Passive or active fluctuations in membranes containing proteins

Local changes in protein filament properties drive large-scale membrane transformations involved in endosome tethering and fusion

Large-scale cellular transformations are triggered by subtle physical and structural changes to individual biomacromolecular and membrane components. A prototypical example of such an event is the orchestrated fusion of membranes within an endosome that enables transport of cargo and processing of biochemical moieties. In this work, we demonstrate how protein filaments on the endosomal membrane surface can leverage a rigid-to-flexible transformation to elicit a large-scale change in membrane flexibility to enable membrane fusion. We develop a polymer field-theoretic model that captures molecular alignment arising from nematic interactions with varying surface density and fraction of flexible filaments, which are biologically controlled within the endosomal membrane. We then predict the collective elasticity of the filament brush in response to changes in the filament alignment, predicting a greater than 20-fold increase of the effective membrane elasticity over the bare membrane elasticity that is triggered by filament alignment. These results show that the endosome can modulate the filament properties to orchestrate membrane fluidization that facilitates vesicle fusion, providing an example of how active processes that modulate local molecular properties can result in large-scale transformations that are essential to cellular survival.

Caveolin-1 protects endothelial cells from extensive expansion of transcellular tunnel by stiffening the plasma membrane

Large transcellular pores elicited by bacterial mono-ADP-ribosyltransferase (mART) exotoxins inhibiting the small RhoA GTPase compromise the endothelial barrier. Recent advances in biophysical modeling point toward membrane tension and bending rigidity as the minimal set of mechanical parameters determining the nucleation and maximal size of transendothelial cell macroaperture (TEM) tunnels induced by bacterial RhoA-targeting mART exotoxins. We report that cellular depletion of caveolin-1, the membrane-embedded building block of caveolae, and depletion of cavin-1, the master regulator of caveolae invaginations, increase the number of TEMs per cell. The enhanced occurrence of TEM nucleation events correlates with a reduction in cell height due to the increase in cell spreading and decrease in cell volume, which, together with the disruption of RhoA-driven F-actin meshwork, favor membrane apposition for TEM nucleation. Strikingly, caveolin-1 specifically controls the opening speed of TEMs, leading to their dramatic 5.4-fold larger widening. Consistent with the increase in TEM density and width in siCAV1 cells, we record a higher lethality in CAV1 KO mice subjected to a catalytically active mART exotoxin targeting RhoA during staphylococcal bloodstream infection. Combined theoretical modeling with independent biophysical measurements of plasma membrane bending rigidity points toward a specific contribution of caveolin-1 to membrane stiffening in addition to the role of cavin-1/caveolin-1-dependent caveolae in the control of membrane tension homeostasis.

Non-Markovian Modeling of Nonequilibrium Fluctuations and Dissipation in Active Viscoelastic Biomatter

Based on a Hamiltonian that incorporates the elastic coupling between a tracer particle and the embedding active viscoelastic biomatter, we derive a generalized non-Markovian Langevin model for the nonequilibrium mechanical tracer response. Our analytical expressions for the frequency-dependent tracer response function and the tracer positional autocorrelation function agree quantitatively with experimental data for red blood cells and actomyosin networks with and without adenosine triphosphate over the entire frequency range and in particular reproduce the low-frequency violation of the fluctuation-dissipation theorem. The viscoelastic power laws, the elastic constants and effective friction coefficients extracted from the experimental data allow straightforward physical interpretation.

Active buckling of pressurized spherical shells: Monte Carlo simulation

We study the buckling of pressurized spherical shells by Monte Carlo simulations in which the detailed balance is explicitly broken-thereby driving the shell to be active, out of thermal equilibrium. Such a shell typically has either higher (active) or lower (sedate) fluctuations compared to one in thermal equilibrium depending on how the detailed balance is broken. We show that, for the same set of elastic parameters, a shell that is not buckled in thermal equilibrium can be buckled if turned active. Similarly a shell that is buckled in thermal equilibrium can unbuckle if sedated. Based on this result, we suggest that it is possible to experimentally design microscopic elastic shells whose buckling can be optically controlled.

Capsule self-oscillating gels showing cell-like nonthermal membrane/shape fluctuations

A primary interest in cell membrane and shape fluctuations is establishing experimental models reflecting only nonthermal active contributions. Here we report a millimeter-scaled capsule self-oscillating gel model mirroring the active contribution effect on cell fluctuations. In the capsule self-oscillating gels, the propagating chemical signals during a Belousov-Zhabotinsky (BZ) reaction induce simultaneous local deformations in the various regions, showing cell-like shape fluctuations. The capsule self-oscillating gels do not fluctuate without the BZ reaction, implying that only the active chemical parameter induces the gel fluctuations. The period and amplitude depend on the gel layer thickness and the concentration of the chemical substrate for the BZ reaction. Our results allow for a solid experimental platform showing actively driven cell-like fluctuations, which can potentially contribute to investigating the active parameter effect on cell fluctuations.

Methods to mechanically perturb and characterize GUV-based minimal cell models

Cells shield organelles and the cytosol via an active boundary predominantly made of phospholipids and membrane proteins, yet allowing communication between the intracellular and extracellular environment. Micron-sized liposome compartments commonly known as giant unilamellar vesicles (GUVs) are used to model the cell membrane and encapsulate biological materials and processes in a cell-like confinement. In the field of bottom-up synthetic biology, many have utilized GUVs as substrates to study various biological processes such as protein-lipid interactions, cytoskeletal assembly, and dynamics of protein synthesis. Like cells, it is ideal that GUVs are also mechanically durable and able to stay intact when the inner and outer environment changes. As a result, studies have demonstrated approaches to tune the mechanical properties of GUVs by modulating membrane composition and lumenal material property. In this context, there have been many different methods developed to test the mechanical properties of GUVs. In this review, we will survey various perturbation techniques employed to mechanically characterize GUVs.

