Membrane viscosity determined from shear-driven flow in giant vesicles

Mfn2-dependent fusion pathway of PE-enriched micron-sized vesicles

Mitofusins (Mfn1 and Mfn2) are the mitochondrial outer-membrane fusion proteins in mammals and belong to the dynamin superfamily of multidomain GTPases. Recent structural studies of truncated variants lacking alpha helical transmembrane domains suggested that Mfns dimerize to promote the approximation and the fusion of the mitochondrial outer membranes upon the hydrolysis of guanine 5'-triphosphate disodium salt (GTP). However, next to the presence of GTP, the fusion activity seems to require multiple regulatory factors that control the dynamics and kinetics of mitochondrial fusion through the formation of Mfn1-Mfn2 heterodimers. Here, we purified and reconstituted the full-length murine Mfn2 protein into giant unilamellar vesicles (GUVs) with different lipid compositions. The incubation with GTP resulted in the fusion of Mfn2-GUVs. High-speed video-microscopy showed that the Mfn2-dependent membrane fusion pathway progressed through a zipper mechanism where the formation and growth of an adhesion patch eventually led to the formation of a membrane opening at the rim of the septum. The presence of physiological concentration (up to 30 mol%) of dioleoyl-phosphatidylethanolamine (DOPE) was shown to be a requisite to observe GTP-induced Mfn2-dependent fusion. Our observations show that Mfn2 alone can promote the fusion of micron-sized DOPE-enriched vesicles without the requirement of regulatory cofactors, such as membrane curvature, or the assistance of other proteins.

Shear-Induced Nonequilibrium Patterns in Lipid Bilayer Membranes Exhibiting Phase Separation

The nonequilibrium dynamics of a fluid lipid membrane under external stimuli is an important issue that spans disciplines such as soft matter, biophysical chemistry, and interface science. This study investigated the dynamic response of lipid vesicles with order-disorder phase separation, which mimics a plasma membrane heterogeneity, to shear flow. Lipid vesicles were immobilized in a microfluidic chamber, and shear-induced nonequilibrium patterns on the membrane surface were observed by an optical microscope. We found that phase-separated membranes exhibit a dissipative structure of stripe patterns along the vortex flow on the membrane surface, and the number of stripes increased with the flow rate. At a high flow rate, the membrane exhibited a stripe-to-wave transition, where striped domains often migrated and the replacement of two different phases happened at vortex centers with time. We obtained a dynamic phase diagram of the shear-induced wave pattern by changing the flow rate, membrane components, and temperature. These findings could provide insight into the dissipative structures of lipid membranes out of equilibrium and flow-mediated mechanotransduction of biological membranes.

Stability of a biomembrane tube covered with proteins

Membrane tubes are essential structural features in cells that facilitate biomaterial transport and inter- and intracellular signaling. The shape of these tubes can be regulated by the proteins that surround and adhere to them. We study the stability of a biomembrane tube coated with proteins by combining linear stability analysis, out-of-equilibrium hydrodynamic calculations, and numerical solutions of a Helfrich-like membrane model. Our analysis demonstrates that both long- and short-wavelength perturbations can destabilize the tubes. Numerical simulations confirm the derived linear stability criteria and yield the nonlinearly perturbed vesicle shapes. Our study highlights the interplay between membrane shape and protein density, where the shape instability concurs with a redistribution of proteins into a banded pattern.

Effects of grafted polymers on the lipid membrane fluidity

Since the membrane fluidity controls the cellular functions, it is important to identify the factors that determine the cell membrane viscosity. Cell membranes are composed of not only lipids and proteins but also polysaccharide chain-anchored molecules, such as glycolipids. To reveal the effects of grafted polymers on the membrane fluidity, in this study, we measured the membrane viscosity of polymer-grafted giant unilamellar vesicles (GUVs), which were prepared by introducing the poly (ethylene glycol) (PEG)-anchored lipids to the ternary GUVs composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), and cholesterol. The membrane viscosity was obtained from the velocity field on the GUV generated by applying a point force, based on the hydrodynamic model proposed by Henle and Levine. The velocity field was visualized by a motion of the circular liquid ordered (Lo) domains formed by a phase separation. With increasing PEG density, the membrane viscosity of PEG-grafted GUVs increased gradually in the mushroom region and significantly in the brush region. We propose a hydrodynamic model that includes the excluded volume effect of PEG chains to explain the increase in membrane viscosity in the mushroom region. This work provides a basic understanding of how grafted polymers affect the membrane fluidity.

Endothelial cells differentially sense laminar and disturbed flows by altering the lipid order of their plasma and mitochondrial membranes

Endothelial cells (ECs) experience two different blood flow patterns: laminar and disturbed flow. Their responses to laminar flow contribute to vascular homeostasis, whereas their responses to disturbed flow result in EC dysfunction and vascular diseases. However, it remains unclear how ECs differentially sense laminar and disturbed flow and trigger signaling that elicits different responses. Here, we showed that ECs differentially sense laminar and disturbed flows by altering the lipid order of their plasma and mitochondrial membranes in opposite directions. This results in distinct changes in mitochondrial function, namely, increased adenosine triphosphate (ATP) production for laminar flow and increased hydrogen peroxide (H2O2) release for disturbed flow, leading to ATP- and H2O2-mediated signaling, respectively. When cultured human aortic ECs were subjected to laminar or disturbed flow in flow-loading devices, the lipid order of their plasma membranes immediately decreased in response to laminar flow and increased in response to disturbed flow. Laminar flow also decreased the lipid order of mitochondrial membranes and increased mitochondrial ATP production. In contrast, disturbed flow increased the lipid order of mitochondrial membranes and increased the release of H2O2 from the mitochondria. The addition of cholesterol to the cells increased the lipid order of both membranes and abrogated laminar flow-induced ATP production, while treatment of the cells with a cholesterol-depleting reagent, methyl-β cyclodextrin, decreased the lipid order of both membranes and abolished disturbed flow-induced H2O2 release, indicating that changes in the membrane lipid order and/or cholesterol content are closely linked to flow-induced changes in mitochondrial functions.NEW & NOTEWORTHY How vascular endothelial cells (ECs) differentially sense laminar and disturbed flows and trigger intracellular signaling remains unclear. Here, we show that EC plasma membranes act as mechanosensors to discriminate between laminar and disturbed flows by undergoing opposite changes in their lipid order. Similar lipid order changes occur simultaneously in the mitochondrial membranes, which are linked to changes in mitochondrial function, that is, increased ATP production for laminar flow and increased H2O2 release for disturbed flow.

