Thermally induced proliferation of pores in a model fluid membrane.

The growth of thermally induced pores in a two-dimensional model fluid membrane is investigated by Monte Carlo simulation. Holes appear in the membrane via an activated process, and their subsequent growth is controlled by an edge energy per unit length or line tension. The barrier height and line tension, together with a lateral tension, are the independent parameters of the model. In the resulting phase diagram, a rupture transition separates an intact membrane from a disintegrated state. The approach to the ruptured state shows distinct regimes. Reducing the barrier height at large line tension produces multiple, quasi-independent, small holes whose behavior is dominated by their edge energy, whereas at lower line tensions shape fluctuations of the holes facilitate their coalescence into a single large hole. At a small value of line tension and large barrier height, a single hole spontaneously permeabilizes the membrane in an entropically driven phase transition. Entropy dominates pore growth for line tensions not far below those measured for artificial vesicles. Permeabilization of lipid bilayers by certain peptides involves perturbing lipid-lipid cohesive energies, and our simulations show that at small line tensions the entropy of hole shape fluctuations destroys the model membrane's stability.     

Dynamic tension spectroscopy and strength of biomembranes

Rupturing fluid membrane vesicles with a steady ramp of micropipette suction produces a distribution of breakage tensions governed by the kinetic process of membrane failure. When plotted as a function of log(tension loading rate), the locations of distribution peaks define a dynamic tension spectrum with distinct regimes that reflect passage of prominent energy barriers along the kinetic pathway. Using tests on five types of giant phosphatidylcholine lipid vesicles over loading rates(tension/time) from 0.01-100 mN/m/s, we show that the kinetic process of membrane breakage can be modeled by a causal sequence of two thermally-activated transitions. At fast loading rates, a steep linear regime appears in each spectrum which implies that membrane failure starts with nucleation of a rare precursor defect. The slope and projected intercept of this regime are set by defect size and frequency of spontaneous formation, respectively. But at slow loading rates, each spectrum crosses over to a shallow-curved regime where rupture tension changes weakly with rate. This regime is predicted by the classical cavitation theory for opening an unstable hole in a two-dimensional film within the lifetime of the defect state. Under slow loading, membrane edge energy and the frequency scale for thermal fluctuations in hole size are the principal factors that govern the level of tension at failure. To critically test the model and obtain the parameters governing the rates of transition under stress, distributions of rupture tension were computed and matched to the measured histograms through solution of the kinetic master (Markov) equations for defect formation and annihilation or evolution to an unstable hole under a ramp of tension. As key predictors of membrane strength, the results for spontaneous frequencies of defect formation and hole edge energies were found to correlate with membrane thicknesses and elastic bending moduli, respectively.     

Evolution of the hemifused intermediate on the pathway to membrane fusion

The pathway to membrane fusion in synthetic and biological systems is thought to pass through hemifusion, in which the outer leaflets are fused while the inner leaflets engage in a hemifusion diaphragm (HD). Fusion has been proposed to be completed by lysis of the expanded HD that matures from a localized stalklike initial connection. However, the process that establishes the expanded HD is poorly understood. Here we mathematically modeled hemifusion of synthetic vesicles, where hemifusion and fusion are most commonly driven by calcium and membrane tension. The model shows that evolution of the hemifused state is driven by these agents and resisted by interleaflet frictional and tensile stresses. Predicted HD growth rates depend on tension and salt concentration, and agree quantitatively with experimental measurements. For typical conditions, we predict that HDs expand at ～30 μm(2)/s, reaching a final equilibrium area ～7% of the vesicle area. Key model outputs are the evolving HD tension and area during the growth transient, properties that may determine whether HD lysis occurs. Applying the model to numerous published experimental studies that reported fusion, our results are consistent with a final fusion step in which the HD ruptures due to super-lysis HD membrane tensions.     

Membrane lysis by gramicidin S visualized in red blood cells and giant vesicles

The cationic amphiphilic antimicrobial peptide gramicidin S (GS) is an effective antibiotic. Its applicability is however restricted to topical infections due to its hemolytic activity. In this study, the process of GS induced hemolysis was investigated in detail for the first time. The morphological changes of red blood cells (RBCs) inflicted by GS were visualized and explained in terms of a physical model. The observed fast rupture events were further investigated with giant unilamellar vesicles (GUVs) as model systems for RBCs. Measurements of membrane fluctuations in GUVs revealed that the membrane surface tension was increased after incubation with GS. These findings are in agreement with the hypothesis that amphiphilic peptides induce membrane rupture by an increase in membrane tension.     