Micromechanics of Biomembranes

Micromechanics techniques are playing an increasing role in characterization of biomembranes. The mechanical properties of membranes play an important role for a whole range of cellular processes. Lipid-protein biomembranes display lateral heterogeneity, domain formation, and morphological changes at mesoscopic and nanoscopic length scales. An attempt is made to introduce how membrane's material properties can be measured. Both fluctuation analysis and micro-pipette aspiration experiments have been used to quantify the micromechanics of membranes. The relationship between the structure and function of biomembranes is a critical concern in modern biology. This overview calls for a deeper understanding of how the cell complexity might be related to the mechanical properties of the lipid-protein membrane. Mechanical properties can influence cellular response to processes like adhesion, transport, differentiation, proliferation and migration.

Active and thermal fluctuations in multi-scale polymer structure and dynamics

The presence of athermal noise or biological fluctuations control and maintain crucial life-processes. In this work, we present an exact analytical treatment of the dynamic behavior of a flexible polymer chain that is subjected to both thermal and active forces. Our model for active forces incorporates temporal correlation associated with the characteristic time scale and processivity of enzymatic function (driven by ATP hydrolysis), leading to an active-force time scale that competes with relaxation processes within the polymer chain. We analyze the structure and dynamics of an active-Brownian polymer using our exact results for the dynamic structure factor and the looping time for the chain ends. The spectrum of relaxation times within a polymer chain implies two different behaviors at small and large length scales. Small length-scale relaxation is faster than the active-force time scale, and the dynamic and structural behavior at these scales are oblivious to active forces and, are thus governed by the true thermal temperature. Large length-scale behavior is governed by relaxation times that are much longer than the active-force time scale, resulting in an effective active-Brownian temperature that dramatically alters structural and dynamic behavior. These complex multi-scale effects imply a time-dependent temperature that governs living and non-equilibrium systems, serving as a unifying concept for interpreting and predicting their physical behavior.

Membrane tension controls the phase equilibrium in fusogenic liposomes

Fusogenic liposomes have been widely used for molecule delivery to cell membranes and cell interior. However, their physicochemical state is still little understood. We tested mechanical material behavior by micropipette aspiration of giant vesicles from fusogenic lipid mixtures and found that the membranes of these vesicles are fluid and under high mechanical tension even before aspiration. Based on this result, we developed a theoretical framework to determine the area expansion modulus and membrane tension of such pre-tensed vesicles from aspiration experiments. Surprisingly high membrane tension of 2.1 mN m^-1 and very low area expansion modulus of 63 mN m^-1 were found. We interpret these peculiar material properties as the result of a mechanically driven phase transition between the usual lamellar phase and an, as of now, not finally determined three dimensional phase of the lipid mixture. The free enthalpy of transition between these phases is very low, i.e. on the order of the thermal energy.

Molecular Shape Solution for Mesoscopic Remodeling of Cellular Membranes

Cellular membranes self-assemble from and interact with various molecular species. Each molecule locally shapes the lipid bilayer, the soft elastic core of cellular membranes. The dynamic architecture of intracellular membrane systems is based on elastic transformations and lateral redistribution of these elementary shapes, driven by chemical and curvature stress gradients. The minimization of the total elastic stress by such redistribution composes the most basic, primordial mechanism of membrane curvature-composition coupling (CCC). Although CCC is generally considered in the context of dynamic compositional heterogeneity of cellular membrane systems, in this article we discuss a broader involvement of CCC in controlling membrane deformations. We focus specifically on the mesoscale membrane transformations in open, reservoir-governed systems, such as membrane budding, tubulation, and the emergence of highly curved sites of membrane fusion and fission. We reveal that the reshuffling of molecular shapes constitutes an independent deformation mode with complex rheological properties.This mode controls effective elasticity of local deformations as well as stationary elastic stress, thus emerging as a major regulator of intracellular membrane remodeling.

Perspective: a stirring role for metabolism in cells

Based on recent findings indicating that metabolism might be governed by a limit on the rate at which cells can dissipate Gibbs energy, in this Perspective, we propose a new mechanism of how metabolic activity could globally regulate biomolecular processes in a cell. Specifically, we postulate that Gibbs energy released in metabolic reactions is used to perform work, allowing enzymes to self‐propel or to break free from supramolecular structures. This catalysis‐induced enzyme movement will result in increased intracellular motion, which in turn can compromise biomolecular functions. Once the increased intracellular motion has a detrimental effect on regulatory mechanisms, this will establish a feedback mechanism on metabolic activity, and result in the observed thermodynamic limit. While this proposed explanation for the identified upper rate limit on cellular Gibbs energy dissipation rate awaits experimental validation, it offers an intriguing perspective of how metabolic activity can globally affect biomolecular functions and will hopefully spark new research.

Statistical behavior of nonequilibrium and living biological systems subjected to active and thermal fluctuations

We present a path-integral formulation of the motion of a particle subjected to fluctuating active and thermal forces. This general framework predicts the statistical behavior associated with the stochastic trajectories of the particle, accounting for all possible realizations of Brownian and active forces, over an arbitrary potential landscape. Temporal correlations in the active forces result in non-Markovian statistics, necessitating the inclusion of a fixed active-force value at specified times within the statistical treatment. We specialize our theory to that of exponentially correlated active forces for a particle in a harmonic potential. We find the exact results for the statistical distributions for the initial position of the particle, accounting for the impact of the correlated active forces at all times prior to the initial time. Our theory is then used to find the two-point distribution for the active Brownian particle, which governs the joint probability that a particle begins and ends at specified locations. Analyses of the active Brownian statistics demonstrate that the impact of active forces can be interpreted through a time-dependent temperature whose influence depends on the competition of timescales of the active-force correlation and the relaxation time of the particle in the harmonic potential. The general results presented in this work are transferable to a broad range of nonequilibrium systems with active and Brownian motion, and the time-dependent temperature serves as a governing principle to describe the competition of timescales associated with active forces and internal relaxation processes.

