Polymer-tethered membranes as quantitative models for the study of integrin-mediated cell adhesion

Why Do Tethered-Bilayer Lipid Membranes Suit for Functional Membrane Protein Reincorporation?

Membrane proteins (MPs) are essential for cellular functions. Understanding the functions of MPs is crucial as they constitute an important class of drug targets. However, MPs are a challenging class of biomolecules to analyze because they cannot be studied outside their native environment. Their structure, function and activity are highly dependent on the local lipid environment, and these properties are compromised when the protein does not reside in the cell membrane. Mammalian cell membranes are complex and composed of different lipid species. Model membranes have been developed to provide an adequate environment to envisage MP reconstitution. Among them, tethered-Bilayer Lipid Membranes (tBLMs) appear as the best model because they allow the lipid bilayer to be decoupled from the support. Thus, they provide a sufficient aqueous space to envisage the proper accommodation of large extra-membranous domains of MPs, extending outside. Additionally, as the bilayer remains attached to tethers covalently fixed to the solid support, they can be investigated by a wide variety of surface-sensitive analytical techniques. This review provides an overview of the different approaches developed over the last two decades to achieve sophisticated tBLMs, with a more and more complex lipid composition and adapted for functional MP reconstitution.

Critical role of lipid membranes in polarization and migration of cells: a biophysical view

Cell migration plays vital roles in many biologically relevant processes such as tissue morphogenesis and cancer metastasis, and it has fascinated biophysicists over the past several decades. However, despite an increasing number of studies highlighting the orchestration of proteins involved in different signaling pathways, the functional roles of lipid membranes have been essentially overlooked. Lipid membranes are generally considered to be a functionless two-dimensional matrix of proteins, although many proteins regulating cell migration gain functions only after they are recruited to the membrane surface and self-organize their functional domains. In this review, we summarize how the logistical recruitment and release of proteins to and from lipid membranes coordinates complex spatiotemporal molecular processes. As predicted from the classical framework of the Smoluchowski equation of diffusion, lipid/protein membranes serve as a 2D reaction hub that contributes to the effective and robust regulation of polarization and migration of cells involving several competing pathways.

Membrane interactions in drug delivery: Model cell membranes and orthogonal techniques

To generate the desired effect in the human body, the active pharmaceutical ingredient usually needs to interact with a receptor located on the cell membrane or inside the cell. Thus, understanding membrane interactions is of great importance when it comes to the development and testing of new drug molecules or new drug delivery systems. Nowadays, there is a tremendous selection of both model cell membranes and of techniques that can be used to characterize interactions between selected model cell membranes and a drug molecule, an excipient, or a drug delivery system. Having such a wide selection of model cell membranes and techniques available makes it sometimes challenging to select the optimal combination for a specific study. Furthermore, it is difficult to compare results obtained using different model cell membranes and techniques, and not all in vitro studies translate as well to an estimation of the in vivo biological activity or understanding of mode of action. This review provides an overview of the available lipid bilayer-based model cell membranes and of the most widely employed techniques for studying membrane interactions. Finally, the need for employing complimentary characterization techniques in order to acquire more reliable and in-depth information is highlighted.

Dynamic Contact Guidance of Myoblasts by Feature Size and Reversible Switching of Substrate Topography: Orchestration of Cell Shape, Orientation, and Nematic Ordering of Actin Cytoskeletons

Biological cells in tissues alter their shapes, positions, and orientations in response to dynamic changes in their physical microenvironments. Here, we investigated the dynamic response of myoblast cells by fabricating substrates displaying microwrinkles that can reversibly change their direction within 60 s by axial compression and relaxation. To quantitatively assess the collective order of cells, we introduced the nematic order parameter of cells that takes not only the distribution of cell-wrinkle angles but also the degree of cell elongation into account. On the subcellular level, we also calculated the nematic order parameter of actin cytoskeletons that takes the rearrangement of actin filaments into consideration. The results obtained on substrates with different wrinkle wavelengths implied the presence of a characteristic wavelength beyond which the order parameters of both cells and actin cytoskeletons level off. Immunofluorescence labeling of vinculin showed that the focal adhesions were all concentrated on the peaks of wrinkles when the wavelength is below the characteristic value. On the other hand, we found focal adhesions on both the peaks and the troughs of wrinkles when the wavelength exceeds the characteristic level. The emergence of collective ordering of cytoskeletons and the adaptation of cell shapes and orientations were monitored by live cell imaging after the seeding of cells from suspensions. After the cells had reached the steady state, the orientation of wrinkles was abruptly changed by 90°. The dynamic response of myoblasts to the drastic change in surface topography was monitored, demonstrating the coordination of the shape and orientation of cells and the nematic ordering of actin cytoskeletons. The "dynamic" substrates established in this study can be used as a powerful tool in mechanobiology that helps us understand how cytoskeletons, cells, and cell ensembles respond to dynamic contact guidance cues.

