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).

Probing the interaction of brain fatty acid binding protein (B-FABP) with model membranes

Brain fatty acid-binding protein (B-FABP) interacts with biological membranes and delivers polyunsaturated fatty acids (FAs) via a collisional mechanism. The binding of FAs in the protein and the interaction with membranes involve a motif called "portal region", formed by two small α-helices, A1 and A2, connected by a loop. We used a combination of site-directed mutagenesis and electron spin resonance to probe the changes in the protein and in the membrane model induced by their interaction. Spin labeled B-FABP mutants and lipidic spin probes incorporated into a membrane model confirmed that BFABP interacts with micelles through the portal region and led to structural changes in the protein as well in the micelles. These changes were greater in the presence of LPG when compared to the LPC models. ESR spectra of B-FABP labeled mutants showed the presence of two groups of residues that responded to the presence of micelles in opposite ways. In the presence of lysophospholipids, group I of residues, whose side chains point outwards from the contact region between the helices, had their mobility decreased in an environment of lower polarity when compared to the same residues in solution. The second group, composed by residues with side chains situated at the interface between the α-helices, experienced an increase in mobility in the presence of the model membranes. These modifications in the ESR spectra of B-FABP mutants are compatible with a less ordered structure of the portal region inner residues (group II) that is likely to facilitate the delivery of FAs to target membranes. On the other hand, residues in group I and micelle components have their mobilities decreased probably as a result of the formation of a collisional complex. Our results bring new insights for the understanding of the gating and delivery mechanisms of FABPs.

Caratterizzazione di membrane da nanofiltrazione

Nanofiltration (NF) is a pressure-driven membrane process, intermediate between reverse osmosis and ultrafiltration. Commercially available polymeric membranes have been used in a wide range of applications, such as drinking, process industry and waste water treatment. For all the applications requiring high stability and harsh washing procedures inorganic membranes are preferred due to their high chemical inertia. Typically, γ – Al2O3 as well as TiO2 and ZrO2 selective layers are used; the latter show higher chemical stability in a wide range of pH and temperatures. In this work the experimental characterization of two different type of membrane has been performed in order to investigate permeation properties, separation performance and efficiency with aqueous solutions containing strong inorganic electrolytes. The influence of salt concentration and feed pH as well as the role of concentration polarization and electrolyte type on the membrane behavior are investigated. Experimentation was performed testing a multi–layer structured NF membrane in α-Al2O3, TiO2 and ZrO2, and a polymeric membrane, in polyamide supported on polysulfone, with binary aqueous solutions containing NaCl, Na2SO4 or CaCl2; the effect of salt composition and pH in the feed side was studied both on flux and salt rejection. All the NF experimental data available for the two membranes were used to evaluate the volumetric membrane charge (X) corresponding to each operative conditions investigated, through the Donnan Steric Pore Model and Dielectric Exclusion (DSPM&DE). The results obtained allow to understand which are the main phenomena at the basis of the different behaviors observed.

Caratterizzazione di membrane metalliche e ionomeriche per applicazioni energetiche