Passive and reversible area regulation of supported lipid bilayers in response to fluid flow

Biological and model membranes are frequently subjected to fluid shear stress. However, membrane mechanical responses to flow remain incompletely described. This is particularly true of membranes supported on a solid substrate, and the influences of membrane composition and substrate roughness on membrane flow responses remain poorly understood. Here, we combine microfluidics, fluorescence microscopy, and neutron reflectivity to explore how supported lipid bilayer patches respond to controlled shear stress. We demonstrate that lipid membranes undergo a significant, passive, and partially reversible increase in membrane area due to flow. We show that these fluctuations in membrane area can be constrained, but not prevented, by increasing substrate roughness. Similar flow-induced changes to membrane structure may contribute to the ability of living cells to sense and respond to flow.

Surface viscosities of lipid bilayers determined from equilibrium molecular dynamics simulations

Lipid membrane viscosity is critical to biological function. Bacterial cells grown in different environments alter their lipid composition in order to maintain a specific viscosity, and membrane viscosity has been linked to the rate of cellular respiration. To understand the factors that determine the viscosity of a membrane, we ran equilibrium all-atom simulations of single component lipid bilayers and calculated their viscosities. The viscosity was calculated via a Green-Kubo relation, with the stress-tensor autocorrelation function modeled by a stretched exponential function. By simulating a series of lipids at different temperatures, we establish the dependence of viscosity on several aspects of lipid chemistry, including hydrocarbon chain length, unsaturation, and backbone structure. Sphingomyelin is found to have a remarkably high viscosity, roughly 20 times that of DPPC. Furthermore, we find that inclusion of the entire range of the dispersion interaction increases viscosity by up to 140%. The simulated viscosities are similar to experimental values obtained from the rotational dynamics of small chromophores and from the diffusion of integral membrane proteins but significantly lower than recent measurements based on the deformation of giant vesicles.

Influence of surface viscosities on the electrodeformation of a prolate viscous drop

Contaminants and other agents are often present at the interface between two fluids, giving rise to rheological properties such as surface shear and dilatational viscosities. The dynamics of viscous drops with interfacial viscosities has attracted greater interest in recent years, due to the influence of surface rheology on deformation and the surrounding flows. We investigate the effects of shear and dilatational viscosities on the electro-deformation of a viscous drop using the Taylor-Melcher leaky dielectric model. We use a large deformation analysis to derive an ordinary differential equation for the drop shape. Our model elucidates the contributions of each force to the overall deformation of the drop and reveals a rich range of dynamic behaviors that show the effects of surface viscosities and their dependence on rheological and electrical properties of the system. We also examine the physical mechanisms underlying the observed behaviors by analyzing the surface dilatation and surface deformation.

Domain dynamics of phase-separated lipid membranes under shear flow

The dynamical behaviour of lateral domains on phase-separated lipid vesicles under external flow is reported. A microfluidic chamber was used for the immobilization of vesicles and the application of shear. Microscopic observation revealed that domains tended to be localized at the vortex center and to exhibit a stripe morphology as the flow speed increased. We clarified the dependency of domain behaviors on the flow speed and lipid mixing fraction. The cholesterol ratio in the membrane affected these domain behaviors. Next, we investigated the growth of domains under flow. We discuss the mechanism of these trends by considering the free energy of phase separation, and reproduce the experimental results by numerical simulations. These findings may lead to a better understanding of the dynamical properties of the membrane under nonequilibrium situations and the biophysical mechanism of cellular mechanotransduction.

Membrane tension propagation couples axon growth and collateral branching

Neuronal axons must navigate a mechanically heterogeneous environment to reach their targets, but the biophysical mechanisms coupling mechanosensation, growth, and branching are not fully understood. Here, we show that local changes in membrane tension propagate along axons at approximately 20 μm/s, more than 1000-fold faster than in most other nonmotile cells where this property has been measured. Local perturbations to tension decay along the axon with a length constant of approximately 41 μm. This rapid and long-range mechanical signaling mediates bidirectional competition between axonal branch initiation and growth cone extension. Our data suggest a mechanism by which mechanical cues at one part of a growing axon can affect growth dynamics remotely.

A vesicle microrheometer for high-throughput viscosity measurements of lipid and polymer membranes

Viscosity is a key property of cell membranes that controls mobility of embedded proteins and membrane remodeling. Measuring it is challenging because existing approaches involve complex experimental designs and/or models, and the applicability of some methods is limited to specific systems and membrane compositions. As a result there is scarcity of systematic data, and the reported values for membrane viscosity vary by orders of magnitude for the same system. Here, we show how viscosity of membranes can be easily obtained from the transient deformation of giant unilamellar vesicles. The approach enables a noninvasive, probe-independent, and high-throughput measurement of the viscosity of membranes made of lipids or polymers with a wide range of compositions and phase state. Using this novel method, we have collected a significant amount of data that provides insights into the relation between membrane viscosity, composition, and structure.

