arXiv subjects

M. E. Cates

Publications and source records attributed to M. E. Cates.

At least 37 records · Page 2Linked to original sources

arXiv2013

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 3D diffusion in the cytoplasm, and 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 3D and 1D diffusion, but leads to surprising robustness of the total search time.

physics.bio-ph↗

arXiv2013

Flexoelectric switching in cholesteric blue phases

We present computer simulations of the response of a flexoelectric blue phase network, either in bulk or under confinement, to an applied field. We find a transition in the bulk between the blue phase I disclination network and a parallel array of disclinations along the direction of the applied field. Upon switching off the field, the system is unable to reconstruct the original blue phase but gets stuck in a metastable phase. Blue phase II is comparatively much less affected by the field. In confined samples, the anchoring at the walls and the geometry of the device lead to the stabilisation of further structures, including field-aligned disclination loops, splayed nematic patterns, and yet more metastable states. Our results are relevant to the understanding of the switching dynamics for a class of new, "superstable", blue phases which are composed of bimesogenic liquid crystals, as these materials combine anomalously large flexoelectric coefficients, and low or near-zero dielectric anisotropy.

cond-mat.soft↗

arXiv2012

Facilitated diffusion on mobile DNA: configurational traps and sequence heterogeneity

We present Brownian dynamics simulations of the facilitated diffusion of a protein, modelled as a sphere with a binding site on its surface, along DNA, modelled as a semi-flexible polymer. We consider both the effect of DNA organisation in 3D, and of sequence heterogeneity. We find that in a network of DNA loops, as 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.

physics.bio-ph↗

arXiv2012

Spontaneous symmetry breaking in active droplets provides a generic route to motility

We explore a generic mechanism whereby a droplet of active matter acquires motility by the spontaneous breakdown of a discrete symmetry. The model we study offers a simple representation of a "cell extract" comprising, e.g., a droplet of actomyosin solution. (Such extracts are used experimentally to model the cytoskeleton.) Actomyosin is an active gel whose polarity describes the mean sense of alignment of actin fibres. In the absence of polymerization and depolymerization processes ('treadmilling'), the gel's dynamics arises solely from the contractile motion of myosin motors; this should be unchanged when polarity is inverted. Our results suggest that motility can arise in the absence of treadmilling, by spontaneous symmetry breaking (SSB) of polarity inversion symmetry. Adapting our model to wall-bound cells in two dimensions, we find that as wall friction is reduced, treadmilling-induced motility falls but SSB-mediated motility rises. The latter might therefore be crucial in three dimensions where frictional forces are likely to be modest. At a supra-cellular level, the same generic mechanism can impart motility to aggregates of non-motile but active bacteria; we show that SSB in this (extensile) case leads generically to rotational as well as translational motion.

cond-mat.soft↗

arXiv2012

When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation

Active Brownian particles (ABPs, such as self-phoretic colloids) swim at fixed speed $v$ along a body-axis ${\bf u}$ that rotates by slow angular diffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with constant $\u$ until a random tumble event suddenly decorrelates the orientation. We show that when the motility parameters depend on density $ρ$ but not on ${\bf u}$, the coarse-grained fluctuating hydrodynamics of interacting ABPs and RTPs can be mapped onto each other and are thus strictly equivalent. In both cases, a steeply enough decreasing $v(ρ)$ causes phase separation in dimensions $d=2,3$, even when no attractive forces act between the particles. This points to a generic role for motility-induced phase separation in active matter. However, we show that the ABP/RTP equivalence does not automatically extend to the more general case of $\u$-dependent motilities.

cond-mat.stat-mech↗

arXiv2012

Bulk rheology and microrheology of active fluids

We simulate macroscopic shear experiments in active nematics and compare them with microrheology simulations where a spherical probe particle is dragged through an active fluid. In both cases we define an effective viscosity: in the case of bulk shear simulations this is the ratio between shear stress and shear rate, whereas in the microrheology case it involves the ratio between the friction coefficient and the particle size. We show that this effective viscosity, rather than being solely a property of the active fluid, is affected by the way chosen to measure it, and strongly depends on details such as the anchoring conditions at the probe surface and on both the system size and the size of the probe particle.

cond-mat.soft↗

arXiv2012

Complex Fluids: The Physics of Emulsions

These lectures start with the mean field theory for a symmetric binary fluid mixture, addressing interfacial tension, the stress tensor, and the equations of motion (Model H). We then consider the phase separation kinetics of such a mixture: coalescence, Ostwald ripening, its prevention by trapped species, coarsening of bicontinuous states, and the role of shear flow. The third topic addressed is the stabilization of emulsions by using surfactants to reduce or even eliminate the interfacial tension between phases; the physics of bending energy, which becomes relevant in the latter case, is then presented briefly. The final topic is the creation of long-lived metastable emulsions by adsorption of colloidal particles or nano-particles at the fluid-fluid interface; alongside spherical droplets, these methods can be used to create a range of unconventional structures with potentially interesting properties that are only now being explored.