The work of this thesis has been focused on the characterization of metallic membranes for the hydrogen purification from steam reforming process and also of perfluorosulphonic acid ionomeric (PFSI) membranes suitable as electrolytes in fuel cell applications. The experimental study of metallic membranes was divided in three sections: synthesis of palladium and silver palladium coatings on porous ceramic support via electroless deposition (ELD), solubility and diffusivity analysis of hydrogen in palladium based alloys (temperature range between 200 and 400 °C up to 12 bar of pressure) and permeation experiments of pure hydrogen and mixtures containing, besides hydrogen, also nitrogen and methane at high temperatures (up to 600 °C) and pressures (up to 10 bar). Sequential deposition of palladium and silver on to porous alumina tubes by ELD technique was carried out using two different procedures: a stirred batch and a continuous flux method. Pure palladium as well as Pd-Ag membranes were produced: the Pd-Ag membranes’ composition is calculated to be close to 77% Pd and 23% Ag by weight which was the target value that correspond to the best performance of the palladium-based alloys. One of the membranes produced showed an infinite selectivity through hydrogen and relatively high permeability value and is suitable for the potential use as a hydrogen separator. The hydrogen sorption in silver palladium alloys was carried out in a gravimetric system on films produced by ELD technique. In the temperature range inspected, up to 400°C, there is still a lack in literature. The experimental data were analyzed with rigorous equations allowing to calculate the enthalpy and entropy values of the Sieverts’ constant; the results were in very good agreement with the extrapolation made with literature data obtained a lower temperature (up to 150 °C). The information obtained in this study would be directly usable in the modeling of hydrogen permeation in Pd-based systems. Pure and mixed gas permeation tests were performed on Pd-based hydrogen selective membranes at operative conditions close to steam-reforming ones. Two membranes (one produced in this work and another produced by NGK Insulators Japan) showed a virtually infinite selectivity and good permeability. Mixture data revealed the existence of non negligible resistances to hydrogen transport in the gas phase. Even if the decrease of the driving force due to polarization concentration phenomena occurs, in principle, in all membrane-based separation systems endowed with high perm-selectivity, an extensive experimental analysis lack, at the moment, in the palladium-based membrane process in literature. Moreover a new procedure has been introduced for the proper comparison of the mass transport resistance in the gas phase and in the membrane. Another object of study was the water vapor sorption and permeation in PFSI membranes with short and long side chains was also studied; moreover the permeation of gases (i.e. He, N2 and O2) in dry and humid conditions was considered. The water vapor sorption showed strong interactions between the hydrophilic groups and the water as revealed from the hysteresis in the sorption-desorption isotherms and thermo gravimetric analysis. The data obtained were used in the modeling of water vapor permeation, that was described as diffusion-reaction of water molecules, and in the humid gases permeation experiments. In the dry gas experiments the permeability and diffusivity was found to increase with temperature and with the equivalent weight (EW) of the membrane. A linear correlation was drawn between the dry gas permeability and the opposite of the equivalent weight of PFSI membranes, based on which the permeability of pure PTFE is retrieved in the limit of high EW. In the other hand O2 ,N2 and He permeability values was found to increase significantly, and in a similar fashion, with water activity. A model that considers the PFSI membrane as a composite matrix with a hydrophilic and a hydrophobic phase was considered allowing to estimate the variation of gas permeability with relative humidity on the basis of the permeability in the dry PFSI membrane and in pure liquid water.

Studio Sperimentale e Modellazione della Separazione di Proteine con Membrane di Affinità

Chromatography represents one of the most important and widely used unit operation in the biotechnology industry. However this technique suffers from several limitations such as high pressure drop, slow mass transfer through the diffusive pores and strong dependence of the binding capacity on flow rate. In this work, affinity membranes with improved capacity have been considered as an alternative technology for the capturing step in antibody manufacturing. Several affinity membranes have been prepared starting from various membrane supports. Different affinity ligands have been utilized like Protein A, the natural ligand of choice for antibodies, as well as synthetic ligands that exhibit affinity for the Fc portion of antibodies. The membranes have been characterized in detail: binding and elution performance was evaluated in adsorption experiments using pure IgG solutions, while membrane selectivity was evaluated using complex solutions like a cell culture supernatant. The most promising affinity membranes were extensively tested in dynamic experiments. The effects of operating parameters like feed concentration and flow rate on separation performances like binding capacity, selectivity and process yield have been studied in detail in order to find the optimal conditions for binding and elution steps. The membranes have been used over several complete chromatographic cycles to evaluate the effects of ageing and of membrane regeneration on dynamic binding capacity. A novel mathematical model is proposed that can describe all the chromatographic steps involved in the membrane affinity chromatography process for protein purification. The mathematical description is based on the species continuity equation coupled with a proper binding kinetic equation, and suitable to describe adequately the dispersion phenomena occurring both in the micro-porous membranes as well as in the extra-column devices used in the system. The model considers specifically all the different chromatographic steps, namely adsorption, washing and elution. The few relevant fitting parameters of the model were derived from a calibration with the experimental affinity cycles performed with pure IgG solutions, then the model is used to describe experimental data obtained in chromatographic cycles carried out with complex feeds as the cell culture supernatant. Simulations reveal a good agreement with experimental data in all the chromatography steps, both in the case of pure IgG solutions and for the cell culture supernatant considered.