Probing lipid membrane bending mechanics using gold nanorod tracking

Lipid bilayer membranes undergo rapid bending undulations with wavelengths from tens of nanometers to tens of microns due to thermal fluctuations. Here, we probe such undulations and the membranes' mechanics by measuring the time-varying orientation of single gold nanorods (GNRs) adhered to the membrane, using high-speed dark field microscopy. In a lipid vesicle, such measurements allow the determination of the membrane's viscosity, bending rigidity, and tension as well as the friction coefficient for sliding of the monolayers over one another. The in-plane rotation of the GNR is hindered by undulations in a tension dependent manner, consistent with simulations. The motion of single GNRs adhered to the plasma membrane of living cultured cells similarly reveals the membrane's complex physics and coupling to the cell's actomyosin cortex.

Absolute vs Convective Instabilities and Front Propagation in Lipid Membrane Tubes

We analyze the stability of biological membrane tubes, with and without a base flow of lipids. Membrane dynamics are completely specified by two dimensionless numbers: the well-known Föppl-von Kármán number Γ and the recently introduced Scriven-Love number SL, respectively quantifying the base tension and base flow speed. For unstable tubes, the growth rate of a local perturbation depends only on Γ, whereas SL governs the absolute versus convective nature of the instability. Furthermore, nonlinear simulations of unstable tubes reveal an initially localized disturbance result in propagating fronts, which leave a thin atrophied tube in their wake. Depending on the value of Γ, the thin tube is connected to the unperturbed regions via oscillatory or monotonic shape transitions-reminiscent of recent experimental observations on the retraction and atrophy of axons. We elucidate our findings through a weakly nonlinear analysis, which shows membrane dynamics may be approximated by a model of the class of extended Fisher-Kolmogorov equations. Our study sheds light on the pattern selection mechanism in axonal shapes by recognizing the existence of two Lifshitz points, at which the front dynamics undergo steady-to-oscillatory bifurcations.

Assessing the use of ellipsoidal microparticles for determining lipid membrane viscosity

The viscosity of lipid membranes sets the timescales of membrane-associated motions, whether driven or diffusive, and therefore influences the dynamics of a wide range of cellular processes. Techniques to measure membrane viscosity remain sparse, however, and reported measurements to date, even of similar systems, give viscosity values that span orders of magnitude. To address this, we improve a method based on measuring both the rotational and translational diffusion of membrane-anchored microparticles and apply this approach and one based on tracking the motion of phase-separated lipid domains to the same system of phase-separated giant vesicles. We find good agreement between the two methods, with inferred viscosities within a factor of two of each other. Our single-particle tracking technique uses ellipsoidal microparticles, and we show that the extraction of physically meaningful viscosity values from their motion requires consideration of their anisotropic shape. The validation of our method on phase-separated membranes makes possible its application to other systems, which we demonstrate by measuring the viscosity of bilayers composed of lipids with different chain lengths ranging from 14 to 20 carbon atoms, revealing a very weak dependence of two-dimensional viscosity on lipid size. The experimental and analysis methods described here should be generally applicable to a variety of membrane systems, both reconstituted and cellular.

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.

PoET: automated approach for measuring pore edge tension in giant unilamellar vesicles

Motivation

A reliable characterization of the membrane pore edge tension of single giant unilamellar vesicles (GUVs) requires the measurement of micrometer sized pores in hundreds to thousands of images. When manually performed, this procedure has shown to be extremely time-consuming and to generate inconsistent results among different users and imaging systems. A user-friendly software for such analysis allowing quick processing and generation of reproducible data had not yet been reported.

Results

We have developed a software (PoET) for automatic pore edge tension measurements on GUVs. The required image processing steps and the characterization of the pore dynamics are performed automatically within the software and its use allowed for a 30-fold reduction in the analysis time. We demonstrate the applicability of the software by comparing the pore edge tension of GUVs of different membrane compositions and surface charges. The approach was applied to electroporated GUVs but is applicable to other means of pore formation.

Availability and implementation

The complete software is implemented in Python and available for Windows at https://dx.doi.org/10.17617/3.7h.

Supplementary information

Supplementary data are available at Bioinformatics Advances online.

How to best estimate the viscosity of lipid bilayers

The viscosity of lipid bilayers is a property relevant to biological function, as it affects the diffusion of membrane macromolecules. To determine its value, and hence portray the membrane, various literature-reported techniques lead to significantly different results. Herein we compare the results issuing from two widely used techniques to determine the viscosity of membranes: the Fluorescence Lifetime Imaging Microscopy (FLIM), and Fluorescence Recovery After Photobleaching (FRAP). FLIM relates the time of rotation of a molecular rotor inserted into the membrane to the macroscopic viscosity of a fluid. Whereas FRAP measures molecular diffusion coefficients. This approach is based on a hydrodynamic model connecting the mobility of a membrane inclusion to the viscosity of the membrane. We show that: This article emphasizes the pitfalls to be avoided and the rules to be observed in order to obtain a value of the bilayer viscosity that characterizes the bilayer instead of interactions between the bilayer and the embedded probe.

Relationship between Viscosity and Acyl Tail Dynamics in Lipid Bilayers

Membrane viscosity is a fundamental property that controls molecular transport and structural rearrangements in lipid membranes. Given its importance in many cell processes, various experimental and computational methods have been developed to measure the membrane viscosity, yet the estimated values depend highly on the method and vary by orders of magnitude. Here we investigate the molecular origins of membrane viscosity by measuring the nanoscale dynamics of the lipid acyl tails using x-ray and neutron spectroscopy techniques. The results show that the membrane viscosity can be estimated from the structural relaxation times of the lipid tails.

