Physical principles of membrane organization

Membranes are the most common cellular structures in both plants and animals. They are now recognized as being involved in almost all aspects of cellular activity ranging from motility and food entrapment in simple unicellular organisms, to energy transduction, immunorecognition, nerve conduction and biosynthesis in plants and higher organisms. This functional diversity is reflected in the wide variety of lipids and particularly of proteins that compose different membranes. An understanding of the physical principles that govern the molecular organization of membranes is essential for an understanding of their physiological roles since structure and function are much more interdependent in membranes than in, say, simple chemical reactions in solution. We must recognize, however, that the word ‘understanding’ means different things in different disciplines, and nowhere is this more apparent than in this multidisciplinary area where biology, chemistry and physics meet.

Using a selective cadmium-binding peplipid to create responsive liquid crystalline nanomaterials.

A specific metal ion-responsive lipid liquid crystalline (LLC) dispersion system was fabricated, which can work in buffer solutions. The LLC matrix was prepared from phytantriol which spontaneously forms the reversed bicontinuous cubic phase in water, and a novel peptide-lipid conjugate (peplipid) consists of a myristate alkyl chain for anchoring into the phytantriol-based cubic bilayer and a peptide sequence for capturing a specific metal ion. The peplipid in its unbound state, when added into the phytantriol-based cubic system induces a positive effect on the bilayer curvature, resulting in the formation of the lamellar phase (vesicles) and the dispersion was transparent in appearance. Upon binding of the cadmium ion, the peplipid induces a negative effect on the lipid bilayer curvature and consequently leading to the formation of cubic phase and opaque appearance. In contrast, other metal ions, including buffering salts, could not sufficiently trigger the phase transition due to weak interaction with the peplipid. The high selectivity of metal ion interaction and triggered phase transition provide potential applications, such as in colloidal-mineral separation, triggered drug release and treatment of cadmium (II) pollution.

Tristearin bilayers: structure of the aqueous interface and stability in the presence of surfactants

We report results of atomistic molecular dynamics simulations of an industrially-relevant, exemplar triacylglycerol (TAG), namely tristearin (TS), under aqueous conditions, at different temperatures and in the presence of an anionic surfactant, sodium dodecylbenzene sulphonate (SDBS). We predict the TS bilayers to be stable and in a gel phase at temperatures of 350 K and below. At 370 K the lipid bilayer was able to melt, but does not feature a stable liquid-crystalline phase bilayer at this elevated temperature. We also predict the structural characteristics of TS bilayers in the presence of SDBS molecules under aqueous conditions, where surfactant molecules are found to spontaneously insert into the TS bilayers. We model TS bilayers containing different amounts of SDBS, with the presence of SDBS imparting only a moderate effect on the structure of the system. Our study represents the first step in applying atomistic molecular dynamics simulations to the investigation of TAG-aqueous interfaces. Our results suggest that the CHARMM36 force-field appears suitable for the simulation of such systems, although the phase behaviour of the system may be shifted to lower temperatures than is the case for the actual system. Our findings provide a foundation for further simulation studies of the TS-aqueous interface.

Papel da localização da carga em determinação dos parâmetros do canal iônico

To aureus α-HL channel, we used the cysteine-scanning mutagenesis technique. Twenty-four mutants were produced from the substitution of a single aminoacid of the primary structure of the α-HL pro this yzed after the incorporation of a mutant channel in planar lipid bilayer membranes. The modified proteins were studied in the absence and presence of watersoluble specific sulphydryl-specific reagents, in order to introduce a strong positive or negative harge at positions of substitution. The introduction of a negative charge in the stem region onverted the selectivity of the channel from weak anionic to more cationic. However, the troduction of a positive charge increased its selectivity to the anion. The degree of these alterations was inversely dependent on the channel radius at the position of the introduced harge (selectivity). As to the asymmetry of the conductance-voltage, the influence of the harge was more complex. The introduction of the negative charge in the stem region (the trans art of the pore) provoked a decrease. The intensity of these alterations depended on the radius, and on the type of free charge at the pore entrance. These results suggest that the free charge at surrounds the pore wall is responsible for the cation-anion selectivity of the channel. The istribution of the charges between the entrances is crucial for determining the asymmetry of e conductance-voltage curves. We hope that these results serve as a model for studies with other nanometric channels, in biological or planar lipid bilayer membranes or in iotechnological applications

