Dynamics of fluid vesicles in shear flow: effect of membrane viscosity and thermal fluctuations

Curvature-sensing and generation by membrane proteins: a review

Membrane proteins are crucial in regulating biomembrane shapes and controlling the dynamic changes in membrane morphology during essential cellular processes. These proteins can localize to regions with their preferred curvatures (curvature sensing) and induce localized membrane curvature. Thus, this review describes the recent theoretical development in membrane remodeling performed by membrane proteins. The mean-field theories of protein binding and the resulting membrane deformations are reviewed. The effects of hydrophobic insertions on the area-difference elasticity energy and that of intrinsically disordered protein domains on the membrane bending energy are discussed. For the crescent-shaped proteins, such as Bin/Amphiphysin/Rvs superfamily proteins, anisotropic protein bending energy and orientation-dependent excluded volume significantly contribute to curvature sensing and generation. Moreover, simulation studies of membrane deformations caused by protein binding are reviewed, including domain formation, budding, and tubulation.

Active polymer behavior in two dimensions: A comparative analysis of tangential and push-pull models

In this work, we compare the structural and dynamic behavior of active filaments in two dimensions using tangential and push-pull models, including a variant with passive end monomers, to bridge the two frameworks. These models serve as valuable frameworks for understanding self-organization in biological polymers and synthetic materials. At low activity, all models exhibit similar behavior; as activity increases, subtle differences emerge in intermediate regimes, but at high activity, their behaviors converge. Adjusting for differences in mean active force reveals nearly identical behavior across models, even across varying filament configurations and bending rigidities. Our results highlight the importance of force definitions in active polymer simulations and provide insights into phase transitions across varying filament configurations.

Density and inertia effects on two-dimensional active semiflexible filament suspensions

We examine the influence of density on the transition between chain and spiral structures in planar assemblies of active semiflexible filaments, utilizing detailed numerical simulations. We focus on how increased density, and higher Péclet numbers, affect the activity-induced transition spiral state in a semiflexible, self-avoiding active chain. Our findings show that increasing the density causes the spiral state to break up, reverting to a motile chain-like shape. This results in a density-dependent reentrant phase transition from spirals back to open chains. We attribute this phenomenon to an inertial effect observed at the single polymer level, where increased persistence length due to inertia has been shown in recent three-dimensional studies to cause polymers to open up. Our two-dimensional simulations further reveal that a reduction in the damping coefficient leads to partial unwinding of the spirals, forming longer arms. In suspension, interactions among these extended arms can trigger a complete unwinding of the spirals, driven by the combined effects of density and inertia.

Shear flow as a tool to distinguish microscopic activities of molecular machines in a chromatin loop

Several types of molecular machines move along biopolymers like chromatin. However, the details about the microscopic activity of these machines and how to distinguish their modes of action are not well understood. We propose that the activity of such machines can be classified by studying looped chromatin under shear flow. Our simulations show that a chromatin-like polymer with two types of activities-constant (type-I) or local curvature-dependent tangential forces (type-II)-exhibits very different behavior under shear flow. We show that one can distinguish both activities by measuring the nature of a globule-to-extended coil transition, tank treading, and tumbling dynamics.

Microscopic origin of tunable assembly forces in chiral active environments

Across a variety of spatial scales, from nanoscale biological systems to micron-scale colloidal systems, equilibrium self-assembly is entirely dictated by-and therefore limited by-the thermodynamic properties of the constituent materials. In contrast, nonequilibrium materials, such as self-propelled active matter, expand the possibilities for driving the assemblies that are inaccessible in equilibrium conditions. Recently, a number of works have suggested that active matter drives or accelerates self-organization, but the emergent interactions that arise between solutes immersed in actively driven environments are complex and poorly understood. Here, we analyze and resolve two crucial questions concerning actively driven self-assembly: (i) how, mechanistically, do active environments drive self-assembly of passive solutes? (ii) Under which conditions is this assembly robust? We employ the framework of odd hydrodynamics to theoretically explain numerical and experimental observations that chiral active matter, i.e., particles driven with a directional torque, produces robust and long-ranged assembly forces. Together, these developments constitute an important step towards a comprehensive theoretical framework for controlling self-assembly in nonequilibrium environments.

Hydrodynamics of a multicomponent vesicle under strong confinement

We numerically investigate the hydrodynamics and membrane dynamics of a multicomponent vesicle in two strongly confined geometries. This serves as a simplified model for red blood cells undergoing large deformations while traversing narrow constrictions. We propose a new parameterization for the bending modulus that remains positive for all lipid phase parameter values. For a multicomponent vesicle passing through a stenosis, we establish connections between various properties: lipid phase coarsening, size and flow profile of the lubrication layers, excess pressure, and the tank-treading velocity of the membrane. For a multicomponent vesicle passing through a contracting channel, we find that the lipid always phase separates so that the vesicle is stiffer in the front as it passes through the constriction. For both cases of confinement we find that lipid coarsening is arrested under strong confinement, and resumes at a high rate upon relief from extreme confinement. The results may be useful for efficient sorting lipid domains using microfluidic flows by controlled release of vesicles passing through strong confinement.

Lift at low Reynolds number

Lift forces are widespread in hydrodynamics. These are typically observed for big and fast objects and are often associated with a combination of fluid inertia (i.e. large Reynolds numbers) and specific symmetry-breaking mechanisms. In contrast, the properties of viscosity-dominated (i.e. low Reynolds numbers) flows make it more difficult for such lift forces to emerge. However, the inclusion of boundary effects qualitatively changes this picture. Indeed, in the context of soft and biological matter, recent studies have revealed the emergence of novel lift forces generated by boundary softness, flow gradients and/or surface charges. The aim of the present review is to gather and analyse this corpus of literature, in order to identify and unify the questioning within the associated communities, and pave the way towards future research.