Hydrodynamic shear dissipation and transmission in lipid bilayers

Vital biological processes, such as trafficking, sensing, and motility, are facilitated by cellular lipid membranes, which interact mechanically with surrounding fluids. Such lipid membranes are only a few nanometers thick and composed of a liquid crystalline structure known as the lipid bilayer. Here, we introduce an active, noncontact, two-point microrheology technique combining multiple optical tweezers probes with planar freestanding lipid bilayers accessible on both sides. We use the method to quantify both fluid slip close to the bilayer surface and transmission of fluid flow across the structure, and we use numerical simulations to determine the monolayer viscosity and the intermonolayer friction. We find that these physical properties are highly dependent on the molecular structure of the lipids in the bilayer. We compare ordered-phase with liquid disordered-phase lipid bilayers, and we find the ordered-phase bilayers to be 10 to 100 times more viscous but with 100 times less intermonolayer friction. When a local shear is applied by the optical tweezers, the ultralow intermonolayer friction results in full slip of the two leaflets relative to each other and as a consequence, no shear transmission across the membrane. Our study sheds light on the physical principles governing the transfer of shear forces by and through lipid membranes, which underpin cell behavior and homeostasis.

Perfusion Chamber for Observing a Liposome-Based Cell Model Prepared by a Water-in-Oil Emulsion Transfer Method

For the construction of a chemical model of contemporary living cells, the so-called water-in-oil emulsion transfer (WOET) method has drawn much attention as one of the promising preparation protocols for cell-sized liposomes encapsulating macromolecules and even micrometer-sized colloidal particles in high yields. Combining the throughput and accuracy of the observation is the key to developing a synthetic approach based on the liposomes prepared by the WOET method. Recent advances in microfluidic technology can provide a solution. By means of surface modification of a poly(dimethylsiloxane)-type microfluidic device integrating size-sorting and trapping modules, here, we enabled a simultaneous direct observation of the liposomes with a narrow size distribution, which were prepared by the WOET method. As a demonstration, we evaluated the variance of encapsulation of polystyrene colloidal particles and water permeability of the cell-sized liposomes prepared by the WOET method in the device. Since the liposomes prepared by the WOET method are useful for constructing cell models with an easy protocol, the current system will lead to a critical development of not only supramolecular chemistry and soft matter physics but also synthetic biology.

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.

Geometry and dynamics of lipid membranes: The Scriven-Love number

The equations governing lipid membrane dynamics in planar, spherical, and cylindrical geometries are presented here. Unperturbed and first-order perturbed equations are determined and nondimensionalized. In membrane systems with a nonzero base flow, perturbed in-plane and out-of-plane quantities are found to vary over different length scales. A new dimensionless number, named the Scriven-Love number, and the well-known Föppl-von Kármán number result from a scaling analysis. The Scriven-Love number compares out-of-plane forces arising from the in-plane, intramembrane viscous stresses to the familiar elastic bending forces, while the Föppl-von Kármán number compares tension to bending forces. Both numbers are calculated in past experimental works, and span a wide range of values in various biological processes across different geometries. In situations with large Scriven-Love and Föppl-von Kármán numbers, the dynamical response of a perturbed membrane is dominated by out-of-plane viscous and surface tension forces-with bending forces playing a negligible role. Calculations of non-negligible Scriven-Love numbers in various biological processes and in vitro experiments show in-plane intramembrane viscous flows cannot generally be ignored when analyzing lipid membrane behavior.

Viscosity Landscape of Phase-Separated Lipid Membrane Estimated from Fluid Velocity Field

In cell membranes, the functional constituents such as peptides, proteins, and polysaccharides diffuse in a sea of lipids as single molecules and molecular aggregates. Thus, the fluidity of the heterogeneous multicomponent membrane is important for understanding the roles of the membrane in cell functionality. Recently, Henle and Levine described the hydrodynamics of molecular diffusion in a spherical membrane. A tangential point force at the north pole induces a pair of vortices whose centers lie on a line perpendicular to the point force and are symmetrical with respect to the point force. The position of the vortex center depends on ηm/Rηw, where R is the radius of the spherical membrane, and ηm and ηw are the viscosities of the membrane and the surrounding medium, respectively. Based on this theoretical prediction, we applied a point force to a phase-separated spherical vesicle composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine/1,2-dioleoyl-sn-glycero-3-phosphocholine/cholesterol by means of a microinjection technique. The pathlines were visualized by trajectories of microdomains. We determined the position of the vortex center and estimated the membrane viscosity using the dependence of the position of the vortex center on ηm/Rηw. The obtained apparent membrane viscosities for various compositions are mapped on the phase diagram. The membrane viscosity is almost constant in the range of 0 <ϕLo ≤ 0.5 (ϕLo: area fraction of the liquid ordered phase), whereas that in the range of 0.5 ≤ ϕLo < 1.0 exponentially increases with increase of ϕLo. The obtained viscosity landscape provides a basic understanding of the fluidity of heterogeneous multicomponent membranes.

Conformational dynamics and phase behavior of lipid vesicles in a precisely controlled extensional flow

Lipid vesicles play a key role in fundamental biological processes. Despite recent progress, we lack a complete understanding of the non-equilibrium dynamics of vesicles due to challenges associated with long-time observation of shape fluctuations in strong flows. In this work, we present a flow-phase diagram for vesicle shape and conformational transitions in planar extensional flow using a Stokes trap, which enables control over the center-of-mass position of single or multiple vesicles in precisely defined flows [A. Shenoy, C. V. Rao and C. M. Schroeder, Proc. Natl. Acad. Sci. U. S. A., 2016, 113(15), 3976-3981]. In this way, we directly observe the non-equilibrium conformations of lipid vesicles as a function of reduced volume ν, capillary number Ca, and viscosity contrast λ. Our results show that vesicle dynamics in extensional flow are characterized by the emergence of three distinct shape transitions, including a tubular to symmetric dumbbell transition, a spheroid to asymmetric dumbbell transition, and quasi-spherical to ellipsoid transition. The experimental phase diagram is in good agreement with recent predictions from simulations [V. Narsimhan, A. P. Spann and E. S. Shaqfeh, J. Fluid Mech., 2014, 750, 144]. We further show that the phase boundary of vesicle shape transitions is independent of the viscosity contrast. Taken together, our results demonstrate the utility of the Stokes trap for the precise quantification of vesicle stretching dynamics in precisely defined flows.