The membrane transporter lactose permease increases lipid bilayer bending rigidity

Cellular life relies on membranes, which provide a resilient and adaptive cell boundary. Many essential processes depend upon the ease with which the membrane is able to deform and bend, features that can be characterized by the bending rigidity. Quantitative investigations of such mechanical properties of biological membranes have primarily been undertaken in solely lipid bilayers and frequently in the absence of buffers. In contrast, much less is known about the influence of integral membrane proteins on bending rigidity under physiological conditions. We focus on an exemplar member of the ubiquitous major facilitator superfamily of transporters and assess the influence of lactose permease on the bending rigidity of lipid bilayers. Fluctuation analysis of giant unilamellar vesicles (GUVs) is a useful means to measure bending rigidity. We find that using a hydrogel substrate produces GUVs that are well suited to fluctuation analysis. Moreover, the hydrogel method is amenable to both physiological salt concentrations and anionic lipids, which are important to mimic key aspects of the native lactose permease membrane. Varying the fraction of the anionic lipid in the lipid mixture DOPC/DOPE/DOPG allows us to assess the dependence of membrane bending rigidity on the topology and concentration of an integral membrane protein in the lipid bilayer of GUVs. The bending rigidity gradually increases with the incorporation of lactose permease, but there is no further increase with greater amounts of the protein in the membrane.

En route to dynamic life processes by SNARE-mediated fusion of polymer and hybrid membranes

A variety of artificial cells springs from the functionalization of liposomes with proteins. However, these models suffer from low durability without repair and replenishment mechanisms, which can be partly addressed by replacing the lipids with polymers. Yet natural membranes are also dynamically remodeled in multiple cellular processes. Here, we show that synthetic amphiphile membranes also undergo fusion, mediated by the protein machinery for synaptic secretion. We integrated fusogenic SNAREs in polymer and hybrid vesicles and observed efficient membrane and content mixing. We determined bending rigidity and pore edge tension as key parameters for fusion and described its plausible progression through cryo-EM snapshots. These findings demonstrate that dynamic membrane phenomena can be reconstituted in synthetic materials, thereby providing new tools for the assembly of synthetic protocells.

Collective dynamics in lipid membranes containing transmembrane peptides

Biological membranes are composed of complex mixtures of lipids and proteins that influence each other's structure and function. The biological activities of many channel-forming peptides and proteins are known to depend on the material properties of the surrounding lipid bilayer. However, less is known about how membrane-spanning channels affect the lipid bilayer properties, and in particular, their collective fluctuation dynamics. Here we use neutron spin echo spectroscopy (NSE) to measure the collective bending and thickness fluctuation dynamics in dimyristoylphosphatidylcholine (di 14 : 0 PC, DMPC) lipid membranes containing two different antimicrobial peptides, alamethicin (Ala) and gramicidin (gD). Ala and gD are both well-studied antimicrobial peptides that form oligomeric membrane-spanning channels with different structures. At low concentrations, the peptides did not have a measurable effect on the average bilayer structure, yet significantly changed the collective membrane dynamics. Despite both peptides forming transmembrane channels, they had opposite effects on the relaxation time of the collective bending fluctuations and associated effective bending modulus, where gD addition stiffened the membrane while Ala addition softened the membrane. Meanwhile, the lowest gD concentrations enhanced the collective thickness fluctuation dynamics, while the higher gD concentrations and all studied Ala concentrations dampened these dynamics. The results highlight the synergy between lipids and proteins in determining the collective membrane dynamics and that not all peptides can be universally treated as rigid bodies when considering their effects on the lipid bilayer fluctuations.

The Mechanics and Thermodynamics of Tubule Formation in Biological Membranes

Membrane tubulation is a ubiquitous process that occurs both at the plasma membrane and on the membranes of intracellular organelles. These tubulation events are known to be mediated by forces applied on the membrane either due to motor proteins, by polymerization of the cytoskeleton, or due to the interactions between membrane proteins binding onto the membrane. The numerous experimental observations of tube formation have been amply supported by mathematical modeling of the associated membrane mechanics and have provided insights into the force-displacement relationships of membrane tubes. Recent advances in quantitative biophysical measurements of membrane-protein interactions and tubule formation have necessitated the need for advances in modeling that will account for the interplay of multiple aspects of physics that occur simultaneously. Here, we present a comprehensive review of experimental observations of tubule formation and provide context from the framework of continuum modeling. Finally, we explore the scope for future research in this area with an emphasis on iterative modeling and experimental measurements that will enable us to expand our mechanistic understanding of tubulation processes in cells.

Comparing physical mechanisms for membrane curvature-driven sorting of BAR-domain proteins

Protein enrichment at specific membrane locations in cells is crucial for many cellular functions. It is well-recognized that the ability of some proteins to sense membrane curvature contributes partly to their enrichment in highly curved cellular membranes. In the past, different theoretical models have been developed to reveal the physical mechanisms underlying curvature-driven protein sorting. This review aims to provide a detailed discussion of the two continuous models that are based on the Helfrich elasticity energy, (1) the spontaneous curvature model and (2) the curvature mismatch model. These two models are commonly applied to describe experimental observations of protein sorting. We discuss how they can be used to explain the curvature-induced sorting data of two BAR proteins, amphiphysin and centaurin. We further discuss how membrane rigidity, and consequently the membrane curvature generated by BAR proteins, could influence protein organization on the curved membranes. Finally, we address future directions in extending these models to describe some cellular phenomena involving protein sorting.