Dynamics of fluid bilayer vesicles: Soft meshes and robust curvature energy discretization

Continuum models like the Helfrich Hamiltonian are widely used to describe fluid bilayer vesicles. Here we study the molecular dynamics compatible dynamics of the vertices of two-dimensional meshes representing the bilayer, whose in-plane motion is only weakly constrained. We show (i) that Jülicher's discretization of the curvature energy offers vastly superior robustness for soft meshes compared to the commonly employed expression by Gommper and Kroll and (ii) that for sufficiently soft meshes, the typical behavior of fluid bilayer vesicles can emerge even if the mesh connectivity remains fixed throughout the simulations. In particular, soft meshes can accommodate large shape transformations, and the model can generate the typical ℓ^{-4} signal for the amplitude of surface undulation modes of nearly spherical vesicles all the way up to the longest wavelength modes. Furthermore, we compare results for Newtonian, Langevin, and Brownian dynamics simulations of the mesh vertices to demonstrate that the internal friction of the membrane model is negligible, making it suitable for studying the internal dynamics of vesicles via coupling to hydrodynamic solvers or particle-based solvent models.

Particle-based mesoscopic model for phase separation in a binary fluid mixture

A mesoscopic simulation model to study the phase separation in a binary fluid mixture in three dimensions (3D) is presented here by augmenting the existing particle-based multiparticle collision dynamics (MPCD) algorithm. The approach describes the nonideal equation of the fluid state by incorporating the excluded-volume interaction between the two components within the framework of stochastic collision, which depends on the local fluid composition and velocity. Calculating the nonideal contribution to the pressure both from simulation and analytics shows the model to be thermodynamically consistent. A phase diagram to explore the range of parameters that give rise to phase separation in the model is investigated. The interfacial width and phase growth obtained from the model agree with the literature for a wide range of temperatures and parameters.

In silico modeling of patient-specific blood rheology in type 2 diabetes mellitus

Increased blood viscosity in type 2 diabetes mellitus (T2DM) is a risk factor for the development of insulin resistance and diabetes-related vascular complications; however, individuals with T2DM exhibit heterogeneous hemorheological properties, including cell deformation and aggregation. Using a multiscale red blood cell (RBC) model with key parameters derived from patient-specific data, we present a computational study of the rheological properties of blood from individual patients with T2DM. Specifically, one key model parameter, which determines the shear stiffness of the RBC membrane (μ) is informed by the high-shear-rate blood viscosity of patients with T2DM. At the same time, the other, which contributes to the strength of the RBC aggregation interaction (D0), is derived from the low-shear-rate blood viscosity of patients with T2DM. The T2DM RBC suspensions are simulated at different shear rates, and the predicted blood viscosity is compared with clinical laboratory-measured data. The results show that the blood viscosity obtained from clinical laboratories and computational simulations are in agreement at both low and high shear rates. These quantitative simulation results demonstrate that the patient-specific model has truly learned the rheological behavior of T2DM blood by unifying the mechanical and aggregation factors of the RBCs, which provides an effective way to extract quantitative predictions of the rheological properties of the blood of individual patients with T2DM.

Disappearance, division, and route change of excitable reaction-diffusion waves in deformable membranes

Shapes of biomembrane in living cells are regulated by curvature-inducing proteins. However, the effects of membrane deformation on signal transductions such as chemical waves have not been researched adequately. Here, we report that membrane deformation can alter the propagation of excitable reaction-diffusion waves using state-of-the-art simulations. Reaction waves can induce large shape transformations, such as membrane budding and necking, that erase or divide the wave, depending on the curvature generated by the waves, feedback to the wave propagation, and the ratio of the reaction and deformation times. In genus-2 vesicles, wave division occurs at branching points and collided waves disappear together. We demonstrate that the occasional disappearance of the waves can alter the pathway of wave propagation. Our findings suggest that membrane deformation and reaction waves can together regulate signal transductions on biomembranes.

Stability of Branched Tubular Membrane Structures

We study the energetics and stability of branched tubular membrane structures by computer simulations of a triangulated network model. We find that triple (Y) junctions can be created and stabilized by applying mechanical forces, if the angle between branches is 120°. The same holds for tetrahedral junctions with tetraeder angles. If the wrong angles are enforced, the branches coalesce to a linear structure, a pure tube. After releasing the mechanical force, Y-branched structures remain metastable if one constrains the enclosed volume and the average curvature (the area difference) to a fixed value; tetrahedral junctions however split up into two Y junctions. Somewhat counterintuitively, the energy cost of adding a Y branch is negative in structures with fixed surface area and tube diameter, even if one accounts for the positive contribution of the additional branch end. For fixed average curvature, however, adding a branch also enforces a thinning of tubes, therefore the overall curvature energy cost is positive. Possible implications for the stability of branched networks structures in cells are discussed.

Non-equilibrium shapes and dynamics of active vesicles

Active vesicles, constructed through the confinement of self-propelled particles (SPPs) inside a lipid membrane shell, exhibit a large variety of non-equilibrium shapes, ranging from the formation of local tethers and dendritic conformations, to prolate and bola-like structures. To better understand the behavior of active vesicles, we perform simulations of membranes modelled as dynamically triangulated surfaces enclosing active Brownian particles. A systematic analysis of membrane deformations and SPP clustering, as a function of SPP activity and volume fraction inside the vesicle is carried out. Distributions of membrane local curvature, and the clustering and mobility of SPPs obtained from simulations of active vesicles are analysed. There exists a feedback mechanism between the enhancement of membrane curvature, the formation of clusters of active particles, and local or global changes in vesicle shape. The emergence of active tension due to the activity of SPPs can well be captured by the Young-Laplace equation. Furthermore, a simple numerical method for tether detection is presented and used to determine correlations between the number of tethers, their length, and local curvature. We also provide several geometrical arguments to explain different tether characteristics for various conditions. These results contribute to the future development of steerable active vesicles or soft micro-robots whose behaviour can be controlled and used for potential applications.