Patterning and polarization of cells by intracellular flows

Beginning with Turing’s seminal work [1], decades of research have demonstrated the fundamental ability of biochemical networks to generate and sustain the formation of patterns. However, it is increasingly appreciated that biochemical networks both shape and are shaped by physical and mechanical processes [2, 3, 4]. One such process is fluid flow. In many respects, the cytoplasm, membrane and actin cortex all function as fluids, and as they flow, they drive bulk transport of molecules throughout the cell. By coupling biochemical activity to long range molecular transport, flows can shape the distributions of molecules in space. Here we review the various types of flows that exist in cells, with the aim of highlighting recent advances in our understanding of how flows are generated and how they contribute to intracellular patterning processes, such as the establishment of cell polarity.

Motion of objects embedded in lipid bilayer membranes: Advection and effective viscosity

An interfacial regularized Stokeslet scheme is presented to predict the motion of solid bodies (e.g., proteins or gel-phase domains) embedded within flowing lipid bilayer membranes. The approach provides a numerical route to calculate velocities and angular velocities in complex flow fields that are not amenable to simple Faxén-like approximations. Additionally, when applied to shearing motions, the calculations yield predictions for the effective surface viscosity of dilute rigid-body-laden membranes. In the case of cylindrical proteins, effective viscosity calculations are compared to two prior analytical predictions from the literature. Effective viscosity predictions for a dilute suspension of rod-shaped objects in the membrane are also presented.

Microfluidic Handling and Analysis of Giant Vesicles for Use as Artificial Cells: A Review

One of the goals of synthetic biology is the bottom-up construction of an artificial cell, the successful realization of which could shed light on how cellular life emerged and could also be a useful tool for studying the function of modern cells. Using liposomes as biomimetic containers is particularly promising because lipid membranes are biocompatible and much of the required machinery can be reconstituted within them. Giant lipid vesicles have been used extensively in other fields such as biophysics and drug discovery, but their use as artificial cells has only recently seen an increase. Despite the prevalence of giant vesicles, many experiments remain challenging or impossible due to their delicate nature compared to biological cells. This review aims to highlight the effectiveness of microfluidic technologies in handling and analyzing giant vesicles. The advantages and disadvantages of different microfluidic approaches and what new insights can be gained from various applications are introduced. Finally, future directions are discussed in which the unique combination of microfluidics and giant lipid vesicles can push forward the bottom-up construction of artificial cells.

Mobility of Molecular Motors Regulates Contractile Behaviors of Actin Networks

Cells generate mechanical forces primarily from interactions between F-actin, cross-linking proteins, myosin motors, and other actin-binding proteins in the cytoskeleton. To understand how molecular interactions between the cytoskeletal elements generate forces, a number of in vitro experiments have been performed but are limited in their ability to accurately reproduce the diversity of motor mobility. In myosin motility assays, myosin heads are fixed on a surface and glide F-actin. By contrast, in reconstituted gels, the motion of both myosin and F-actin is unrestricted. Because only these two extreme conditions have been used, the importance of mobility of motors for network behaviors has remained unclear. In this study, to illuminate the impacts of motor mobility on the contractile behaviors of the actin cytoskeleton, we employed an agent-based computational model based on Brownian dynamics. We find that if motors can bind to only one F-actin like myosin I, networks are most contractile at intermediate mobility. In this case, less motor mobility helps motors stably pull F-actins to generate tensile forces, whereas higher motor mobility allows F-actins to aggregate into larger clustering structures. The optimal intermediate motor mobility depends on the stall force and affinity of motors that are regulated by mechanochemical rates. In addition, we find that the role of motor mobility can vary drastically if motors can bind to a pair of F-actins. A network can exhibit large contraction with high motor mobility because motors bound to antiparallel pairs of F-actins can exert similar forces regardless of their mobility. Results from this study imply that the mobility of molecular motors may critically regulate contractile behaviors of actin networks in cells.

Microwave measurement of giant unilamellar vesicles in aqueous solution

A microwave technique is demonstrated to measure floating giant unilamellar vesicle (GUV) membranes in a 25 μm wide and 18.8 μm high microfluidic channel. The measurement is conducted at 2.7 and 7.9 GHz, at which a split-ring resonator (SRR) operates at odd modes. A 500 nm wide and 100 μm long SRR split gap is used to scan GUVs that are slightly larger than 25 μm in diameter. The smaller fluidic channel induces flattened GUV membrane sections, which make close contact with the SRR gap surface. The used GUVs are synthesized with POPC (16:0–18:1 PC 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine), SM (16:0 Egg Sphingomyelin) and cholesterol at different molecular compositions. It is shown that SM and POPC bilayers have different dielectric permittivity values, which also change with measurement frequencies. The obtained membrane permittivity values, e.g. 73.64-j6.13 for POPC at 2.7 GHz, are more than 10 times larger than previously reported results. The discrepancy is likely due to the measurement of dielectric polarization parallel with, other than perpendicular to, the membrane surface. POPC and SM-rich GUV surface sections are also clearly identified. Further work is needed to verify the obtained large permittivity values and enable accurate analysis of membrane composition.

Hydrodynamic mobility of confined polymeric particles, vesicles, and cancer cells in a square microchannel

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 a square cross-section. Our operating conditions are such that the mobility is measured as a function of geometric confinement over the range 0.3 < λ < 1.5 and at specified particle Reynolds numbers that are within 0.1 < Rep < 2.5. The experimental mobility data of each of these systems is compared with the circular-tube theory of Hestroni, Haber, and Wacholder [J. Fluid Mech. 41, 689-705 (1970)] with modifications made for a square cross-section. For polymeric particles, we find that the mobility data agrees well over a large confinement range with the theory but under predicts for vesicles. The mobility of vesicles is higher in a square channel than in a circular tube, and does not depend significantly on membrane mechanical properties. The mobility of cancer cells is in good agreement with the theory up to λ ≈ 0.8, after which it deviates. Comparison of the mobility data of the three systems reveals that cancer cells have higher mobility than rigid particles but lower than vesicles, suggesting that the cell membrane frictional properties are in between a solid-like interface and a fluid bilayer. We explain further the differences in the mobility of the three systems by considering their shape deformation and surface flow on the interface. The results of this study may find potential applications in drug delivery and biomedical diagnostics.