On the Role of Curved Membrane Nanodomains, and Passive and Active Skeleton Forces in the Determination of Cell Shape and Membrane Budding

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding.

Constructing artificial respiratory chain in polymer compartments: Insights into the interplay between bo3 oxidase and the membrane

Cytochrome bo3 ubiquinol oxidase is a transmembrane protein, which oxidizes ubiquinone and reduces oxygen, while pumping protons. Apart from its combination with F1Fo-ATPase to assemble a minimal ATP regeneration module, the utility of the proton pump can be extended to other applications in the context of synthetic cells such as transport, signaling, and control of enzymatic reactions. In parallel, polymers have been speculated to be phospholipid mimics with respect to their ability to self-assemble in compartments with increased stability. However, their usability as interfaces for complex membrane proteins has remained questionable. In the present work, we optimized a fusion/electroformation approach to reconstitute bo3 oxidase in giant unilamellar vesicles made of PDMS-g-PEO and/or phosphatidylcholine (PC). This enabled optical access, while microfluidic trapping allowed for online analysis of individual vesicles. The tight polymer membranes and the inward oriented enzyme caused 1 pH unit difference in 30 min, with an initial rate of 0.35 pH·min-1 To understand the interplay in these composite systems, we studied the relevant mechanical and rheological membrane properties. Remarkably, the proton permeability of polymer/lipid hybrids decreased after protein insertion, while the latter also led to a 20% increase of the polymer diffusion coefficient in polymersomes. In addition, PDMS-g-PEO increased the activity lifetime and the resistance to free radicals. These advantageous properties may open diverse applications, ranging from cell-free biotechnology to biomedicine. Furthermore, the presented study serves as a comprehensive road map for studying the interactions between membrane proteins and synthetic membranes, which will be fundamental for the successful engineering of such hybrid systems.

How a lipid bilayer membrane responds to an oscillating nanoparticle: Promoted membrane undulation and directional wave propagation

Mechanical forces acting on a plasma membrane are of essential importance to cellular functioning via inducing delicate change of the membrane shape with the underlying mechanism yet to be elucidated. Here, we introduce an oscillating nanoparticle (NP) interaction with a lipid bilayer membrane, using the coarse-grained simulation to investigate the dynamic membrane response to constrained mechanical stimulation, which is ubiquitous in biology. Our results demonstrate that, the membrane responds to an oscillating NP by generating nanoscale undulation waves, which immediately propagate through the membrane. In dynamics, propagation of the generated membrane undulation waves always starts from flattening of the region where the NP locates, thus producing a lateral force to propel the waves away from the point of stimulation. The speed of membrane undulation wave propagation is proportional to that of NP oscillation and accelerated by increasing the integral membrane surface tension, suggesting that both the membrane bending and stretching contribute to the energy driving the unique response of membrane undulation wave propagation.

Statistical Mechanics of an Elastically Pinned Membrane: Equilibrium Dynamics and Power Spectrum

In biological settings, membranes typically interact locally with other membranes: the extracellular matrix in the exterior or internal cellular structures such as the cytoskeleton, locally pinning the membrane. Characterizing the dynamical properties of such interactions presents a difficult task. Significant progress has been achieved through simulations and experiments, yet analytical progress in modeling pinned membranes has been impeded by the complexity of governing equations. Here, we circumvent these difficulties by calculating analytically the time-dependent Green's function of the operator governing the dynamics of an elastically pinned membrane in a hydrodynamic surrounding and subject to external forces. This enables us to calculate the equilibrium power spectral density for an overdamped membrane pinned by an elastic, permanently attached spring subject to thermal excitations. By considering the effects of the finite experimental resolution on the measured spectra, we show that the elasticity of the pinning can be extracted from the experimentally measured spectrum. Membrane fluctuations can thus be used as a tool to probe mechanical properties of the underlying structures. Such a tool may be particularly relevant in the context of cell mechanics, in which the elasticity of the membrane's attachment to the cytoskeleton could be measured.

Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces

Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins. Furthermore, these curved membrane proteins are often associated with the recruitment of the cytoskeleton, which then applies active forces that deform the membrane. This coupling between curvature and activity was previously explored theoretically in the linear limit of small deformations, and low dimensionality. Here we explore the unrestricted shapes of vesicles that contain active curved membrane proteins, in three-dimensions, using Monte-Carlo numerical simulations. The activity of the proteins is in the form of protrusive forces that push the membrane outwards, as may arise from the cytoskeleton of the cell due to actin or microtubule polymerization occurring near the membrane. For proteins that have an isotropic convex shape, the additional protrusive force enhances their tendency to aggregate and form membrane protrusions (buds). In addition, we find another transition from deformed spheres with necklace type aggregates, to flat pancake-shaped vesicles, where the curved proteins line the outer rim. This second transition is driven by the active forces, coupled to the spontaneous curvature, and the resulting configurations may shed light on the formation of sheet-like protrusions and lamellipodia of adhered and motile cells.

Giant Vesicles and Their Use in Assays for Assessing Membrane Phase State, Curvature, Mechanics, and Electrical Properties

Giant unilamellar vesicles represent a promising and extremely useful model biomembrane system for systematic measurements of mechanical, thermodynamic, electrical, and rheological properties of lipid bilayers as a function of membrane composition, surrounding media, and temperature. The most important advantage of giant vesicles over other model membrane systems is that the membrane responses to external factors such as ions, (macro)molecules, hydrodynamic flows, or electromagnetic fields can be directly observed under the microscope. Here, we briefly review approaches for giant vesicle preparation and describe several assays used for deducing the membrane phase state and measuring a number of material properties, with further emphasis on membrane reshaping and curvature.

