This thesis describes for the first time, how the membrane capacitance of pluripotent human embryonic stem cells (H1, H9, RCM1) increases with their differentiation (H1-MSC, H9-MSC, RCM1-trophoblast) based on the literature review. The method used to determine membrane capacitance was dielectrophoresis (DEP), which is an electrokinetic technique capable of characterising and sorting cells without the need for antibody-based cell surface markers, magnetic beads, or other chemical tags. This finding has potential biomedical importance because human embryonic stem cell (hESCs) isolated from early blastocyst-stage embryos and differentiated progeny have been identified to be of possible use in drug screening and regenerative cell based therapeutic treatment. Current cell sorting methods require membrane surface markers that limit their applicability in stem cell therapeutics, a limitation that is either removed or reduced if DEP-based sorting was used. The work described in this thesis consists of the design, fabrication and testing of DEP based microfluidic devices for characterization and separation of human embryonic stem cells. The cells studied were human undifferentiated hESC lines (H1, H9, RCM1, RH1, and T8) and their differentiated progeny (H1-MSC, H9-MSC, RCM1-trophoblast, hES-MP). The cell membrane capacitance (Cm) of the cells was determined by measuring a parameter known as the DEP cross-over frequency (fxo), where the electrical polarisability of a cell equals that of its suspending electrolyte and so experiences no DEP force. The studies of hESC lines cultured from different sources indicate, on the basis of their similar Cm values, that they have similar membrane morphologies. The change in calculated Cm value upon differentiation of these hESCs indicates that changes occur in their membrane morphology, texturing and possibly of their membrane thickness. Subsequent enrichment of these hESCs from human dermal fibroblasts (hDFs) has been achieved based on fxo measurements. The results presented in this thesis confirm the existence, previously indicated in the literature, of distinctive parameters for undifferentiated and differentiating cells on which future application of DEP in hESC manufacturing can be based.

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Droplet Interface Bilayers (DIBs) have a number of attributes that distinguish them from conventional artificial lipid bilayers. In particular, the ability to manipulate bilayers mechanically is explored in this thesis. Directed bilayer area changes are used to make precise measurements of the specific capacitance of DIBs and to control the two dimensional concentration of a membrane protein reconstituted in the bilayer. Chapter 1 provides a general introduction to the role of the lipid membrane en- vironment in the function of biological membranes and their integral proteins. An overview of model lipid bilayer systems is given. Chapter 2 introduces work carried out in this laboratory previously and illustrates the experimental setup of DIBs. Some important bilayer biophysical concepts are covered to provide the theoretical background to experiments in this and in later chapters. Results from the characterisation of DIBs are reported, and an account of the development of methods to manipulate the bilayer by mechanical means is given. Chapter 3 describes experiments that apply bilayer area manipulation in DIBs to achieve precise measurement of specific capacitance in a range of lipid systems. Chapter 4 reports results from experiments investigating the response of bilayer specific capacitance to an applied potential. Chapter 5 covers the background and experimental setup for total internal fluo- rescence microscopy experiments in DIBs and describes the expression, purification and characterisation of the bacterial β-barrel membrane protein pore α-Hemolysin. Chapter 6 describes experiments that apply the mechanical manipulation of bilayer area in DIBs to the corralling and control of the surface density of α-Hemolysin.