The Effects of Shear Force Transmission Across Vesicle Membranes

We report a comprehensive study on mechanotransmission of shear forces across lipid bilayer membranes of giant unilamellar vesicles (GUVs). GUVs containing fluorescent tracer particles were immobilized on a microfluidic platform and exposed to shear flows. A method was developed for the visualization of three-dimensional flows at high precision by defocusing microscopy. We quantify the symmetry of external flow around the GUV and show its effects on vortex flows and luminal dynamics. With increasing asymmetry, luminal vortices merged while liquid exchange in between them increased. The effect of membrane composition was studied through addition of cholesterol. Mechanotransmission efficacy, quantified by the ratio of luminal flow to external flow, ranged from ε = 0.094 (0 mol % cholesterol) to ε = 0.043 (16 mol % cholesterol). Our findings give new cues to the mechanisms underlying the sensing of strength and spatial distribution of shear forces by cells and the impact of membrane composition.

Probing Elastic and Viscous Properties of Phospholipid Bilayers Using Neutron Spin Echo Spectroscopy

The elastic and viscous properties of self-assembled amphiphilic membranes dictate the intricate hierarchy of their structure and dynamics ranging from the diffusion of individual molecules to the large-scale deformation of the membrane. We previously demonstrated that neutron spin echo spectroscopy measurements of model amphiphilic membranes can access the naturally occurring submicrosecond membrane motions, such as bending and thickness fluctuations. Here we show how the experimentally measured fluctuation parameters can be used to determine the inherent membrane properties and demonstrate how membrane viscosity and compressibility modulus are influenced by lipid composition in a series of simple phosphatidylcholine bilayers with different tail lengths as a function of temperature. This approach highlights the interdependence of the bilayer elastic and viscous properties and the collective membrane dynamics and opens new avenues to investigating the mechanical properties of more complex and biologically inspired systems.

Electrohydrodynamics of a compound vesicle under an AC electric field

Compound vesicles are relevant as simplified models for biological cells as well as in technological applications such as drug delivery. Characterization of these compound vesicles, especially the inner vesicle, remains a challenge. Similarly their response to electric field assumes importance in light of biomedical applications such as electroporation. Fields lower than that required for electroporation cause electrodeformation in vesicles and can be used to characterize their mechanical and electrical properties. A theoretical analysis of the electrohydrodynamics of a compound vesicle with outer vesicle of radius R _o and an inner vesicle of radius [Formula: see text], is presented. A phase diagram for the compound vesicle is presented and elucidated using detailed plots of electric fields, free charges and electric stresses. The electrohydrodynamics of the outer vesicle in a compound vesicle shows a prolate-sphere and prolate-oblate-sphere shape transitions when the conductivity of the annular fluid is greater than the outer fluid, and vice-versa respectively, akin to single vesicle electrohydrodynamics reported in the literature. The inner vesicle in contrast shows sphere-prolate-sphere and sphere-prolate-oblate-sphere transitions when the inner fluid conductivity is greater and smaller than the annular fluid, respectively. Equations and methodology are provided to determine the bending modulus and capacitance of the outer as well as the inner membrane, thereby providing an easy way to characterize compound vesicles and possibly biological cells.

Energy dissipation in flows through curved spaces

Fluid dynamics in intrinsically curved geometries is encountered in many physical systems in nature, ranging from microscopic bio-membranes all the way up to general relativity at cosmological scales. Despite the diversity of applications, all of these systems share a common feature: the free motion of particles is affected by inertial forces originating from the curvature of the embedding space. Here we reveal a fundamental process underlying fluid dynamics in curved spaces: the free motion of fluids, in the complete absence of solid walls or obstacles, exhibits loss of energy due exclusively to the intrinsic curvature of space. We find that local sources of curvature generate viscous stresses as a result of the inertial forces. The curvature- induced viscous forces are shown to cause hitherto unnoticed and yet appreciable energy dissipation, which might play a significant role for a variety of physical systems involving fluid dynamics in curved spaces.

Lipid and Peptide Diffusion in Bilayers: The Saffman-Delbrück Model and Periodic Boundary Conditions

The periodic Saffman-Delbrück (PSD) model, an extension of the Saffman-Delbrück model developed to describe the effects of periodic boundary conditions on the diffusion constants of lipids and proteins obtained from simulation, is tested using the coarse-grained Martini and all-atom CHARMM36 (C36) force fields. Simulations of pure Martini dipalmitoylphosphatidylcholine (DPPC) bilayers and those with one embedded gramicidin A (gA) dimer or one gA monomer with sizes ranging from 512 to 2048 lipids support the PSD model. Underestimates of D^∞ (the value of the diffusion constant for an infinite system) from the 512-lipid system are 35% for DPPC, 45% for the gA monomer, and 70% for the gA dimer. Simulations of all-atom DPPC and dioleoylphosphatidylcholine (DOPC) bilayers yield diffusion constants not far from experiment. However, the PSD model predicts that diffusion constants at the sizes of the simulation should underestimate experiment by approximately a factor of 3 for DPPC and 2 for DOPC. This likely implies a deficiency in the C36 force field. A Bayesian method for extrapolating diffusion constants of lipids and proteins in membranes obtained from simulation to infinite system size is provided.

