Passive or active fluctuations in membranes containing proteins

Intrinsic reaction-cycle time scale of Na+,K+-ATPase manifests itself in the lipid-protein interactions of nonequilibrium membranes

Interaction between integral membrane proteins and the lipid-bilayer component of biological membranes is expected to mutually influence the proteins and the membrane. We present quantitative evidence of a manifestation of the lipid-protein interactions in liposomal membranes, reconstituted with actively pumping Na(+),K(+)-ATPase, in terms of nonequilibrium shape fluctuations that contain a relaxation time, τ, which is robust and independent of the specific fluctuation modes of the membrane. In the case of pumping Na(+)-ions, analysis of the flicker-noise temporal correlation spectrum of the liposomes leads to τ ~/= 0.5 s, comparing favorably with an intrinsic reaction-cycle time of about 0.4 s from enzymology.

Nonthermal ATP-dependent fluctuations contribute to the in vivo motion of chromosomal loci

Chromosomal loci jiggle in place between segregation events in prokaryotic cells and during interphase in eukaryotic nuclei. This motion seems random and is often attributed to brownian motion. However, we show here that locus dynamics in live bacteria and yeast are sensitive to metabolic activity. When ATP synthesis is inhibited, the apparent diffusion coefficient decreases, whereas the subdiffusive scaling exponent remains constant. Furthermore, the magnitude of locus motion increases more steeply with temperature in untreated cells than in ATP-depleted cells. This "superthermal" response suggests that untreated cells have an additional source of molecular agitation, beyond thermal motion, that increases sharply with temperature. Such ATP-dependent fluctuations are likely mechanical, because the heat dissipated from metabolic processes is insufficient to account for the difference in locus motion between untreated and ATP-depleted cells. Our data indicate that ATP-dependent enzymatic activity, in addition to thermal fluctuations, contributes to the molecular agitation driving random (sub)diffusive motion in the living cell.

Effective tension and fluctuations in active membranes

We calculate the fluctuation spectrum of the shape of a lipid vesicle or cell exposed to a nonthermal source of noise. In particular, we take constraints on the membrane area and the volume of fluid that it encapsulates into account when obtaining expressions for the dependency of the membrane tension on the noise. We then investigate three possible origins of the nonthermal noise taken from the literature: A direct force, which models an external medium pushing on the membrane, a curvature force, which models a fluctuating spontaneous curvature, and a permeation force coming from an active transport of fluid through the membrane. For the direct force and curvature force cases, we compare our results to existing experiments on active membranes.

Model answers to lipid membrane questions

Ever since it was discovered that biological membranes have a core of a bimolecular sheet of lipid molecules, lipid bilayers have been a model laboratory for investigating physicochemical and functional properties of biological membranes. Experimental and theoretical models help the experimental scientist to plan experiments and interpret data. Theoretical models are the theoretical scientist's preferred toys to make contact between membrane theory and experiments. Most importantly, models serve to shape our intuition about which membrane questions are the more fundamental and relevant ones to pursue. Here we review some membrane models for lipid self-assembly, monolayers, bilayers, liposomes, and lipid-protein interactions and illustrate how such models can help answering questions in modern lipid cell biology.

Lipids, curvature, and nano-medicine

The physical properties of the lamellar lipid-bilayer component of biological membranes are controlled by a host of thermodynamic forces leading to overall tensionless bilayers with a conspicuous lateral pressure profile and build-in curvature-stress instabilities that may be released locally or globally in terms of morphological changes. In particular, the average molecular shape and the propensity of the different lipid and protein species for forming non-lamellar and curved structures are a source of structural transitions and control of biological function. The effects of different lipids, sterols, and proteins on membrane structure are discussed and it is shown how one can take advantage of the curvature-stress modulations brought about by specific molecular agents, such as fatty acids, lysolipids, and other amphiphilic solutes, to construct intelligent drug-delivery systems that function by enzymatic triggering via curvature.Practical applications: The simple concept of lipid molecular shape and how it impacts on the structure of lipid aggregates, in particular the curvature and curvature stress in lipid bilayers and liposomes, can be exploited to construct liposome-based drug-delivery systems, e.g., for use as nano-medicine in cancer therapy. Non-lamellar-forming lysolipids and fatty acids, some of which may be designed to be prodrugs, can be created by phospholipase action in diseased tissues thereby providing for targeted drug release and proliferation of molecular entities with conical shape that break down the permeability barrier of the target cells and may hence enhance efficacy.

