Diffusion on membrane tubes: a highly discriminatory test of the Saffman-Delbruck theory

Research progress on the regulatory role of cell membrane surface tension in cell behavior

Cell membrane surface tension has emerged as a pivotal biophysical factor governing cell behavior and fate. This review systematically delineates recent advances in techniques for cell membrane surface tension quantification, mechanosensing mechanisms, and regulatory roles of cell membrane surface tension in modulating major cellular processes. Micropipette aspiration, tether pulling, and newly developed fluorescent probes enable the measurement of cell membrane surface tension with spatiotemporal precision. Cells perceive cell membrane surface tension via conduits including mechanosensitive ion channels, curvature-sensing proteins (e.g. BAR domain proteins), and cortex-membrane attachment proteins (e.g. ERM proteins). Through membrane receptors like integrins, cells convert mechanical cues into biochemical signals. This conversion triggers cytoskeletal remodeling and extracellular matrix interactions in response to environmental changes. Elevated cell membrane surface tension suppresses cell spreading, migration, and endocytosis while facilitating exocytosis. Moreover, reduced cell membrane surface tension promotes embryonic stem cell differentiation and cancer cell invasion, underscoring cell membrane surface tension as a regulator of cell plasticity. Outstanding questions remain regarding cell membrane surface tension regulatory mechanisms and roles in tissue development/disease in vivo. Emerging tools to manipulate cell membrane surface tension with high spatiotemporal control in combination with omics approaches will facilitate the elucidation of cell membrane surface tension-mediated effects on signaling networks across various cell types/states. This will accelerate the development of cell membrane surface tension-based biomarkers and therapeutics for regenerative medicine and cancer. Overall, this review provides critical insights into cell membrane surface tension as a potent orchestrator of cell function, with broader impacts across mechanobiology.

A Diffusion Model to Quantify Membrane Repair Process in Listeria monocytogenes Exposed to High Pressure Processing Based on Fluorescence Microscopy Data

The effects of environmental stresses on microorganisms have been well-studied, and cellular responses to stresses such as heat, cold, acids, and salts have been extensively discussed. Although high pressure processing (HPP) is becoming more popular as a preservation method in the food industry, the characteristics of the cellular damage caused by high pressure are unclear, and the microbial response to this stress has not yet been well-explored. We exposed the pathogen Listeria monocytogenes to HPP (400 MPa, 8 min, 8°C) and found that the high pressure created plasma membrane pores. Using a common staining technique involving propidium iodide (PI) combined with high-frequency fluorescence microscopy, we monitored the rate of diffusion of PI molecules into hundreds of bacterial cells through these pores on days 0, 1, 2, 3, and 4 after pressurization. We also developed a mathematical dynamic model based on mass transfer and passive diffusion laws, calibrated using our microscopy experiments, to evaluate the response of bacteria to HPP. We found that the rate of diffusion of PI into the cells decreased over the 4 consecutive days after exposure to HPP, indicating repair of the pressure-created membrane pores. The model suggested a temporal change in the size of pores until closure. To the best of our knowledge, this is the first time that pressure-created membrane pores have been quantitatively described and shown to diminish with time. In addition, we found that the membrane repair rate in response to HPP was linear, and growth was temporarily arrested at the population level during the repair period. These results support the existence of a progressive repair process in some of the cells that take up PI, which can therefore be considered as being sub-lethally injured rather than dead. Hence, we showed that a subgroup of bacteria survived HPP and actively repaired their membrane pores.

Diffusion on Membrane Domes, Tubes, and Pearling Structures

Diffusion is a fundamental mechanism for protein distribution in cell membranes. These membranes often exhibit complex shapes, which range from shallow domes to elongated tubular or pearl-like structures. Shape complexity of the membrane influences the diffusive spreading of proteins and molecules. Despite the importance membrane geometry plays in these diffusive processes, it is challenging to establish the dependence between diffusion and membrane morphology. We solve the diffusion equation numerically on various static curved shapes representative for experimentally observed membrane shapes. Our results show that membrane necks become diffusion barriers. We determine the diffusive half-time, i.e., the time that is required to reduce the amount of protein in the budded region by one half, and find a quadratic relation between the diffusive half-time and the averaged mean curvature of the membrane shape, which we rationalize by a scaling law. Our findings thus help estimate the characteristic diffusive timescale based on the simple measure of membrane mean curvature.