Binding equilibrium and kinetics of membrane-anchored receptors and ligands in cell adhesion: Insights from computational model systems and theory

The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the binding equilibrium and kinetics of these proteins is affected by the membranes and by the membrane anchoring and molecular properties of the proteins. Simulations and theory both indicate that the binding equilibrium constant [Formula: see text] and the on- and off-rate constants of anchored receptors and ligands in their 2-dimensional (2D) membrane environment strongly depend on the membrane roughness from thermally excited shape fluctuations on nanoscales. Recent theory corroborated by simulations provides a general relation between [Formula: see text] and the binding constant [Formula: see text] of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in 3 dimensions (3D).

Tethered and Polymer Supported Bilayer Lipid Membranes: Structure and Function

Solid supported bilayer lipid membranes are model systems to mimic natural cell membranes in order to understand structural and functional properties of such systems. The use of a model system allows for the use of a wide variety of analytical tools including atomic force microscopy, impedance spectroscopy, neutron reflectometry, and surface plasmon resonance spectroscopy. Among the large number of different types of model membranes polymer-supported and tethered lipid bilayers have been shown to be versatile and useful systems. Both systems consist of a lipid bilayer, which is de-coupled from an underlying support by a spacer cushion. Both systems will be reviewed, with an emphasis on the effect that the spacer moiety has on the bilayer properties.

Reconstitution of Fusion Proteins in Supported Lipid Bilayers for the Study of Cell Surface Receptor-Ligand Interactions in Cell-Cell Contact

Bioactive molecules such as adhesion ligands, growth factors, or enzymes play an important role in modulating cell behavior such as cell adhesion, spreading, and differentiation. Deciphering the mechanism of ligand-mediated cell adhesion and associated signaling is of great interest not only for fundamental biophysical investigations but also for applications in medicine and biotechnology. In the presented work, we developed a new biomimetic platform that enables culturing primary neurons and testing cell surface-receptor ligand interactions in cell-cell contacts as, e.g., in neuronal synapses. This platform consists of a supported lipid bilayer modified with incorporated neuronal adhesion proteins conjugated with the Fc-domain of IgG (ephrin A5 Fc-chimera). We extensively characterized properties of these protein containing bilayers using fluorescence recovery after photobleaching (FRAP), quartz crystal microbalance with dissipation (QCM-D), and immunostaining. We conclude that the Fc-domain is the part responsible for the incorporation of the protein into the bilayer. The biomimetic platform prepared by this new approach was able to promote neuronal cell adhesion and maintain growth as well as facilitate neuronal maturation as shown by electrophysiological measurements. We believe that our approach can be extended to insert other proteins to create a general culture platform for neurons and other cell types.

The lateral diffusion and fibrinogen induced clustering of platelet integrin αIIbβ3 reconstituted into physiologically mimetic GUVs