Trasporto di materia in membrane polimeriche e nanocomposite per la separazione di gas

Membrane-based separation processes are acquiring, in the last years, an increasing importance because of their intrinsic energetic and environmental sustainability: some types of polymeric materials, showing adequate perm-selectivity features, appear rather suitable for these applications, because of their relatively low cost and easy processability. In this work have been studied two different types of polymeric membranes, in view of possible applications to the gas separation processes, i.e. Mixed Matrix Membranes (MMMs) and high free volume glassy polymers. Since the early 90’s, it has been understood that the performances of polymeric materials in the field of gas separations show an upper bound in terms of permeability and selectivity: in particular, an increase of permeability is often accompanied by a decrease of selectivity and vice-versa, while several inorganic materials, like zeolites or silica derivates, can overcome this limitation. As a consequence, it has been developed the idea of dispersing inorganic particles in polymeric matrices, in order to obtain membranes with improved perm-selectivity features. In particular, dispersing fumed silica nanoparticles in high free volume glassy polymers improves in all the cases gases and vapours permeability, while the selectivity may either increase or decrease, depending upon material and gas mixture: that effect is due to the capacity of nanoparticles to disrupt the local chain packing, increasing the dimensions of excess free volume elements trapped in the polymer matrix. In this work different kinds of MMMs were fabricated using amorphous Teflon® AF or PTMSP and fumed silica: in all the cases, a considerable increase of solubility, diffusivity and permeability of gases and vapours (n-alkanes, CO2, methanol) was observed, while the selectivity shows a non-monotonous trend with filler fraction. Moreover, the classical models for composites are not able to capture the increase of transport properties due to the silica addition, so it has been necessary to develop and validate an appropriate thermodynamic model that allows to predict correctly the mass transport features of MMMs. In this work, another material, called poly-trimethylsilyl-norbornene (PTMSN) was examined: it is a new generation high free volume glassy polymer that, like PTMSP, shows unusual high permeability and selectivity levels to the more condensable vapours. These two polymer differ each other because PTMSN shows a more pronounced chemical stability, due to its structure double-bond free. For this polymer, a set of Lattice Fluid parameters was estimated, making possible a comparison between experimental and theoretical solubility isotherms for hydrocarbons and alcoholic vapours: the successfully modelling task, based on application of NELF model, offers a reliable alternative to direct sorption measurement, which is extremely time-consuming due to the relevant relaxation phenomena showed by each sorption step. For this material also dilation experiments were performed, in order to quantify its dimensional stability in presence of large size, swelling vapours.

Expressions- und Funktionsanalysen von "Tetraspan Vesicle Membrane Proteins" in Caenorhabditis elegans