Dynamics of passive and active membrane tubes

Utilising Onsager's variational formulation, we derive dynamical equations for the relaxation of a fluid membrane tube in the limit of small deformation, allowing for a contrast of solvent viscosity across the membrane and variations in surface tension due to membrane incompressibility. We compute the relaxation rates, recovering known results in the case of purely axis-symmetric perturbations and making new predictions for higher order (azimuthal) m-modes. We analyse the long and short wavelength limits of these modes by making use of various asymptotic arguments. We incorporate stochastic terms to our dynamical equations suitable to describe both passive thermal forces and non-equilibrium active forces. We derive expressions for the fluctuation amplitudes, an effective temperature associated with active fluctuations, and the power spectral density for both the thermal and active fluctuations. We discuss an experimental assay that might enable measurement of these fluctuations to infer the properties of the active noise. Finally we discuss our results in the context of active membranes more generally and give an overview of some open questions in the field.

Getting around the cell: physical transport in the intracellular world

Eukaryotic cells face the challenging task of transporting a variety of particles through the complex intracellular milieu in order to deliver, distribute, and mix the many components that support cell function. In this review, we explore the biological objectives and physical mechanisms of intracellular transport. Our focus is on cytoplasmic and intra-organelle transport at the whole-cell scale. We outline several key biological functions that depend on physically transporting components across the cell, including the delivery of secreted proteins, support of cell growth and repair, propagation of intracellular signals, establishment of organelle contacts, and spatial organization of metabolic gradients. We then review the three primary physical modes of transport in eukaryotic cells: diffusive motion, motor-driven transport, and advection by cytoplasmic flow. For each mechanism, we identify the main factors that determine speed and directionality. We also highlight the efficiency of each transport mode in fulfilling various key objectives of transport, such as particle mixing, directed delivery, and rapid target search. Taken together, the interplay of diffusion, molecular motors, and flows supports the intracellular transport needs that underlie a broad variety of biological phenomena.

Conventional analysis of movement on non-flat surfaces like the plasma membrane makes Brownian motion appear anomalous

Cells are neither flat nor smooth, which has serious implications for prevailing plasma membrane models and cellular processes like cell signalling, adhesion and molecular clustering. Using probability distributions from diffusion simulations, we demonstrate that 2D and 3D Euclidean distance measurements substantially underestimate diffusion on non-flat surfaces. Intuitively, the shortest within surface distance (SWSD), the geodesic distance, should reduce this problem. The SWSD is accurate for foldable surfaces but, although it outperforms 2D and 3D Euclidean measurements, it still underestimates movement on deformed surfaces. We demonstrate that the reason behind the underestimation is that topographical features themselves can produce both super- and subdiffusion, i.e. the appearance of anomalous diffusion. Differentiating between topography-induced and genuine anomalous diffusion requires characterising the surface by simulating Brownian motion on high-resolution cell surface images and a comparison with the experimental data.

Many-particle mobility and diffusion tensors for objects in viscous sheets

We derive a mobility tensor for many cylindrical objects embedded in a viscous sheet. This tensor guarantees a positive dissipation rate for any configuration of particles and forces, analogous to the Rotne-Prager-Yamakawa tensor for spherical particles in a three-dimensional viscous fluid. We test our result for a ring of radially driven particles, demonstrating the positive-definite property at all particle densities. The derived tensor can be utilized in Brownian dynamics simulations with hydrodynamic interactions for such systems as proteins in biomembranes and inclusions in free-standing liquid films.