Construction of an alkaline phosphatase-liposome system: a tool for biomineralization study

Alkaline phosphatase is required for the mineralization of bone and cartilage. This enzyme is localized in the matrix vesicle, which plays a role key in calcifying cartilage. In this paper. we standardize a method for construction an alkaline phosphatase liposome system to mimic matrix vesicles and examine a some kinetic behavior of the incorporated enzyme. Polidocanol-solubilized alkaline phosphatase, free of detergent, was incorporated into liposomes constituted from dimyristoylphosphatidylcholine (DMPC), dilaurilphosphatidylcholine (DLPC) or dipalmitoylphosphatidylcholine (DPPC). This process was time-dependent and >95% of the enzyme was incorporated into the liposome after 4 h of incubation at 25 degreesC. Although, incorporation was more rapid when vesicles constituted from DPPC were used, the incorporation was more efficient using vesicles constituted from DMPC. The 395 nm diameter of the alkaline phosphatase-liposome system was relatively homogeneous and more stable when stored at 4 degreesC.Alkaline phosphatase was completely released from liposome system only using purified phosphatidylinositol-specific phospholipase C (PIPLC). These experiments confirm that the interaction between alkaline phosphatase and lipid bilayer of liposome is via GPI anchor of the enzyme, alone. An important point shown is that an enzyme bound to liposome does not lose the ability to hydrolyze ATP, pyrophosphate and p-nitrophenyl phosphate (PNPP), but a liposome environment affects its kinetic properties, specifically for pyrophosphate.The standardization of such system allows the study of the effect of phospholipids and the enzyme in in vitro and in vivo mineralization, since it reproduces many essential features of the matrix vesicle. (C) 2002 Elsevier B.V. Ltd. All rights reserved.

Erythrocyte ghost cell-alkaline phosphatase: construction and characterization of a vesicular system for use in biomineralization studies

Alkaline phosphatase is required for the mineralization of bone and cartilage. This enzyme is localized in the matrix vesicle, which plays a role key in calcifying cartilage. In this paper we standardize a method to construction a resealed ghost cell-alkaline phosphatase system to mimic matrix vesicles and examine the kinetic behavior of the incorporated enzyme. Polidocanol-solubilized alkaline phosphatase, free of detergent, was incorporated into resealed ghost cells. This process was time-dependent and practically 50% of the enzyme was incorporated into the vesicles in 40 h of incubation, at 25 degreesC. Alkaline phosphatase-ghost cell systems were relatively homogeneous with diameters of about 300 nm and were more stable when stored at -20 degreesC.Alkaline phosphatase was completely released from the resealed ghost cell-system using only phospholipase C. These experiments confirm that the interaction between alkaline phosphatase and the lipid bilayer of resealed ghost cell is exclusively via glycosylphosphatidylinositol (GPI) anchor of the enzyme.An important point shown is that an enzyme bound to resealed ghost cell does not lose the ability to hydrolyze ATP, pyrophosphate and p-nitrophenyl phosphate (PNPP), but the presence of a ghost membrane, as a support of the enzyme, affects its kinetic properties. Moreover, calcium ions stimulate and phosphate ions inhibit the PNPPase activity of alkaline phosphatase present in resealed ghost cells. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Interaction of amphiphilic derivatives of chitosan with DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Desenvolvimento e caracterização físico-química de sistemas líquido cristalinos contendo palmitato de retinol: quantificação química, avaliação da atividade antioxidante, estudos de liberação e bioadesão in vitro

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Rotational diffusion membrane and fluorescence anisotropy.

