Self-assembly and organization of lipid-protein membranes

Phospholipid Membranes as Chemically and Functionally Tunable Materials

The sheet-like lipid bilayer is the fundamental structural component of all cell membranes. Its building blocks are phospholipids and cholesterol. Their amphiphilic structure spontaneously leads to the formation of a bilayer in aqueous environment. Lipids are not just structural elements. Individual lipid species, the lipid membrane structure, and lipid dynamics influence and regulate membrane protein function. An exciting field is emerging where the membrane-associated material properties of different bilayer systems are used in designing innovative solutions for widespread applications across various fields, such as the food industry, cosmetics, nano- and biomedicine, drug storage and delivery, biotechnology, nano- and biosensors, and computing. Here, the authors summarize what is known about how lipids determine the properties and functions of biological membranes and how this has been or can be translated into innovative applications. Based on recent progress in the understanding of membrane structure, dynamics, and physical properties, a perspective is provided on how membrane-controlled regulation of protein functions can extend current applications and even offer new applications.

Nanostructured Antimicrobial Peptides: Crucial Steps of Overcoming the Bottleneck for Clinics

The security issue of human health is faced with dispiriting threats from multidrug-resistant bacteria infections induced by the abuse and misuse of antibiotics. Over decades, the antimicrobial peptides (AMPs) hold great promise as a viable alternative to treatment with antibiotics due to their peculiar antimicrobial mechanisms of action, broad-spectrum antimicrobial activity, lower drug residue, and ease of synthesis and modification. However, they universally express a series of disadvantages that hinder their potential application in the biomedical field (e.g., low bioavailability, poor protease resistance, and high cytotoxicity) and extremely waste the abundant resources of AMP database discovered over the decades. For all these reasons, the nanostructured antimicrobial peptides (Ns-AMPs), based on a variety of nanosystem modification, have made up for the deficiencies and pushed the development of novel AMP-based antimicrobial therapies. In this review, we provide an overview of the advantages of Ns-AMPs in improving therapeutic efficacy and biological stability, reducing side effects, and gaining the effect of organic targeting and drug controlled release. Then the different material categories of Ns-AMPs are described, including inorganic material nanosystems containing AMPs, organic material nanosystems containing AMPs, and self-assembled AMPs. Additionally, this review focuses on the Ns-AMPs for the effect of biological activities, with emphasis on antimicrobial activity, biosecurity, and biological stability. The "state-of-the-art" antimicrobial modes of Ns-AMPs, including controlled release of AMPs under a specific environment or intrinsic antimicrobial properties of Ns-AMPs, are also explicated. Finally, the perspectives and conclusions of the current research in this field are also summarized.

A New Hope: Self-Assembling Peptides with Antimicrobial Activity

Peptide drugs hold great promise for the treatment of infectious diseases thanks to their novel mechanisms of action, low toxicity, high specificity, and ease of synthesis and modification. Naturally developing self-assembly in nature has inspired remarkable interest in self-assembly of peptides to functional nanomaterials. As a matter of fact, their structural, mechanical, and functional advantages, plus their high bio-compatibility and bio-degradability make them excellent candidates for facilitating biomedical applications. This review focuses on the self-assembly of peptides for the fabrication of antibacterial nanomaterials holding great interest for substituting antibiotics, with emphasis on strategies to achieve nano-architectures of self-assembly. The antibacterial activities achieved by these nanomaterials are also described.

Self-assembly of anionic, ligand-coated nanoparticles in lipid membranes

Ligand-functionalized nanoparticles (NPs) are a promising platform for imaging and drug delivery applications. A number of recent molecular simulation and theoretical studies explored how these NPs interact with model lipid membranes. However, interactions between ligand-coated NPs leading to possible cooperative effects and association have not been investigated. In this coarse-grained molecular dynamics study, we focus on a specific case of several anionic, ligand-coated NPs embedded in a lipid membrane. Several new effects are observed. Specifically, in the presence of cholesterol in the membrane, NPs tend to form linear clusters, or chains. Analysis of the driving forces for this association reveals an important role of the recently discovered orderphobic effect, although we acknowledge that a combination of factors must be at play. At the same time, we argue that the specific linear shape of the clusters is a result of a subtle balance between the forces that stabilize a NP in the membrane and the forces that drive the NP-NP association processes. These effects, observed for the first time in the NP-membrane systems, have also direct correspondence to similar effects in protein-membrane systems and these links between the two realms should be explored further.