Tetraspan vesicle membrane proteins (TVPs) sind ubiquitäre Komponenten von Transportvesikeln. Bei den Säugetieren unterscheidet man drei Familien, die Physine, Gyrine und SCAMPs (secretory carrier-associated membrane proteins). Ihre Funktion ist weitgehend unbekannt, es wird jedoch vermutet, dass sie eine Rolle bei der Vesikelbildung und der Vesikelrezirkulierung spielen. In Caenorhabditis elegans existiert von jeder Familie jeweils nur ein einziges Polypeptid: für die Physine Synaptophysin (SPH-1), für die Gyrine Synaptogyrin (SNG-1) und für die SCAMPs SCAMP (SCM-1). Ziel der Arbeit war es die Verteilung der C. elegans TVPs zu untersuchen und ihre Funktion unter besonderer Berücksichtigung der vesikelvermittelten synaptischen Kopplung zu bestimmen. Wenn die C. elegans TVPs in humanen Epithelzellen synthetisiert werden, lokalisieren sie in zytoplasmatischen Vesikeln. In Kotransfektionsexperimenten wurde gezeigt, dass sie größtenteils in den gleichen Strukturen enthalten sind. In C. elegans synthetisierte TVP-Reporterkonstrukte können in unterschiedlichen Geweben nachgewiesen werden. Dabei ist SNG-1 fast ausschließlich in Neuronen zu finden. SPH-1 und SCM-1 hingegen weisen komplexe und teilweise überlappende Verteilungsmuster auf. Während für SPH-1 eine starke Fluoreszenz im Pharynx, auf der apikalen Seite der Darmzellen oberhalb des sog. terminal webs und in adluminalen Regionen von exkretorischen Geweben gefunden wurde, war SCM-1 stark in der Muskulatur und den Coelomozyten vertreten. Die Expression von SCM-1 in Pharynx und Darm war deutlich schwächer. Die C. elegans TVPs werden früh in der Entwicklung ab der Gastrulation (SPH-1 und SCM-1) bzw. ab der Neurulation im sog. Komma-Stadium (SNG-1) produziert. Um die Funktion der TVPs in C. elegans zu untersuchen, wurden TVP-Mutanten analysiert. Durch Kombination aller drei TVP-Gen-Mutanten wurden TVP-Dreifachmutanten generiert. Diese wiesen keinen offensichtlichen Defekt im Bewegungsmuster auf, entwickelten sich normal und bildeten ein normales Nervensystem aus. Auch auf unterschiedliche chemische und physikalische Reize in sensorischen Tests reagierten die TVP-Dreifachmutanten in gleicher Weise wie Wildtyptiere. Ebenso zeigen die TVP-Dreifachmutanten elektrophysiologisch unter normalen Bedingungen keine anormalen Reaktionsmuster. In ultrastrukturellen Untersuchungen wurde lediglich eine signifikant erhöhte Anzahl Clathrin-ummantelter Vesikel in cholinergen Synapsen gefunden. Erst unter Stressbedingungen, hervorgerufen durch den GABA-Antagonisten Pentylentetrazol (PTZ), wiesen sowohl die TVP-Dreifach- als auch die TVP-Einzelmutanten eine deutlich erhöhte Krampfbereitschaft auf. Zusammengenommen zeigen die Analysen, dass TVPs zwar für grundlegende neuronale Prozesse nicht notwendig sind, dass sie aber auf der anderen Seite vermutlich an alternativen redundanten Wegen der Neurotransmitterfreisetzung beteiligt sind.

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.

EPR spectroscopic investigation of membrane protein structure and folding on light harvesting complex LHCIIb

Structure and folding of membrane proteins are important issues in molecular and cell biology. In this work new approaches are developed to characterize the structure of folded, unfolded and partially folded membrane proteins. These approaches combine site-directed spin labeling and pulse EPR techniques. The major plant light harvesting complex LHCIIb was used as a model system. Measurements of longitudinal and transversal relaxation times of electron spins and of hyperfine couplings to neighboring nuclei by electron spin echo envelope modulation(ESEEM) provide complementary information about the local environment of a single spin label. By double electron electron resonance (DEER) distances in the nanometer range between two spin labels can be determined. The results are analyzed in terms of relative water accessibilities of different sites in LHCIIb and its geometry. They reveal conformational changes as a function of micelle composition. This arsenal of methods is used to study protein folding during the LHCIIb self assembly and a spatially and temporally resolved folding model is proposed. The approaches developed here are potentially applicable for studying structure and folding of any protein or other self-assembling structure if site-directed spin labeling is feasible and the time scale of folding is accessible to freeze-quench techniques.