Structural properties of model membranes, such as lipid vesicles, may be investigated through the addition of fluorescent probes. After incorporation, the fluorescent molecules are excited with linearly polarized light and the fluorescence emission is depolarized due to translational as well as rotational diffusion during the lifetime of the excited state. The monitoring of emitted light is undertaken through the technique of time-resolved fluorescence: the intensity of the emitted light informs on fluorescence decay times, and the decay of the components of the emitted light yield rotational correlation times which inform on the fluidity of the medium. The fluorescent molecule DPH, of uniaxial symmetry, is rather hydrophobic and has collinear transition and emission moments. It has been used frequently as a probe for the monitoring of the fluidity of the lipid bilayer along the phase transition of the chains. The interpretation of experimental data requires models for localization of fluorescent molecules as well as for possible restrictions on their movement. In this study, we develop calculations for two models for uniaxial diffusion of fluorescent molecules, such as DPH, suggested in several articles in the literature. A zeroth order test model consists of a free randomly rotating dipole in a homogeneous solution, and serves as the basis for the study of the diffusion of models in anisotropic media. In the second model, we consider random rotations of emitting dipoles distributed within cones with their axes perpendicular to the vesicle spherical geometry. In the third model, the dipole rotates in the plane of the of bilayer spherical geometry, within a movement that might occur between the monolayers forming the bilayer. For each of the models analysed, two methods are used by us in order to analyse the rotational diffusion: (I) solution of the corresponding rotational diffusion equation for a single molecule, taking into account the boundary conditions imposed by the models, for the probability of the fluorescent molecule to be found with a given configuration at time t. Considering the distribution of molecules in the geometry proposed, we obtain the analytical expression for the fluorescence anisotropy, except for the cone geometry, for which the solution is obtained numerically; (II) numerical simulations of a restricted rotational random walk in the two geometries corresponding to the two models. The latter method may be very useful in the cases of low-symmetry geometries or of composed geometries.

Statistical models for experimental model membranes.

Biological membranes are constituted from lipid bilayers and proteins. Investigation of protein-membrane interaction, essential for biological function of cells, must rest upon solid knowledge of lipid bilayer behavior. Thus, extensive studies of an experimental model for membranes, lipid bilayers in water solution, have been undertaken in the last decades. These systems present structural, thermal and electrical properties which depend on temperature, ionic strength or concentration. In this talk, we shall discuss statistical models for lipid bilayers, as well as the relation between their properties and results for properties of lipid dispersions investigated by the laboratories supervised by Teresa Lamy (IF-USP) and Amando Ito (FFCL-USP).

