In active matter systems, deformable boundaries provide a mechanism to organize internal active stresses and perform work on the external environment. To study a minimal model of such a system, we perform particle-based simulations of an elastic vesicle containing a collection of polar active filaments. The interplay between the active stress organization due to interparticle interactions and that due to the deformability of the confinement leads to a variety of filament spatiotemporal organizations that have not been observed in bulk systems or under rigid confinement, including highly-aligned rings and caps. In turn, these filament assemblies drive dramatic and tunable transformations of the vesicle shape and its dynamics. We present simple scaling models that reveal the mechanisms underlying these emergent behaviors and yield design principles for engineering active materials with targeted shape dynamics.
We use numerical simulations to study the dynamics of three dimensional vesicles in unconfined and confined Poiseuille flow. Previous numerical studies have shown that when the fluid viscosity inside and outside the vesicle is same (no viscosity contrast), a transition from asymmetric slippers to symmetric parachutes takes place as viscous forcing or capillary number is increased. At higher viscosity contrast, an outward migration tendency has also been observed in unconfined flow simulations. In this paper, we study how the presence of viscosity contrast and confining walls affect the dynamic…
One of the most promising features of active systems is that they can extract energy from their environment and convert it to mechanical work. Self propelled particles enable rectification when in contact with rigid boundaries. They can rectify their own motion when confined in asymmetric channels and that of microgears. In this paper, we study the shape fluctuations of two dimensional flexible vesicles containing active Brownian particles. We show how these fluctuations not only are capable of easily squeezing a vesicle through narrow openings, but are also responsible for its rectification w…
The dynamics and rheology of a vesicle confined in a channel under shear flow are studied at finite temperature. The effect of finite temperature on vesicle motion and system viscosity is investigated. A two-dimensional numerical model, which includes thermal fluctuations and is based on a combination of molecular dynamics and mesoscopic hydrodynamics, is used to perform a detailed analysis in a wide range of the Peclet numbers (the ratio of the shear rate to the rotational diffusion coefficient). The suspension viscosity is found to be a monotonous increasing function of the viscosity contras…
Narrow membrane tubes are commonly pulled out from the surface of phospholipid vesicles using forces applied either through laser or magnetic tweezers or through the action of processive motor proteins. Recent examples have emerged where such tubes spontaneously grow from vesicles coated with bioactive cytoskeletal filaments (e.g. FtsZ, microtubule) in the presence GTP. We show how a soft vesicle deforms due to the interplay between its topology, local curvature and the forces due to the active filaments. We present results from Dynamically Triangulated Monte Carlo simulations of a spherical c…
The shape deformation of a three-dimensional axisymmetric vesicle with encapsulated filaments or impurities is analyzed by integrating a dissipation dynamics. This method can incorporate systematically the constraint of a fixed surface area and/or a fixed volume. The filament encapsulated in a vesicle is assumed to take a form of a rod or a ring so as to imitate cytoskeletons. In both cases, results of the shape transition of the vesicle are summarized in phase diagrams in the phase space of the vesicular volume and a rod length or a ring radius. We also study the dynamics of a vesicle with im…
The transport of deformable objects including polymer particles, vesicles and cells, has been a subject of interest for several decades where the majority of experimental and theoretical studies have been focused on circular tubes. Due to advances in microfluidics, there is a need to study the transport of individual deformable particles in rectangular microchannels where corner flows can be important. In this study, we report measurements of hydrodynamic mobility of confined polymeric particles, vesicles and cancer cells in a linear microchannel with square cross-section. Our operating condit…
Morphologies of a vesicle confined in a spherical vesicle were explored experimentally by fast confocal laser microscopy and numerically by a dynamically-triangulated membrane model with area-difference elasticity. The confinement was found to induce several novel shapes of the inner vesicles, that had been never observed in unilamellar vesicles: double and quadruple stomatocytes, slit vesicle, and vesicles of two or three compartments with various shapes. The simulations reproduced the experimental results very well and some of the shape transitions can be understood by a simple theoretical m…
Red blood cells (RBCs) are the major component of blood and the flow of blood is dictated by that of RBCs. We employ vesicles, which consist of closed bilayer membranes enclosing a fluid, as a model system to study the behavior of RBCs under a confined Poiseuille flow. We extensively explore two main parameters: i) the degree of confinement of vesicles within the channel, and ii) the flow strength. Rich and complex dynamics for vesicles are revealed ranging from steady-state shapes (in the form of parachute and slipper) to chaotic dynamics of shape. Chaos occurs through a cascade of multiple p…
We present a numerical study of the time-dependent motion of a two-dimensional vesicle in a channel under an imposed flow. In a Poiseuille flow the shape of the vesicle depends on the flow strength, the mechanical properties of the membrane, and the width of the channel as reported in the past. This study is focused on the centered snaking (CSn) shape, where the vesicle shows an oscillatory motion like a swimmer flagella even though the flow is stationary. We quantify this behavior by the amplitude and frequency of the oscillations of the vesicle's center of mass. We observe regions in paramet…