Platelet integrin αIIbβ3 is a key mediator of platelet activation and thrombosis. Upon activation αIIbβ3 undergoes significant conformational rearrangement, inducing complex bidirectional signalling and protein recruitment leading to platelet activation. Reconstituted lipid models of the integrin can enhance our understanding of the structural and mechanistic details of αIIbβ3 behaviour away from the complexity of the platelet machinery. Here, a novel method of αIIbβ3 insertion into Giant Unilamellar Vesicles (GUVs) is described that allows for effective integrin reconstitution unrestricted by lipid composition. αIIbβ3 was inserted into two GUV lipid compositions that seek to better mimic the platelet membrane. First, "nature's own", comprising 32% DOPC, 25% DOPE, 20% CH, 15% SM and 8% DOPS, intended to mimic the platelet cell membrane. Fluorescence Lifetime Correlation Spectroscopy (FLCS) reveals that exposure of the integrin to the activators Mn(2+) or DTT does not influence the diffusion coefficient of αIIbβ3. Similarly, exposure to αIIbβ3's primary ligand fibrinogen (Fg) alone does not affect αIIbβ3's diffusion coefficient. However, addition of Fg with either activator reduces the integrin diffusion coefficient from 2.52 ± 0.29 to μm(2) s(-1) to 1.56 ± 0.26 (Mn(2+)) or 1.49 ± 0.41 μm(2) s(-1) (DTT) which is consistent with aggregation of activated αIIbβ3 induced by fibrinogen binding. The Multichannel Scaler (MCS) trace shows that the integrin-Fg complex diffuses through the confocal volume in clusters. Using the Saffman-Delbrück model as a first approximation, the diffusion coefficient of the complex suggests at least a 20-fold increase in the radius of membrane bound protein, consistent with integrin clustering. Second, αIIbβ3 was also reconstituted into a "raft forming" GUV with well defined liquid disordered (Ld) and liquid ordered (Lo) phases. Using confocal microscopy and lipid partitioning dyes, αIIbβ3 showed an affinity for the DOPC rich Ld phase of the raft forming GUVs, and was effectively excluded from the cholesterol and sphingomyelin rich Lo phase. Activation and Fg binding of the integrin did not alter the distribution of αIIbβ3 between the lipid phases. This observation suggests partitioning of the activated fibrinogen bound αIIbβ3 into cholesterol rich domains is not responsible for the integrin clustering observed.

Membrane adhesion and the formation of heterogeneities: biology, biophysics, and biotechnology

Membrane adhesion is essential to many vital biological processes. Sites of membrane adhesion are often associated with heterogeneities in the lipid and protein composition of the membrane. These heterogeneities are thought to play functional roles by facilitating interactions between proteins. However, the causal links between membrane adhesion and membrane heterogeneities are not known. Here we survey the state of the field and indicate what we think are understudied areas ripe for development.

Ligand binding alters dimerization and sequestering of urokinase receptors in raft-mimicking lipid mixtures

Lipid heterogeneities, such as lipid rafts, are widely considered to be important for the sequestering of membrane proteins in plasma membranes, thereby influencing membrane protein functionality. However, the underlying mechanisms of such sequestration processes remain elusive, in part, due to the small size and often transient nature of these functional membrane heterogeneities in cellular membranes. To overcome these challenges, here we report the sequestration behavior of urokinase receptor (uPAR), a glycosylphosphatidylinositol-anchored protein, in a planar model membrane platform with raft-mimicking lipid mixtures of well-defined compositions using a powerful optical imaging platform consisting of confocal spectroscopy XY-scans, photon counting histogram, and fluorescence correlation spectroscopy analyses. This methodology provides parallel information about receptor sequestration, oligomerization state, and lateral mobility with single molecule sensitivity. Most notably, our experiments demonstrate that moderate changes in uPAR sequestration are not only associated with modifications in uPAR dimerization levels, but may also be linked to ligand-mediated allosteric changes of these membrane receptors. Our data show that these modifications in uPAR sequestration can be induced by exposure to specific ligands (urokinase plasminogen activator, vitronectin), but not via adjustment of the cholesterol level in the planar model membrane system. Good agreement of our key findings with published results on cell membranes confirms the validity of our model membrane approach. We hypothesize that the observed mechanism of receptor translocation in the presence of raft-mimicking lipid mixtures is also applicable to other glycosylphosphatidylinositol-anchored proteins.

Polymer-tethered lipid multi-bilayers: a biomembrane-mimicking cell substrate to probe cellular mechano-sensing

Cells tiptoe through their environment forming highly localized and dynamic focal contacts. Experiments on polymeric gels of adjustable elasticity have shown that cells probe the viscoelasticity of their environment through an adaptive process of focal contact assembly/disassembly that critically affects cell adhesion, morphology, and motility. However, the specific mechanisms of this process have not yet been fully revealed. Here we report, for the first time, that fibroblast adhesion, morphology, and migration can also be controlled by altering the number of bilayers in a stack of multiple polymer-tethered lipid bilayers stabilized via maleimide-sulfhydral coupling chemistry. The observed changes in cell morphology, migration, and cytoskeletal organization in response to bilayer stacking correspond well with those previously observed on polymeric substrates of different polymer crosslinking density suggesting that variations in bilayer stacking are associated with changes in substrate viscoelasticity. This is in conceptual agreement with the existing knowledge about the structural, dynamic, and mechanical properties of polymer-lipid composite materials. Several distinct features, such as the lateral mobility of individual cell linkers and the immobilization of linker clusters, make the described substrates highly attractive tools for the study of dynamic, mechano-regulated cell linkages and cellular mechano-sensing.