Active rheology of phospholipid vesicles

Optical tweezers are used to manipulate the shape of artificial dioleoyl-phosphatidylcholine (DOPC) phospholipid vesicles of around 30 μm diameter. Using a time-shared trapping system, a complex of traps drives oscillations of the vesicle equator, with a sinusoidal time dependence and over a range of spatial and temporal frequencies. The mechanical response of the vesicle membrane as a function of the frequency and wavelength of the driving oscillation is monitored. A simple model of the vesicles as spherical elastic membranes immersed in a newtonian fluid, driven by a harmonic trapping potential, describes the experimental data. The bending modulus of the membrane is recovered. The method has potential for future investigation of nonthermally driven systems, where comparison of active and passive rheology can help to distinguish nonthermal forces from equilibrium fluctuations.

Continuum simulations of biomembrane dynamics and the importance of hydrodynamic effects

Traditional particle-based simulation strategies are impractical for the study of lipid bilayers and biological membranes over the longest length and time scales (microns, seconds and longer) relevant to cellular biology. Continuum-based models developed within the frameworks of elasticity theory, fluid dynamics and statistical mechanics provide a framework for studying membrane biophysics over a range of mesoscopic to macroscopic length and time regimes, but the application of such ideas to simulation studies has occurred only relatively recently. We review some of our efforts in this direction with emphasis on the dynamics in model membrane systems. Several examples are presented that highlight the prominent role of hydrodynamics in membrane dynamics and we argue that careful consideration of fluid dynamics is key to understanding membrane biophysics at the cellular scale.

Effective temperature of red-blood-cell membrane fluctuations

Biologically driven nonequilibrium fluctuations are often characterized by their non-Gaussianity or by an "effective temperature", which is frequency dependent and higher than the ambient temperature. We address these two measures theoretically by examining a randomly kicked particle, with a variable number of kicking motors, and show how these two indicators of nonequilibrium behavior can contradict. Our results are compared with new experiments on shape fluctuations of red-blood cell membranes, and demonstrate how the physical nature of the motors in this system can be revealed using these global measures of nonequilibrium.

Curvature-driven lipid sorting in biomembranes

It has often been suggested that the high curvature of transport intermediates in cells may be a sufficient means to segregate different lipid populations based on the relative energy costs of forming bent membranes. In this review, we present in vitro experiments that highlight the essential physics of lipid sorting at thermal equilibrium: It is driven by a trade-off between bending energy, mixing entropy, and interactions between species. We collect evidence that lipid sorting depends strongly on lipid-lipid and protein-lipid interactions, and hence on the underlying composition of the membrane and on the presence of bound proteins.

Stretching and relaxation of vesicles

We study the shape relaxation of spherical giant unilamellar vesicles which have been deformed far from equilibrium into ellipsoids using optical tweezers. The relaxation back to a sphere is determined by elastic constants of the vesicles, and their excess area, parameters that are obtained for each stretched vesicle from shape fluctuations in thermal equilibrium, as well as low Reynolds number fluid flow. The relaxation time could be compared favorably to a simple formula which encompasses the joint effect of membrane rigidity and fluid flow. The time constant of the stretched vesicle is slower than that of its thermal fluctuations, which agrees with a recent theory; however, it is one order of magnitude faster than predicted.

The vesicle trafficking protein Sar1 lowers lipid membrane rigidity

The sculpting of membranes into dynamic, curved shapes is central to intracellular cargo trafficking. Though the generation of membrane curvature during trafficking necessarily involves both lipids and membrane-associated proteins, current mechanistic views focus primarily on the formation of rigid cages and curved scaffolds by protein assemblies. Here we report on a different mechanism for the control of membrane deformation, unrelated to the imposition of predefined curvature, involving modulation of membrane material properties: Sar1, a GTPase that regulates vesicle trafficking from the endoplasmic reticulum, lowers the rigidity of the lipid bilayer membrane to which it binds. In vitro assays in which optically trapped microspheres create controlled membrane deformations revealed a monotonic decline in bending modulus as a function of Sar1 concentration, down to nearly zero rigidity, indicating a dramatic lowering of the energetic cost of curvature generation. This is the first demonstration that a vesicle trafficking protein lowers the rigidity of its target membrane, leading to a new conceptual framework for vesicle biogenesis.