Excitable reaction-diffusion waves of curvature-inducing proteins on deformable membrane tubes

Living cells employ excitable reaction-diffusion waves for internal cellular functions, in which curvature-inducing proteins are often involved. However, the role of their mechanochemical coupling is not well understood. Here, we report the membrane deformation induced by the excitable reaction-diffusion waves of curvature-inducing proteins and the alternation in the waves due to the deformation, using a coarse-grained simulation of tubular membranes with a modified FitzHugh-Nagumo model. Protein-propagating waves deform tubular membranes and large deformations induce budding and erase waves. The wave speed and shape are determined by a combination of membrane deformation and spatial distribution of the curvature-inducing protein. Waves are also undulated in the azimuthal direction depending on the condition. Rotationally symmetric waves locally deform the tubes into a symmetric shape but maintain a straight shape on average. Our simulation method can be applied to other chemical reaction models and used to investigate various biomembrane phenomena.

Membrane shape deformation induced by curvature-inducing proteins consisting of chiral crescent binding and intrinsically disordered domains

Curvature-inducing proteins containing a bin/amphiphysin/Rvs domain often have intrinsically disordered domains. Recent experiments have shown that these disordered chains enhance curvature sensing and generation. Here, we report on the modification of protein–membrane interactions by disordered chains using meshless membrane simulations. The protein and bound membrane are modeled together as a chiral crescent protein rod with two excluded-volume chains. As the chain length increases, the repulsion between them reduces the cluster size of the proteins. It induces spindle-shaped vesicles and a transition between arc-shaped and circular protein assemblies in a disk-shaped vesicle. For flat membranes, an intermediate chain length induces many tubules owing to the repulsion between the protein assemblies, whereas longer chains promote perpendicular elongation of tubules. Moreover, protein rods with zero rod curvature and sufficiently long chains stabilize the spherical buds. For proteins with a negative rod curvature, an intermediate chain length induces a rugged membrane with branched protein assemblies, whereas longer chains induce the formation of tubules with periodic concave-ring structures.

Nonlinear Transient and Steady State Stretching of Deflated Vesicles in Flow

Membrane-bound vesicles and organelles exhibit a wide array of nonspherical shapes at equilibrium, including biconcave and tubular morphologies. Despite recent progress, the stretching dynamics of deflated vesicles is not fully understood, particularly far from equilibrium where complex nonspherical shapes undergo large deformations in flow. Here, we directly observe the transient and steady-state nonlinear stretching dynamics of deflated vesicles in extensional flow using a Stokes trap. Automated flow control is used to observe vesicle dynamics over a wide range of flow rates, shape anisotropy, and viscosity contrast. Our results show that deflated vesicle membranes stretch into highly deformed shapes in flow above a critical capillary number Ca_c1. We further identify a second critical capillary number Ca_c2, above which vesicle stretch diverges in flow. Vesicles are robust to multiple nonlinear stretch-relax cycles, evidenced by relaxation of dumbbell-shaped vesicles containing thin lipid tethers following flow cessation. An analytical model is developed for vesicle deformation in flow, which enables comparison of nonlinear steady-state stretching results with theories for different reduced volumes. Our results show that the model captures the steady-state stretching of moderately deflated vesicles; however, it underpredicts the steady-state nonlinear stretching of highly deflated vesicles. Overall, these results provide a new understanding of the nonlinear stretching dynamics and membrane mechanics of deflated vesicles in flow.

Lattice Boltzmann simulations on the tumbling to tank-treading transition: effects of membrane viscosity

The tumbling to tank-treading (TB-TT) transition for red blood cells (RBCs) has been widely investigated, with a main focus on the effects of the viscosity ratio [Formula: see text] (i.e., the ratio between the viscosities of the fluids inside and outside the membrane) and the shear rate [Formula: see text] applied to the RBC. However, the membrane viscosity [Formula: see text] plays a major role in a realistic description of RBC dynamics, and only a few works have systematically focused on its effects on the TB-TT transition. In this work, we provide a parametric investigation on the effect of membrane viscosity [Formula: see text] on the TB-TT transition for a single RBC. It is found that, at fixed viscosity ratios [Formula: see text], larger values of [Formula: see text] lead to an increased range of values of capillary number at which the TB-TT transition occurs; moreover, we found that increasing [Formula: see text] or increasing [Formula: see text] results in a qualitatively but not quantitatively similar behaviour. All results are obtained by means of mesoscale numerical simulations based on the lattice Boltzmann models. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Hydrodynamic coupling for particle-based solvent-free membrane models

The great challenge with biological membrane systems is the wide range of scales involved, from nanometers and picoseconds for individual lipids to the micrometers and beyond millisecond for cellular signaling processes. While solvent-free coarse-grained membrane models are convenient for large-scale simulations and promising to provide insight into slow processes involving membranes, these models usually have unrealistic kinetics. One major obstacle is the lack of an equally convenient way of introducing hydrodynamic coupling without significantly increasing the computational cost of the model. To address this, we introduce a framework based on anisotropic Langevin dynamics, for which major in-plane and out-of-plane hydrodynamic effects are modeled via friction and diffusion tensors from analytical or semi-analytical solutions to Stokes hydrodynamic equations. Using this framework, in conjunction with our recently developed membrane model, we obtain accurate dispersion relations for planar membrane patches, both free-standing and in the vicinity of a wall. We briefly discuss how non-equilibrium dynamics is affected by hydrodynamic interactions. We also measure the surface viscosity of the model membrane and discuss the affecting dissipative mechanisms.