Iterative layer-by-layer assembly of polymer-tethered multi-bilayers using maleimide–thiol coupling chemistry

The current study reports on the layer-by-layer assembly of a polymer-tethered lipid multi-bilayer stack using the iterative addition and roll out of giant unilamellar vesicles (GUVs) containing constituents with thiol and maleimide functional groups, respectively. Confocal microscopy and photobleaching experiments confirm stack integrity and stability over time, as well as the lateral fluidity of individual bilayers within the stacks. Complementary wide-field single molecule fluorescence microscopy and atomic force microscopy experiments show that increasing bilayer-substrate distances are associated with changes in lipid lateral mobility and bilayer morphology. Importantly, the described iterative approach can be employed to assemble multi-bilayer stacks with more than two bilayers, thus further reducing the influence of the underlying solid substrate on membrane behavior. Furthermore, the presence of lipopolymers within the multi-bilayer stacks results in fascinating membrane dynamics and organization properties, with interesting parallels to those found in plasma membranes. In that sense, the described multi-bilayer architecture represents an attractive model membrane platform for a variety of different biophysical studies.

Bilayer asymmetry influences integrin sequestering in raft-mimicking lipid mixtures

There is growing recognition that lipid heterogeneities in cellular membranes play an important role in the distribution and functionality of membrane proteins. However, the detection and characterization of such heterogeneities at the cellular level remains challenging. Here we report on the poorly understood relationship between lipid bilayer asymmetry and membrane protein sequestering in raft-mimicking model membrane mixtures using a powerful experimental platform comprised of confocal spectroscopy XY-scan and photon-counting histogram analyses. This experimental approach is utilized to probe the domain-specific sequestering and oligomerization state of αvβ3 and α5β1 integrins in bilayers, which contain coexisting liquid-disordered/liquid-ordered (ld/lo) phase regions exclusively in the top leaflet of the bilayer (bottom leaflet contains ld phase). Comparison with previously reported integrin sequestering data in bilayer-spanning lo-ld phase separations demonstrates that bilayer asymmetry has a profound influence on αvβ3 and α5β1 sequestering behavior. For example, both integrins sequester preferentially to the lo phase in asymmetric bilayers, but to the ld phase in their symmetric counterparts. Furthermore, our data show that bilayer asymmetry significantly influences the role of native ligands in integrin sequestering.

Biomimetic membrane platform: fabrication, characterization and applications

A facile method for assembly of biomimetic membranes serving as a platform for expression and insertion of membrane proteins is described. The membrane architecture was constructed in three steps: (i) assembly/printing of α-laminin peptide (P19) spacer on gold to separate solid support from the membrane architecture; (ii) covalent coupling of different lipid anchors to the P19 layer to serve as stabilizers of the inner leaflet during bilayer formation; (iii) lipid vesicle spreading to form a complete bilayer. Two different lipid membrane systems were examined and two different P19 architectures prepared by either self-assembly or μ-contact printing were tested and characterized using contact angle (CA) goniometry, surface plasmon resonance (SPR) spectroscopy and imaging surface plasmon resonance (iSPR). It is shown that surface coverage of cushion layer is significantly improved by μ-contact printing thereby facilitating bilayer formation as compared to self-assembly. To validate applicability of proposed methodology, incorporation of Cytochrome bo(3) ubiquinol oxidase (Cyt-bo(3)) into biomimetic membrane was performed by in vitro expression technique which was further monitored by surface plasmon enhanced fluorescence spectroscopy (SPFS). The results showed that solid supported planar membranes, tethered by α-laminin peptide cushion layer, provide an attractive environment for membrane protein insertion and characterization.

Poly(2-oxazoline)s as polymer therapeutics

Poly(2-oxazoline)s (POx) are currently discussed as an upcoming polymer platform for biomaterials design and especially for polymer therapeutics. POx meet specific requirements needed for the development of next-generation polymer therapeutics such as biocompatibility, high modulation of solubility, variation of size, architecture as well as chemical functionality. Although in the early 1990s first and promising POx-based systems were presented, the field lay dormant for almost two decades. Only very recently, POx-based polymer therapeutics came back into the focus of very intensive research. In this review, we give an overview on the chemistry and physicochemical properties of POx and summarize the research of POx-protein conjugates, POx-drug conjugates, POx-based polyplexes and POx micelles for drug delivery.