Precise and millidegree stable temperature control for fluorescence imaging: application to phase transitions in lipid membranes

We present the design of a custom temperature-controlled chamber suitable for water or oil immersion fluorescence microscopy and its application to phase behavior in lipid bilayer vesicles. The apparatus is self-contained and portable, suitable for multiuser microscopy facilities. It offers a higher temperature resolution and stability than any comparable commercial apparatus, on the order of millidegrees. We demonstrate the utility of the system in the study of miscibility transitions in model membranes. The temperature-dependent phase behavior of model membrane systems that display liquid-ordered (L(o)) phase coexistence with the liquid-disordered (L(d)) phase is relevant to understanding the existence of heterogeneities in biological cell plasma membranes, ubiquitously termed "lipid rafts."

Dynamics of biomembranes with active multiple-state inclusions

Nonequilibrium dynamics of biomembranes with active multiple-state inclusions is considered. The inclusions represent protein molecules which perform cyclic internal conformational motions driven by the energy brought with adenosine triphosphate (ATP) ligands. As protein conformations cyclically change, this induces hydrodynamical flows and also directly affects the local curvature of a membrane. On the other hand, variations in the local curvature of the membrane modify the transition rates between conformational states in a protein, leading to a feedback in the considered system. Moreover, active inclusions can move diffusively through the membrane so that their surface concentration varies. The kinetic description of this system is constructed and the stability of the uniform stationary state is analytically investigated. We show that, as the rate of supply of chemical energy is increased above a certain threshold, this uniform state becomes unstable and stationary or traveling waves spontaneously develop in the system. Such waves are accompanied by periodic spatial variations of the membrane curvature and the inclusion density. For typical parameter values, their characteristic wavelengths are of the order of hundreds of nanometers. For traveling waves, the characteristic frequency is of the order of a thousand Hz or less. The predicted instabilities are possible only if at least three internal inclusion states are present.

Diffusing proteins on a fluctuating membrane: analytical theory and simulations

Using analytical calculations and computer simulations, we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the membrane shape through its spontaneous curvature and bending rigidity. The lateral motion of the protein may be viewed as diffusion in an effective potential, hence, the effective mobility is always reduced compared to the case of free diffusion. Using a rigorous path-integral approach, we derive an analytical expression for the effective diffusion coefficient for small ratios of temperature and bending rigidity, which is the biologically relevant limit. Simulations show very good quantitative agreement with our analytical result. The analysis of the correlation functions contributing to the diffusion coefficient shows that the correlations between the stochastic force of the protein and the response in the membrane shape are responsible for the reduction. Our quantitative analysis of the membrane height correlation spectrum shows an influence of the protein-membrane interaction causing a distinctly altered wave-vector dependence compared to a free membrane. Furthermore, the time correlations exhibit the two relevant time scales of the system: that of membrane fluctuations and that of lateral protein diffusion with the latter typically much longer than the former. We argue that the analysis of the long-time decay of membrane height correlations can thus provide a new means to determine the effective diffusion coefficient of proteins in the membrane.

Domain-driven morphogenesis of cellular membranes

Cellular membrane systems delimit and organize the intracellular space. Most of the morphological rearrangements in cells involve the coordinated remodeling of the lipid bilayer, the core of the membranes. This process is generally thought to be initiated and coordinated by specialized protein machineries. Nevertheless, it has become increasingly evident that the most essential part of the geometric information and energy required for membrane remodeling is supplied via the cooperative and synergistic action of proteins and lipids, as cellular shapes are constructed using the intrinsic dynamics, plasticity and self-organizing capabilities provided by the lipid bilayer. Here, we analyze the essential role of proteo-lipid membrane domains in conducting and coordinating morphological remodeling in cells.

Dynamics of vesicle unbinding under axisymmetric flow

The competition between adhesion and external flow to unbind settled vesicles from substrates is investigated. An experimental setup is developed to apply a hydrodynamic pulling force in the range of a few piconewtons to a vesicle with retained axisymmetry. In the limit of a small excess of membrane area, vesicles are found to transit during unbinding from a process of fluid film thickening at constant contact area to a finite-time process of contact radius drop to zero with an exponent 1/2. Both characteristic times vary linearly with the inverse flow rate. On the contrary, deflated vesicles under a moderate pulling force exhibit a decrease of contact area at a constant film thickness before a film thickening.