Scaling of lipid membrane rigidity with domain area fraction

Biological membranes are highly heterogeneous in composition which in turn leads to local variations in the physical properties. Here we quantify how heterogeneity in stiffness determines the effective bending modulus, κ_eff, of model phase-separated membranes with coexisting soft fluid and rigid gel domains. We find that the temperature- and composition- dependent trends in membrane rigidity collapse onto a single curve, such that κ_eff directly scales with the area fraction of the rigid gel domains. Using no adjustable parameters, the measurements are found to agree with theoretical predictions for inhomogenous membranes and indicate that κ_eff is sensitive to the lateral distribution of the rigid phase within the membrane. This key finding confirms that the properties of heterogeneous membranes can be quantitatively predicted if the area fraction and properties of the individual phases are known.

Signatures of motor susceptibility to forces in the dynamics of a tracer particle in an active gel

We study a model for the motion of a tracer particle inside an active gel, exposing the properties of the van Hove distribution of the particle displacements. Active events of a typical force magnitude can give rise to non-Gaussian distributions having exponential tails or side peaks. The side peaks are predicted to appear when the local bulk elasticity of the gel is large enough and few active sources are dominant. We explain the regimes of the different distributions and study the structure of the side peaks for active sources that are susceptible to the elastic stress that they cause inside the gel. We show how the van Hove distribution is altered by both the duty cycle of the active sources and their susceptibility, and suggest it as a sensitive probe to analyze microrheology data in active systems with restoring elastic forces.

The fluid membrane determines mechanics of erythrocyte extracellular vesicles and is softened in hereditary spherocytosis

Extracellular vesicles (EVs) are widely studied regarding their role in cell-to-cell communication and disease, as well as for applications as biomarkers or drug delivery vehicles. EVs contain membrane and intraluminal proteins, affecting their structure and thereby likely their functioning. Here, we use atomic force microscopy for mechanical characterization of erythrocyte, or red blood cell (RBC), EVs from healthy individuals and from patients with hereditary spherocytosis (HS) due to ankyrin deficiency. While these EVs are packed with proteins, their response to indentation resembles that of fluid liposomes lacking proteins. The bending modulus of RBC EVs of healthy donors is ~15 k_bT, similar to the RBC membrane. Surprisingly, whereas RBCs become more rigid in HS, patient EVs have a significantly (~40%) lower bending modulus than donor EVs. These results shed light on the mechanism and effects of EV budding and might explain the reported increase in vesiculation of RBCs in HS patients.

Red blood cell disorders are often accompanied by increased release of extracellular vesicles (EVs), but their structural and mechanical properties are not fully understood. Here, the authors show that red blood cell EVs show liposome-like mechanical features and are softened in blood disorder patients.

Living Matter: Mesoscopic Active Materials

An introduction to the physical properties of living active matter at the mesoscopic scale (tens of nanometers to micrometers) and their unique features compared with "dead," nonactive matter is presented. This field of research is increasingly denoted as "biological physics" where physics includes chemical physics, soft matter physics, hydrodynamics, mechanics, and the related engineering sciences. The focus is on the emergent properties of these systems and their collective behavior, which results in active self-organization and how they relate to cellular-level biological function. These include locomotion (cell motility and migration) forces that give rise to cell division, the growth and form of cellular assemblies in development, the beating of heart cells, and the effects of mechanical perturbations such as shear flow (in the bloodstream) or adhesion to other cells or tissues. An introduction to the fundamental concepts and theory with selected experimental examples related to the authors' own research is presented, including red-blood-cell membrane fluctuations, motion of the nucleus within an egg cell, self-contracting acto-myosin gels, and structure and beating of heart cells (cardiomyocytes), including how they can be driven by an oscillating, mechanical probe.

Nanomechanics of Extracellular Vesicles Reveals Vesiculation Pathways

Extracellular vesicles (EVs) are emerging as important mediators of cell-cell communication as well as potential disease biomarkers and drug delivery vehicles. However, the mechanical properties of these vesicles are largely unknown, and processes leading to microvesicle-shedding from the plasma membrane are not well understood. Here an in depth atomic force microscopy force spectroscopy study of the mechanical properties of natural EVs is presented. It is found that several natural vesicles of different origin have a different composition of lipids and proteins, but similar mechanical properties. However, vesicles generated by red blood cells (RBC) at different temperatures/incubation times are different mechanically. Quantifying the lipid content of EVs reveals that their stiffness decreases with the increase in their protein/lipid ratio. Further, by maintaining RBC at "extreme" nonphysiological conditions, the cells are pushed to utilize different vesicle generation pathways. It is found that RBCs can generate protein-rich soft vesicles, possibly driven by protein aggregation, and low membrane-protein content stiff vesicles, likely driven by cytoskeleton-induced buckling. Since similar cortical cytoskeleton to that of the RBC exists on the membranes of most mammalian cells, our findings help advancing the understanding of the fundamental process of vesicle generation.

Mapping Cell Membrane Fluctuations Reveals Their Active Regulation and Transient Heterogeneities

Shape fluctuations of the plasma membrane occur in all cells, are incessant, and are proposed to affect membrane functioning. Although studies show how membrane fluctuations are affected by cellular activity in adherent cells, their spatial regulation and the corresponding change in membrane mechanics remain unclear. In this article, we study how ATP-driven activities and actomyosin cytoskeleton impact basal membrane fluctuations in adherent cells. Using interference imaging, we map height fluctuations within single cells and compare the temporal spectra with existing theoretical models to gain insights about the underlying membrane mechanics. We find that ATP-dependent activities enhance the nanoscale z fluctuations but stretch out the membrane laterally. Although actin polymerization or myosin-II activity individually enhances fluctuations, the cortex in unperturbed cells stretches out the membrane and dampens fluctuations. Fitting with models suggest this dampening to be due to confinement by the cortex. However, reduced fluctuations on mitosis or on ATP-depletion/stabilization of cortex correlate with increased tension. Both maps of fluctuations and local temporal autocorrelation functions reveal ATP-dependent transient short-range (<2 μm) heterogeneities. Together, our results show how various ATP-driven processes differently affect membrane mechanics and hence fluctuations, while creating distinct local environments whose functional role needs future investigation.