Die elektrische Signalverarbeitung in Nervenzellen basiert auf deren erregbarer Zellmembran. Üblicherweise wird angenommen, dass die in der Membran eingebetteten leitfähigen Ionenkanäle nicht auf direkte Art gekoppelt sind und dass die Kapazität des von der Membran gebildeten Kondensators konstant ist. Allerdings scheinen diese Annahmen nicht für alle Nervenzellen zu gelten. Im Gegenteil, verschiedene Ionenkanäle “kooperieren” und auch die Vorstellung von einer konstanten spezifischen Membrankapazität wurde kürzlich in Frage gestellt. Die Auswirkungen dieser Abweichungen auf die elektrischen Eigenschaften von Nervenzellen ist das Thema der folgenden kumulativen Dissertationsschrift. Im ersten Projekt wird gezeigt, auf welche Weise stark kooperative spannungsabhängige Ionenkanäle eine Form von zellulärem Kurzzeitspeicher für elektrische Aktivität bilden könnten. Solche kooperativen Kanäle treten in der Membran häufig in kleinen räumlich getrennte Clustern auf. Basierend auf einem mathematischen Modell wird nachgewiesen, dass solche Kanalcluster als eine bistabile Leitfähigkeit agieren. Die dadurch entstehende große Speicherkapazität eines Ensembles dieser Kanalcluster könnte von Nervenzellen für stufenloses persistentes Feuern genutzt werden -- ein Feuerverhalten von Nutzen für das Kurzzeichgedächtnis. Im zweiten Projekt wird ein neues Dynamic Clamp Protokoll entwickelt, der Capacitance Clamp, das erlaubt, Änderungen der Membrankapazität in biologischen Nervenzellen zu emulieren. Eine solche experimentelle Möglichkeit, um systematisch die Rolle der Kapazität zu untersuchen, gab es bisher nicht. Nach einer Reihe von Tests in Simulationen und Experimenten wurde die Technik mit Körnerzellen des *Gyrus dentatus* genutzt, um den Einfluss von Kapazität auf deren Feuerverhalten zu studieren. Die Kombination beider Projekte zeigt die Relevanz dieser oft vernachlässigten Facetten von neuronalen Membranen für die Signalverarbeitung in Nervenzellen. / Electrical signaling in neurons is shaped by their specialized excitable cell membranes. Commonly, it is assumed that the ion channels embedded in the membrane gate independently and that the electrical capacitance of neurons is constant. However, not all excitable membranes appear to adhere to these assumptions. On the contrary, ion channels are observed to gate cooperatively in several circumstances and also the notion of one fixed value for the specific membrane capacitance (per unit area) across neuronal membranes has been challenged recently. How these deviations from the original form of conductance-based neuron models affect their electrical properties has not been extensively explored and is the focus of this cumulative thesis. In the first project, strongly cooperative voltage-gated ion channels are proposed to provide a membrane potential-based mechanism for cellular short-term memory. Based on a mathematical model of cooperative gating, it is shown that coupled channels assembled into small clusters act as an ensemble of bistable conductances. The correspondingly large memory capacity of such an ensemble yields an alternative explanation for graded forms of cell-autonomous persistent firing – an observed firing mode implicated in working memory. In the second project, a novel dynamic clamp protocol -- the capacitance clamp -- is developed to artificially modify capacitance in biological neurons. Experimental means to systematically investigate capacitance, a basic parameter shared by all excitable cells, had previously been missing. The technique, thoroughly tested in simulations and experiments, is used to monitor how capacitance affects temporal integration and energetic costs of spiking in dentate gyrus granule cells. Combined, the projects identify computationally relevant consequences of these often neglected facets of neuronal membranes and extend the modeling and experimental techniques to further study them.

Signalverarbeitung im Nervensystem hängt sowohl von der Netzwerkstruktur, als auch den zellulären Eigenschaften der Nervenzellen ab. In dieser Abhandlung werden zwei zelluläre Eigenschaften im Hinblick auf ihre funktionellen Anpassungsmöglichkeiten untersucht: Es wird gezeigt, dass neuronale Morphologie die Signalweiterleitung unter Berücksichtigung energetischer Beschränkungen verstärken kann, und dass selbst kleine Änderungen in biophysikalischen Parametern die Aktivierungsbifurkation in Nervenzellen, und damit deren Informationskodierung, wechseln können. Im ersten Teil dieser Abhandlung wird, unter Verwendung von mathematischen Modellen und Daten, die Hypothese aufgestellt, dass Energie-effiziente Signalweiterleitung als starker Evolutionsdruck für unterschiedliche Zellkörperlagen bei Nervenzellen wirkt. Um Energie zu sparen, kann die Signalweiterleitung vom Dendrit zum Axon verstärkt werden, indem relativ kleine Zellkörper zwischen Dendrit und Axon eingebaut werden, während relativ große Zellkörper besser ausgelagert werden. Im zweiten Teil wird gezeigt, dass biophysikalische Parameter, wie Temperatur, Membranwiderstand oder Kapazität, den Feuermechanismus des Neurons ändern, und damit gleichfalls Aktionspotential-basierte Informationsverarbeitung. Diese Arbeit identifiziert die sogenannte "saddle-node-loop" (Sattel-Knoten-Schlaufe) Bifurkation als den Übergang, der besonders drastische funktionale Auswirkungen hat. Neben der Änderung neuronaler Filtereigenschaften sowie der Ankopplung an Stimuli, führt die "saddle-node-loop" Bifurkation zu einer Erhöhung der Netzwerk-Synchronisation, was möglicherweise für das Auslösen von Anfällen durch Temperatur, wie bei Fieberkrämpfen, interessant sein könnte. / Signal processing in nervous systems is shaped by the connectome as well as the cellular properties of nerve cells. In this thesis, two cellular properties are investigated with respect to the functional adaptations they provide: It is shown that neuronal morphology can improve signal transmission under energetic constraints, and that even small changes in biophysical parameters can switch spike generation, and thus information encoding. In the first project of the thesis, mathematical modeling and data are deployed to suggest energy-efficient signaling as a major evolutionary pressure behind morphological adaptations of cell body location: In order to save energy, the electrical signal transmission from dendrite to axon can be enhanced if a relatively small cell body is located between dendrite and axon, while a relatively large cell body should be externalized. In the second project, it is shown that biophysical parameters, such as temperature, membrane leak or capacitance, can transform neuronal excitability (i.e., the spike onset bifurcation) and, with that, spike-based information processing. This thesis identifies the so-called saddle-node-loop bifurcation as the transition with particularly drastic functional implications. Besides altering neuronal filters and stimulus locking, the saddle-node-loop bifurcation leads to an increase in network synchronization, which may potentially be relevant for the initiation of seizures in response to increased temperature, such as during fever cramps.