Computational analyses on the structure-function relation in ion channels

Ion channels are protein molecules, embedded in the lipid bilayer of the cell membranes. They act as powerful sensing elements switching chemicalphysical stimuli into ion-fluxes. At a glance, ion channels are water-filled pores, which can open and close in response to different stimuli (gating), and one once open select the permeating ion species (selectivity). They play a crucial role in several physiological functions, like nerve transmission, muscular contraction, and secretion. Besides, ion channels can be used in technological applications for different purpose (sensing of organic molecules, DNA sequencing). As a result, there is remarkable interest in understanding the molecular determinants of the channel functioning. Nowadays, both the functional and the structural characteristics of ion channels can be experimentally solved. The purpose of this thesis was to investigate the structure-function relation in ion channels, by computational techniques. Most of the analyses focused on the mechanisms of ion conduction, and the numerical methodologies to compute the channel conductance. The standard techniques for atomistic simulation of complex molecular systems (Molecular Dynamics) cannot be routinely used to calculate ion fluxes in membrane channels, because of the high computational resources needed. The main step forward of the PhD research activity was the development of a computational algorithm for the calculation of ion fluxes in protein channels. The algorithm - based on the electrodiffusion theory - is computational inexpensive, and was used for an extensive analysis on the molecular determinants of the channel conductance. The first record of ion-fluxes through a single protein channel dates back to 1976, and since then measuring the single channel conductance has become a standard experimental procedure. Chapter 1 introduces ion channels, and the experimental techniques used to measure the channel currents. The abundance of functional data (channel currents) does not match with an equal abundance of structural data. The bacterial potassium channel KcsA was the first selective ion channels to be experimentally solved (1998), and after KcsA the structures of four different potassium channels were revealed. These experimental data inspired a new era in ion channel modeling. Once the atomic structures of channels are known, it is possible to define mathematical models based on physical descriptions of the molecular systems. These physically based models can provide an atomic description of ion channel functioning, and predict the effect of structural changes. Chapter 2 introduces the computation methods used throughout the thesis to model ion channels functioning at the atomic level. In Chapter 3 and Chapter 4 the ion conduction through potassium channels is analyzed, by an approach based on the Poisson-Nernst-Planck electrodiffusion theory. In the electrodiffusion theory ion conduction is modeled by the drift-diffusion equations, thus describing the ion distributions by continuum functions. The numerical solver of the Poisson- Nernst-Planck equations was tested in the KcsA potassium channel (Chapter 3), and then used to analyze how the atomic structure of the intracellular vestibule of potassium channels affects the conductance (Chapter 4). As a major result, a correlation between the channel conductance and the potassium concentration in the intracellular vestibule emerged. The atomic structure of the channel modulates the potassium concentration in the vestibule, thus its conductance. This mechanism explains the phenotype of the BK potassium channels, a sub-family of potassium channels with high single channel conductance. The functional role of the intracellular vestibule is also the subject of Chapter 5, where the affinity of the potassium channels hEag1 (involved in tumour-cell proliferation) and hErg (important in the cardiac cycle) for several pharmaceutical drugs was compared. Both experimental measurements and molecular modeling were used in order to identify differences in the blocking mechanism of the two channels, which could be exploited in the synthesis of selective blockers. The experimental data pointed out the different role of residue mutations in the blockage of hEag1 and hErg, and the molecular modeling provided a possible explanation based on different binding sites in the intracellular vestibule. Modeling ion channels at the molecular levels relates the functioning of a channel to its atomic structure (Chapters 3-5), and can also be useful to predict the structure of ion channels (Chapter 6-7). In Chapter 6 the structure of the KcsA potassium channel depleted from potassium ions is analyzed by molecular dynamics simulations. Recently, a surprisingly high osmotic permeability of the KcsA channel was experimentally measured. All the available crystallographic structure of KcsA refers to a channel occupied by potassium ions. To conduct water molecules potassium ions must be expelled from KcsA. The structure of the potassium-depleted KcsA channel and the mechanism of water permeation are still unknown, and have been investigated by numerical simulations. Molecular dynamics of KcsA identified a possible atomic structure of the potassium-depleted KcsA channel, and a mechanism for water permeation. The depletion from potassium ions is an extreme situation for potassium channels, unlikely in physiological conditions. However, the simulation of such an extreme condition could help to identify the structural conformations, so the functional states, accessible to potassium ion channels. The last chapter of the thesis deals with the atomic structure of the !- Hemolysin channel. !-Hemolysin is the major determinant of the Staphylococcus Aureus toxicity, and is also the prototype channel for a possible usage in technological applications. The atomic structure of !- Hemolysin was revealed by X-Ray crystallography, but several experimental evidences suggest the presence of an alternative atomic structure. This alternative structure was predicted, combining experimental measurements of single channel currents and numerical simulations. This thesis is organized in two parts, in the first part an overview on ion channels and on the numerical methods adopted throughout the thesis is provided, while the second part describes the research projects tackled in the course of the PhD programme. The aim of the research activity was to relate the functional characteristics of ion channels to their atomic structure. In presenting the different research projects, the role of numerical simulations to analyze the structure-function relation in ion channels is highlighted.

Analysis of ion channel stochastic signals for biosensing

In biological world, life of cells is guaranteed by their ability to sense and to respond to a large variety of internal and external stimuli. In particular, excitable cells, like muscle or nerve cells, produce quick depolarizations in response to electrical, mechanical or chemical stimuli: this means that they can change their internal potential through a quick exchange of ions between cytoplasm and the external environment. This can be done thanks to the presence of ion channels, proteins that span the lipid bilayer and act like switches, allowing ionic current to flow opening and shutting in a stochastic way. For a particular class of ion channels, ligand-gated ion channels, the gating processes is strongly influenced by binding between receptive sites located on the channel surface and specific target molecules. These channels, inserted in biomimetic membranes and in presence of a proper electronic system for acquiring and elaborating the electrical signal, could give us the possibility of detecting and quantifying concentrations of specific molecules in complex mixtures from ionic currents across the membrane; in this thesis work, this possibility is investigated. In particular, it reports a description of experiments focused on the creation and the characterization of artificial lipid membranes, the reconstitution of ion channels and the analysis of their electrical and statistical properties. Moreover, after a chapter about the basis of the modelling of the kinetic behaviour of ligand gated ion channels, a possible approach for the estimation of the target molecule concentration, based on a statistical analysis of the ion channel open probability, is proposed. The fifth chapter contains a description of the kinetic characterisation of a ligand gated ion channel: the homomeric α2 isoform of the glycine receptor. It involved both experimental acquisitions and signal analysis. The last chapter represents the conclusions of this thesis, with some remark on the effective performance that may be achieved using ligand gated ion channels as sensing elements.