Nonequilibrium fluctuations of lipid membranes by the rotating motor protein F1F0-ATP synthase

The shape of biological membranes is constantly remodeled and maintained out of equilibrium by active proteins. The functional capacity of membrane deformation is mainly determined by the mechanical interplay between protein activity and bending elasticity. In our experiments, we find that ATP synthase, a rotating membrane protein that synthesizes the biochemical energy in cells through proton-pumping activity across the membrane, promotes localized nonequilibrium membrane fluctuations when reconstituted in giant lipid vesicles. The large membrane deformations emerge from the pumping action of rotating proteins clustered at specific emplacements in the membrane. Our results pave the way to new experimental realizations to explore the collective effects of rotating ATP synthases and their possible biological implications for biomembrane organization and protein functionality.

ATP synthase is a rotating membrane protein that synthesizes ATP through proton-pumping activity across the membrane. To unveil the mechanical impact of this molecular active pump on the bending properties of its lipid environment, we have functionally reconstituted the ATP synthase in giant unilamellar vesicles and tracked the membrane fluctuations by means of flickering spectroscopy. We find that ATP synthase rotates at a frequency of about 20 Hz, promoting large nonequilibrium deformations at discrete hot spots in lipid vesicles and thus inducing an overall membrane softening. The enhanced nonequilibrium fluctuations are compatible with an accumulation of active proteins at highly curved membrane sites through a curvature−protein coupling mechanism that supports the emergence of collective effects of rotating ATP synthases in lipid membranes.

Permeability modes in fluctuating lipid membranes with DNA-translocating pores

Membrane pores can significantly alter not only the permeation dynamics of biological membranes but also their elasticity. Large membrane pores able to transport macromolecular contents represent an interesting model to test theoretical predictions that assign active-like (non-equilibrium) behavior to the permeability contributions to the enhanced membrane fluctuations existing in permeable membranes [Maneville et al. Phys. Rev. Lett. 82, 4356 (1999)]. Such high-amplitude active contributions arise from the forced transport of solvent and solutes through the open pores, which becomes even dominant at large permeability. In this paper, we present a detailed experimental analysis of the active shape fluctuations that appear in highly permeable lipid vesicles with large macromolecular pores inserted in the lipid membrane, which are a consequence of transport permeability events occurred in an osmotic gradient. The experimental results are found in quantitative agreement with theory, showing a remarkable dependence with the density of membrane pores and giving account of mechanical compliances and permeability rates that are compatible with the large size of the membrane pore considered. The presence of individual permeation events has been detected in the fluctuation time-series, from which a stochastic distribution of the permeation events compatible with a shot-noise has been deduced. The non-equilibrium character of the membrane fluctuations in a permeation field, even if the membrane pores are mere passive transporters, is clearly demonstrated. Finally, a bio-nano-technology outlook of the proposed synthetic concept is given on the context of prospective uses as active membrane DNA-pores exploitable in gen-delivery applications based on lipid vesicles.

Studying the effects of asymmetry on the bending rigidity of lipid membranes formed by microfluidics

In this article we detail a robust high-throughput microfluidic platform capable of fabricating either symmetric or asymmetric giant unilamellar vesicles (GUVs) and characterise the mechanical properties of their membranes.

Fluctuations of a membrane nanotube revealed by high-resolution force measurements

Pulling membrane nanotubes from liposomes presents a powerful method to gain access to membrane mechanics. Here we extend classical optical tweezers studies to infer membrane nanotube dynamics with high spatial and temporal resolution. We first validate our force measurement setup by accurately measuring the bending modulus of EPC membrane in tube pulling experiments. Then we record the position signal of a trapped bead when it is connected, or not, to a tube. We derive the fluctuation spectrum of these signals and find that the presence of a membrane nanotube induces higher fluctuations, especially at low frequencies (10-1000 Hz). We analyse these spectra by taking into account the peristaltic modes of nanotube fluctuations. This analysis provides a new experimental framework for a quantitative study of the fluctuations of nanotubular membrane structures that are present in living cells, and now classically used for in vitro biomimetic approaches.

Membrane stiffness is modified by integral membrane proteins

The ease with which a cell membrane can bend and deform is important for a wide range of biological functions. Peripheral proteins that induce curvature in membranes (e.g. BAR domains) have been studied for a number of years. Little is known, however, about the effect of integral membrane proteins on the stiffness of a membrane (characterised by the bending rigidity, Kc). We demonstrate by computer simulation that adding integral membrane proteins at physiological densities alters the stiffness of the membrane. First we establish that the coarse-grained MARTINI forcefield is able to accurately reproduce the bending rigidity of a small patch of 1500 phosphatidyl choline lipids by comparing the calculated value to both experiment and an atomistic simulation of the same system. This enables us to simulate the dynamics of large (ca. 50 000 lipids) patches of membrane using the MARTINI coarse-grained description. We find that altering the lipid composition changes the bending rigidity. Adding integral membrane proteins to lipid bilayers also changes the bending rigidity, whilst adding a simple peripheral membrane protein has no effect. Our results suggest that integral membrane proteins can have different effects, and in the case of the bacterial outer membrane protein, BtuB, the greater the density of protein, the larger the reduction in stiffness.