Reaction-diffusion waves coupled with membrane curvature

The reaction-diffusion waves of proteins are known to be involved in fundamental cellular functions, such as cell migration, cell division, and vesicular transportation. In some of these phenomena, pattern formation on the membranes is induced by the coupling between membrane deformation and the reaction-diffusion system through curvature-inducing proteins that bend the biological membranes. Although the membrane shape and the dynamics of the curvature-inducing proteins affect each other in these systems, the effect of such mechanochemical feedback loops on the waves has not been studied in detail. In this study, reaction-diffusion waves coupled with membrane deformation are investigated using simulations combining a dynamically triangulated membrane model with the Brusselator model extended to include the effect of membrane curvature. It is found that the propagating wave patterns change into nonpropageting patterns and spiral wave patterns due to the mechanochemical effects. Moreover, the wave speed is positively or negatively correlated with the local membrane curvature depending on the spontaneous curvature and bending rigidity. In addition, self-oscillation of the vesicle shape occurs, associated with the reaction-diffusion waves of curvature-inducing proteins. This agrees with the experimental observation of GUVs with a reconstituted Min system, which plays a key role in the cell division of Escherichia coli. The findings of this study demonstrate the importance of mechanochemical coupling in biological phenomena.

Effects of polymers on the cavitating flow around a cylinder: A large-scale molecular dynamics analysis

The cavitation flow of linear-polymer solutions around a cylinder is studied by performing a large-scale molecular dynamics simulation. The addition of polymer chains remarkably suppresses cavitation. The polymers are stretched into a linear shape near the cylinder and entrained in the vortex behind the cylinder. As the polymers stretch, the elongational viscosity increases, which suppresses the vortex formation. Furthermore, the polymers exhibit an entropic elasticity owing to stretching. This elastic energy increases the local temperature, which inhibits the cavitation inception. These effects of polymers result in the dramatic suppression of cavitation.

Loading and relaxation dynamics of a red blood cell

We use mesoscale numerical simulations to investigate the unsteady dynamics of a single red blood cell (RBC) subjected to an external mechanical load. We carry out a detailed comparison between the loading (L) dynamics, following the imposition of the mechanical load on the RBC at rest, and the relaxation (R) dynamics, allowing the RBC to relax to its original shape after the sudden arrest of the mechanical load. Such a comparison is carried out by analyzing the characteristic times of the two corresponding dynamics, i.e., t_L and t_R. When the intensity of the mechanical load is small enough, the two kinds of dynamics are symmetrical (t_L≈t_R) and independent of the typology of mechanical load (intrinsic dynamics); otherwise, in marked contrast, an asymmetry is found, wherein the loading dynamics is typically faster than the relaxation one. This asymmetry manifests itself with non-universal characteristics, e.g., dependency on the applied load and/or on the viscoelastic properties of the RBC membrane. To deepen such a non-universal behaviour, we consider the viscosity of the erythrocyte membrane as a variable parameter and focus on three different typologies of mechanical load (mechanical stretching, shear flow, elongational flow): this allows to clarify how non-universality builds up in terms of the deformation and rotational contributions induced by the mechanical load on the membrane. Finally, we also investigate the effect of the elastic shear modulus on the characteristic times t_L and t_R. Our results provide crucial and quantitative information on the unsteady dynamics of RBC and its membrane response to the imposition/cessation of external mechanical loads.

In-Flow dynamics of an area-difference-energy spring-particle red blood cell model on non-uniform grids

In this paper the area-difference-energy spring-particle (ADE-SP) red blood cell (RBC) structural model developed by Chen and Boyle is coupled with a lattice Boltzmann flux solver to simulate RBC dynamics. The novel ADE-SP model accounts for bending resistance due to the membrane area difference of RBCs while the lattice Boltzmann flux solver offers reduced computational runtimes through GPU parallelisation and enabling the employment of non-uniform meshes. This coupled model is used to simulate RBC dynamics and predictions are compared with existing experimental measurements. The simulations successfully predict tumbling, tank-treading, swinging and intermittent behaviour of an RBC in shear flow, and demonstrate the capability of the model in capturing in-flow RBC behaviours.

Pattern formation in reaction-diffusion system on membrane with mechanochemical feedback

Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently, chemical reaction propagation has been experimentally observed in plasma membranes. Thus, it is important to understand how the reaction-diffusion dynamics are modified on deformable curved membranes. Here, we investigated nonequilibrium pattern formation on vesicles induced by mechanochemical feedback between membrane deformation and chemical reactions, using dynamically triangulated membrane simulations combined with the Brusselator model. We found that membrane deformation changes stable patterns relative to those that occur on a non-deformable curved surface, as determined by linear stability analysis. We further found that budding and multi-spindle shapes are induced by Turing patterns, and we also observed the transition from oscillation patterns to stable spot patterns. Our results demonstrate the importance of mechanochemical feedback in pattern formation on deforming membranes.

