(s):  
Konstantinos Manikas ◽  
Markus Hütter ◽  
Patrick D. Anderson
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Brownian Dynamics ◽  
Thermal Fluctuations ◽  
Time Dependent ◽  
Structure Evolution ◽  
Strength Increase ◽  
Large Rotation ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations

AbstractThe effect of time-dependent external fields on the structures formed by particles with induced dipoles dispersed in a viscous fluid is investigated by means of Brownian Dynamics simulations. The physical effects accounted for are thermal fluctuations, dipole-dipole and excluded volume interactions. The emerging structures are characterised in terms of particle clusters (orientation, size, anisotropy and percolation) and network structure. The strength of the external field is increased in one direction and then kept constant for a certain amount of time, with the structure formation being influenced by the slope of the field-strength increase. This effect can be partially rationalized by inhomogeneous time re-scaling with respect to the field strength, however, the presence of thermal fluctuations makes the scaling at low field strength inappropriate. After the re-scaling, one can observe that the lower the slope of the field increase, the more network-like and the thicker the structure is. In the second part of the study the field is also rotated instantaneously by a certain angle, and the effect of this transition on the structure is studied. For small rotation angles ($$\theta \le 20^{{\circ }}$$ θ ≤ 20 ∘ ) the clusters rotate but stay largely intact, while for large rotation angles ($$\theta \ge 80^{{\circ }}$$ θ ≥ 80 ∘ ) the structure disintegrates and then reforms, due to the nature of the interactions (parallel dipoles with perpendicular inter-particle vector repel each other). For intermediate angles ($$20<\theta <80^{{\circ }}$$ 20 < θ < 80 ∘ ), it seems that, during rotation, the structure is altered towards a more network-like state, as a result of cluster fusion (larger clusters). The details provided in this paper concern an electric field, however, all results can be projected into the case of a magnetic field and paramagnetic particles.

The effect of Brownian motion on the stability of sedimenting suspensions of polarizable rods in an electric field

2009 ◽  
Vol 624 ◽  
pp. 361-388 ◽  
Author(s):  
BRENDAN D. HOFFMAN ◽  
ERIC S. G. SHAQFEH
Keyword(s):  
Brownian Motion ◽  
Electric Fields ◽  
Brownian Dynamics ◽  
Mean Field ◽  
Thermal Motion ◽  
Particle Orientation ◽  
Induced Charge ◽  
The Stability ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations

We examine the collective dynamics of polarizable, Brownian, sedimenting rods of high aspect ratio. Previous work of Koch and Shaqfeh (J. Fluids Mech., vol. 209, 1989 pp. 521–542) has shown that in the absence of Brownian motion, sedimenting suspensions of rods are unstable to concentration fluctuations and form dense streamers via interparticle hydrodynamic interactions. Recently, Saintillan, Shaqfeh & Darve (Phys. Fluids, vol. 18 (121701), 2006b p. 1) demonstrated that electric fields can act to stabilize these non-Brownian suspensions of polarizable rods through induced-charge electrokinetic rotation, which forces particle alignment. In this paper, we employ a mean-field linear stability analysis as well as Brownian dynamics simulations to study the effect of thermal motion on the onset of instability. We find that in the absence of electric fields, Brownian motion consistently suppresses instability formation through randomization of particle orientation. However, when electric fields are applied, thermal motion can act to induce instability by counteracting the stabilizing effect of induced-charge orientation.

scholarly journals Structure formation in suspensions under uniform electric or magnetic field

2021 ◽  
Author(s):  
Konstantinos Manikas ◽  
Georgios G. Vogiatzis ◽  
Markus Hütter ◽  
Patrick D. Anderson
Keyword(s):  
Magnetic Field ◽  
External Field ◽  
Structure Formation ◽  
Brownian Dynamics ◽  
Volume Fraction ◽  
Structural Evolution ◽  
Thermal Fluctuations ◽  
Branch Points ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations

AbstractThe structure formation of particles with induced dipoles dispersed in a viscous fluid, under a spatially and temporarily uniform external electric or magnetic field, is investigated by means of Brownian Dynamics simulations. Dipole–dipole interactions forces, excluded volume forces and thermal fluctuations are accounted for. The resulting structures are characterized in terms of average orientation of their inter-particle vectors (second Legendre polynomial), network structure, size of particle clusters, anisotropy of the gyration tensor of every cluster and existence of (cluster) percolation. The magnitude of the strength of the external field and the volume fraction of particles are varied and the structural evolution of the system is followed in time. The results show that the characteristic timescale calculated from the interaction of only two dipoles is also valid for the collective dynamics of many-particle simulations. In addition, the magnitude of the strength of the external field in the range of values we investigate influences only the magnitude of the deviations around the average behavior. The main characteristics (number density of branch-points and thickness of branches) of the structure are mainly affected by the volume fraction. The possibility of 3D printing these systems is explored. While the paper provides the details about the case of an electric field, all results presented here can be translated directly into the case of a magnetic field and paramagnetic particles.

scholarly journals Thermally Fluctuating, Semiflexible Sheets in Simple Shear Flow

Soft Matter ◽  
2022 ◽  
Author(s):  
Kevin S. Silmore ◽  
Michael Strano ◽  
James W. Swan
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Brownian Dynamics ◽  
Thermal Fluctuations ◽  
Hydrodynamic Interactions ◽  
Simple Shear Flow ◽  
Bending Rigidity ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations ◽  
Shear Energy

We perform Brownian dynamics simulations of semiflexible colloidal sheets with hydrodynamic interactions and thermal fluctuations in shear flow. As a function of the ratio of bending rigidity to shear energy...

scholarly journals Effect of chromatin flexibility on diffusive loop extrusion via molecular slip-links

2018 ◽  
Author(s):  
C. A. Brackley ◽  
J. Johnson ◽  
D. Michieletto ◽  
D. Marenduzzo
Keyword(s):  
Physical Properties ◽  
Brownian Dynamics ◽  
Dynamical Process ◽  
Base Pairs ◽  
Chromatin Fibre ◽  
Chromatin Loops ◽  
Eukaryotic Chromatin ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations

AbstractWe use Brownian dynamics simulations to study the formation of chromatin loops through diffusive sliding of molecular slip links, mimicking the behaviour of cohesin-like 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 elasticity of the chromatin fibre strongly affects this dynamical process, and find that diffusive loop extrusion is more efficient on stiffer chromatin regions. Efficiency is also enhanced if cohesin loading sites are close to regions where CTCF is bound. In light of the heterogeneous physical properties of eukaryotic chromatin, we suggest that our results should be relevant to the looping and organisation of interphase chromosomes in vivo.

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