Stability and phase separation in mixed self-assembled monolayers

Recent single molecule experiments rely on the self-assembly of binary mixtures of molecules with very different properties in a stable monolayer, in order to probe the characteristics of the interspersed molecule of interest in a controlled environment. However, not all efforts at coassembly have been successful. To study systematically the behavior of such systems, we derive the free energy of multicomponent systems of rods with configurational degrees of freedom, localized on a surface, starting from a generalized van der Waals description. The molecular parameters are determined by geometrical factors of the molecules and by their pairwise van der Waals interactions computed using molecular mechanics. Applying the model to two experimental situations, we are able to use the stability analysis of the respective mixtures to explain why coassembly was successful in one set of experiments (carotene and alkanethiol) and not in another (benzenethiols and alkanethiol). We outline general guidelines for suitable choices of molecules to achieve coassembly.

Modelling of proteins in membranes

This review describes some recent theories and simulations of mesoscopic and microscopic models of lipid membranes with embedded or attached proteins. We summarize results supporting our understanding of phenomena for which the activities of proteins in membranes are expected to be significantly affected by the lipid environment. Theoretical predictions are pointed out, and compared to experimental findings, if available. Among others, the following phenomena are discussed: interactions of interfacially adsorbed peptides, pore-forming amphipathic peptides, adsorption of charged proteins onto oppositely charged lipid membranes, lipid-induced tilting of proteins embedded in lipid bilayers, protein-induced bilayer deformations, protein insertion and assembly, and lipid-controlled functioning of membrane proteins.

Observation of the main phase transition of dinervonoylphosphocholine giant liposomes by fluorescence microscopy

The phase heterogeneity of giant unilamellar dinervonoylphosphocholine (DNPC) vesicles in the course of the main phase transition was investigated by confocal fluorescence microscopy observing the fluorescence from the membrane incorporated lipid analog, 1-palmitoyl-2-(N-4-nitrobenz-2-oxa-1,3-diazol)aminocaproyl-sn-glycero-3-phosphocholine (NBDPC). These data were supplemented by differential scanning calorimetry (DSC) of DNPC large unilamellar vesicles (LUV, diameter approximately 0.1 and 0.2 microm) and multilamellar vesicles (MLV). The present data collected upon cooling reveal a lack of micron-scale gel and fluid phase coexistence in DNPC GUVs above the temperature of 20.5 degrees C, this temperature corresponding closely to the heat capacity maxima (T(em)) of DNPC MLVs and LUVs (T(em) approximately 21 degrees C), measured upon DSC cooling scans. This is in keeping with the model for phospholipid main transition inferred from our previous fluorescence spectroscopy data for DMPC, DPPC, and DNPC LUVs. More specifically, the current experiments provide further support for the phospholipid main transition involving a first-order process, with the characteristic two-phase coexistence converting into an intermediate phase in the proximity of T(em). This at least macroscopically homogenous intermediate phase would then transform into the liquid crystalline state by a second-order process, with further increase in acyl chain trans-->gauche isomerization.

The significance of lipid composition for membrane activity: New concepts and ways of assessing function

In the last decade or so, it has been realised that membranes do not just have a lipid-bilayer structure in which proteins are embedded or with which they associate. Structures are dynamic and contain areas of heterogeneity which are vital for their formation. In this review, we discuss some of the ways in which these dynamic and heterogeneous structures have implications during stress and in relation to certain human diseases. A particular stress is that of temperature which may instigate adaptation in poikilotherms or appropriate defensive responses during fever in mammals. Recent data emphasise the role of membranes in sensing temperature changes and in controlling a regulatory loop with chaperone proteins. This loop seems to need the existence of specific membrane microdomains and also includes association of chaperone (heat stress) proteins with the membrane. The role of microdomains is then discussed further in relation to various human pathologies such as cardiovascular disease, cancer and neurodegenerative diseases. The concept of modifying membrane lipids (lipid therapy) as a means for treating such pathologies is then introduced. Examples are given when such methods have been shown to have benefit. In order to study membrane microheterogeneity in detail and to elucidate possible molecular mechanisms that account for alteration in membrane function, new methods are needed. In the second part of the review, we discuss ultra-sensitive and ultra-resolution imaging techniques. These include atomic force microscopy, single particle tracking, single particle tracing and various modern fluorescence methods. Finally, we deal with computing simulation of membrane systems. Such methods include coarse-grain techniques and Monte Carlo which offer further advances into molecular dynamics. As computational methods advance they will have more application by revealing the very subtle interactions that take place between the lipid and protein components of membranes - and which are so essential to their function.