Role of combined cell membrane and wall mechanical properties regulated by polarity signals in cell budding

Budding yeast, Saccharomyces cerevisiae, serves as a prime biological model to study mechanisms underlying asymmetric growth. Previous studies have shown that prior to bud emergence, polarization of a conserved small GTPase Cdc42 must be established on the cell membrane of a budding yeast. Additionally, such polarization contributes to the delivery of cell wall remodeling enzymes and hydrolase from cytosol through the membrane, to change the mechanical properties of the cell wall. This leads to the hypothesis that Cdc42 and its associated proteins at least indirectly regulate cell surface mechanical properties. However, how the surface mechanical properties in the emerging bud are changed and whether such change is important are not well understood. To test several hypothesised mechanisms, a novel three-dimensional coarse-grained particle-based model has been developed which describes inhomogeneous mechanical properties of the cell surface. Model simulations predict alternation of the levels of stretching and bending stiffness of the cell surface in the bud region by the polarized Cdc42 signals is essential for initiating bud formation. Model simulations also suggest that bud shape depends strongly on the distribution of the polarized signaling molecules while the neck width of the emerging bud is strongly impacted by the mechanical properties of the chitin and septin rings. Moreover, the temporal change of the bud mechanical properties is shown to affect the symmetry of the bud shape. The 3D model of asymmetric cell growth can also be used for studying viral budding and other vegetative reproduction processes performed via budding, as well as detailed studies of cell growth.

Active particles induce large shape deformations in giant lipid vesicles

Biological cells generate intricate structures by sculpting their membrane from within to actively sense and respond to external stimuli or to explore their environment^1-4. Several pathogenic bacteria also provide examples of how localized forces strongly deform cell membranes from inside, leading to the invasion of neighbouring healthy mammalian cells⁵. Giant unilamellar vesicles have been successfully used as a minimal model system with which to mimic biological cells^6-11, but the realization of a minimal system with localized active internal forces that can strongly deform lipid membranes from within and lead to dramatic shape changes remains challenging. Here we present a combined experimental and simulation study that demonstrates how self-propelled particles enclosed in giant unilamellar vesicles can induce a plethora of non-equilibrium shapes and active membrane fluctuations. Using confocal microscopy, in the experiments we explore the membrane response to local forces exerted by self-phoretic Janus microswimmers. To quantify dynamic membrane changes, we perform Langevin dynamics simulations of active Brownian particles enclosed in thin membrane shells modelled by dynamically triangulated surfaces. The most pronounced shape changes are observed at low and moderate particle loadings, with the formation of tether-like protrusions and highly branched, dendritic structures, whereas at high volume fractions globally deformed vesicle shapes are observed. The resulting state diagram predicts the conditions under which local internal forces generate various membrane shapes. A controlled realization of such distorted vesicle morphologies could improve the design of artificial systems such as small-scale soft robots and synthetic cells.

Microstreaming inside Model Cells Induced by Ultrasound and Microbubbles

Studies on the bioeffects produced by ultrasound and microbubbles have focused primarily on transport in bulk tissue, drug uptake by individual cells, and disruption of biological membranes. Relatively little is known about the physical perturbations and fluid dynamics of the intracellular environment during ultrasound exposure. To investigate this, a custom acoustofluidic chamber was designed to expose model cells, in the form of giant unilamellar vesicles, to ultrasound and microbubbles. The motion of fluorescent tracer beads within the lumen of the vesicles was tracked during exposure to laminar flow (∼1 mm s^-1), ultrasound (1 MHz, ∼150 kPa, 60 s), and phospholipid-coated microbubbles, alone and in combination. To decouple the effects of fluid flow and ultrasound exposure, the system was also modeled numerically by using boundary-driven streaming field equations. Both the experimental and numerical results indicate that all conditions produced internal streaming within the vesicles. Ultrasound alone produced an average bead velocity of 6.5 ± 1.3 μm/s, which increased to 8.5 ± 3.8 μm/s in the presence of microbubbles compared to 12 ± 0.12 μm/s under laminar flow. Further research on intracellular forces in mammalian cells and the associated biological effects in vitro and in vivo are required to fully determine the implications for safety and/or therapy.

Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models

Biomembranes are two-dimensional assemblies of phospholipids that are only a few nanometres thick, but form micrometre-sized structures vital to cellular function. Explicit molecular modelling of biologically relevant membrane systems is computationally expensive due to the large number of solvent particles and slow membrane kinetics. Coarse-grained solvent-free membrane models offer efficient sampling but sacrifice realistic kinetics, thereby limiting the ability to predict pathways and mechanisms of membrane processes. Here, we present a framework for integrating coarse-grained membrane models with continuum-based hydrodynamics. This framework facilitates efficient simulation of large biomembrane systems with large timesteps, while achieving realistic equilibrium and non-equilibrium kinetics. It helps to bridge between the nanometer/nanosecond spatiotemporal resolutions of coarse-grained models and biologically relevant time- and lengthscales. As a demonstration, we investigate fluctuations of red blood cells, with varying cytoplasmic viscosities, in 150-milliseconds-long trajectories, and compare kinetic properties against single-cell experimental observations.

Nanoparticle transport phenomena in confined flows

Nanoparticles submerged in confined flow fields occur in several technological applications involving heat and mass transfer in nanoscale systems. Describing the transport with nanoparticles in confined flows poses additional challenges due to the coupling between the thermal effects and fluid forces. Here, we focus on the relevant literature related to Brownian motion, hydrodynamic interactions and transport associated with nanoparticles in confined flows. We review the literature on the several techniques that are based on the principles of non-equilibrium statistical mechanics and computational fluid dynamics in order to simultaneously preserve the fluctuation-dissipation relationship and the prevailing hydrodynamic correlations. Through a review of select examples, we discuss the treatments of the temporal dynamics from the colloidal scales to the molecular scales pertaining to nanoscale fluid dynamics and heat transfer. As evident from this review, there, indeed has been little progress made in regard to the accurate modeling of heat transport in nanofluids flowing in confined geometries such as tubes. Therefore the associated mechanisms with such processes remain unexplained. This review has revealed that the information available in open literature on the transport properties of nanofluids is often contradictory and confusing. It has been very difficult to draw definitive conclusions. The quality of work reported on this topic is non-uniform. A significant portion of this review pertains to the treatment of the fluid dynamic aspects of the nanoparticle transport problem. By simultaneously treating the energy transport in ways discussed in this review as related to momentum transport, the ultimate goal of understanding nanoscale heat transport in confined flows may be achieved.

