arXiv subjects

John J. Williamson

Publications and source records attributed to John J. Williamson.

10 recordsLinked to original sources

arXiv2018

Stability and roughness of interfaces in mechanically-regulated tissues

Cell division and death can be regulated by the mechanical forces within a tissue. We study the consequences for the stability and roughness of a propagating interface, by analysing a model of mechanically-regulated tissue growth in the regime of small driving forces. For an interface driven by homeostatic pressure imbalance or leader-cell motility, long and intermediate-wavelength instabilities arise, depending respectively on an effective viscosity of cell number change, and on substrate friction. A further mechanism depends on the strength of directed motility forces acting in the bulk. We analyse the fluctuations of a stable interface subjected to cell-level stochasticity, and find that mechanical feedback can help preserve reproducibility at the tissue scale. Our results elucidate mechanisms that could be important for orderly interface motion in developing tissues.

physics.bio-ph↗

arXiv2018

Effects of passive phospholipid flip-flop and asymmetric external fields on bilayer phase equilibria

Compositional asymmetry between the leaflets of bilayer membranes modifies their phase behaviour, and is thought to influence other important features such as mechanical properties and protein activity. We address here how phase behaviour is affected by passive phospholipid \textit{flip-flop}, such that the compositional asymmetry is not fixed. We predict transitions from "pre flip-flop" behaviour to a restricted set of phase equilibria that can persist in the presence of passive flip-flop. Surprisingly, such states are not necessarily symmetric. We further account for external symmetry-breaking, such as a preferential substrate interaction, and show how this can stabilise strongly asymmetric equilibrium states. Our theory explains several experimental observations of flip-flop mediated changes in phase behaviour, and shows how domain formation and compositional asymmetry can be controlled in concert, by manipulating passive flip-flop rates and applying external fields.

cond-mat.soft↗

arXiv2016

Comment on "Elastic Membrane Deformations Govern Interleaflet Coupling of Lipid-Ordered Domains"

In lieu of abstract, first paragraph reads: Galimzyanov et al. [1] find that line tension between thick liquid-ordered ($L_{o}$) and thinner liquid-disordered ($L_{d}$) registered lipid bilayer phases is minimised by an asymmetric "slip region", length $L\!\sim\!5\,\textrm{nm}$ (Fig. 1). They claim that line tensions alone explain domain registration, without "direct" (area-dependent) inter-leaflet interaction [2,3]. We show this is unfounded, without direct interaction their results would predict \textit{antiregistration}, dependent on composition. To find equilibrium from line energies, line \textit{tensions} must be combined with interfacial lengths for given states at given composition. This was not done in [1].

cond-mat.soft↗

arXiv2015

Kinetics of symmetry and asymmetry in a phase-separating bilayer membrane

We simulate a phase-separating a bilayer in which the leaflets experience a direct coupling favouring local compositional symmetry ("registered" bilayer phases), and an indirect coupling due to hydrophobic mismatch that favours strong local asymmetry ("antiregistered" bilayer phases). For wide ranges of overall leaflet compositions, multiple competing states are possible. For estimated physical parameters, a quenched bilayer may first evolve toward a metastable state more asymmetric than if the leaflets were uncorrelated;\ subsequently, it must nucleate to reach its equilibrium, more symmetric, state. These phase-transition kinetics exhibit characteristic signatures through which fundamental and opposing inter-leaflet interactions may be probed. We emphasise how bilayer phase diagrams with a separate axis for each leaflet can account for overall and local symmetry/asymmetry, and capture a range of observations in the experiment and simulation literature.

cond-mat.soft↗

arXiv2015

Nucleation of symmetric domains in the coupled leaflets of a bilayer

We study the kinetics governing the attainment of inter-leaflet domain symmetry in a phase-separating amphiphilic bilayer. "Indirect" inter-leaflet coupling via hydrophobic mismatch can induce an instability towards a metastable pattern of locally asymmetric domains upon quenching from high temperature. This necessitates a nucleation step to form the conventional symmetric pattern of domains, which are favoured by a "direct" inter-leaflet coupling. We model the energetics for a symmetric domain to nucleate from the metastable state, and find that an interplay between hydrophobic mismatch and thickness stretching/compression causes the effective hydrophobic mismatch, and thus line tension, to depend on domain size. This leads to strong departure from classical nucleation theory. We speculate on implications for cell membrane rafts or clusters, whose size may be of similar magnitude to estimated critical radii for domain symmetry.