Flexible charged macromolecules on mixed fluid lipid membranes: theory and Monte Carlo simulations

Fluid membranes containing charged lipids enhance binding of oppositely charged proteins by mobilizing these lipids into the interaction zone, overcoming the concomitant entropic losses due to lipid segregation and lower conformational freedom upon macromolecule adsorption. We study this energetic-entropic interplay using Monte Carlo simulations and theory. Our model system consists of a flexible cationic polyelectrolyte, interacting, via Debye-Hückel and short-ranged repulsive potentials, with membranes containing neutral lipids, 1% tetravalent, and 10% (or 1%) monovalent anionic lipids. Adsorption onto a fluid membrane is invariably stronger than to an equally charged frozen or uniform membrane. Although monovalent lipids may suffice for binding rigid macromolecules, polyvalent counter-lipids (e.g., phosphatidylinositol 4,5 bisphosphate), whose entropy loss upon localization is negligible, are crucial for binding flexible macromolecules, which lose conformational entropy upon adsorption. Extending Rosenbluth's Monte Carlo scheme we directly simulate polymer adsorption on fluid membranes. Yet, we argue that similar information could be derived from a biased superposition of quenched membrane simulations. Using a simple cell model we account for surface concentration effects, and show that the average adsorption probabilities on annealed and quenched membranes coincide at vanishing surface concentrations. We discuss the relevance of our model to the electrostatic-switch mechanism of, e.g., the myristoylated alanine-rich C kinase substrate protein.

Simulation studies of protein-induced bilayer deformations, and lipid-induced protein tilting, on a mesoscopic model for lipid bilayers with embedded proteins

Biological membranes are complex and highly cooperative structures. To relate biomembrane structure to their biological function it is often necessary to consider simpler systems. Lipid bilayers composed of one or two lipid species, and with embedded proteins, provide a model system for biological membranes. Here we present a mesoscopic model for lipid bilayers with embedded proteins, which we have studied with the help of the dissipative particle dynamics simulation technique. Because hydrophobic matching is believed to be one of the main physical mechanisms regulating lipid-protein interactions in membranes, we considered proteins of different hydrophobic length (as well as different sizes). We studied the cooperative behavior of the lipid-protein system at mesoscopic time- and lengthscales. In particular, we correlated in a systematic way the protein-induced bilayer perturbation, and the lipid-induced protein tilt, with the hydrophobic mismatch (positive and negative) between the protein hydrophobic length and the pure lipid bilayer hydrophobic thickness. The protein-induced bilayer perturbation was quantified in terms of a coherence length, xi(P), of the lipid bilayer hydrophobic thickness profile around the protein. The dependence on temperature of xi(P), and the protein tilt-angle, were studied above the main-transition temperature of the pure system, i.e., in the fluid phase. We found that xi(P) depends on mismatch, i.e., the higher the mismatch is, the longer xi(P) becomes, at least for positive values of mismatch; a dependence on the protein size appears as well. In the case of large model proteins experiencing extreme mismatch conditions, in the region next to the so-called lipid annulus, there appears an undershooting (or overshooting) region where the bilayer hydrophobic thickness is locally lower (or higher) than in the unperturbed bilayer, depending on whether the protein hydrophobic length is longer (or shorter) than the pure lipid bilayer hydrophobic thickness. Proteins may tilt when embedded in a too-thin bilayer. Our simulation data suggest that, when the embedded protein has a small size, the main mechanism to compensate for a large hydrophobic mismatch is the tilt, whereas large proteins react to negative mismatch by causing an increase of the hydrophobic thickness of the nearby bilayer. Furthermore, for the case of small, peptidelike proteins, we found the same type of functional dependence of the protein tilt-angle on mismatch, as was recently detected by fluorescence spectroscopy measurements.