Shape Transformations of Vesicles Induced by Swim Pressure

While the behavior of vesicles in thermodynamic equilibrium has been studied extensively, how active forces control vesicle shape transformations is not understood. Here, we combine theory and simulations to study the shape behavior of vesicles containing active Brownian particles. We show that the combination of active forces, dimensionality, and membrane bending free energy creates a plethora of novel phase transitions. At low swim pressure, the vesicle exhibits a discontinuous transition from a spherical to a prolate shape, which has no counterpart in two dimensions. At high swim pressure it exhibits stochastic spatiotemporal oscillations. Our work helps researchers to understand and control the shape dynamics of membranes in active-matter systems.

A theoretical study on the dynamics of a compound vesicle in shear flow

The dynamics of nucleate cells in shear flow is of great relevance in cancer cells and circulatory tumor cells where they determine the flow properties of blood. Buoyed by the success of giant unilamellar vesicles in explaining the dynamics of anucleate cells such as red blood cells, compound vesicles have been suggested as a simple model for nucleate cells. A compound vesicle consists of two concentric unilamellar vesicles with the inner, annular and outer regions filled with aqueous Newtonian solvents. In this work, a theoretical model is presented to study the deformation and dynamics of a compound vesicle in linear shear flow using small deformation theory and spherical harmonics with higher order approximation to the membrane forces. A coupling of viscous and membrane stresses at the membrane interface of the two vesicles results in highly nonlinear shape evolution equations for the inner and the outer vesicles which are solved numerically. The results indicate that the size of the inner vesicle (χ) does not affect the tank-treading dynamics of the outer vesicle. The inner vesicle admits a greater inclination angle than the outer vesicle. However, the transition to trembling/swinging and tumbling is significantly affected. The inner and outer vesicles exhibit identical dynamics in the parameter space defined by the nondimensional rotational (Λ_an) and extensional (S) strength of the general shear flow. At moderate χ, a swinging mode is observed for the inner vesicle while the outer vesicle exhibits tumbling. The inner vesicle also exhibits modification of the TU mode to IUS (intermediate tumbling swinging) mode. Moreover, synchronization of the two vesicles at higher χ and a Capillary number sensitive motion at lower χ is observed in the tumbling regime. These results are in accordance with the few experimental observations reported by Levant and Steinberg. A reduction in the inclination angle is observed with an increase in χ when the inner vesicle is replaced by a solid inclusion. Additionally, a very elaborate phase diagram is presented in the Λ_an-S parameter space, which could be tested in future experiments or numerical simulations.

Oblate to prolate transition of a vesicle in shear flow

Vesicles are micrometric soft particles whose 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. We characterize the transition from oblate to prolate and analyse the divergence of the transition time near the critical capillary number. We then analyse the lift dynamics of an oblate vesicle in the weak flow regime.

State diagram for wall adhesion of red blood cells in shear flow: from crawling to flipping

Red blood cells in shear flow show a variety of different shapes due to the complex interplay between hydrodynamics and membrane elasticity. Malaria-infected red blood cells become generally adhesive and less deformable. Adhesion to a substrate leads to a reduction in shape variability and to a flipping motion of the non-spherical shapes during the mid-stage of infection. Here, we present a complete state diagram for wall adhesion of red blood cells in shear flow obtained by simulations, using a particle-based mesoscale hydrodynamics approach, multiparticle collision dynamics. We find that cell flipping at a substrate is replaced by crawling beyond a critical shear rate, which increases with both membrane stiffness and viscosity contrast between the cytosol and suspending medium. This change in cell dynamics resembles the transition between tumbling and tank-treading for red blood cells in free shear flow. In the context of malaria infections, the flipping-crawling transition would strongly increase the adhesive interactions with the vascular endothelium, but might be suppressed by the combined effect of increased elasticity and viscosity contrast.

A finite difference method with subsampling for immersed boundary simulations of the capsule dynamics with viscoelastic membranes

The membrane or interfacial viscosity is an important property in many multiphase and biofluidic situations, such as the red blood cell dynamics and emulsion stability. The immersed boundary method (IBM), which incorporates the dynamic flow-membrane interaction via force distribution and velocity interpolation, has been extensively employed in simulations of such systems. Unfortunately, direct implementation of membrane viscosity in IBM suffers severe numerical instability, which causes an IBM calculation to break down before generating any useful results. Few attempts have been recently reported; however, several concerns exist in these attempts, such as the inconsistency to the classical definition of membrane viscosity, the inability to model the shear and dilatational viscosities separately, the unjustified mathematical formulations, and the complicated algorithms and computation. To overcome these concerns, in this paper, we propose a finite difference approach for implementing membrane viscosity in immersed boundary simulations. The viscous stress is obtained via finite difference approximations to the differential strain-stress relationship, with the help of a subsampling scheme to reduce the numerical noise in the calculated strain rates. This simple method has also avoided the complicated matrix calculations in previous attempts, and hence, a better computational efficiency is expected. Detailed mathematical description of the method and key steps for its implementation in immersed boundary programs are provided. Validation and illustration calculations are performed, and our results are compared with analytical solutions and previous publications with satisfactory agreement. The influences of membrane mesh resolution and simulation time step are also examined; and the results show no indication that our finite difference method has downgraded the general IBM accuracy. Based on these simulations and analysis, we believe that our method would be a better choice for future IBM simulations of capsule dynamics with viscoelastic membranes.