Machine-learning methods for structure prediction of β-barrel membrane proteins

Different types of proteins exist with diverse functions that are essential for living organisms. An important class of proteins is represented by transmembrane proteins which are specifically designed to be inserted into biological membranes and devised to perform very important functions in the cell such as cell communication and active transport across the membrane. Transmembrane β-barrels (TMBBs) are a sub-class of membrane proteins largely under-represented in structure databases because of the extreme difficulty in experimental structure determination. For this reason, computational tools that are able to predict the structure of TMBBs are needed. In this thesis, two computational problems related to TMBBs were addressed: the detection of TMBBs in large datasets of proteins and the prediction of the topology of TMBB proteins. Firstly, a method for TMBB detection was presented based on a novel neural network framework for variable-length sequence classification. The proposed approach was validated on a non-redundant dataset of proteins. Furthermore, we carried-out genome-wide detection using the entire Escherichia coli proteome. In both experiments, the method significantly outperformed other existing state-of-the-art approaches, reaching very high PPV (92%) and MCC (0.82). Secondly, a method was also introduced for TMBB topology prediction. The proposed approach is based on grammatical modelling and probabilistic discriminative models for sequence data labeling. The method was evaluated using a newly generated dataset of 38 TMBB proteins obtained from high-resolution data in the PDB. Results have shown that the model is able to correctly predict topologies of 25 out of 38 protein chains in the dataset. When tested on previously released datasets, the performances of the proposed approach were measured as comparable or superior to the current state-of-the-art of TMBB topology prediction.

Statistical problems related to excitation threshold and reset value of membrane potentials

Die vorliegende Arbeit ist motiviert durch biologische Fragestellungen bezüglich des Verhaltens von Membranpotentialen in Neuronen. Ein vielfach betrachtetes Modell für spikende Neuronen ist das Folgende. Zwischen den Spikes verhält sich das Membranpotential wie ein Diffusionsprozess X der durch die SDGL dX_t= beta(X_t) dt+ sigma(X_t) dB_t gegeben ist, wobei (B_t) eine Standard-Brown'sche Bewegung bezeichnet. Spikes erklärt man wie folgt. Sobald das Potential X eine gewisse Exzitationsschwelle S überschreitet entsteht ein Spike. Danach wird das Potential wieder auf einen bestimmten Wert x_0 zurückgesetzt. In Anwendungen ist es manchmal möglich, einen Diffusionsprozess X zwischen den Spikes zu beobachten und die Koeffizienten der SDGL beta() und sigma() zu schätzen. Dennoch ist es nötig, die Schwellen x_0 und S zu bestimmen um das Modell festzulegen. Eine Möglichkeit, dieses Problem anzugehen, ist x_0 und S als Parameter eines statistischen Modells aufzufassen und diese zu schätzen. In der vorliegenden Arbeit werden vier verschiedene Fälle diskutiert, in denen wir jeweils annehmen, dass das Membranpotential X zwischen den Spikes eine Brown'sche Bewegung mit Drift, eine geometrische Brown'sche Bewegung, ein Ornstein-Uhlenbeck Prozess oder ein Cox-Ingersoll-Ross Prozess ist. Darüber hinaus beobachten wir die Zeiten zwischen aufeinander folgenden Spikes, die wir als iid Treffzeiten der Schwelle S von X gestartet in x_0 auffassen. Die ersten beiden Fälle ähneln sich sehr und man kann jeweils den Maximum-Likelihood-Schätzer explizit angeben. Darüber hinaus wird, unter Verwendung der LAN-Theorie, die Optimalität dieser Schätzer gezeigt. In den Fällen OU- und CIR-Prozess wählen wir eine Minimum-Distanz-Methode, die auf dem Vergleich von empirischer und wahrer Laplace-Transformation bezüglich einer Hilbertraumnorm beruht. Wir werden beweisen, dass alle Schätzer stark konsistent und asymptotisch normalverteilt sind. Im letzten Kapitel werden wir die Effizienz der Minimum-Distanz-Schätzer anhand simulierter Daten überprüfen. Ferner, werden Anwendungen auf reale Datensätze und deren Resultate ausführlich diskutiert.