Lysozyme effect on structural state of model membranes as revealed by pyrene excimerization studies

Steady-state measurements of pyrene fluorescence in the model bilayer membranes composed of phosphatidylcholine (PC) and its mixtures with cardiolipin (CL) have been performed to gain insight into the effect of lysozyme on molecular organization of lipid bilayer. Analysis of vibronic structure of the probe emission spectra revealed no changes in transverse distribution of pyrene monomers on varying CL contents or increasing the extent of lysozyme binding to liposomes. Excimer-to-monomer fluorescence intensity ratio has been found to reduce on lysozyme association with lipids. The magnitude of this effect increased with increasing CL content from 0 to 40 mol%. These results have been interpreted as indicating decrease in the membrane free volume on formation of both electrostatic and hydrophobic protein-lipid contacts.

Direct determination by capillary electrophoresis of cardiovascular drugs, previously included in liposomes

The lipophilicity of some cardiovascular drugs was determined by capillary electrophoresis (CE). Mexiletine, amlodipine and indapamide, the drugs considered, were in contact with liposomial vescicles for 2, 4 or 6 h. After the contact time the drugs, penetrated into liposomial vesicles, were determined by CE using phosphate buffer (pH 6.3 or 7.4) or borate buffer (pH 9). The lipophilicity of three drugs was determined considering the drug percentage penetrated into liposomial vesicles. The found lipohilicity order was amlodipine > mexiletine > indapamide.

Lipids do influence protein function-the hydrophobic matching hypothesis revisited

A topical review of the current state of lipid-protein interactions is given with focus on the physical interactions between lipids and integral proteins in lipid-bilayer membranes. The concepts of hydrophobic matching and curvature stress are revisited in light of recent data obtained from experimental and theoretical studies which demonstrate that not only do integral proteins perturb the lipids, but the physical state of the lipids does also actively influence protein function. The case of the trans-membrane water-channel protein aquaporin GlpF from E. coli imbedded in lipid-bilayer membranes is discussed in some detail. Numerical data obtained from Molecular Dynamics simulations show on the one side that the lipid bilayer adapts to the channel by a hydrophobic matching condition which reflects the propensity of the lipid molecules for forming curved structures. On the other side, it is demonstrated that the transport function of the channel is modulated by the matching condition and/or the curvature stress in a lipid-specific manner.

Diffusion in two-component lipid membranes--a fluorescence correlation spectroscopy and monte carlo simulation study

Using fluorescence correlation spectroscopy, calorimetry, and Monte Carlo simulations, we studied diffusion processes in two-component membranes close to the chain melting transition. The aim is to describe complex diffusion behavior in lipid systems in which gel and fluid domains coexist. Diffusion processes in gel membranes are significantly slower than in fluid membranes. Diffusion processes in mixed phase regions are therefore expected to be complex. Due to statistical fluctuations the gel-fluid domain patterns are not uniform in space and time. No models for such diffusion processes are available. In this article, which is both experimental and theoretical, we investigated the diffusion in DMPC-DSPC lipid mixtures as a function of temperature and composition. We then modeled the fluorescence correlation spectroscopy experiment using Monte Carlo simulations to analyze the diffusion process. It is shown that the simulations yield a very good description of the experimental diffusion processes, and that predicted autocorrelation profiles are superimposable with the experimental curves. We believe that this study adds to the discussion on the physical nature of rafts found in biomembranes.

Evidence for the lack of a specific interaction between cholesterol and sphingomyelin

The putative specific interaction and complex formation by sphingomyelin and cholesterol was investigated. Accordingly, low contents (1 mol % each) of fluorescently labeled derivatives of these lipids, namely 1-palmitoyl-2[10-(pyren-1-yl)]decanoyl-sn-glycero-3-phosphocholine (PyrPC), n-[10-(1-pyrenyl)decanoyl]sphingomyelin (PyrSM), and increasing concentrations of cholesterol (up to 5 mol %), were included in large unilamellar vesicles composed of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) or 1,2-dinervonoyl-sn-glycero-3-phosphocholine (DNPC), and the excimer/monomer fluorescence emission ratio (I(e)/I(m)) was measured. In DNPC below the main phase transition, the addition of up to 5 mol % cholesterol reduced I(e)/I(m) significantly. Except for this, cholesterol had only a negligible effect in both matrices and for both probes. We then compared the efficiency of resonance energy transfer from PyrPC and PyrSM to 22-(n-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-23,24-bisnor-5-cholen-3beta-ol (NBDchol). An augmenting colocalization of the latter resonance energy transfer pair with temperature was observed in a DMPC matrix below the main phase transition. In contrast, compared to PyrSM the colocalization of PyrPC with NBDchol was more efficient in the longer DNPC matrix. These results could be confirmed using 5,6-dibromo-cholestan-3beta-ol as a collisional quencher for the pyrene-labeled lipids. The results indicate lack of a specific interaction between sphingomyelin and cholesterol, and further imply that hydrophobic mismatch between the lipid constituents could provide the driving force for the cosegregation of sphingomyelin and cholesterol in fluid phospholipid bilayers of thicknesses comparable to those found for biomembranes.