Lateral Diffusion of a Submicrometer Particle on a Lipid Bilayer Membrane

In past decades, nanoparticles and nanomaterials have been actively used for applications such as visualizing nano/submicrometer cell structure, killing cancer cells, and using drug delivery systems. It is important to understand the physicochemical mechanisms that govern the motion of nanoparticles on a plasma membrane surface. However, the motion of small particles of <1000 nm on lipid membranes is poorly understood. In this study, we investigated the diffusion of particles with a diameter of 200-800 nm on a lipid membrane using cell-sized liposomes. Particle-associated liposomes were obtained by applying centrifugal force to a mixture of liposomes and particle solutions. We measured the thermal motion of the particles by phase-contrast microscopy. We found that (i) the particle-size dependence of the diffusion of particles adhering to membranes was better described by the DADL model rather than the Einstein-Stokes model, (ii) the diffusion coefficient of a particle strongly depends on the adsorption state of the particle, such as fully or partially wrapped by the membrane, and (iii) anomalous diffusion was induced by the localization of particles on the neck of budded vesicles.

Effect of charge on the mechanical properties of surfactant bilayers

Charge effects on the mechanical properties of surfactant bilayers have been measured, for a system with a low ionic strength, using small-angle neutron scattering and neutron spin echo spectroscopy. We report that, not only does increasing the surface charge density lead to greater structural ordering and a stiffening of the membrane, which is consistent with classical theory of charge effects on membranes, but also that the relaxation rate of the membrane thickness fluctuations decreases without affecting the fluctuation amplitude. From the relaxation rate we demonstrate, using recent theory, that the viscosity of the surfactant membrane is increased with surface charge density, which suggests that the amount of charge controls the diffusion behavior of inclusions inside the membrane. The present results confirm that the thickness fluctuation relaxation rate and amplitude are tuned independently since the membrane viscosity is only influencing the relaxation rate. This work demonstrates that charge stabilization of lamellar bilayers is not merely affected by intermembrane interactions and structural ordering but that intramembrane dynamics also have a significant contribution.

Strong influence of periodic boundary conditions on lateral diffusion in lipid bilayer membranes

The Saffman-Delbrück hydrodynamic model for lipid-bilayer membranes is modified to account for the periodic boundary conditions commonly imposed in molecular simulations. Predicted lateral diffusion coefficients for membrane-embedded solid bodies are sensitive to box shape and converge slowly to the limit of infinite box size, raising serious doubts for the prospects of using detailed simulations to accurately predict membrane-protein diffusivities and related transport properties. Estimates for the relative error associated with periodic boundary artifacts are 50% and higher for fully atomistic models in currently feasible simulation boxes. MARTINI simulations of LacY membrane protein diffusion and LacY dimer diffusion in DPPC membranes and lipid diffusion in pure DPPC bilayers support the underlying hydrodynamic model.

Transbilayer Colocalization of Lipid Domains Explained via Measurement of Strong Coupling Parameters

When micron-scale compositional heterogeneity develops in membranes, the distribution of lipids on one face of the membrane strongly affects the distribution on the other. Specifically, when lipid membranes phase separate into coexisting liquid phases, domains in each monolayer leaflet of the membrane are colocalized with domains in the opposite leaflet. Colocalized domains have never been observed to spontaneously move out of registry. This result indicates that the lipid compositions in one leaflet are strongly coupled to compositions in the opposing leaflet. Predictions of the interleaflet coupling parameter, Λ, vary by a factor of 50. We measure the value of Λ by applying high shear forces to supported lipid bilayers. This causes the upper leaflet to slide over the lower leaflet, moving domains out of registry. We find that the threshold shear stress required to deregister domains in the upper and lower leaflets increases with the inverse length of domains. We derive a simple, closed-form expression relating the threshold shear to Λ, and find Λ = 0.016 ± 0.004 kBT/nm2.

Morphological changes of the red blood cells treated with metal oxide nanoparticles

The toxic effect of Al₂O₃, SiО₂ and ZrО₂ nanoparticles on red blood cells of Wistar rats was studied in vitro using the atomic force microscopy and the fluorescence analysis. Transformation of discocytes into echinocytes and spherocytes caused by the metal oxide nanoparticles was revealed. It was shown that only extremely high concentration of the nanoparticles (2mg/ml) allows correct estimating of their effect on the cell morphology. Besides, it was found out that the microviscosity changes of red blood cell membranes treated with nanoparticles began long before morphological modifications of the cells. On the contrary, the negatively charged ZrO₂ and SiO₂ nanoparticles did not affect ghost microviscosity up to concentrations of 1μg/ml and 0.1mg/ml, correspondingly. In its turn, the positively charged Al₂O₃ nanoparticles induced structural changes in the lipid bilayer of the red blood cells already at a concentration of 0.05μg/ml. A decrease in microviscosity of the erythrocyte ghosts treated with Al₂O₃ and SiO₂ nanoparticles was shown. It was detected that the interaction of ZrO₂ nanoparticles with the cells led to an increase in the membrane microviscosity and cracking of swollen erythrocytes.

Hydrodynamic coupling of particle inclusions embedded in curved lipid bilayer membranes

We develop theory and computational methods to investigate particle inclusions embedded within curved lipid bilayer membranes. We consider the case of spherical lipid vesicles where inclusion particles are coupled through (i) intramembrane hydrodynamics, (ii) traction stresses with the external and trapped solvent fluid, and (iii) intermonolayer slip between the two leaflets of the bilayer. We investigate relative to flat membranes how the membrane curvature and topology augment hydrodynamic responses. We show how both the translational and rotational mobility of protein inclusions are effected by the membrane curvature, ratio of intramembrane viscosity to solvent viscosity, and intermonolayer slip. For general investigations of many-particle dynamics, we also discuss how our approaches can be used to treat the collective diffusion and hydrodynamic coupling within spherical bilayers.