Struktur- und Funktionsuntersuchungen des C 4-Dicarboxylat-Sensors DcuS von Escherichia coli

Das Zweikomponentensystem DcuSR reguliert die Expression der Gene der anaeroben Fumaratatmung in E. coli in Abhängigkeit von externen C4-Dicarbonsäuren. Die membranständige Histidinkinase DcuS detektiert den Reiz und leitet ihn über die Membran an den Responseregulaor DcuR weiter, der die Aktivität der Zielgene reguliert. Das Substratspektrum von DcuS wurde näher untersucht und strukturelle Eigenschaften der Substrate sowie ihre Affinität zu DcuS bestimmt. Es wird vermutet, dass Histidinkinasen im aktiven Zustand als Dimere oder höhere Oligomere vorliegen. Der Oligomerisierungszustand von DcuS in der Membran wurde mittels EPR-Spektroskopie untersucht. Es wurden funktionelle Cysteinmutanten von DcuS hergestellt, die nur an bestimmten Positionen der periplasmatischen Domäne Cysteinreste, aber sonst keine weiteren Cysteinreste, enthielten. Die Proteine wurden isoliert, über die Cysteinreste mit Nitroxiden markiert und in Liposomen rekonstituiert. Erste EPR-Messungen zeigten, dass rekonstituiertes DcuS in einem geordneten Zustand in der Membran vorliegt, der diskrete Abstände zwischen den Monomeren aufweist. Die Struktur von rekonstituiertem DcuS in der Membran soll durch Festkörper-NMR aufgeklärt werden. Ein geeignetes C-terminal verkürztes Konstrukt, DcuS-PD/PAS wurde zu diesem Zweck hergestellt. Das Protein ließ sich in hoher Reinheit isolieren und konnte wieder in Liposomen rekonstituiert werden. Vorbereitende NMR-Messungen zeigten, dass eine Strukturaufklärung an diesem Protein möglich ist. Weitere Strukturuntersuchungen werden zur Zeit durchgeführt.