The effect of chain length on protein solubilization in polymer-based vesicles (polymersomes)

Using a mean-field analysis we derive a consistent model for the perturbation of a symmetric polymeric bilayer due to the incorporation of transmembrane proteins, as a function of the polymer molecular weight and the protein dimensions. We find that the mechanism for the inhibition of protein incorporation in polymeric bilayers differs from that of their inclusion in polymer-carrying lipid vesicles; in polymersomes, the equilibrium concentration of transmembrane proteins decreases as a function of the thickness mismatch between the protein and the bilayer core, whereas in liposomes the presence of polymer chains affects the protein adsorption kinetics. Despite the increased stiffness of polymer bilayers (when compared to lipid ones), their perturbation decay length and range of protein-protein interaction is found to be relatively long. The energetic penalty due to protein adsorption increases relatively slowly as a function of the polymer chain length due to the self-assembled nature of the polymer bilayer. As a result, we predict that transmembrane proteins may be incorporated in significant numbers even in bilayers where the thickness mismatch is large.

Docosahexaenoic acid: membrane properties of a unique fatty acid

Docosahexaenoic acid (DHA) with 22-carbons and 6 double bonds is the extreme example of an omega-3 polyunsaturated fatty acid (PUFA). DHA has strong medical implications since its dietary presence has been positively linked to the prevention of numerous human afflictions including cancer and heart disease. The PUFA, moreover, is essential to neurological function. It is remarkable that one simple molecule has been reported to affect so many seemingly unrelated biological processes. Although details of a molecular mode of action remain elusive, DHA must be acting at a fundamental level common to many tissues that is related to the high degree of conformational flexibility that the multiple double bonds have been identified to confer. One likely target for DHA action is at the cell membrane where the fatty acid is known to readily incorporate into membrane phospholipids. Once esterified into phospholipids DHA has been demonstrated to significantly alter many basic properties of membranes including acyl chain order and "fluidity", phase behavior, elastic compressibility, permeability, fusion, flip-flop and protein activity. It is concluded that DHA's interaction with other membrane lipids, particularly cholesterol, may play a prominent role in modulating the local structure and function of cell membranes.

Analyzing heat capacity profiles of peptide-containing membranes: cluster formation of gramicidin A

The analysis of peptide and protein partitioning in lipid membranes is of high relevance for the understanding of biomembrane function. We used statistical thermodynamics analysis to demonstrate the effect of peptide mixing behavior on heat capacity profiles of lipid membranes with the aim to predict peptide aggregation from c(P)-profiles. This analysis was applied to interpret calorimetric data on the interaction of the antibiotic peptide gramicidin A with lipid membranes. The shape of the heat capacity profiles was found to be consistent with peptide clustering in both gel and fluid phase. Applying atomic force microscopy, we found gramicidin A aggregates and established a close link between thermodynamics data and microscopic imaging. On the basis of these findings we described the effect of proteins on local fluctuations. It is shown that the elastic properties of the membrane are influenced in the peptide environment.

A computational model of membrane lipid electronic properties in relation to neural signaling

We present a computational model of a transiently-organized neural membrane molecular system with possible information-processing capacity. The model examines field-induced dipole and quadrupole moments and polarizability in monomeric, dimeric, and trimeric ethenes. Polarization of the ethenes is strongly indicated. This result is interpreted as a significant electronic feature of a molecular computing system based on organization of membrane lipids into a transient ( approximately 10(-4) s) crystalline state due to lipid-protein hydrophobic mismatch at the membrane-ion-channel interface. Predictive implications of the model's electronic features are briefly discussed.