Rhythmic pore dynamics in a shrinking lipid vesicle

The rhythmic motion of membrane pore behavior under nonequilibrium conditions was studied. Application of the surfactant triton X-100 (TX-100) caused lipid vesicles to exhibit two types of shrinking dynamics with pore generation, which depended on both the size of the vesicles and the concentration of added TX-100. Small vesicles and the addition of a low concentration of TX-100 resulted in rhythmic-pore dynamics, where a transient pore was generated within a vesicle in a repetitive manner. In contrast, large vesicles and a high concentration of TX-100 led to continuous-pore dynamics, where the vesicle maintained an open pore during the shrinking process. In the rhythmic-pore membrane, long-cycle oscillation was observed with large vesicles and a low concentration TX-100. The period of one cycle decreased with a decrease in the vesicle size and an increase in the TX-100 concentration. We discuss the mechanism of these trends by considering the elastic free energy of the membrane.

Physical model for the width distribution of axons

The distribution of widths of axons was recently investigated, and was found to have a distinct peak at an optimized value. The optimized axon width at the peak may arise from the conflicting demands of minimizing energy consumption and assuring signal transmission reliability. The distribution around this optimized value is found to have a distinct non-Gaussian shape, with an exponential "tail". We propose here a mechanical model whereby this distribution arises from the interplay between the elastic energy of the membrane surrounding the axon core, the osmotic pressure induced by the neurofilaments inside the axon bulk, and active processes that remodel the microtubules and neurofilaments inside the axon. The axon's radius of curvature can be determined by the cell's control of the osmotic pressure difference across the membrane, the membrane tension or by changing the composition of the different components of the membrane. We find that the osmotic pressure, determined by the neurofilaments, seems to be the dominant control parameter.

Hybrid elastic and discrete-particle approach to biomembrane dynamics with application to the mobility of curved integral membrane proteins

We introduce a simulation strategy to consistently couple continuum biomembrane dynamics to the motion of discrete biological macromolecules residing within or on the membrane. The methodology is used to study the diffusion of integral membrane proteins that impart a curvature on the bilayer surrounding them. Such proteins exhibit a substantial reduction in diffusion coefficient relative to "flat" proteins; this effect is explained by elementary hydrodynamic considerations.

Membrane tension lowering induced by protein activity

Using videomicroscopy we present measurements of the fluctuation spectrum of giant vesicles containing bacteriorhodopsin pumps. When the pumps are activated, we observe a significant increase of the fluctuations in the low wave vector region, which we interpret as due to a lowering of the effective tension of the membrane.

Direct calculation from the stress tensor of the lateral surface tension of fluctuating fluid membranes

From the tangential and normal stresses associated with the Helfrich Hamiltonian, we calculate the lateral force per unit length, tau, exerted by a planar, fluctuating membrane, as a function of the membrane tension sigma and bending rigidity kappa. We unveil a confusion in the literature concerning the derivation of tau, and we argue, contrary to the present understanding, that tau should differ from the tensionlike coefficient of the fluctuation spectrum. Nontrivial implications concerning the Laplace pressure in vesicles and its relation with the excess area are discussed.

The stochastic dynamics of filopodial growth

A filopodium is a cytoplasmic projection, exquisitely built and regulated, which extends from the leading edge of the migrating cell, exploring the cell's neighborhood. Commonly, filopodia grow and retract after their initiation, exhibiting rich dynamical behaviors. We model the growth of a filopodium based on a stochastic description which incorporates mechanical, physical, and biochemical components. Our model provides a full stochastic treatment of the actin monomer diffusion and polymerization of each individual actin filament under stress of the fluctuating membrane. We investigated the length distribution of individual filaments in a growing filopodium and studied how it depends on various physical parameters. The distribution of filament lengths turned out to be narrow, which we explained by the negative feedback created by the membrane load and monomeric G-actin gradient. We also discovered that filopodial growth is strongly diminished upon increasing retrograde flow, suggesting that regulating the retrograde flow rate would be a highly efficient way to control filopodial extension dynamics. The filopodial length increases as the membrane fluctuations decrease, which we attributed to the unequal loading of the membrane force among individual filaments, which, in turn, results in larger average polymerization rates. We also observed significant diffusional noise of G-actin monomers, which leads to smaller G-actin flux along the filopodial tube compared with the prediction using the diffusion equation. Overall, partial cancellation of these two fluctuation effects allows a simple mean field model to rationalize most of our simulation results. However, fast fluctuations significantly renormalize the mean field model parameters. The biological significance of our filopodial model and avenues for future development are also discussed.