Photofixierung von Lipidmembranen aus Glykolipopolymeren auf Goldoberflächen

Ziel war Herstellung und Charakterisierung festkörperunterstützter Membransysteme aus Glykolipopolymeren auf Goldoberflächen, mit elektrischen Eigenschaften, die denen der Schwarzfilmmembranen entsprechen. Um diese Eigenschaften mit impedanzspektroskopischen Techniken messen zu können, ist die Präparation der Membranen auf Goldfilmen notwendig. Eine direkte Verankerung der Glykolipopolymermoleküle (GLP) auf der Goldoberfläche ist nicht möglich, daher werden die untersuchten GLP mit Hilfe von photoreaktiven Molekülen kovalent auf der Goldoberfläche immobilisiert. Untersuchten Abstandhalter waren Thio-Polyethylenglykol und eine Mischung zweier Alkanthiole, bestehend aus 1-Thiohexanol und Bis-(Aminododecyl)-disulfid. Thio-PEG-Monoschichten zeigten sehr unterschiedliche Schichtdicken, weil die Moleküle auf der Oberfläche sehr unterschiedliche Konformationen annehmen können, die eine regelmässige Anordnung erschweren. Langmuir-Blodgett Übertrag sowie die durchgeführte photochemische Fixierung der GLP-Moleküle auf Thio-PEG Schichten führte zu Eigenschaften, die auf den Aufbau einer Lipidmonolage hinweisen. Diese stellte jedoch im Bereich der Lipidmoleküle keine geschlossene Schicht dar. Es kommen als Abstandhaltermoleküle für die Photofunktionalisierung nur Moleküle in Frage, die aufgrund ihrer Eigenschaften eine regelmässige Anordnung auf der Goldoberfläche anstreben. Diese Voraussetzung erfüllt am besten die Gruppe der Alkanthiole. Terminal funktionalisierte Alkanthiole müssen jedoch mit nicht oder anderweitig funktionalisierten Alkanthiolen verdünnt assembliert werden, um weitergehende Funktionalisierungen einzugehen. Die untersuchten GLP lassen sich aufgrund ihrer amphiphilen Struktur an der Wasser-Luft Grenzfläche vororientieren. In allen Fällen gelingt auch der Langmuir-Blodgett Übertrag der komprimierten Schicht, sowie, nach der für die Anbindung notwendigen Trocknung, die photochemisch kovalente Fixierung der Monoschicht durch Bestrahlung mit UV-Licht. Damit konnte erstmals die photochemisch kovalente Fixierung von GLPs auf der Goldoberfläche gezeigt werden. Untersuchungen erfolgten an einem Copolymer sowie zwei unterschiedlichen Homopolymermolekülen. Der unterschiedliche molekulare Aufbau der GLP spiegelt sich in ihrem Verhalten an der Wasser-Luft Grenzfläche sowie in den Eigenschaften der gebildeten Monoschichten wieder. Die Copolymer-Schichten zeigten sehr unterschiedliche Schichtdicken. Auch die EIS-Daten sind schlecht reproduzierbar. Dies ist auf die molekulare Struktur des Copolymers zurückzuführen. Gänzlich unterschiedlich verhalten sich die Homopolymere. Aufgrund ihrer Struktur lassen sie sich zu dichten Schichten komprimieren. Messungen der Fluoreszenzerholung nach Photobleichung (FRAP) zeigen homogene aber nicht fluide Schichten. Die photochemisch kovalente Fixierung des Moleküls auf der Goldoberfläche konnte durch SPR- sowie EIS-Messungen nachgewiesen werden. Die EIS-Messungen zeigen Werte, die sich in Bereichen der idealen Modellmembran bewegen. Der erfolgreiche Einbau von Valinomycin konnte bestätigt werden. FRAP Untersuchungen zeigten die Bildung homogener Schichten. Diese sind jedoch im Bereich der proximalen Lipidschicht nicht fluide. Um die Fluidität in Anlehnung an die Eigenschaften der natürlichen Membranen zu erhöhen, wurden die photochemisch kovalent fixierten Anker-Glykolipopolymer-Moleküle durch Mischung mit freien Lipiden lateral verdünnt. Auch die kovalente Fixierung der GLP-Bausteine innerhalb gemischten Schichten konnte erfolgreich demonstriert werden. Die Schichten zeigten sich jedoch, mit Ausnahme der Schichten aus 50mol% Homopolymer und 50mol% Lipid, inhomogen. Nach Photobleichung durch den Laserblitz kam es nur bei den 50mol%:50mol% -Schichten (Ho: Lipid) zur Erholung der Fluoreszenz, was auf das Vorliegen von beweglichen Lipidmolekülen innerhalb der Membran schliessen lässt. Der Versuch der Inkorporation von Valinomycin gelang ebenfalls. Alle genannten Ergebnisse deuten darauf hin, dass die molekulare Architektur der hergestellten Schichten durch die unterschiedlichen Längendimensionen des Homopolymer-Moleküls einerseits, sowie des Lipids andererseits nicht für alle Mischungsverhältnisse ausreichend stabil ist. Die für die kovalente Fixierung erforderliche Trocknung der Schicht führt zu einer deutlichen Verminderung des Wassergehaltes des Systems und einer daraus resultierenden starken Destabilisierung der aufgebauten Schichten. Insgesamt gesehen stellt somit die photochemische Fixierung der glykosidischen Homopolymer-Membranen ein vielversprechendes Modellsystem dar.