Cholesterol dependent recruitment of di22:6-PC by a G protein-coupled receptor into lateral domains

Bovine rhodopsin was reconstituted into mixtures of didocosahexaenoylphosphatidylcholine (di22:6-PC), dipalmitoylphosphatidylcholine (di16:0-PC), sn-1-palmitoyl-sn-2-docosahexaenoylphosphatidylcholine (16:0, 22:6-PC) and cholesterol. Rhodopsin denaturation was examined by using high-sensitivity differential scanning calorimetry. The unfolding temperature was increased at lower levels of lipid unsaturation, but the highest temperature was detected for native disk membranes: di22:6-PC < 16:0,22:6-PC < di16:0,18:1-PC < native disks. The incorporation of 30 mol% of cholesterol resulted in 2-4 degrees C increase of denaturation temperature in all reconstituted systems examined. From the analysis of van't Hoff's and calorimetric enthalpies, it was concluded that the presence of cholesterol in di22:6-PC-containing bilayers induces a level of cooperativity in rhodopsin unfolding. Fluorescence resonance energy transfer (FRET), using lipids labeled at the headgroup with pyrene (Py) as donors and rhodopsin retinal group as acceptor of fluorescence, was used to study rhodopsin association with lipids. Higher FRET efficiencies detected for di22:6-PE-Py, compared to di16:0-PE-Py, in mixed di22:6-PC-di16:0-PC-cholesterol bilayers, indicate preferential segregation of rhodopsin with polyunsaturated lipids. The effective range of the rhodopsin-lipid interactions facilitating cluster formation exceeds two adjacent lipid layers. In similar mixed bilayers containing no cholesterol, cluster formation was absent at temperatures above lipid phase transition, indicating a crucial role of cholesterol in microdomain formation.

Indirect interaction of colloidal particles adsorbed on smectic films

Colloidal particles like peptides and proteins adsorbed on a stack of lipid bilayers cause elastic deformations which disturb the smectic order. Two adsorbed particles attract each other due to the superposition of their deformation fields. The effective pair potential attributed to this substrate-mediated force decays exponentially with the particle distance. The range of this potential coincides with the decay length of elastic deformations, and is found to be proportional to the square root of the stack thickness. If the stack is sufficiently thick, the substrate-mediated interaction is estimated to be strong enough to overcome the entropic barrier and enforce aggregation or even crystallization of the adsorbate.

Resonance energy transfer study of hemoglobin complexes with model phospholipid membranes

By examining the resonance energy transfer between fluorescent probes, embedded in the lipid bilayer (4-(dimethylaminostyryl)-1-methylpiridine, 4-(dimethylaminostyryl)-1-dodecylpiridine, N,N'-bishexamethylenrhodamine, rhodamine 6G) as donors, and the heme group of hemoglobin as acceptor, the structure of the protein complexes with the model membranes composed of phosphatidylcholine and cardiolipin was characterized. Quantitative interpretation of the experimental data was performed in terms of the model of energy transfer in two-dimensional systems, using a set of parameters including the distance of closest approach between donor and acceptor, the vertical separation of donor planes, the acceptor distance from the donor plane and the orientation factor. The limits for the heme distance from the lipid bilayer center and the depth of the protein penetration in the membrane interior were estimated. The results obtained suggest that the depth of hemoglobin insertion into liposomal membranes decreases upon increasing CL content in the lipid bilayer.

Theoretical analysis of protein organization in lipid membranes

The fundamental physical principles of the lateral organization of trans-membrane proteins and peptides as well as peripheral membrane proteins and enzymes are considered from the point of view of the lipid-bilayer membrane, its structure, dynamics, and cooperative phenomena. Based on a variety of theoretical considerations and model calculations, the nature of lipid-protein interactions is considered both for a single protein and an assembly of proteins that can lead to aggregation and protein crystallization in the plane of the membrane. Phenomena discussed include lipid sorting and selectivity at protein surfaces, protein-lipid phase equilibria, lipid-mediated protein-protein interactions, wetting and capillary condensation as means of protein organization, mechanisms of two-dimensional protein crystallization, as well as non-equilibrium organization of active proteins in membranes. The theoretical findings are compared with a variety of experimental data.