Tailored poly(2-oxazoline) polymer brushes to control protein adsorption and cell adhesion

POx bottle-brush brushes (BBBs) are synthesized by SIPGP of 2-isopropenyl-2-oxazoline and consecutive LCROP of 2-oxazolines on 3-aminopropyltrimethoxysilane-modified silicon substrates. The side chain hydrophilicity and polarity are varied. The impact of the chemical composition and architecture of the BBB upon protein (fibronectin) adsorption and endothelial cell adhesion are investigated and prove extremely low protein adsorption and cell adhesion on BBBs with hydrophilic side chains such as poly(2-methyl-2-oxazoline) and poly(2-ethyl-2-oxazoline). The influence of the POx side chain terminal function upon adsorption and adhesion is minor but the side chain length has a significant effect on bioadsorption.

Native ligands change integrin sequestering but not oligomerization in raft-mimicking lipid mixtures

Distinct lipid environments, including lipid rafts, are increasingly recognized as a crucial factor affecting membrane protein function in plasma membranes. Unfortunately, an understanding of their role in membrane protein activation and oligomerization has remained elusive due to the challenge of characterizing these often small and transient plasma membrane heterogeneities in live cells. To address this difficulty, we present an experimental model membrane platform based on polymer-supported lipid bilayers containing stable raft-mimicking domains (type I) and homogeneous cholesterol-lipid mixtures (type II) into which transmembrane proteins are incorporated (α(v)β(3) and α(5)β(1) integrins). These flexible lipid platforms enable the use of confocal fluorescence spectroscopy, including the photon counting histogram method, in tandem with epifluorescence microscopy to quantitatively probe the effect of the binding of native ligands from the extracellular matrix ligands (vitronectin and fibronectin for α(v)β(3) and α(5)β(1), respectively) on domain-specific protein sequestration and on protein oligomerization state. We found that both α(v)β(3) and α(5)β(1) sequester preferentially to nonraft domains in the absence of extracellular matrix ligands, but upon ligand addition, α(v)β(3) sequesters strongly into raft-like domains and α(5)β(1) loses preference for either raft-like or nonraft-like domains. A corresponding photon counting histogram analysis showed that integrins exist predominantly in a monomeric state. No change was detected in oligomerization state upon ligand binding in either type I or type II bilayers, but a moderate increase in oligomerization state was observed for increasing concentrations of cholesterol. The combined findings suggest a mechanism in which changes in integrin sequestering are caused by ligand-induced changes in integrin conformation and/or dynamics that affect integrin-lipid interactions without altering the integrin oligomerization state.

Hydrogen-bond-directed giant unilamellar vesicles of guanosine derivative: preparation, properties, and fusion

By mixing a small volume of THF containing guanosine derivative 1 and tetraethylenegrycol dodecyl ether (TEGDE) with water and subsequently removing TEGDE by gel permeation chromatography, micrometer-sized giant unilamellar vesicles (GUV) of 1 were successfully prepared. The vesicle membrane was a 2-D sheet assembly of thickness 2.5 nm, composed of a 2-D inter-guanine hydrogen-bond network. The GUV dispersion showed high stability because of a large negative zeta potential, which allowed repeated sedimentation and redispersion by centrifugation and subsequent gentle agitation. TEGDE-triggered fusion of GUVs took place within 350 ms, which proceeded by fusion of the vesicle membranes in contact. These unique static and dynamic properties of the GUV membrane assembled by the 2-D hydrogen-bond network are discussed.

Quartz crystal microbalance with dissipation monitoring of supported lipid bilayers on various substrates

Supported lipid bilayers (SLBs) mimic biological membranes and are a versatile platform for a wide range of biophysical research fields including lipid-protein interactions, protein-protein interactions and membrane-based biosensors. The quartz crystal microbalance with dissipation monitoring (QCM-D) has had a pivotal role in understanding SLB formation on various substrates. As shown by its real-time kinetic monitoring of SLB formation, QCM-D can probe the dynamics of biomacromolecular interactions. We present a protocol for constructing zwitterionic SLBs supported on silicon oxide and titanium oxide, and discuss technical issues that need to be considered when working with charged lipid compositions. Furthermore, we explain a recently developed strategy that uses an amphipathic, alpha-helical (AH) peptide to form SLBs on gold and titanium oxide substrates. The protocols can be completed in less than 3 h.

Biomimetic approaches for studying membrane processes

This short review focuses on recent innovative systems and experimental approaches designed to investigate membrane processes and biomolecular interactions associated with membranes. Our emphasis is on "biomimetics" which reflects the significance and contributions of the chemistry/biology interface in addressing complex biological questions. We have not limited this review to discussion of new "sensors" or "assays"per se, but rather we tried to review new concepts employed for analysis of membrane processes.