Limiting shapes of confined lipid vesicles

We theoretically study the shapes of lipid vesicles confined to a spherical cavity, elaborating a framework based on the so-called limiting shapes constructed from geometrically simple structural elements such as double-membrane walls and edges. Partly inspired by numerical results, the proposed non-compartmentalized and compartmentalized limiting shapes are arranged in the bilayer-couple phase diagram which is then compared to its free-vesicle counterpart. We also compute the area-difference-elasticity phase diagram of the limiting shapes and we use it to interpret shape transitions experimentally observed in vesicles confined within another vesicle. The limiting-shape framework may be generalized to theoretically investigate the structure of certain cell organelles such as the mitochondrion.

Particle-based membrane model for mesoscopic simulation of cellular dynamics

We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on interacting and reacting particles, each representing a coarse patch of a lipid monolayer. Particle interactions include nearest-neighbor bond-stretching and angle-bending and are parameterized so as to reproduce the local membrane mechanics given by the Helfrich energy density over a range of relevant curvatures. In-plane fluidity is implemented with Monte Carlo bond-flipping moves. The physical accuracy of the model is verified by five tests: (i) Power spectrum analysis of equilibrium thermal undulations is used to verify that the particle-based representation correctly captures the dynamics predicted by the continuum model of fluid membranes. (ii) It is verified that the input bending stiffness, against which the potential parameters are optimized, is accurately recovered. (iii) Isothermal area compressibility modulus of the membrane is calculated and is shown to be tunable to reproduce available values for different lipid bilayers, independent of the bending rigidity. (iv) Simulation of two-dimensional shear flow under a gravity force is employed to measure the effective in-plane viscosity of the membrane model and show the possibility of modeling membranes with specified viscosities. (v) Interaction of the bilayer membrane with a spherical nanoparticle is modeled as a test case for large membrane deformations and budding involved in cellular processes such as endocytosis. The results are shown to coincide well with the predicted behavior of continuum models, and the membrane model successfully mimics the expected budding behavior. We expect our model to be of high practical usability for ultra coarse-grained molecular dynamics or particle-based reaction-diffusion simulations of biological systems.

Bilayer sheet protrusions and budding from bilayer membranes induced by hydrolysis and condensation reactions

Shape transformations of flat bilayer membranes and vesicles induced by hydrolysis and condensation reactions of amphiphilic molecules are studied using coarse-grained molecular dynamics simulations. The hydrolysis and condensation reactions result in the formation and dissociation of amphiphilic molecules, respectively. Asymmetric reactions between the inner and outer leaflets of a vesicle can transport amphiphilic molecules between the leaflets. It is found that the resulting area difference between the two leaflets induces bilayer sheet protrusion (BP) and budding at low reduced volumes of the vesicles, whereas BP only occurs at high reduced volumes. The probabilities of these two types of transformations depend on the shear viscosity of the surrounding fluids compared to the membrane as well as the reaction rates. A higher surrounding fluid viscosity leads to more BP formation. The inhomogeneous spatial distribution of the hydrophobic reaction products forms the nuclei of BP formation, and faster diffusion of the products enhances BP formation. Our results suggest that adjustment of the viscosity is important to control membrane shape transformations in experiments.

Elastic particle deformation in rectangular channel flow as a measure of particle stiffness

In this study, we experimentally observed and characterized soft elastic particle deformation in confined flow in a microchannel with a rectangular cross-section. Hydrogel microparticles of pNIPAM were produced using two different concentrations of crosslinker. This resulted in particles with two different shear moduli of 13.3 ± 5.5 Pa and 32.5 ± 15.7 Pa and compressive moduli of 66 ± 10 Pa and 79 ± 15 Pa, respectively, as measured by capillary micromechanics. Under flow, the particle shapes transitioned from circular to egg, triangular, arrowhead, and ultimately parachute shaped with increasing shear rate. The shape changes were reversible, and deformed particles relaxed back to circular/spherical in the absence of flow. The thresholds for each shape transition were quantified using a non-dimensional radius of curvature at the tip, particle deformation, circularity, and the depth of the concave dimple at the trailing edge. Several of the observed shapes were distinct from those previously reported in the literature for vesicles and capsules; the elastic particles had a narrower leading tip and a lower circularity. Due to variations in the shear moduli between particles within a batch of particles, each flow rate corresponded to a small but finite range of capillary number (Ca) and resulted in a series of shapes. By arranging the images on a plot of Ca versus circularity, a direct correlation was developed between shape and Ca and thus between particle deformation and shear modulus. As the shape was very sensitive to differences in shear modulus, particle deformation in confined flow may allow for better differentiation of microparticle shear modulus than other methods.

Particle-based modeling of heterogeneous chemical kinetics including mass transfer

Connecting the macroscopic world of continuous fields to the microscopic world of discrete molecular events is important for understanding several phenomena occurring at physical boundaries of systems. An important example is heterogeneous catalysis, where reactions take place at active surfaces, but the effective reaction rates are determined by transport limitations in the bulk fluid and reaction limitations on the catalyst surface. In this work we study the macro-micro connection in a model heterogeneous catalytic reactor by means of stochastic rotation dynamics. The model is able to resolve the convective and diffusive interplay between participating species, while including adsorption, desorption, and reaction processes on the catalytic surface. Here we apply the simulation methodology to a simple straight microchannel with a catalytic strip. Dimensionless Damkohler numbers are used to comment on the spatial concentration profiles of reactants and products near the catalyst strip and in the bulk. We end the discussion with an outlook on more complicated geometries and increasingly complex reactions.