cond-mat.soft↗

arXiv2015

Registered and antiregistered phase separation of mixed amphiphilic bilayers

We derive a mean-field free energy for the phase behaviour of coupled bilayer leaflets, which is implicated in cellular processes and important to the design of artificial membranes. Our model accounts for amphiphile-level structural features, particularly hydrophobic mismatch, which promotes antiregistration (AR), in competition with the `direct' trans-midplane coupling usually studied, promoting registration (R). We show that the phase diagram of coupled leaflets allows multiple \textit{metastable} coexistences, then illustrate the kinetic implications with a detailed study of a bilayer of equimolar overall composition. For approximate parameters estimated to apply to phospholipids, equilibrium coexistence is typically registered, but metastable antiregistered phases can be kinetically favoured by hydrophobic mismatch. Thus a bilayer in the spinodal region can require nucleation to equilibrate, in a novel manifestation of Ostwald's `rule of stages'. Our results provide a framework for understanding disparate existing observations, elucidating a subtle competition of couplings, and a key role for phase transition kinetics in bilayer phase behaviour.

cond-mat.soft↗

arXiv2014

Measuring local volume fraction, long-wavelength correlations and fractionation in a phase-separating polydisperse fluid

We dynamically simulate fractionation (partitioning of particle species) during spinodal gas-liquid separation of a size-polydisperse colloid, using polydispersity up to ~40% and a skewed parent size distribution. We introduce a novel coarse-grained Voronoi method to minimise size bias in measuring local volume fraction, along with a variety of spatial correlation functions which detect fractionation without requiring a clear distinction between the phases. These can be applied whether or not a system is phase separated, to determine structural correlations in particle size, and generalise easily to other kinds of polydispersity (charge, shape, etc.). We measure fractionation in both mean size and polydispersity between the phases, its direction differing between model interaction potentials which are identical in the monodisperse case. These qualitative features are predicted by a perturbative theory requiring only a monodisperse reference as input. The results show that intricate fractionation takes place almost from the start of phase separation, so can play a role even in nonequilibrium arrested states. The methods for characterisation of inhomogeneous polydisperse systems could in principle be applied to experiment as well as modelling.

cond-mat.soft↗

arXiv2014

Effects of the Carnahan-Starling free energy within theories of fluids with short-range attraction

Within the Free-Volume Asakura-Oosawa-Vrij (FVAO) theory of colloid-polymer mixtures, we show that unphysical gas-liquid binodals predicted in the regime of small attraction range (i.e. polymer size) are caused in part by the use of the Carnahan-Starling (CS) hard sphere (HS) reference free energy. Replacement of the CS expression with an alternative dramatically affects predicted phase behaviour and, for polydisperse colloid, the resultant fractionation predictions. Although short-range attractions render FVAO, as a perturbative HS-based theory, less accurate anyway, we argue that the particular effects of CS in this regime are an important consideration -- usually ignored -- in the evaluation of such theories. We refer to a variety of literature exhibiting similarly inaccurate gas-liquid binodals, and suggest CS's status as the de facto choice of hard sphere reference should be carefully considered where short-range attractions are present.

cond-mat.soft↗

arXiv2013

The effects of polydispersity and metastability on crystal growth kinetics

We investigate the effect of metastable gas-liquid (G-L) separation on crystal growth in a system of either monodisperse or slightly size-polydisperse square well particles, using a simulation setup that allows us to focus on the growth of a single crystal. Our system parameters are such that, inside the metastable G-L binodal, a macroscopic layer of the gas phase "coats" the crystal as it grows, consistent with experiment and theoretical free energy considerations. Crucially, the effect of this metastable G-L separation on the crystal growth rate depends qualitatively on whether the system is polydisperse. We measure reduced polydispersity and qualitatively different local size ordering in the crystal relative to the fluid, proposing that the required fractionation is dynamically facilitated by the gas layer. Our results show that polydispersity and metastability, both ubiquitous in soft matter, must be considered in tandem if their dynamical effects are to be understood.

cond-mat.soft↗

arXiv2012

Spinodal fractionation in a polydisperse square well fluid

Using Kinetic Monte Carlo simulation, we model gas-liquid spinodal decomposition in a size-polydisperse square well fluid, representing a 'near-monodisperse' colloidal dispersion. We find that fractionation (demixing) of particle sizes between the phases begins asserting itself shortly after the onset of phase ordering. Strikingly, the direction of size fractionation can be reversed by a seemingly trivial choice between two inter-particle potentials which, in the monodisperse case, are identical -- we rationalise this in terms of a perturbative, equilibrium theory of polydispersity. Furthermore, our quantitative results show that Kinetic Monte Carlo simulation can provide detailed insight into the role of fractionation in real colloidal systems.

cond-mat.soft↗