Editorial

Stimulated secretion in endocrine cells and neuronal synapses causes a rise in endocytosis rates to recover the added membrane. The endocytic process involves the mechanical deformation of the membrane to produce an invagination. Studies of osmotic swelling effects on endocytosis indicate that the increased surface tension is tightly correlated to a significant decrease of endocytosis. When rat basophilic leukemia (RBL) cells are stimulated to secrete, there is a dramatic drop in the membrane tension and only small changes in membrane bending stiffness. Neither the shape change that normally accompanies secretion nor the binding of ligand without secretion causes a drop in tension. Further, tension decreases within 6 s, preceding shape change and measurable changes in endocytosis. After secretion stops, tension recovers. On the basis of these results we suggest that the physical parameter of membrane tension is a major regulator of endocytic rate in RBL cells. Low tensions would stimulate endocytosis and high tensions would stall the endocytic machinery.     

Membrane Fluctuations Destabilize Clathrin Protein Lattice Order

We develop a theoretical model of a clathrin protein lattice on a flexible cell membrane. The clathrin subunit is modeled as a three-legged pinwheel with elastic deformation modes and intersubunit binding interactions. The pinwheels are constrained to lie on the surface of an elastic sheet that opposes bending deformation and is subjected to tension. Through Monte Carlo simulations, we predict the equilibrium phase behavior of clathrin lattices at various levels of tension. High membrane tensions, which correspond to suppressed membrane fluctuations, tend to stabilize large, flat crystalline structures similar to plaques that have been observed in vivo on cell membranes that are adhered to rigid surfaces. Low tensions, on the other hand, give rise to disordered, defect-ridden lattices that behave in a fluidlike manner. The principles of two-dimensional melting theory are applied to our model system to further clarify how high tensions can stabilize crystalline order on flexible membranes. These results demonstrate the importance of environmental physical cues in dictating the collective behavior of self-assembled protein structures.     

Membrane Fluctuations Destabilize Clathrin Protein Lattice Order

We develop a theoretical model of a clathrin protein lattice on a flexible cell membrane. The clathrin subunit is modeled as a three-legged pinwheel with elastic deformation modes and intersubunit binding interactions. The pinwheels are constrained to lie on the surface of an elastic sheet that opposes bending deformation and is subjected to tension. Through Monte Carlo simulations, we predict the equilibrium phase behavior of clathrin lattices at various levels of tension. High membrane tensions, which correspond to suppressed membrane fluctuations, tend to stabilize large, flat crystalline structures similar to plaques that have been observed in vivo on cell membranes that are adhered to rigid surfaces. Low tensions, on the other hand, give rise to disordered, defect-ridden lattices that behave in a fluidlike manner. The principles of two-dimensional melting theory are applied to our model system to further clarify how high tensions can stabilize crystalline order on flexible membranes. These results demonstrate the importance of environmental physical cues in dictating the collective behavior of self-assembled protein structures.     

Intramembrane electrostatic interactions destabilize lipid vesicles

Membrane stability is of central concern in many biology and biotechnology processes. It has been suggested that intramembrane electrostatic interactions play a key role in membrane stability. However, due primarily to a lack of supporting experimental evidence, they are not commonly considered in mechanical analyses of lipid membranes. In this paper, we use the micropipette aspiration technique to characterize the elastic moduli and critical tensions of lipid vesicles with varying surface charge. Charge was induced by doping neutral phosphatidylcholine vesicles with anionic lipids phosphatidylglycerol and phosphatidic acid. Measurements were taken in potassium chloride (moderate ion-lipid binding) and tetramethylammonium chloride (low ion-lipid binding) solutions. We show that inclusion of anionic lipid does not appreciably alter the areal dilation elasticity of lipid vesicles. However, the tension required for vesicle rupture decreases with increasing anionic lipid fraction and is a function of electrolyte composition. Using vesicles with 30% charged (i.e., unbound) anionic lipid, we measured critical tension reductions of 75%, demonstrating the important role of electrostatic interactions in membrane stability.     