Development of a Virtual Cell Model to Predict Cell Response to Substrate Topography

Cells can sense and respond to changes in the topographical, chemical, and mechanical information in their environment. Engineered substrates are increasingly being developed that exploit these physical attributes to direct cell responses (most notably mesenchymal stem cells) and therefore control cell behavior toward desired applications. However, there are very few methods available for robust and accurate modeling that can predict cell behavior prior to experimental evaluations, and this typically means that many cell test iterations are needed to identify best material features. Here, we developed a unifying computational framework to create a multicomponent cell model, called the "virtual cell model" that has the capability to predict changes in whole cell and cell nucleus characteristics (in terms of shape, direction, and even chromatin conformation) on a range of cell substrates. Modeling data were correlated with cell culture experimental outcomes in order to confirm the applicability of the virtual cell model and demonstrating the ability to reflect the qualitative behavior of mesenchymal stem cells. This may provide a reliable, efficient, and fast high-throughput approach for the development of optimized substrates for a broad range of cellular applications including stem cell differentiation.

Hybrid smoothed dissipative particle dynamics and immersed boundary method for simulation of red blood cells in flows

In biofluid flow systems, often the flow problems of fluids of complex structures, such as the flow of red blood cells (RBCs) through complex capillary vessels, need to be considered. The smoothed dissipative particle dynamics (SDPD), a particle-based method, is one of the easy and flexible methods to model such complex structure fluids. It couples the best features of the smoothed particle hydrodynamics (SPH) and dissipative particle dynamics (DPD), with parameters having specific physical meaning (coming from SPH discretization of the Navier-Stokes equations), combined with thermal fluctuations in a mesoscale simulation, in a similar manner to the DPD. On the other hand, the immersed boundary method (IBM), a preferred method for handling fluid-structure interaction problems, has also been widely used to handle the fluid-RBC interaction in RBC simulations. In this paper, we aim to couple SDPD and IBM together to carry out the simulations of RBCs in complex flow problems. First, we develop the SDPD-IBM model in details, including the SDPD model for the evolving fluid flow, the RBC model for calculating RBC deformation force, the IBM for treating fluid-RBC interaction, and the solid boundary treatment model as well. We then conduct the verification and validation of the combined SDPD-IBM method. Finally, we demonstrate the capability of the SDPD-IBM method by simulating the flows of RBCs in rectangular, cylinder, curved, bifurcated, and constricted tubes, respectively.

Construction of Nuclear Envelope Shape by a High-Genus Vesicle with Pore-Size Constraint

Nuclear pores have an approximately uniform distribution in the nuclear envelope of most living cells. Hence, the morphology of the nuclear envelope is a spherical stomatocyte with a high genus. We have investigated the morphology of high-genus vesicles under pore-size constraint using dynamically triangulated membrane simulations. Bending-energy minimization without volume or other constraints produces a circular-cage stomatocyte, where the pores are aligned in a circular line on an oblate bud. As the pore radius is reduced, the circular-pore alignment is more stabilized than a random pore distribution on a spherical bud. However, we have clarified the conditions for the formation of a spherical stomatocyte: a small perinuclear volume, osmotic pressure within nucleoplasm, and repulsion between the pores. When area-difference elasticity is taken into account, the formation of cylindrical or budded tubules from the stomatocyte and discoidal stomatocyte is found.

Role of molecular turnover in dynamic deformation of a three-dimensional cellular membrane

In cells, the molecular constituents of membranes are dynamically turned over by transportation from one membrane to another. This molecular turnover causes the membrane to shrink or expand by sensing the stress state within the cell, changing its morphology. At present, little is known as to how this turnover regulates the dynamic deformation of cellular membranes. In this study, we propose a new physical model by which molecular turnover is coupled with three-dimensional membrane deformation to explore mechanosensing roles of turnover in cellular membrane deformations. In particular, as an example of microscopic machinery, based on a coarse-graining description, we suppose that molecular turnover depends on the local membrane strain. Using the proposed model, we demonstrate computational simulations of a single vesicle. The results show that molecular turnover adaptively facilitates vesicle deformation, owing to its stress dependence; while the vesicle drastically expands in the case with low bending rigidity, it shrinks in that with high bending rigidity. Moreover, localized active tension on the membrane causes cellular migration by driving the directional transport of molecules within the cell. These results illustrate the use of the proposed model as well as the role of turnover in the dynamic deformations of cellular membranes.

Theory and algorithms to compute Helfrich bending forces: a review

Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.

Lattice Boltzmann Simulation of Healthy and Defective Red Blood Cell Settling in Blood Plasma

In this paper, an attempt has been made to study sedimentation of a red blood cell (RBC) in a plasma-filled tube numerically. Such behaviors are studied for a healthy and a defective cell which might be created due to human diseases, such as diabetes, sickle-cell anemia, and hereditary spherocytosis. Flow-induced deformation of RBC is obtained using finite-element method (FEM), while flow and fluid-membrane interaction are handled using lattice Boltzmann (LB) and immersed boundary methods (IBMs), respectively. The effects of RBC properties as well as its geometry and orientation on its sedimentation rate are investigated and discussed. The results show that decreasing frontal area of an RBC and/or increasing tube diameter results in a faster settling. Comparison of healthy and diabetic cells reveals that less cell deformability leads to slower settling. The simulation results show that the sicklelike and spherelike RBCs have lower settling velocity as compared with a biconcave discoid cell.