Fluctuations of coupled fluid and solid membranes with application to red blood cells

The fluctuation spectra and the intermembrane interaction of two membranes at a fixed average distance are investigated. Each membrane can either be a fluid or a solid membrane, and in isolation, its fluctuations are described by a bare or a wave-vector-dependent bending modulus, respectively. The membranes interact via their excluded-volume interaction; the average distance is maintained by an external, homogeneous pressure. For strong coupling, the fluctuations can be described by a single, effective membrane that combines the elastic properties. For weak coupling, the fluctuations of the individual, noninteracting membranes are recovered. The case of a composite membrane consisting of one fluid and one solid membrane can serve as a microscopic model for the plasma membrane and cytoskeleton of the red blood cell. We find that, despite the complex microstructure of bilayers and cytoskeletons in a real cell, the fluctuations with wavelengths lambda greater, similar 400 nm are well described by the fluctuations of a single, polymerized membrane (provided that there are no inhomogeneities of the microstructure). The model is applied to the fluctuation data of discocytes ("normal" red blood cells), a stomatocyte, and an echinocyte. The elastic parameters of the membrane and an effective temperature that quantifies active, metabolically driven fluctuations are extracted from the experiments.

Responsive viscoelastic giant lipid vesicles filled with a poly(N-isopropylacrylamide) artificial cytoskeleton

Responsive giant lipid vesicles filled with aqueous PolyNipam sol (SFV) or gel (GFV) were prepared by ultra-violet polymerisation performed in situ. Upon crossing the lower critical transition temperature of PolyNipam, SFVs and GFVs undergo a significant change of their structural and mechanical properties or a drastic volume transition, respectively. Rheometric and micropipette experiments show that both internal viscosity of SFVs and internal shear modulus of GFVs are tunable over several orders of magnitude and lie in the range observed for living cells. Moreover, the vesicle membrane is strongly bound to the internal polymer medium, making these systems interesting for mimicking the basic mechanical behaviour of passive living cells.

Active membranes studied by X-ray scattering

In view of recent theories of "active" membranes, we have studied multilamellar phospholipid membrane stacks with reconstituted transmembrane protein bacteriorhodopsin (BR) under different illumination conditions by X-ray scattering. The light-active protein is considered as an active constituent which drives the system out of equilibrium and is predicted to change the collective fluctuation properties of the membranes. Using X-ray reflectivity, X-ray non-specular (diffuse) scattering, and grazing incidence scattering, we find no detectable change in the scattering curves when changing the illumination condition. In particular the intermembrane spacing d remains constant, after eliminating hydration-related artifacts by design of a suitable sample environment. The absence of any observable non-equilibrium effects in the experimental window is discussed in view of the relevant parameters and recent theories.

1/f ruffle oscillations in plasma membranes of amphibian epithelial cells under normal and inverted gravitational orientations

Membrane ruffle fluctuations of amphibian epithelial cells A6 (CCL102) cultured in normal and upside down oriented plates have been analyzed through video microscopy. Our results reveal that their edge ruffle fluctuations exhibit a stochastic dynamics with 1/f(alpha) power spectrum over at least two decades at low frequencies and long range correlated, self-affine lateral border profiles. In a few and small areas of the membrane, probably nearby focal contacts, we found periodic oscillations which could be induced by myosin driven contraction of stress fibers. Furthermore, whereas the different gravitational orientations had none or little effect on the structure (power spectra and surface roughness) of these membrane ruffle fluctuations, their dynamic parameters were differentially affected. Indeed, the decay time of ruffles remained unchanged, but the period of lamellipodia oscillations near the focal adhesion points was significantly altered in A6 cells cultured upside down.

Negative tension induced by lipid uptake

Membrane fusion is an important process in cell biology. While the molecular mechanisms of fusion are actively studied at a very local scale, the consequences of fusion at a larger scale on the shape and stability of the membrane are still not explored. In this Letter, the evolution of the membrane tension during the fusion of positive small unilamellar vesicles with a negative giant unilamellar vesicle has been experimentally investigated and compared to an existing theoretical model. The tension has been deduced using videomicroscopy from the measurement of the fluctuation spectrum and of the time correlation function of the fluctuations. We show that fusion induces a strong decrease in the effective tension of the membrane which eventually reaches negative values. Under these conditions, we show that localized instabilities appear on the vesicle. The membrane finally collapses, forming dense lipid structures.