Mechanical aspects of the lungs as cancer cell-killing organs during hematogenous metastasis

A substantial proportion of many different types of circulating cancer cells appear to be killed during their interactions with the pulmonary microcirculation. Different tensions exist during respiration within alveolar units, and hence the pulmonary capillaries. We have calculated the effects of these tensions on the entry and subsequent fate of circulating cancer cells. Our calculations indicate that during expiration, when tension in the capillary walls is low, cancer cells can enter and travel along the capillaries without damage, because the vessels are deformed by the cells and the hydrodynamic field surrounding them. During normal inspiration when the alveoli are stretched, the increased tension within the capillary walls serves to compress the contained cancer cells. This compression, together with previously calculated blood pressure differentials between the ends of the cells, is thought in some cases, to increase their membrane tensions above the critical level for rupture, resulting in cytolysis, in accord with experimental observations. In deep inspiration, when a very substantial increase in capillary wall tension occurs, cancer cells already within the capillaries, entering them and in transit along them are expected to develop membrane tensions greatly exceeding the critical values for rupture. It is suggested that these respiration-induced effects may act as an important rate-regulating step in the metastatic process, where the development of pulmonary metastases plays a central role. Furthermore, induced deep inspiration may conceivably be utilized in the inhibition of pulmonary metastasis.     

Lateral tensions and pressures in membranes and lipid monolayers

The effects of lateral tension on the properties of membranes are often explained in comparison with analogous experiments on monolayers, which yield more detailed data. To calculate the effects of changes in tension on the composition of, or incorporation of amphiphiles into membranes we examine (i) the fidelity of the monolayer analogy, (ii) the range of possible tensions in a membrane, and the way in which tensions arise and (iii) the equilibrium partitioning of amphiphiles between aqueous solution and a bilayer under tension. We argue that, at the same areas per molecule, a monolayer at an $\text{n-}\text{alkane}\text{/}\text{water}$ interface is a closer analogy of the lipid bilayer than a monolayer at an air/water interface. Next, we show from a thermodynamic argument that changes in membrane tension can affect the absorption of very large amphiphiles such as proteins, but that physiological tensions are unlikely to affect the absorption of lipids or drugs. Finally we consider the possibility that the measured bulk tension in a complicated membrane such as that of the erythrocyte may be larger than the local tension in the fluid mosaic portions, and suggest a model which explains the ability of the erythrocyte membrane to withstand much higher tensions than other biological membranes and lipid bilayers.     

Three dimensional (temperature–tension–composition) phase map of mixed DOPC–DPPC vesicles: Two solid phases and a fluid phase coexist on three intersecting planes

Mapping the phase behavior of multicomponent phospholipid membranes has been an ongoing pursuit, motivated by interest in both fundamental physics and cell function. Prior investigations addressed temperature-composition space and the features of the associated domains. The current study additionally considers membrane tension, analogous to pressure in bulk materials. Focusing on model mixed 1,2-dioleoyl-sn-glycero-3-phosphocholine and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DOPC and DPPC respectively) membranes, we examine the thermodynamic impact of tension on fluid-solid coexistence and the nature of phase-separated domains. Reported here is the 3 dimensional composition-temperature-tension phase map containing three intersecting curved surfaces. Depending on the system’s position in this 3D space, giant unilamellar vesicles containing DOPC and DPPC may exhibit, in addition to a 2-component fluid Lα phase, two different types of solid DPPC-rich domains: tracer-excluding hexagonal patches or tracer-selective stripes. The fluid phase occurs at high temperatures. At cool temperatures striped solid DPPC-rich domains coexist with the fluid at elevated tensions. These stripes occur independent of tension, at the coolest temperatures. At low tensions and intermediate temperatures, patchy solid DPPC-rich domains coexist with the Lα fluid and may persist, if kinetically trapped, at lower temperatures. We associate the striped DPPC domains with a tilt-gel (Lβ’) morphology and the hexagonal DPPC patches with a dense corrugated ripple phase (Pβ’). These assignments, based on the reported areal densities of the corrugated and tilt solids, enabled first principles estimates of the coexistence boundaries that match the experiments well, including the tension sensitivity of coexistence curves and triple-point-like features for fixed composition.     

Interactions of a charged nanoparticle with a lipid membrane: implications for gene delivery

We employ self-consistent field theory to study the thermodynamics of membrane-particle interactions in the context of gene delivery systems, with the aim to guide the design of dendrimers that can overcome the endosomal escape barrier by inserting into membranes and creating pores. We consider the interaction between a model polyamidoamine dendrimer and a membrane under controlled tension as a function of the separation between the dendrimer and the membrane. In all the cases we have studied, the lowest free energy state corresponds to the membrane partially wrapping the dendrimer. However, with moderate tension, we find that a G5 (or larger) generation dendrimer, through thermal fluctuation, can induce the formation of metastable pores. These metastable pores are subsequently shown to significantly lower the critical tension necessary for membrane rupture, thus possibly enhancing the release of the trapped genetic material from the endosome.     