Revealing the Effects of Nanoscale Membrane Curvature on Lipid Mobility

Recent advances in nanoengineering and super-resolution microscopy have enabled new capabilities for creating and observing membrane curvature. However, the effects of curvature on single-lipid diffusion have yet to be revealed. The simulations presented here describe the capabilities of varying experimental methods for revealing the effects of nanoscale curvature on single-molecule mobility. Traditionally, lipid mobility is revealed through fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS), and single particle tracking (SPT). However, these techniques vary greatly in their ability to detect the effects of nanoscale curvature on lipid behavior. Traditionally, FRAP and FCS depend on diffraction-limited illumination and detection. A simulation of FRAP shows minimal effects on lipids diffusion due to a 50 nm radius membrane bud. Throughout the stages of the budding process, FRAP detected minimal changes in lipid recovery time due to the curvature versus flat membrane. Simulated FCS demonstrated small effects due to a 50 nm radius membrane bud that was more apparent with curvature-dependent lipid mobility changes. However, SPT achieves a sub-diffraction-limited resolution of membrane budding and lipid mobility through the identification of the single-lipid positions with ≤15 nm spatial and ≤20 ms temporal resolution. By mapping the single-lipid step lengths to locations on the membrane, the effects of membrane topography and curvature could be correlated to the effective membrane viscosity. Single-fluorophore localization techniques, such SPT, can detect membrane curvature and its effects on lipid behavior. These simulations and discussion provide a guideline for optimizing the experimental procedures in revealing the effects of curvature on lipid mobility and effective local membrane viscosity.

Analysis of diffusion in curved surfaces and its application to tubular membranes

Diffusion of particles in curved surfaces is inherently complex compared with diffusion in a flat membrane, owing to the nonplanarity of the surface. The consequence of such nonplanar geometry on diffusion is poorly understood but is highly relevant in the case of cell membranes, which often adopt complex geometries. To address this question, we developed a new finite element approach to model diffusion on curved membrane surfaces based on solutions to Fick's law of diffusion and used this to study the effects of geometry on the entry of surface-bound particles into tubules by diffusion. We show that variations in tubule radius and length can distinctly alter diffusion gradients in tubules over biologically relevant timescales. In addition, we show that tubular structures tend to retain concentration gradients for a longer time compared with a comparable flat surface. These findings indicate that sorting of particles along the surfaces of tubules can arise simply as a geometric consequence of the curvature without any specific contribution from the membrane environment. Our studies provide a framework for modeling diffusion in curved surfaces and suggest that biological regulation can emerge purely from membrane geometry.

Curvature correction to the mobility of fluid membrane inclusions

Using rigorous low-Reynolds-number hydrodynamic theory on curved surfaces, we provide, via a Stokeslet-type approach, a general and concise expression for the leading-order curvature correction to the canonical, planar, Saffman-Delbrück value of the diffusion constant for a small inclusion embedded in an arbitrarily (albeit weakly) curved fluid membrane. In order to demonstrate the efficacy and utility of this general result, we apply our theory to the specific case of calculating the diffusion coefficient of a locally curvature inducing membrane inclusion. By including both the effects of inclusion and membrane elasticity, as well as their respective thermal shape fluctuations, excellent agreement is found with recently published experimental data on the surface tension dependent mobility of membrane bound inclusions.

Mobility Measurements Probe Conformational Changes in Membrane Proteins due to Tension

The function of membrane-embedded proteins such as ion channels depends crucially on their conformation. We demonstrate how conformational changes in asymmetric membrane proteins may be inferred from measurements of their diffusion. Such proteins cause local deformations in the membrane, which induce an extra hydrodynamic drag on the protein. Using membrane tension to control the magnitude of the deformations, and hence the drag, measurements of diffusivity can be used to infer-via an elastic model of the protein-how conformation is changed by tension. Motivated by recent experimental results [Quemeneur et al., Proc. Natl. Acad. Sci. U.S.A. 111, 5083 (2014)], we focus on KvAP, a voltage-gated potassium channel from Aeropyrum pernix. The conformation of KvAP is found to change considerably due to tension, with its "walls," where the protein meets the membrane, undergoing significant angular strains. The torsional stiffness is determined to be 26.8k(B)T per radian at room temperature. This has implications for both the structure and the function of such proteins in the environment of a tension-bearing membrane.

Dynamic assembly of polymer nanotube networks via kinesin powered microtubule filaments

We describe for the first time how biological nanomotors may be used to actively self-assemble mesoscale networks composed of diblock copolymer nanotubes. The collective force generated by multiple kinesin nanomotors acting on a microtubule filament is large enough to overcome the energy barrier required to extract nanotubes from polymer vesicles comprised of poly(ethylene oxide-b-butadiene) in spite of the higher force requirements relative to extracting nanotubes from lipid vesicles. Nevertheless, large-scale polymer networks were dynamically assembled by the motors. These networks displayed enhanced robustness, persisting more than 24 h post-assembly (compared to 4-5 h for corresponding lipid networks). The transport of materials in and on the polymer membranes differs substantially from the transport on analogous lipid networks. Specifically, our data suggest that polymer mobility in nanotubular structures is considerably different from planar or 3D structures, and is stunted by 1D confinement of the polymer subunits. Moreover, quantum dots adsorbed onto polymer nanotubes are completely immobile, which is related to this 1D confinement effect and is in stark contrast to the highly fluid transport observed on lipid tubules.