Membranes under shear stress: visualization of non-equilibrium domain patterns and domain fusion in a microfluidic device

In this study we investigate the effect of shear force on lipid membranes induced by external fluid flow. We use giant unilamellar vesicles (GUVs) as simple cell models and chose a ternary lipid mixture that exhibits liquid-ordered and liquid-disordered domains. These domains are stained with different dyes to allow visualization of changes within the membrane after the application of flow. A microfluidic device served as a valuable platform to immobilize the vesicles and apply shear forces of a defined strength. Moreover, integration of valves allowed us to stop the flow instantaneously and visualize the relaxing domain patterns by means of high-resolution fluorescence microscopy. We observed the formation of transient, non-deterministic patterns of the formerly round domains during application of flow. When the flow is stopped, round domains are formed again on a time scale of ms to s. At longer time scales of several seconds to minutes, the domains fuse into larger domains until they reach equilibrium. These processes are accelerated with increasing temperature and vesicles with budding domains do not fuse unless the temperature is elevated. Our results show the strong effect of the flow on the lipid membrane and we believe that this phenomenon plays a crucial role in the processes of mechanotransduction in living cells.

Brownian Dynamics of Electrostatically Adhering Small Vesicles to a Membrane Surface Induces Domains and Probes Viscosity

Using single-particle tracking, we investigate the interaction of small unilamellar vesicles (SUVs) that are electrostatically tethered to the freestanding membrane of a giant unilamellar vesicle (GUV). We find that the surface mobility of the GUV-riding SUVs is Brownian, insensitive to the bulk viscosity, vesicle size, and vesicle fluidity but strongly altered by the viscosity of the underlying membrane. Analyzing the diffusional behavior of SUVs within the Saffman-Delbrück model for the dynamics of membrane inclusions supports the notion that the mobility of the small vesicles is coupled to that of dynamically induced lipid clusters within the target GUV membrane. The reversible binding also offers a nonperturbative means for measuring the viscosity of biomembranes, which is an important parameter in cell physiology and function.

Hydrodynamics of bilayer membranes with diffusing transmembrane proteins

We consider the hydrodynamics of lipid bilayers containing transmembrane proteins of arbitrary shape. This biologically-motivated problem is relevant to the cell membrane, whose fluctuating dynamics play a key role in phenomena ranging from cell migration, intercellular transport, and cell communication. Using Onsager's variational principle, we derive the equations that govern the relaxation dynamics of the membrane shape, of the mass densities of the bilayer leaflets, and of the diffusing proteins' concentration. With our generic formalism, we obtain several results on membrane dynamics. We find that proteins that span the bilayer increase the intermonolayer friction coefficient. The renormalization, which can be significant, is in inverse proportion to the protein's mobility. Second, we find that asymmetric proteins couple to the membrane curvature and to the difference in monolayer densities. For practically all accessible membrane tensions (σ > 10(-8) N m(-1)) we show that the protein density is the slowest relaxing variable. Furthermore, its relaxation rate decreases at small wavelengths due to the coupling to curvature. We apply our formalism to the large-scale diffusion of a concentrated protein patch. We find that the diffusion profile is not self-similar, owing to the wavevector dependence of the effective diffusion coefficient.

Hydrodynamic Forces on Macromolecules Protruding from Lipid Bilayers Due to External Liquid Flows

It has previously been observed that an externally applied hydrodynamic shear flow above a fluid lipid bilayer can change the local concentration of macromolecules that are associated with the lipid bilayer. The external liquid flow results in a hydrodynamic force on molecules protruding from the lipid bilayer, causing them to move in the direction of the flow. However, there has been no quantitative study about the magnitude of these forces. We here use finite element simulations to investigate how the magnitude of the external hydrodynamic forces varies with the size and shape of the studied macromolecule. The simulations show that the hydrodynamic force is proportional to the effective hydrodynamic area of the studied molecule, Ahydro, multiplied by the mean hydrodynamic shear stress acting on the membrane surface, σhydro. The parameter Ahydro depends on the size and shape of the studied macromolecule above the lipid bilayer and scales with the cross-sectional area of the molecule. We also investigate how hydrodynamic shielding from other surrounding macromolecules decreases Ahydro when the surface coverage of the shielding macromolecules increases. Experiments where the protein streptavidin is anchored to a supported lipid bilayer on the floor of a microfluidic channel were finally performed at three different surface concentrations, Φ = 1%, 6%, and 10%, where the protein is being moved relative to the lipid bilayer by a liquid flow through the channel. From photobleaching measurements of fluorescently labeled streptavidin we found the experimental drift data to be within good accuracy of the simulated results, less than 12% difference, indicating the validity of the results obtained from the simulations. In addition to giving a deeper insight into how a liquid flow can affect membrane-associated molecules in a lipid bilayer, we also see an interesting potential of using hydrodynamic flow experiments together with the obtained results to study the size and the intermolecular forces between macromolecules in membranes and lipid bilayers.

Nodal versus Total Axonal Strain and the Role of Cholesterol in Traumatic Brain Injury

Traumatic brain injury (TBI) is a health threat that affects every year millions of people involved in motor vehicle and sporting accidents, and thousands of soldiers in battlefields. Diffuse axonal injury (DAI) is one of the most frequent types of TBI leading to death. In DAI, the initial traumatic event is followed by a cascade of biochemical changes that take time to develop in full, so that symptoms may not become apparent until days or weeks after the original injury. Hence, DAI is a dynamic process, and the opportunity exists to prevent its progression provided the initial trauma can be predicted at the molecular level. Here, we present preliminary evidence from micro-finite element (FE) simulations that the mechanical response of central nervous system myelinated fibers is dependent on the axonal diameter, the ratio between axon diameter and fiber diameter (g-ratio), the microtubules density, and the cholesterol concentration in the axolemma and myelin. A key outcome of the simulations is that there is a significant difference between the overall level of strain in a given axonal segment and the level of local strain in the Ranvier nodes contained in that segment, with the nodal strain being much larger than the total strain. We suggest that the acquisition of this geometric and biochemical information by means of already available high resolution magnetic resonance imaging techniques, and its incorporation in current FE models of the brain will enhance the models capacity to predict the site and magnitude of primary axonal damage upon TBI.