Endocytosis and exocytosis protect cells against severe membrane tension variations

The ability of cells to regulate their shape and volume is critical for many cell functions. How endocytosis and exocytosis, as important ways of membrane trafficking, affect cellular volume regulation is still unclear. Here, we develop a theoretical framework to study the dynamics of cell volume, endocytosis, and exocytosis in response to osmotic shocks and mechanical loadings. This model can not only explain observed dynamics of endocytosis and exocytosis during osmotic shocks but also predict the dynamics of endocytosis and exocytosis during cell compressions. We find that a hypotonic shock stimulates exocytosis, while a hypertonic shock stimulates endocytosis; and exocytosis in turn allows cells to have a dramatic change in cell volume but a small change in membrane tension during hyposmotic swelling, protecting cells from rupture under high tension. In addition, we find that cell compressions with various loading speeds induce three distinct dynamic modes of endocytosis and exocytosis. Finally, we show that increasing endocytosis and exocytosis rates reduce the changes in cell volume and membrane tension under fast cell compression, whereas they enhance the changes in cell volume and membrane tension under slow cell compression. Together, our findings reveal critical roles of endocytosis and exocytosis in regulating cell volume and membrane tension.     

Oxytropism: a new twist in pollen tube orientation

Chemical gradients and structural features within the pistil have been previously proposed as factors determining the directionality of pollen tube growth. In this study, we examine the behavior of pollen of eight species germinated in a dynamic oxygen gradient. While the germination rates of some species decreased directly with decreasing oxygen tension, other species showed no decrease in germination at oxygen tensions as low as 2 kPa. In one species, germination was consistently greater at decreased oxygen tensions than at ambient atmospheric levels. In three of the eight species tested, the developing pollen tube showed clear directional growth away from the more-oxygenated regions of the growth medium, while in one species growth was towards the more-oxygenated region. The remaining four species showed random tube growth. The pattern of oxytropic responses among the taxa suggests that this tropic behavior is both widespread and phylogenetically unpredictable.     

Measurement of low levels of oxygen and their effect on respiration in cell suspensions maintained in an open system

The presence of low levels of oxygen may have profound effects on the cytotoxic activity of radiation, radiosensitizers, and bioreductive alkylating agents. As others have shown, low oxygen tensions may significantly alter rates of cellular and chemical oxygen consumption. When experiments are performed at very low oxygen concentrations, the opposing effects of oxygen leakage into and cellular/chemical oxygen consumption from the system can lead to unpredictable results. Use of a newly designed, highly sensitive Clark-type oxygen sensor has permitted accurate and reproducible measurement of low levels of oxygen. Cellular depletion of oxygen at various cell densities has been monitored for a series of oxygen tensions in solution and the corresponding respiration rates have been calculated. Although oxygen depletion was found to be quite significant at low oxygen tensions, not all oxygen present could be removed by cellular respiration. Respiration rate decreased as oxygen tension decreased and approached zero at low oxygen tensions. This result was independent of cell density. A model is presented to account for the observed effect of oxygen tension on cellular oxygen utilization.     

Membrane Expansion Increases Endocytosis Rate during Mitosis

Mitosis in mammalian cells is accompanied by a dramatic inhibition of endocytosis. We have found that the addition of amphyphilic compounds to metaphase cells increases the endocytosis rate even to interphase levels. Detergents and solvents all increased endocytosis rate, and the extent of increase was in direct proportion to the concentration added. Although the compounds could produce a variety of different effects, we have found a strong correlation with a physical alteration in the membrane tension as measured by the laser tweezers. Plasma membrane tethers formed by latex beads pull back on the beads with a force that was related to the in-plane bilayer tension and membrane– cytoskeletal adhesion. We found that as cells enter mitosis, the membrane tension rises as the endocytosis rate decreases; and as cells exited mitosis, the endocytosis rate increased as the membrane tension decreased. The addition of amphyphilic compounds decreased membrane tension and increased the endocytosis rate. With the detergent, deoxycholate, the endocytosis rate was restored to interphase levels when the membrane tension was restored to interphase levels. Although biochemical factors are clearly involved in the alterations in mitosis, we suggest that endocytosis is blocked primarily by the increase in apparent plasma membrane tension. Higher tensions inhibit both the binding of the endocytic complex to the membrane and mechanical deformation of the membrane during invagination. We suggest that membrane tension is an important regulator of the endocytosis rate and alteration of tension is sufficient to modify endocytosis rates during mitosis. Further, we postulate that the rise in membrane tension causes cell rounding and the inhibition of motility, characteristic of mitosis.     