Barriers in the brain: resolving dendritic spine morphology and compartmentalization

Dendritic spines are micron-sized protrusions that harbor the majority of excitatory synapses in the central nervous system. The head of the spine is connected to the dendritic shaft by a 50-400 nm thin membrane tube, called the spine neck, which has been hypothesized to confine biochemical and electric signals within the spine compartment. Such compartmentalization could minimize interspinal crosstalk and thereby support spine-specific synapse plasticity. However, to what extent compartmentalization is governed by spine morphology, and in particular the diameter of the spine neck, has remained unresolved. Here, we review recent advances in tool development - both experimental and theoretical - that facilitate studying the role of the spine neck in compartmentalization. Special emphasis is given to recent advances in microscopy methods and quantitative modeling applications as we discuss compartmentalization of biochemical signals, membrane receptors and electrical signals in spines. Multidisciplinary approaches should help to answer how dendritic spine architecture affects the cellular and molecular processes required for synapse maintenance and modulation.

Confined mobility in biomembranes modeled by early stage Brownian motion

An equation of motion, derived from the fractal analysis of the Brownian particle trajectory, makes it possible to calculate the time dependence of the mean square displacement for early times, before the Einstein formula becomes valid. The diffusion coefficient increases with the distance travelled which can be restricted by the geometrical conditions. The corresponding diffusion coefficient cannot increase further to achieve a value characteristic for unrestricted environment. Explicit formula is derived for confined diffusivity related to the unrestricted one as dependent on the maximum particle mean square displacement possible normalized by the square of its mean free path. The model describes the lipid and protein diffusion in tubular membranes with different radii, originally fitted by the modified Saffman-Delbrück equation, and the lateral mobility of synthetic model peptides for which the diffusion coefficient is inversely proportional to the radius of the diffusing object and to the thickness of the membrane.

Membrane shape modulates transmembrane protein distribution

Although membrane shape varies greatly throughout the cell, the contribution of membrane curvature to transmembrane protein targeting is unknown because of the numerous sorting mechanisms that take place concurrently in cells. To isolate the effect of membrane shape, we used cell-sized giant unilamellar vesicles (GUVs) containing either the potassium channel KvAP or the water channel AQP0 to form membrane nanotubes with controlled radii. Whereas the AQP0 concentrations in flat and curved membranes were indistinguishable, KvAP was enriched in the tubes, with greater enrichment in more highly curved membranes. Fluorescence recovery after photobleaching measurements showed that both proteins could freely diffuse through the neck between the tube and GUV, and the effect of each protein on membrane shape and stiffness was characterized using a thermodynamic sorting model. This study establishes the importance of membrane shape for targeting transmembrane proteins and provides a method for determining the effective shape and flexibility of membrane proteins.

A continuous network of lipid nanotubes fabricated from the gliding motility of kinesin powered microtubule filaments

Synthetic interconnected lipid nanotube networks were fabricated on the millimeter scale based on the simple, cooperative interaction between phospholipid vesicles and kinesin-microtubule (MT) transport systems. More specifically, taxol-stabilized MTs, in constant 2D motion via surface absorbed kinesin, extracted and extended lipid nanotube networks from large Lα phase multilamellar liposomes (5-25 μm). Based on the properties of the inverted motility geometry, the total size of these nanofluidic networks was limited by MT surface density, molecular motor energy source (ATP), and total amount and physical properties of lipid source material. Interactions between MTs and extended lipid nanotubes resulted in bifurcation of the nanotubes and ultimately the generation of highly branched networks of fluidically connected nanotubes. The network bifurcation was easily tuned by changing the density of microtubules on the surface to increase or decrease the frequency of branching. The ability of these networks to capture nanomaterials at the membrane surface with high fidelity was subsequently demonstrated using quantum dots as a model system. The diffusive transport of quantum dots was also characterized with respect to using these nanotube networks for mass transport applications.