Theoretical studies of fluid membrane mechanics

Biologische Membranen sind Fettmolekül-Doppelschichten, die sich wie zweidimensionale Flüssigkeiten verhalten. Die Energie einer solchen fluiden Oberfläche kann häufig mit Hilfe eines Hamiltonians beschrieben werden, der invariant unter Reparametrisierungen der Oberfläche ist und nur von ihrer Geometrie abhängt. Beiträge innerer Freiheitsgrade und der Umgebung können in den Formalismus mit einbezogen werden. Dieser Ansatz wird in der vorliegenden Arbeit dazu verwendet, die Mechanik fluider Membranen und ähnlicher Oberflächen zu untersuchen. Spannungen und Drehmomente in der Oberfläche lassen sich durch kovariante Tensoren ausdrücken. Diese können dann z. B. dazu verwendet werden, die Gleichgewichtsposition der Kontaktlinie zu bestimmen, an der sich zwei aneinander haftende Oberflächen voneinander trennen. Mit Ausnahme von Kapillarphänomenen ist die Oberflächenenergie nicht nur abhängig von Translationen der Kontaktlinie, sondern auch von Änderungen in der Steigung oder sogar Krümmung. Die sich ergebenden Randbedingungen entsprechen den Gleichgewichtsbedingungen an Kräfte und Drehmomente, falls sich die Kontaktlinie frei bewegen kann. Wenn eine der Oberflächen starr ist, muss die Variation lokal dieser Fläche folgen. Spannungen und Drehmomente tragen dann zu einer einzigen Gleichgewichtsbedingung bei; ihre Beiträge können nicht mehr einzeln identifiziert werden. Um quantitative Aussagen über das Verhalten einer fluiden Oberfläche zu machen, müssen ihre elastischen Eigenschaften bekannt sein. Der "Nanotrommel"-Versuchsaufbau ermöglicht es, Membraneigenschaften lokal zu untersuchen: Er besteht aus einer porenüberspannenden Membran, die während des Experiments durch die Spitze eines Rasterkraftmikroskops in die Pore gedrückt wird. Der lineare Verlauf der resultierenden Kraft-Abstands-Kurven kann mit Hilfe der in dieser Arbeit entwickelten Theorie reproduziert werden, wenn der Einfluss von Adhäsion zwischen Spitze und Membran vernachlässigt wird. Bezieht man diesen Effekt in die Rechnungen mit ein, ändert sich das Resultat erheblich: Kraft-Abstands-Kurven sind nicht länger linear, Hysterese und nichtverschwindende Trennkräfte treten auf. Die Voraussagen der Rechnungen könnten in zukünftigen Experimenten dazu verwendet werden, Parameter wie die Biegesteifigkeit der Membran mit einer Auflösung im Nanometerbereich zu bestimmen. Wenn die Materialeigenschaften bekannt sind, können Probleme der Membranmechanik genauer betrachtet werden. Oberflächenvermittelte Wechselwirkungen sind in diesem Zusammenhang ein interessantes Beispiel. Mit Hilfe des oben erwähnten Spannungstensors können analytische Ausdrücke für die krümmungsvermittelte Kraft zwischen zwei Teilchen, die z. B. Proteine repräsentieren, hergeleitet werden. Zusätzlich wird das Gleichgewicht der Kräfte und Drehmomente genutzt, um mehrere Bedingungen an die Geometrie der Membran abzuleiten. Für den Fall zweier unendlich langer Zylinder auf der Membran werden diese Bedingungen zusammen mit Profilberechnungen kombiniert, um quantitative Aussagen über die Wechselwirkung zu treffen. Theorie und Experiment stoßen an ihre Grenzen, wenn es darum geht, die Relevanz von krümmungsvermittelten Wechselwirkungen in der biologischen Zelle korrekt zu beurteilen. In einem solchen Fall bieten Computersimulationen einen alternativen Ansatz: Die hier präsentierten Simulationen sagen voraus, dass Proteine zusammenfinden und Membranbläschen (Vesikel) bilden können, sobald jedes der Proteine eine Mindestkrümmung in der Membran induziert. Der Radius der Vesikel hängt dabei stark von der lokal aufgeprägten Krümmung ab. Das Resultat der Simulationen wird in dieser Arbeit durch ein approximatives theoretisches Modell qualitativ bestätigt.