The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules.For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the…
We investigate the morphology of a toroidal fluid membrane vesicle confined inside a spherical container. The equilibrium shapes are assembled in a geometrical phase diagram as a function of scaled area and reduced volume of the membrane. For small area the vesicle can adopt its free form. When increasing the area, the membrane cannot avoid contact and touches the confining sphere along a circular contact line, which extends to a zone of contact for higher area. The elastic energies of the equilibrium shapes are compared to those of their confined counterparts of spherical topology to predict …
The morphology of spherically confined flexoelectric fluid membrane vesicles in an external uniform electric field is studied numerically. Due to the deformations induced by the confinement, the membrane becomes polarized resulting in an interaction with the external field. The equilibrium shapes of the vesicle without electric field can be classified in a geometrical phase diagram as a function of scaled area and reduced volume [1,2]. When the area of the membrane is only slightly larger than the area of the confining sphere, a single axisymmetric invagination appears. A non-vanishing electri…
Vesicles are micrometric soft particles whose the membrane is a two-dimensional incompressible fluid governed by bending resistance leading to a zoology of shapes. The dynamics of deflated vesicles in shear flow with a bottom wall, a first minimal configuration to consider confined vesicles is investigated using numerical simulations. Coexistence under flow of oblate (metastable) and prolate (stable) shapes is studied in details. In particular, we discuss the boundaries of the region of coexistence in the (v, Ca) plane where v is the reduced volume of the vesicle and Ca the Capillary number. W…
Biological systems exploit self-assembly to create complex structures whose arrangements are finely controlled from molecular to mesoscopic level. Herein we report an example of using fully synthetic systems that mimic two levels of self-assembly. We show the formation of vesicles using amphiphilic copolymers whose chemical nature is chosen to control both membrane formation and membrane-confined interactions. We report polymersomes with patterns that emerge by engineering interfacial tension within the polymersome surface. This allows the formation of domains whose topology is tailored by the…
Phase-contrast microscopy is used to monitor the shapes of micron-scale fluid-phase phospholipid-bilayer vesicles in aqueous solution. At fixed temperature, each vesicle undergoes thermal shape fluctuations. We are able experimentally to characterize the thermal shape ensemble by digitizing the vesicle outline in real time and storing the time-sequence of images. Analysis of this ensemble using the area-difference-elasticity (ADE) model of vesicle shapes allows us to associate (map) each time-sequence to a point in the zero-temperature (shape) phase diagram. Changing the laboratory temperature…
Confinement of filamentary objects is ubiquitous in numerous biological, medical, and engineering scenarios. Quantitatively determining the mechanical interaction between flexible filaments and surface confinement is particularly challenging due to the unknown contact force induced by elasticity interacting with geometric constraints. Here, we consider a simplified model of confined filamentary object: an elastic curve under surface confinement. Local force and moment balance equation incorporating the role of contact is utilized to derive the contact force exerted by surface on the confined e…
The steady motion and deformation of a lipid-bilayer vesicle translating through a circular tube in low Reynolds number pressure-driven flow are investigated numerically using an axisymmetric boundary element method. This fluid-structure interaction problem is determined by three dimensionless parameters: reduced volume (a measure of the vesicle asphericity), geometric confinement (the ratio of the vesicle effective radius to the tube radius), and capillary number (the ratio of viscous to bending forces). The physical constraints of a vesicle -- fixed surface area and enclosed volume when it i…
An analytic expression is derived for the distribution $G(\vec{R})$ of the end-to-end distance $\vec{R}$ of semiflexible polymers in external potentials to elucidate the effect of confinement on the mechanical and statistical properties of biomolecules. For parabolic confinement the result is exact whereas for realistic potentials a self-consistent ansatz is developed, so that $G(\vec{R})$ is given explicitly even for hard wall confinement. The theoretical result is in excellent quantitative agreement with fluorescence microscopy data for actin filaments confined in rectangularly shaped microc…
Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside of deformable vesicles or soft tissue like cell walls, chorions, and buds. Surprisingly little is known about morphogenesis due to growth in flexible confinements - perhaps owing to the daunting complexity lying in the nonlinear feedback between packed material and expandable cavity. Here we show by experiments and simulations how geometric and material properties lead…
Despite its significance in microfluidics, the effect of confinement on the transition from the tank-treading (steady motion) to the tumbling (unsteady motion) dynamical state of deformable micro-particles has not been studied in detail. In this paper, we investigate the dynamics of a single viscous vesicle under confining shear as a general model system for red blood cells, capsules, or viscous droplets. The transition from tank-treading to tumbling motion can be triggered by the ratio between internal and external fluid viscosities. Here, we show that the transition can be induced solely by …
Pattern of confined chemical garden was controlled by the speed of injected fluid, and their mechanism is discussed. A confined chemical garden system was constructed where an aqueous solution of cobalt chloride was injected into a cell filled with sodium silicate solution. The reaction of these two solutions resulted in the formation of precipitation. The viscosities of the prepared aqueous solutions were set to be similar in order to rule out the possibility of Saffman-Taylor instability. The injection front showed three distinctive patterns: algaes, shells, and filaments, which were depende…