Nonlinear sorting, curvature generation, and crowding of endophilin N-BAR on tubular membranes

The curvature of biological membranes is controlled by membrane-bound proteins. For example, during endocytosis, the sorting of membrane components, vesicle budding, and fission from the plasma membrane are mediated by adaptor and accessory proteins. Endophilin is a peripherally binding membrane protein that functions as an endocytic accessory protein. Endophilin's membrane tubulation capacity is well known. However, to understand the thermodynamic and mechanical aspects of endophilin function, experimental measurements need to be compared to quantitative theoretical models. We present measurements of curvature sorting and curvature generation of the endophilin A1 N-BAR domain on tubular membranes pulled from giant unilamellar vesicles. At low concentration, endophilin functions primarily as a membrane curvature sensor; at high concentrations, it also generates curvature. We determine the spontaneous curvature induced by endophilin and observe sigmoidal curvature/composition coupling isotherms that saturate at high membrane tensions and protein solution concentrations. The observation of saturation is supported by a strong dependence of lateral diffusion coefficients on protein density on the tether membrane. We develop a nonlinear curvature/composition coupling model that captures our experimental observations. Our model predicts a curvature-induced phase transition among two states with varying protein density and membrane curvature. This transition could act as a switch during endocytosis.

Processivity and collectivity of biomolecular motors extracting membrane nanotubes

Biomolecular motors can pull and viscously drag membranes. The resulting elongations include cell protrusions, tether networks, and sensorial tentacles. Here we focus on the extraction of a single tube from a vesicle. Via a force balance coupled to binding kinetics, we analytically determine the phase diagram of tube formation as function of the motor processivity, the surface viscosity of the membrane η'(m), and the density of motors on the vesicle ρ. Three tubulation mechanisms are identified: (i) tip pulling, due to the accumulation of motors at the leading edge of the membrane, (ii) viscous drag, emergent from the translation of motors along the tube, and (iii) hybrid extraction, such that tip pulling and viscous drag are equally important. For experimental values of η'(m) and ρ, we find that the growth of bionanotubes tends to be driven by viscous forces, whereas artificial membranes are dominated by tip pulling.

Lateral diffusion on tubular membranes: quantification of measurements bias

Single Particle Tracking (SPT) is a powerful technique for the analysis of the lateral diffusion of the lipid and protein components of biological membranes. In neurons, SPT allows the study of the real-time dynamics of receptors for neurotransmitters that diffuse continuously in and out synapses. In the simplest case where the membrane is flat and is parallel to the focal plane of the microscope the analysis of diffusion from SPT data is relatively straightforward. However, in most biological samples the membranes are curved, which complicates analysis and may lead to erroneous conclusions as for the mode of lateral diffusion. Here we considered the case of lateral diffusion in tubular membranes, such as axons, dendrites or the neck of dendritic spines. Monte Carlo simulations allowed us to evaluate the error in diffusion coefficient (D) calculation if the curvature is not taken into account. The underestimation is determined by the diameter of the tubular surface, the frequency of image acquisition and the degree of mobility itself. We found that projected trajectories give estimates that are 25 to 50% lower than the real D in case of 2D-SPT over the tubular surface. The use of 3D-SPT improved the measurements if the frequency of image acquisition was fast enough in relation to the mobility of the molecules and the diameter of the tube. Nevertheless, the calculation of D from the components of displacements in the axis of the tubular structure gave accurate estimate of D, free of geometrical artefacts. We show the application of this approach to analyze the diffusion of a lipid on model tubular membranes and of a membrane-bound GFP on neurites from cultured rat hippocampal neurons.

Mobility in geometrically confined membranes

Lipid and protein lateral mobility is essential for biological function. Our theoretical understanding of this mobility can be traced to the seminal work of Saffman and Delbrück, who predicted a logarithmic dependence of the protein diffusion coefficient (i) on the inverse of the size of the protein and (ii) on the "membrane size" for membranes of finite size [Saffman P, Delbrück M (1975) Proc Natl Acad Sci USA 72:3111-3113]. Although the experimental proof of the first prediction is a matter of debate, the second has not previously been thought to be experimentally accessible. Here, we construct just such a geometrically confined membrane by forming lipid bilayer nanotubes of controlled radii connected to giant liposomes. We followed the diffusion of individual molecules in the tubular membrane using single particle tracking of quantum dots coupled to lipids or voltage-gated potassium channels KvAP, while changing the membrane tube radius from approximately 250 to 10 nm. We found that both lipid and protein diffusion was slower in tubular membranes with smaller radii. The protein diffusion coefficient decreased as much as 5-fold compared to diffusion on the effectively flat membrane of the giant liposomes. Both lipid and protein diffusion data are consistent with the predictions of a hydrodynamic theory that extends the work of Saffman and Delbrück to cylindrical geometries. This study therefore provides strong experimental support for the ubiquitous Saffman-Delbrück theory and elucidates the role of membrane geometry and size in regulating lateral diffusion.