Characterizing stability properties of supported bilayer membranes on nanoglassified substrates using surface plasmon resonance

Supported bilayer membranes (SBMs) formed on solid substrates, in particular glass, provide an ideal cell mimicking model system that has been found to be highly useful for biosensing applications. Although the stability of the membrane structures is known to determine the applicability, the subject has not been extensively investigated, largely because of the lack of convenient methods to monitor changes of membrane properties on glass in real time. This work reports the evaluation of the stability properties of a series of SBMs against chemical and air damage by use of surface plasmon resonance spectroscopy and nanoglassified gold substrates. Seven SBMs composed of phosphatidylcholine and DOPC+, including single-component, mixed, protein-reinforced SBMs (rSBMs) and protein-tethered bilayer membranes (ptBLMs), are studied. The stability properties under various conditions, especially the effects of surfactants, organic solvents, and dehydration damage on the bilayers, are compared. PC membranes are found to be easily removed from the glassy surfaces using relatively low concentrations of the surfactants, while DOPC+ is markedly more stable toward nonionic surfactant. DOPC+ membranes also demonstrated remarkable air stability while PC films exhibited considerable damage from dehydration. Doping of cholesterol does not improve PC's stability against SDS and Triton but changes the lipid membrane packing enough to protect against dehydration damage. Although rSBMs and ptBLMs improve air stability to a certain degree, they are still quite susceptible to significant damage/removal from ionic and nonionic surfactants at lower concentrations. Overall, DOPC+ has noted higher stability on glass, likely due to the favorable electrostatic interaction between the silicate surface and the lipid headgroup, making it a good candidate for application. Nanoglassy SPR proves to be an attractive platform capable of rapidly screening film stability in real-time, providing critical information for future work using supported membranes for sensing applications.

Two-dimensional center-of-mass diffusion of lipid-tethered poly(2-methyl-2-oxazoline) at the air-water interface studied at the single molecule level

The two-dimensional (2D) center-of-mass diffusion, D, of end-tethered poly(2-methyl-2-oxazoline) (PMOx) lipopolymer chains was studied in a Langmuir monolayer at the air-water interface using wide-field single molecule fluorescence microscopy. In this case, tethering and stabilization of hydrophilic PMOx chains at the air-water interface is accomplished via end-tethering to lipid molecules forming a hydrophobic anchor. To explore the influence of molecular weight, M n, and surface concentration, c s, on lateral mobility, two different PMOx chain lengths of n = 30 and 50 ( n, number of monomer units) were analyzed over a wide range of c s. Using multiparticle tracking analysis of TRITC-labeled PMOx lipopolymers, we found two regimes of lipopolymer lateral mobility. At low c s, D is independent of surface concentration but increases with decreasing n. Here diffusion properties are well described by the Rouse model. In contrast, at more elevated c s, the data do not follow Rouse scaling but are in good agreement with a free area-area model of diffusion. The current study provides for the first time experimental insight into the 2D center-of-mass diffusion of end-tethered polymers at the air-water interface. The obtained results will be of importance for the understanding of diffusion processes in polymer-tethered phospholipid bilayers mimicking biomembranes at low and high tethering concentrations.

Fluctuation spectra of free and supported membrane pairs

Fluctuation spectra of fluid compound membrane systems are calculated. The systems addressed contain two (or more) almost parallel membranes that are connected by harmonic tethers or by a continuous, harmonic confining potential. Additionally, such a compound system can be attached to a supporting substrate. We compare quasi-analytical results for tethers with analytical results for corresponding continuous models and investigate under what circumstances the discrete nature of the tethers actually influences the fluctuations. A tethered, supported membrane pair with similar bending rigidities and stiff tethers can possess a nonmonotonic fluctuation spectrum with a maximum. A nonmonotonic spectrum with a maximum and a minimum can occur for an either free or supported membrane pair of rather different bending rigidities and for stiff tethers. Typical membrane displacements are calculated for supported membrane pairs with discrete or continuous interacting potentials. Thereby an estimate of how close the constituent two membranes and the substrate typically approach each other is given. For a supported membrane pair with discrete or continuous interactions, the typical displacements of each membrane are altered with respect to a single supported membrane, where those of the membrane near the substrate are diminished and those of the membrane further away are enhanced.