Fusion peptides and the mechanism of viral fusion

Segments of viral fusion proteins play an important role in viral fusion. They are defined by a number of criteria, including the sensitivity of this region of the viral fusion protein to loss of function as a consequence of mutation. In addition, small model peptides designed to mimic this segment of viral fusion proteins often have some membrane perturbing activity. The properties of viral fusion peptides are quite varied. Many are found at the amino terminus of viral fusion proteins. As isolated peptides, they have been found to form both α-helical as well as β-structure. In addition, some viruses have internal fusion peptides. Just as there are several structural motifs for viral fusion peptides, there are also several mechanisms by which they accelerate the process of membrane fusion. These include the promotion of negative curvature, lowering the rupture tension of the lipid monolayer, acting as an anchor to join the fusion membranes, transmitting a force to the membrane or imparting energy to the system by other means. It is not likely that the fusion peptide can fulfill all of these diverse roles and future studies will elucidate which of these mechanisms is most important for the action of individual viral fusion peptides.     

Entropy-driven instability and rupture of fluid membranes.

A computer simulation is used to investigate hole formation in a model membrane. The model parameters are the stress applied to the membrane, and the edge energy per unit length along the hole boundary (edge tension). Even at zero stress, the membrane has an entropically driven instability against hole formation. Within the model, the minimum edge tension required for the stability of a typical biological membrane is in the region of 1 x 10(-11) J/m, which is similar to the edge tension obtained in many measurements of biomembranes. At the zero-stress instability threshold, the hole shape is the same as a self-avoiding ring, but under compression, the hole shape assumes a branched polymer form. In the presence of large holes at zero stress, the membrane itself behaves like a branched polymer. The boundaries of the phase diagram for membrane stability are obtained, and general features of the rate of membrane rupture under stress are investigated. A model in which the entropy of hole formation is proportional to the hole perimeter is used to interpret the simulation results at small stress near the instability threshold.     

Cytomechanics of axonal development

Mechanical tension is a robust regulator of axonal development of cultured neurons. We review work from our laboratory, using calibrated glass needles to measure or apply tension to chick sensory neurons, chick forebrain neurons, and rat PC12 cells. We survey direct evidence for two different regimes of tension effects on neurons, a fluid-like growth regime, and a nongrowth, elastic regime. Above a minimum tension threshold, we observe growth effects of tension regulating four phases of axonal development:

1. Initiation of process outgrowth from the cell body;
2. Growth cone-mediated elongation of the axon;
3. Elongation of the axon after synaptogenesis, which normally accommodates the skeletal growth of vertebrates; and
4. Axonal elimination by retraction.

Significantly, the quantitative relationship between the force and the growth response is suprisingly similar to the simple relationship characteristic of Newtonian fluid mechanical elements: elongation rate is directly proportional to tension (above the threshold), and this robust linear relationship extends from physiological growth rates to far-above-physiological rates. Thus, tension apparently integrates the complex biochemistry of axonal elongation, including cytoskeletal and membrane dynamics, to produce a simple “force input/growth output” relationship. In addition to this fluid-like growth response, peripheral neurons show elastic behaviors at low tensions (below the threshold tension for growth), as do most cell types. Thus, neurites could exert small static forces without diminution for long periods. In addition, axons of peripheral neurons can actively generate modest tensions, presumably similar to muscle contraction, at tensions near zero. The elastic and force-generating capability of neural axons has recently been proposed to play a major role in the morphogenesis of the brain.     

Correlating a protein structure with function of a bacterial mechanosensitive channel

MscL, a mechanosensitive channel found in many bacteria, protects cells from hypotonic shock by reducing intracellular pressure through release of cytoplasmic osmolytes. First isolated from Escherichia coli, this protein has served as a model for how a protein senses and responds to membrane tension. Recently the structure of a functionally uncharacterized MscL homologue from Mycobacterium tuberculosis was solved by x-ray diffraction to a resolution of 3.5 A. Here we demonstrate that the protein forms a functional MscL-like mechanosensitive channel in E. coli membranes and azolectin proteoliposomes. Furthermore, we show that M. tuberculosis MscL crystals, when re-solubilized and reconstituted, yield wild-type channel currents in patch clamp, demonstrating that the protein does not irreversibly change conformation upon crystallization. Finally, we apply functional clues acquired from the E. coli MscL to the M. tuberculosis channel and show a mechanistic correlation between these channels. However, the inability of the M. tuberculosis channel to gate at physiological membrane tensions, demonstrated by in vivo E. coli expression and in vitro reconstitution, suggests that the membrane environment or other additional factors influence the gating of this channel.