cond-mat.soft↗

arXiv2012

Modeling the Relaxation of Polymer Glasses under Shear and Elongational Loads

Glassy polymers show strain hardening: at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flow-induced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymer-borne stress, slowing the deformation enough for the segmental (or solvent) modes to then re-vitrify. Here we present new results for the corresponding behavior under step-stress shear loading, to which very similar physics applies. To explain the unloading behavior in the extensional case requires introduction of a crinkle factor describing a rapid loss of segmental ordering. We discuss in more detail here the physics of this, which we argue involves non-entropic contributions to the polymer stress, and which might lead to some important differences between shear and elongation. We also discuss some fundamental and possibly testable issues concerning the physical meaning of entropic elasticity in vitrified polymers. Finally we present new results for the startup of steady shear flow, addressing the possible role of transient shear banding.

cond-mat.soft↗

arXiv2012

Colloids in active fluids: Anomalous micro-rheology and negative drag

We simulate an experiment in which a colloidal probe is pulled through an active nematic fluid. We find that the drag on the particle is non-Stokesian (not proportional to its radius). Strikingly, a large enough particle in contractile fluid (such as an actomyosin gel) can show negative viscous drag in steady state: the particle moves in the opposite direction to the externally applied force. We explain this, and the qualitative trends seen in our simulations, in terms of the disruption of orientational order around the probe particle and the resulting modifications to the active stress.

cond-mat.soft↗

arXiv2012

Diffusive transport without detailed balance in motile bacteria: Does microbiology need statistical physics?

Microbiology is the science of microbes, particularly bacteria. Many bacteria are motile: they are capable of self-propulsion. Among these, a significant class execute so-called run-and-tumble motion: they follow a fairly straight path for a certain distance, then abruptly change direction before repeating the process. This dynamics has something in common with Brownian motion (it is diffusive at large scales), and also something in contrast. Specifically, motility parameters such as the run speed and tumble rate depend on the local environment and hence can vary in space. When they do so, even if a steady state is reached, this is not generally invariant under time-reversal: the principle of detailed balance, which restores the microscopic time-reversal symmetry of systems in thermal equilibrium, is mesoscopically absent in motile bacteria. This lack of detailed balance (allowed by the flux of chemical energy that drives motility) creates pitfalls for the unwary modeller. Here I review some statistical mechanical models for bacterial motility, presenting them as a paradigm for exploring diffusion without detailed balance. I also discuss the extent to which statistical physics is useful in understanding real or potential microbiological experiments.

cond-mat.stat-mech↗

arXiv2012

First-Principles Constitutive Equation for Suspension Rheology

We provide a detailed derivation of a recently developed first-principles approach to calculating averages in systems of interacting, spherical Brownian particles under time-dependent flow. Although we restrict ourselves to flows which are both homogeneous and incompressible, the time-dependence and geometry (e.g. shear, extension) are arbitrary. The approximations formulated within mode-coupling theory are particularly suited to dense colloidal suspensions and capture the slow relaxation arising from particle interactions and the resulting glass transition to an amorphous solid. The delicate interplay between slow structural relaxation and time-dependent external flow in colloidal suspensions may thus be studied within a fully tensorial theory.

cond-mat.soft↗

arXiv2012

Phase separation and rotor self-assembly in active particle suspensions

Adding a non-adsorbing polymer to passive colloids induces an attraction between the particles via the `depletion' mechanism. High enough polymer concentrations lead to phase separation. We combine experiments, theory and simulations to demonstrate that using active colloids (such as motile bacteria) dramatically changes the physics of such mixtures. First, significantly stronger inter-particle attraction is needed to cause phase separation. Secondly, the finite size aggregates formed at lower inter-particle attraction show unidirectional rotation. These micro-rotors demonstrate the self assembly of functional structures using active particles. The angular speed of the rotating clusters scales approximately as the inverse of their size, which may be understood theoretically by assuming that the torques exerted by the outermost bacteria in a cluster add up randomly. Our simulations suggest that both the suppression of phase separation and the self assembly of rotors are generic features of aggregating swimmers, and should therefore occur in a variety of biological and synthetic active particle systems.