Periodicities in the Hodgkin-Huxley model and versions of this model with stochastic input

A field of computational neuroscience develops mathematical models to describe neuronal systems. The aim is to better understand the nervous system. Historically, the integrate-and-fire model, developed by Lapique in 1907, was the first model describing a neuron. In 1952 Hodgkin and Huxley [8] described the so called Hodgkin-Huxley model in the article “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve”. The Hodgkin-Huxley model is one of the most successful and widely-used biological neuron models. Based on experimental data from the squid giant axon, Hodgkin and Huxley developed their mathematical model as a four-dimensional system of first-order ordinary differential equations. One of these equations characterizes the membrane potential as a process in time, whereas the other three equations depict the opening and closing state of sodium and potassium ion channels. The membrane potential is proportional to the sum of ionic current flowing across the membrane and an externally applied current. For various types of external input the membrane potential behaves differently. This thesis considers the following three types of input: (i) Rinzel and Miller [15] calculated an interval of amplitudes for a constant applied current, where the membrane potential is repetitively spiking; (ii) Aihara, Matsumoto and Ikegaya [1] said that dependent on the amplitude and the frequency of a periodic applied current the membrane potential responds periodically; (iii) Izhikevich [12] stated that brief pulses of positive and negative current with different amplitudes and frequencies can lead to a periodic response of the membrane potential. In chapter 1 the Hodgkin-Huxley model is introduced according to Izhikevich [12]. Besides the definition of the model, several biological and physiological notes are made, and further concepts are described by examples. Moreover, the numerical methods to solve the equations of the Hodgkin-Huxley model are presented which were used for the computer simulations in chapter 2 and chapter 3. In chapter 2 the statements for the three different inputs (i), (ii) and (iii) will be verified, and periodic behavior for the inputs (ii) and (iii) will be investigated. In chapter 3 the inputs are embedded in an Ornstein-Uhlenbeck process to see the influence of noise on the results of chapter 2.

Chemopreventive effects of eicosapentaenoic acid free fatty acid in a murine model of colitis-associated colorectal cancer

Inflammatory bowel diseases are associated with increased risk of developing colitis-associated colorectal cancer (CAC). Epidemiological data show that the consumption of ω-3 polyunsaturated fatty acids (ω-3 PUFAs) decreases the risk of sporadic colorectal cancer (CRC). Importantly, recent data have shown that eicosapentaenoic acid-free fatty acid (EPA-FFA) reduces polyps formation and growth in models of familial adenomatous polyposis. However, the effects of dietary EPA-FFA are unknown in CAC. We tested the effectiveness of substituting EPA-FFA, for other dietary fats, in preventing inflammation and cancer in the AOM-DSS model of CAC. The AOM-DSS protocols were designed to evaluate the effect of EPA-FFA on both initiation and promotion of carcinogenesis. We found that EPA-FFA diet strongly decreased tumor multiplicity, incidence and maximum tumor size in the promotion and initiation arms. Moreover EPA-FFA, in particular in the initiation arm, led to reduced cell proliferation and nuclear β-catenin expression, whilst it increased apoptosis. In both arms, EPA-FFA treatment led to increased membrane switch from ω-6 to ω-3 PUFAs and a concomitant reduction in PGE2 production. We observed no significant changes in intestinal inflammation between EPA-FFA treated arms and AOM-DSS controls. Importantly, we found that EPA-FFA treatment restored the loss of Notch signaling found in the AOM-DSS control, resulted in the enrichment of Lactobacillus species in the gut microbiota and led to tumor suppressor miR34-a induction. In conclusion, our data suggest that EPA-FFA is an effective chemopreventive agent in CAC.

Excitability properties of mouse motor axons in the mutant SOD1(G93A) model of amyotrophic lateral sclerosis

Non-invasive excitability studies of motor axons in patients with amyotrophic lateral sclerosis (ALS) have revealed a changing pattern of abnormal membrane properties with disease progression, but the heterogeneity of the changes has made it difficult to relate them to pathophysiology. The SOD1(G93A) mouse model of ALS displays more synchronous motoneuron pathology. Multiple excitability measures of caudal and sciatic nerves in mutant and wild-type mice were compared before onset of signs and during disease progression (4-19 weeks), and they were related to changes in muscle fiber histochemistry. Excitability differences indicated a modest membrane depolarization in SOD1(G93A) axons at about the time of symptom onset (8 weeks), possibly due to deficient energy supply. Previously described excitability changes in ALS patients, suggesting altered sodium and potassium conductances, were not seen in the mice. This suggests that those changes relate to features of the human disease that are not well represented in the animal model.