Pulling nanotubes from supported bilayers

The force required to form a nanoscale tube from a supported lipid bilayer (SLB) by pulling was measured using an atomic force microscope (AFM). The equilibrium membrane shape during an AFM pulling experiment was calculated and used to derive a general force-distance relationship for pulling a tube from an SLB. We compare these theoretical results with our experimental data and determine the tube radius, the force required to elongate the tube, and, consequently, the surface tension. For a dioleoylphosphatidylcholine (DOPC) SLB, the tension was found to be close to membrane rupture during the pulling experiment.

Rotational diffusion of the α(2a) adrenergic receptor revealed by FlAsH labeling in living cells

The fluorescein arsenical hairpin binder (FlAsH) shows much promise to determine the relative orientations of protein regions and structures even in living cells and in the plasma membrane. In this study, we characterized FlAsH's photophysical properties by steady-state anisotropy and time-resolved single photon counting for further applications with G-protein coupled receptors. We find that FlAsH has a relatively high initial anisotropy of 0.31 ± 0.01 and a three-component fluorescence lifetime with an average of 4.1 ± 0.1 ns. We characterized the FlAsH fluorophore orientation in the α(2A) adrenergic receptor revealing rigid orientations of FlAsH in the membrane plane for rotational correlation times of ∼50 ns in living cells. To elucidate the fluorophore-membrane orientation and rotational correlation time, an anisotropy treatment similar to that of another researcher (Axelrod, D. 1979. Biophys. J. 26:557-573) was developed. The rotational correlation times were observed to increase by up to 16 ns after agonist addition. The rotational correlation time also allowed for a comparison to the theoretical relationship between translational and rotational diffusion (originally proposed by Saffman, P. G., and M. Delbrück. 1975. Proc. Natl. Acad. Sci. USA. 72:3111-3113) and revealed a discrepancy of a factor between 10 and 100.

Recent applications of fluorescence recovery after photobleaching (FRAP) to membrane bio-macromolecules

This review examines some recent applications of fluorescence recovery after photobleaching (FRAP) to biopolymers, while mainly focusing on membrane protein studies. Initially, we discuss the lateral diffusion of membrane proteins, as measured by FRAP. Then, we talk about the use of FRAP to probe interactions between membrane proteins by obtaining fundamental information such as geometry and stoichiometry of the interacting complex. Afterwards, we discuss some applications of FRAP at the cellular level as well as the level of organisms. We conclude by comparing diffusion coefficients obtained by FRAP and several other alternative methods.

Dynamic sorting of lipids and proteins in membrane tubes with a moving phase boundary

Cellular organelle membranes maintain their integrity, global shape, and composition despite vigorous exchange among compartments of lipids and proteins during trafficking and signaling. Organelle homeostasis involves dynamic molecular sorting mechanisms that are far from being understood. In contrast, equilibrium thermodynamics of membrane mixing and sorting, particularly the phase behavior of binary and ternary model membrane mixtures and its coupling to membrane mechanics, is relatively well characterized. Elucidating the continuous turnover of live cell membranes, however, calls for experimental and theoretical membrane models enabling manipulation and investigation of directional mass transport. Here we introduce the phenomenon of curvature-induced domain nucleation and growth in membrane mixtures with fluid phase coexistence. Membrane domains were consistently observed to nucleate precisely at the junction between a strongly curved cylindrical (tube) membrane and a pipette-aspirated giant unilamellar vesicle. This experimental geometry mimics intracellular sorting compartments, because they often show tubular-vesicular membrane regions. Nucleated domains at tube necks were observed to present diffusion barriers to the transport of lipids and proteins. We find that curvature-nucleated domains grow with characteristic parabolic time dependence that is strongly curvature-dependent. We derive an analytical model that reflects the observed growth dynamics. Numerically calculated membrane shapes furthermore allow us to elucidate mechanical details underlying curvature-dependent directed lipid transport. Our observations suggest a novel dynamic membrane sorting principle that may contribute to intracellular protein and lipid sorting and trafficking.