Hydrodynamic collective effects of active proteins in biological membranes

Lipid bilayers forming biological membranes are known to behave as viscous two-dimensional fluids on submicrometer scales; usually they contain a large number of active protein inclusions. Recently, it was shown [A. S. Mikhailov and R. Kapral, Proc. Natl. Acad. Sci. USA 112, E3639 (2015)PNASA60027-842410.1073/pnas.1506825112] that such active proteins should induce nonthermal fluctuating lipid flows leading to diffusion enhancement and chemotaxislike drift for passive inclusions in biomembranes. Here, a detailed analytical and numerical investigation of such effects is performed. The attention is focused on the situations when proteins are concentrated within lipid rafts. We demonstrate that passive particles tend to become attracted by active rafts and are accumulated inside them.

Membrane mechanical properties of synthetic asymmetric phospholipid vesicles

Synthetic lipid vesicles have served as important model systems to study cellular membrane biology. Research has shown that the mechanical properties of bilayer membranes significantly affects their biological behavior. The properties of a lipid bilayer are governed by lipid acyl chain length, headgroup type, and the presence of membrane proteins. However, few studies have explored how membrane architecture, in particular trans-bilayer lipid asymmetry, influences membrane mechanical properties. In this study, we investigated the effects of lipid bilayer architecture (i.e. asymmetry) on the mechanical properties of biological membranes. This was achieved using a customized micropipette aspiration system and a novel microfluidic technique previously developed by our team for building asymmetric phospholipid vesicles with tailored bilayer architecture. We found that the bending modulus and area expansion modulus of the synthetic asymmetric bilayers were up to 50% larger than the values acquired for symmetric bilayers. This was caused by the dissimilar lipid distribution in each leaflet of the bilayer for the asymmetric membrane. To the best of our knowledge, this is the first report on the impact of trans-bilayer asymmetry on the area expansion modulus of synthetic bilayer membranes. Since the mechanical properties of bilayer membranes play an important role in numerous cellular processes, these results have significant implications for membrane biology studies.

Membrane remodeling and mechanics: Experiments and simulations of α-Synuclein

We review experimental and simulation approaches that have been used to determine curvature generation and remodeling of lipid bilayers by membrane-bending proteins. Particular emphasis is placed on the complementary approaches used to study α-Synuclein (αSyn), a major protein involved in Parkinson's disease (PD). Recent cellular and biophysical experiments have shown that the protein 1) deforms the native structure of mitochondrial and model membranes; and 2) inhibits vesicular fusion. Today's advanced experimental and computational technology has made it possible to quantify these protein-induced changes in membrane shape and material properties. Collectively, experiments, theory and multi-scale simulation techniques have established the key physical determinants of membrane remodeling and rigidity: protein binding energy, protein partition depth, protein density, and membrane tension. Despite the exciting and significant progress made in recent years in these areas, challenges remain in connecting biophysical insights to the cellular processes that lead to disease. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Dynamics of a membrane interacting with an active wall

Active motions of a biological membrane can be induced by nonthermal fluctuations that occur in the outer environment of the membrane. We discuss the dynamics of a membrane interacting hydrodynamically with an active wall that exerts random velocities on the ambient fluid. Solving the hydrodynamic equations of a bound membrane, we first derive a dynamic equation for the membrane fluctuation amplitude in the presence of different types of walls. Membrane two-point correlation functions are calculated for three different cases: (i) a static wall, (ii) an active wall, and (iii) an active wall with an intrinsic time scale. We focus on the mean squared displacement (MSD) of a tagged membrane describing the Brownian motion of a membrane segment. For the static wall case, there are two asymptotic regimes of MSD (∼t^{2/3} and ∼t^{1/3}) when the hydrodynamic decay rate changes monotonically. In the case of an active wall, the MSD grows linearly in time (∼t) in the early stage, which is unusual for a membrane segment. This linear-growth region of the MSD is further extended when the active wall has a finite intrinsic time scale.

Nanometric thermal fluctuations of weakly confined biomembranes measured with microsecond time-resolution

We probe the bending fluctuations of bio-membranes using highly deflated giant unilamellar vesicles (GUVs) bound to a substrate by a weak potential arising from generic interactions. The substrate is either homogeneous, with GUVs bound only by the weak potential, or is chemically functionalized with a micro-pattern of very strong specific binders. In both cases, the weakly adhered membrane is seen to be confined at a well-defined distance above the surface while it continues to fluctuate strongly. We quantify the fluctuations of the weakly confined membrane at the substrate proximal surface as well as of the free membrane at the distal surface of the same GUV. This strategy enables us to probe in detail the damping of fluctuations in the presence of the substrate, and to independently measure the membrane tension and the strength of the generic interaction potential. Measurements were done using two complementary techniques - dynamic optical displacement spectroscopy (DODS, resolution: 20 nm, 10 μs), and dual wavelength reflection interference contrast microscopy (DW-RICM, resolution: 4 nm, 50 ms). After accounting for the spatio-temporal resolution of the techniques, an excellent agreement between the two measurements was obtained. For both weakly confined systems we explore in detail the link between fluctuations on the one hand and membrane tension and the interaction potential on the other hand.

Dynamics of two-component membranes surrounded by viscoelastic media

We discuss the dynamics of two-component fluid membranes which are surrounded by viscoelastic media. We assume that membrane-embedded proteins can diffuse laterally and induce a local membrane curvature. The mean squared displacement of a tagged membrane segment is obtained as a generalized Einstein relation. When the elasticity of the surrounding media obeys a power-law behavior in frequency, an anomalous diffusion of the membrane segment is predicted. We also consider the situation where the proteins generate active non-equilibrium forces. The generalized Einstein relation is further modified by an effective temperature that depends on the force dipole energy. The obtained generalized Einstein relations are useful for membrane microrheology experiments.