Fluctuation spectrum of quasispherical membranes with force-dipole activity

The fluctuation spectrum of a quasispherical vesicle with active membrane proteins is calculated. The activity of the proteins is modeled as the proteins pushing on their surroundings giving rise to nonlocal force distributions. Both the contributions from the thermal fluctuations of the active protein densities and the temporal noise in the individual active force distributions of the proteins are taken into account. The noise in the individual force distributions is found to become significant at short wavelengths.

Mechanics of nonplanar membranes with force-dipole activity

A study is made of how active membrane proteins can modify the long wavelength mechanics of fluid membranes. The activity of the proteins is modelled as disturbing the protein surroundings through nonlocal force distributions of which a force-dipole distribution is the simplest example. An analytic expression describing how the activity modifies the force-balance equation for the membrane surface is obtained in the form of a moment expansion of the force distribution. This expression allows for further studies of the consequences of the activity for nonplanar membranes. In particular the active contributions to mechanical properties such as tension and bending moments become apparent. It is also explained how the activity can induce a hydrodynamic attraction between the active proteins in the membrane.

Diffusion in curved fluid membranes

We analyze theoretically the effects of curvature on the diffusion in a fluid membrane, within the Saffman-Delbrück hydrodynamic model. We calculate the effect of curvature on the intrinsic fluidity of a membrane through changes in its thickness, for both static or fluctuating curvature. We treat both thermal curvature fluctuations, and fluctuations due to active processes. Such curvature fluctuations increase the average membrane thickness and diminish the projected area, thereby decreasing the diffusion coefficient. This calculation allows us to predict the effect of shear flow on the membrane diffusion, and to compare to observations on living cells.

Nonequilibrium membrane fluctuations driven by active proteins

We extend a model for nonthermal membrane undulations driven by active (adenosine triphosphate-dependent or light-harvesting) membrane proteins [N. Gov, Phys. Rev. Lett. 93, 268104 (2004)]. The present model accounts for the fact that proteins can diffuse laterally across the membrane surface and that individual proteins are expected to exert forces preferentially in one normal direction over the other (due to their orientation within the bilayer). The addition of these effects alters the scaling of fluctuation amplitudes with system size. Additionally, theoretical arguments and dynamic simulations both suggest that, in certain regimes, the probability distribution of fluctuation amplitudes is expected to be non-Gaussian (in contrast to thermal systems).

Autonomously moving nanorods at a viscous interface

We study the autonomous motion of catalytic nanorods in Gibbs monolayers. The catalytic activity of the rods on a hydrogen peroxide aqueous subphase gives rise to anomalous translational and rotational diffusion. The rods perform a Levy-walk superdiffusive motion that can be decomposed into thermal orientation fluctuations and an active motion of the rods with a constant velocity along their long axis. Since interfacial dissipation increases relative to bulk phase dissipation when miniaturizing the size of objects moving in the interface, the autonomous nanorods allow for precise measurements of surface shear viscosities as low as a few nN s/m. The cross over from active motion toward passive diffusion when increasing the surfactant concentration is explained by a loss of friction asymmetry of the rods.

Dynamics of membranes driven by actin polymerization

A motile cell, when stimulated, shows a dramatic increase in the activity of its membrane, manifested by the appearance of dynamic membrane structures such as lamellipodia, filopodia, and membrane ruffles. The external stimulus turns on membrane bound activators, like Cdc42 and PIP2, which cause increased branching and polymerization of the actin cytoskeleton in their vicinity leading to a local protrusive force on the membrane. The emergence of the complex membrane structures is a result of the coupling between the dynamics of the membrane, the activators, and the protrusive forces. We present a simple model that treats the dynamics of a membrane under the action of actin polymerization forces that depend on the local density of freely diffusing activators on the membrane. We show that, depending on the spontaneous membrane curvature associated with the activators, the resulting membrane motion can be wavelike, corresponding to membrane ruffling and actin waves, or unstable, indicating the tendency of filopodia to form. Our model also quantitatively explains a variety of related experimental observations and makes several testable predictions.

Reversible photoswitching in a cell-sized vesicle

A photosensitive amphiphilic molecule can switch the shape of an assembled vesicle as determined by microscopic observation. Photoisomerization induces a change in membrane fluctuation behavior or a morphological transition between ellipsoid and bud shapes, depending on the asymmetrical degree of the initial shape. The mechanism of this reversible photoswitching in the vesicle morphology is interpreted in terms of a change in the effective cross-sectional area of the photosensitive molecule.