We present a general dynamical theory of a membrane coupled to an actin cortex containing polymerizing filaments with active stresses and currents, and demonstrate that active membrane dynamics [Phys. Rev. Lett \textbf{84}, 3494 (2000)] and spontaneous shape oscillations emerge from this description. We also consider membrane instabilities and patterns induced by the presence of filaments with polar orientational correlations in the tangent plane of the membrane. The dynamical features we predict should be seen in a variety of cellular contexts involving the dynamics of the membrane-cytoskelet…
We systematically explore the self-assembly of semi-flexible polymers in deformable spherical confinement across a wide regime of chain stiffness, contour lengths and packing fractions by means of coarse-grained molecular dynamics simulations. Compliant, DNA-like filaments are found to undergo a continuous crossover from two distinct surface-ordered quadrupolar states, both characterized by tetrahedral patterns of topological defects, to either longitudinal or latitudinal bipolar structures with increasing polymer concentrations. These transitions, along with the intermediary arrangements that…
The steady-state behavior of a dilute suspension of self-propelled filaments confined between planar walls subjected to the Couette-flow is reported herein. The effect of hydrodynamics has been taken into account using a mesoscale simulation approach. We present a detailed analysis of positional and angular probability distributions of filaments with varying propulsive force and shear-flow. Distribution of centre-of-mass of the filament shows adsorption near the surfaces, which diminishes with the flow. The excess density of filaments decreases with Weissenberg number as $Wi^{-β}$ with an expo…
Using agent-based simulations of self-propelled particles subject to short-range repulsion and nematic alignment we explore the dynamical phases of a dense active material confined to the surface of a sphere. We map the dynamical phase diagram as a function of curvature, alignment strength and activity and reproduce phases seen in recent experiments on active microtubules moving on the surfaces of vesicles. At low driving, we recover the equilibrium nematic ground state with four +1/2 defects. As the driving is increased, geodesic forces drive the transition to a band of polar matter wrapping …
We use numerical simulations to study the dynamics of red blood cells (RBCs) in unconfined and confined Poiseuille flow. Previous numerical studies with 3D vesicles have indicated that the slipper shape observed in experiments at high capillary number can be attributed to the bistability due to the interplay of wall push and outward migration tendency at higher viscosity contrasts. In this paper, we study this outward migration and bistability using numerical simulations for 3D capsules and provide phase diagrams of RBC dynamics with and without viscosity contrast. We observe a bistability of …
Optimal Translocation of Living \& Active Filaments in Confinement
University of Padova（帕多瓦大学）；ICTP South American Institute for Fundamental Research, Instituto de Física Teórica, Universidade Estadual Paulista（国际理论物理中心南美基础研究所，理论物理研究所，圣保罗州立大学）；van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam（范德瓦耳斯-泽曼研究所，物理研究所，阿姆斯特丹大学）；Universidad Complutense de Madrid（马德里康普顿斯大学）；GISC - Grupo Interdisciplinar de Sistemas Complejos, Universidad Complutense de Madrid（跨学科复杂系统小组，马德里康普顿斯大学）；INFN, Sezione di Padova（意大利国家核物理研究所，帕多瓦分部）
Many active fluid systems encountered in biology are set in total geometric confinement. Cytoplasmic streaming in plant cells is a prominent and ubiquitous example, in which cargo-carrying molecular motors move along polymer filaments and generate coherent cell-scale flow. When filaments are not fixed to the cell periphery, a situation found both in vivo and in vitro, we observe that the basic dynamics of streaming are closely related to those of a non-motile stresslet suspension. Under this model, it is demonstrated that confinement makes possible a stable circulating state; a linear stabilit…
Helically coiled filaments are a frequent motif in nature. In situations commonly encountered in experiments coiled helices are squeezed flat onto two dimensional surfaces. Under such 2-D confinement helices form "squeelices" - peculiar squeezed conformations often resembling looped waves, spirals or circles. Using theory and Monte-Carlo simulations we illuminate here the mechanics and the unusual statistical mechanics of confined helices and show that their fluctuations can be understood in terms of moving and interacting discrete particle-like entities - the "twist-kinks". We show that confi…
While semi-flexible polymers and fibers are an important class of material due to their rich mechanical properties, it remains unclear how these properties relate to the microscopic conformation of the polymers. Actin filaments constitute an ideal model polymer system due to their micron-sized length and relatively high stiffness that allow imaging at the single filament level. Here we study the effect of entanglements on the conformational dynamics of actin filaments in shear flow. We directly measure the full three-dimensional conformation of single actin filaments, using confocal microscopy…
We theoretically study the conformations of a helical semi-flexible filament confined to a flat surface. This squeezed helix exhibits a variety of unexpected shapes resembling circles, waves or spirals depending on the material parameters. We explore the conformation space in detail and show that the shapes can be understood as the mutual elastic interaction of conformational quasi-particles. Our theoretical results are potentially useful to determine the material parameters of such helical filaments in an experimental setting.
In the presence of ATP, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modelling can help to quantify the relationship between individual motors plus filaments to organisation and dynamics on molecular and supra-molecular length scales. Here we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between fil…