Lipid domains in model membranes: a brief historical perspective

All biological membranes consist of a complex composite of macromolecules and macromolecular assemblies, of which the fluid lipid-bilayer component is a core element with regard to cell encapsulation and barrier properties. The fluid lipid bilayer also supports the functional machinery of receptors, channels and pumps that are associated with the membrane. This bilayer is stabilized by weak physical and colloidal forces, and its nature is that of a self-assembled system of amphiphiles in water. Being only approximately 5 nm in thickness and still encapsulating a cell that is three orders of magnitude larger in diameter, the lipid bilayer as a material has very unusual physical properties, both in terms of structure and dynamics. Although the lipid bilayer is a fluid, it has a distinct and structured trans-bilayer profile, and in the plane of the bilayer the various molecular components, viz different lipid species and membrane proteins, have the capacity to organize laterally in terms of differentiated domains on different length and time scales. These elements of small-scale structure and order are crucial for the functioning of the membrane. It has turned out to be difficult to quantitatively study the small-scale structure of biological membranes. A major part of the insight into membrane micro- and nano-domains and the concepts used to describe them have hence come from studies of simple lipid bilayers as models of membranes, by use of a wide range of theoretical, experimental and simulational approaches. Many questions remain to be answered as to which extent the result from model studies can carry over to real biological membranes.

Reconstitution of a transmembrane protein, the voltage-gated ion channel, KvAP, into giant unilamellar vesicles for microscopy and patch clamp studies

Giant Unilamellar Vesicles (GUVs) are a popular biomimetic system for studying membrane associated phenomena. However, commonly used protocols to grow GUVs must be modified in order to form GUVs containing functional transmembrane proteins. This article describes two dehydration-rehydration methods - electroformation and gel-assisted swelling - to form GUVs containing the voltage-gated potassium channel, KvAP. In both methods, a solution of protein-containing small unilamellar vesicles is partially dehydrated to form a stack of membranes, which is then allowed to swell in a rehydration buffer. For the electroformation method, the film is deposited on platinum electrodes so that an AC field can be applied during film rehydration. In contrast, the gel-assisted swelling method uses an agarose gel substrate to enhance film rehydration. Both methods can produce GUVs in low (e.g., 5 mM) and physiological (e.g., 100 mM) salt concentrations. The resulting GUVs are characterized via fluorescence microscopy, and the function of reconstituted channels measured using the inside-out patch-clamp configuration. While swelling in the presence of an alternating electric field (electroformation) gives a high yield of defect-free GUVs, the gel-assisted swelling method produces a more homogeneous protein distribution and requires no special equipment.

Recent developments in the field of bending rigidity measurements on membranes

This review gives a brief overview of experimental approaches used to assess the bending rigidity of membranes. Emphasis is placed on techniques based on the use of giant unilamellar vesicles. We summarize the effect on the bending rigidity of membranes as a function of membrane composition, presence of various inclusions in the bilayer and molecules and ions in the bathing solutions. Examples for the impact of temperature, cholesterol, some peptides and proteins, sugars and salts are provided and the literature data are discussed critically. Future directions, open questions and possible developments in this research field are also included.

Bending lipid membranes: experiments after W. Helfrich's model

Current description of biomembrane mechanics originates for a large part from W. Helfrich's model. Based on his continuum theory, many experiments have been performed in the past four decades on simplified membranes in order to characterize the mechanical properties of lipid membranes and the contribution of polymers or proteins. The long-term goal was to develop a better understanding of the mechanical properties of cell membranes. In this paper, we will review representative experimental approaches that were developed during this period and the main results that were obtained.

Nonequilibrium collective dynamics in photoexcited lipid multilayers by time resolved diffuse x-ray scattering

We study the nonequilibrium shape fluctuations in fluorescence labeled phospholipid multibilayers composed of the model lipid DOPC and the well-known lipid dye Texas red, driven out of equilibrium by short laser pulses. The temporal evolution of the lipid bilayer undulations after excitation was recorded by time resolved x-ray diffraction. Already at moderate peak intensities (Pp≤10(5)  W/cm2), pulsed laser illumination leads to significant changes of the undulation modes in a well-defined lateral wavelength band. The observed phenomena evolve on nano- to microsecond time scales after optical excitation, and can be described in terms of a modulation instability in the lipid multilamellar stack.

Is the fluid mosaic (and the accompanying raft hypothesis) a suitable model to describe fundamental features of biological membranes? What may be missing?

The structure, dynamics, and stability of lipid bilayers are controlled by thermodynamic forces, leading to overall tensionless membranes with a distinct lateral organization and a conspicuous lateral pressure profile. Bilayers are also subject to built-in curvature-stress instabilities that may be released locally or globally in terms of morphological changes leading to the formation of non-lamellar and curved structures. A key controller of the bilayer's propensity to form curved structures is the average molecular shape of the different lipid molecules. Via the curvature stress, molecular shape mediates a coupling to membrane-protein function and provides a set of physical mechanisms for formation of lipid domains and laterally differentiated regions in the plane of the membrane. Unfortunately, these relevant physical features of membranes are often ignored in the most popular models for biological membranes. Results from a number of experimental and theoretical studies emphasize the significance of these fundamental physical properties and call for a refinement of the fluid mosaic model (and the accompanying raft hypothesis).

Optical stretching as a tool to investigate the mechanical properties of lipid bilayers

Measurements of lipid bilayer bending modulus by various techniques produce widely divergent results. We attempt to resolve some of this ambiguity by measuring bending modulus in a system that can rapidly process large numbers of samples, yielding population statistics. This system is based on optical stretching of giant unilamellar vesicles (GUVs) in a microfluidic dual-beam optical trap (DBOT). The microfluidic DBOT system is used here to measure three populations of GUVs with distinct lipid compositions. We find that gel-phase membranes are significantly stiffer than liquid-phase membranes, consistent with previous reports. We also find that the addition of cholesterol does not alter the bending modulus of membranes composed of a monounsaturated phospholipid.