cond-mat.soft↗

arXiv2012

Schematic Mode Coupling Theory of Glass Rheology: Single and Double Step Strains

Mode coupling theory (MCT) has had notable successes in addressing the rheology of hard-sphere colloidal glasses, and also soft colloidal glasses such as star-polymers. Here, we explore the properties of a recently developed MCT-based schematic constitutive equation under idealized experimental protocols involving single and then double step strains. We find strong deviations from expectations based on factorable, BKZ-type constitutive models. Specifically, a nonvanishing stress remains long after the application of two equal and opposite step strains; this residual stress is a signature of plastic deformation. We also discuss the distinction between hypothetically instantaneous step strains and fast ramps. These are not generally equivalent in our MCT approach, with the latter more likely to capture the physics of experimental `step' strains. The distinction points to the different role played by reversible anelastic, and irreversible plastic rearrangements.

cond-mat.soft↗

arXiv2012

Rheology of Lamellar Liquid Crystals in Two and Three Dimensions: A Simulation Study

We present large scale computer simulations of the nonlinear bulk rheology of lamellar phases (smectic liquid crystals) at moderate to large values of the shear rate (Peclet numbers 10-100), in both two and three dimensions. In two dimensions we find that modest shear rates align the system and stabilise an almost regular lamellar phase, but high shear rates induce the nucleation and proliferation of defects, which in steady state is balanced by the annihilation of defects of opposite sign. The critical shear rate at onset of this second regime is controlled by thermodynamic and kinetic parameters; we offer a scaling analysis that relates the critical shear rate to a critical "capillary number" involving those variables. Within the defect proliferation regime, the defects may be partially annealed by slowly decreasing the applied shear rate; this causes marked memory effects, and history-dependent rheology. Simulations in three dimensions show instead shear-induced ordering even at the highest shear rates studied here. This suggests that the critical shear rate shifts markedly upward on increasing dimensionality. This may in part reflect the reduced constraints on defect motion, allowing them to find and annihilate each other more easily. Residual edge defects in the 3D aligned state mostly point along the flow velocity, an orientation impossible in two dimensions.

cond-mat.soft↗

arXiv2012

Confined Cubic Blue Phases under Shear

We study the behaviour of confined cubic blue phases under shear flow via lattice Boltzmann simulations. We focus on the two experimentally observed phases, blue phase I and blue phase II. The disinclination network of blue phase II continuously breaks and reforms under shear, leading to an oscillatory stress response in time. The oscillations are only regular for very thin samples. For thicker samples, the shear leads to a "stick-slip" motion of part of the network along the vorticity direction. Blue phase I responds very differently: its defect network undergoes seemingly chaotic rearrangements under shear, irrespective of system size.

cond-mat.soft↗

arXiv2012

Cytoplasmic streaming in plant cells: the role of wall slip

We present a computer simulation study, via lattice Boltzmann simulations, of a microscopic model for cytoplasmic streaming in algal cells such as those of Chara corallina. We modelled myosin motors tracking along actin lanes as spheres undergoing directed motion along fixed lines. The sphere dimension takes into account the fact that motors drag vesicles or other organelles, and, unlike previous work, we model the boundary close to which the motors move as walls with a finite slip layer. By using realistic parameter values for actin lane and myosin density, as well as for endoplasmic and vacuole viscosity and the slip layer close to the wall, we find that this simplified view, which does not rely on any coupling between motors, cytoplasm and vacuole other than that provided by viscous Stokes flow, is enough to account for the observed magnitude of streaming velocities in intracellular fluid in living plant cells.

physics.bio-ph↗

arXiv2012

Self-Assembly and Nonlinear Dynamics of Dimeric Colloidal Rotors in Cholesterics

We study by simulation the physics of two colloidal particles in a cholesteric liquid crystal with tangential order parameter alignment at the particle surface. The effective force between the pair is attractive at short range and favors assembly of colloid dimers at specific orientations relative to the local director field. When pulled through the fluid by a constant force along the helical axis, we find that such a dimer rotates, either continuously or stepwise with phase-slip events. These cases are separated by a sharp dynamical transition and lead, respectively, to a constant or an ever-increasing phase lag between the dimer orientation and the local nematic director.

cond-mat.soft↗

arXiv2011

On the structure of blue phase III

We report large scale simulations of the blue phases of cholesteric liquid crystals. Our results suggest a structure for blue phase III, the blue fog, which has been the subject of a long debate in liquid crystal physics. We propose that blue phase III is an amorphous network of disclination lines, which is thermodynamically and kinetically stabilised over crystalline blue phases at intermediate chiralities}. This amorphous network becomes ordered under an applied electric field, as seen in experiments.

cond-mat.soft↗