Hydrodynamics in curved membranes: the effect of geometry on particulate mobility

We determine the particulate transport properties of fluid membranes with nontrivial geometries that are surrounded by viscous Newtonian solvents. Previously, this problem in membrane hydrodynamics was discussed for the case of flat membranes by Saffman and Delbrück [P. G. Saffman and M. Delbrück, Proc. Natl. Acad. Sci. U.S.A. 72, 3111 (1975)]. We review and develop the formalism necessary to consider the hydrodynamics of membranes with arbitrary curvature and show that the effect of local geometry is twofold. First, local Gaussian curvature introduces in-plane viscous stresses even for situations in which the velocity field is coordinate-independent. Secondly, even in the absence of Gaussian curvature, the geometry of the membrane modifies the momentum transport between the bulk fluids and the membrane. We illustrate these effects by examining in detail the mobilities of particles bound to spherical and cylindrical membranes. These two examples provide experimentally testable predictions for particulate mobilities and membrane velocity fields on giant unilamellar vesicles and membrane tethers. Finally, we use the examples of spherical and cylindrical membranes to demonstrate how the global geometry and topology of the membrane influences the membrane velocities and the particle mobilities.

Correlated diffusion of membrane proteins and their effect on membrane viscosity

We extend the Saffman theory of membrane hydrodynamics to account for the correlated motion of membrane proteins, along with the effect of protein concentration on that correlation and on the response of the membrane to stresses. Expressions for the coupling diffusion coefficients of protein pairs and their concentration dependence are derived in the limit of small protein size relative to the interprotein separation. The additional role of membrane viscosity as determining the characteristic length scale for membrane response leads to unusual concentration effects at large separation-the transverse coupling increases with protein concentration, whereas the longitudinal one becomes concentration-independent.

Sorting of lipids and proteins in membrane curvature gradients

The sorting of lipids and proteins in cellular trafficking pathways is a process of central importance in maintaining compartmentalization in eukaryotic cells. However, the mechanisms behind these sorting phenomena are currently far from being understood. Among several mechanistic suggestions, membrane curvature has been invoked as a means to segregate lipids and proteins in cellular sorting centers. To assess this hypothesis, we investigate the sorting of lipid analog dye trace components between highly curved tubular membranes and essentially flat membranes of giant unilamellar vesicles. Our experimental findings indicate that intracellular lipid sorting, contrary to frequent assumptions, is unlikely to occur by lipids fitting into membrane regions of appropriate curvature. This observation is explained in the framework of statistical mechanical lattice models that show that entropy, rather than curvature energy, dominates lipid distribution in the absence of strongly preferential lateral intermolecular interactions. Combined with previous findings of curvature induced phase segregation, we conclude that lipid cooperativity is required to enable efficient sorting. In contrast to lipid analog dyes, the peripheral membrane binding protein Cholera toxin subunit B is effectively curvature-sorted. The sorting of Cholera toxin subunit B is rationalized by statistical models. We discuss the implications of our findings for intracellular sorting mechanisms.

Membrane nanotubes physically connect T cells over long distances presenting a novel route for HIV-1 transmission

Transmission of HIV-1 via intercellular connections has been estimated as 100-1000 times more efficient than a cell-free process, perhaps in part explaining persistent viral spread in the presence of neutralizing antibodies. Such effective intercellular transfer of HIV-1 could occur through virological synapses or target-cell filopodia connected to infected cells. Here we report that membrane nanotubes, formed when T cells make contact and subsequently part, provide a new route for HIV-1 transmission. Membrane nanotubes are known to connect various cell types, including neuronal and immune cells, and allow calcium-mediated signals to spread between connected myeloid cells. However, T-cell nanotubes are distinct from open-ended membranous tethers between other cell types, as a dynamic junction persists within T-cell nanotubes or at their contact with cell bodies. We also report that an extracellular matrix scaffold allows T-cell nanotubes to adopt variably shaped contours. HIV-1 transfers to uninfected T cells through nanotubes in a receptor-dependent manner. These data lead us to propose that HIV-1 can spread using nanotubular connections formed by short-term intercellular unions in which T cells specialize.