Role of nitric oxide and endocannabinoids in synaptic plasticity in the perirhinal cortex and in visual recognition memory

Introduction and aims of the research Nitric oxide (NO) and endocannabinoids (eCBs) are major retrograde messengers, involved in synaptic plasticity (long-term potentiation, LTP, and long-term depression, LTD) in many brain areas (including hippocampus and neocortex), as well as in learning and memory processes. NO is synthesized by NO synthase (NOS) in response to increased cytosolic Ca2+ and mainly exerts its functions through soluble guanylate cyclase (sGC) and cGMP production. The main target of cGMP is the cGMP-dependent protein kinase (PKG). Activity-dependent release of eCBs in the CNS leads to the activation of the Gαi/o-coupled cannabinoid receptor 1 (CB1) at both glutamatergic and inhibitory synapses. The perirhinal cortex (Prh) is a multimodal associative cortex of the temporal lobe, critically involved in visual recognition memory. LTD is proposed to be the cellular correlate underlying this form of memory. Cholinergic neurotransmission has been shown to play a critical role in both visual recognition memory and LTD in Prh. Moreover, visual recognition memory is one of the main cognitive functions impaired in the early stages of Alzheimer’s disease. The main aim of my research was to investigate the role of NO and ECBs in synaptic plasticity in rat Prh and in visual recognition memory. Part of this research was dedicated to the study of synaptic transmission and plasticity in a murine model (Tg2576) of Alzheimer’s disease. Methods Field potential recordings. Extracellular field potential recordings were carried out in horizontal Prh slices from Sprague-Dawley or Dark Agouti juvenile (p21-35) rats. LTD was induced with a single train of 3000 pulses delivered at 5 Hz (10 min), or via bath application of carbachol (Cch; 50 μM) for 10 min. LTP was induced by theta-burst stimulation (TBS). In addition, input/output curves and 5Hz-LTD were carried out in Prh slices from 3 month-old Tg2576 mice and littermate controls. Behavioural experiments. The spontaneous novel object exploration task was performed in intra-Prh bilaterally cannulated adult Dark Agouti rats. Drugs or vehicle (saline) were directly infused into the Prh 15 min before training to verify the role of nNOS and CB1 in visual recognition memory acquisition. Object recognition memory was tested at 20 min and 24h after the end of the training phase. Results Electrophysiological experiments in Prh slices from juvenile rats showed that 5Hz-LTD is due to the activation of the NOS/sGC/PKG pathway, whereas Cch-LTD relies on NOS/sGC but not PKG activation. By contrast, NO does not appear to be involved in LTP in this preparation. Furthermore, I found that eCBs are involved in LTP induction, but not in basal synaptic transmission, 5Hz-LTD and Cch-LTD. Behavioural experiments demonstrated that the blockade of nNOS impairs rat visual recognition memory tested at 24 hours, but not at 20 min; however, the blockade of CB1 did not affect visual recognition memory acquisition tested at both time points specified. In three month-old Tg2576 mice, deficits in basal synaptic transmission and 5Hz-LTD were observed compared to littermate controls. Conclusions The results obtained in Prh slices from juvenile rats indicate that NO and CB1 play a role in the induction of LTD and LTP, respectively. These results are confirmed by the observation that nNOS, but not CB1, is involved in visual recognition memory acquisition. The preliminary results obtained in the murine model of Alzheimer’s disease indicate that deficits in synaptic transmission and plasticity occur very early in Prh; further investigations are required to characterize the molecular mechanisms underlying these deficits.

Stochastic models and dynamic measures for the characterization of bistable circuits

During the last few years, a great deal of interest has risen concerning the applications of stochastic methods to several biochemical and biological phenomena. Phenomena like gene expression, cellular memory, bet-hedging strategy in bacterial growth and many others, cannot be described by continuous stochastic models due to their intrinsic discreteness and randomness. In this thesis I have used the Chemical Master Equation (CME) technique to modelize some feedback cycles and analyzing their properties, including experimental data. In the first part of this work, the effect of stochastic stability is discussed on a toy model of the genetic switch that triggers the cellular division, which malfunctioning is known to be one of the hallmarks of cancer. The second system I have worked on is the so-called futile cycle, a closed cycle of two enzymatic reactions that adds and removes a chemical compound, called phosphate group, to a specific substrate. I have thus investigated how adding noise to the enzyme (that is usually in the order of few hundred molecules) modifies the probability of observing a specific number of phosphorylated substrate molecules, and confirmed theoretical predictions with numerical simulations. In the third part the results of the study of a chain of multiple phosphorylation-dephosphorylation cycles will be presented. We will discuss an approximation method for the exact solution in the bidimensional case and the relationship that this method has with the thermodynamic properties of the system, which is an open system far from equilibrium.In the last section the agreement between the theoretical prediction of the total protein quantity in a mouse cells population and the observed quantity will be shown, measured via fluorescence microscopy.

Analysis of the memory B cell response against glycoconjugate vaccines

The development of vaccines directed against polysaccharide capsules of S. pneumoniae, H. influenzae and N. meningitidis have been of great importance in preventing potentially fatal infections. Bacterial capsular polysaccharides are T-cell-independent antigens that induce specific antibody response characterized by IgM immunoglobulins, with a very low IgG class switched response and lack of capability of inducing a booster response. The inability of pure polysaccharides to induce sustained immune responses has required the development of vaccines containing polysaccharides conjugated to a carrier protein, with the aim to generate T cell help. It is clear that the immunogenicity of glycoconjugate vaccines can vary depending on different factors, e.g. chemical nature of the linked polysaccharide, carrier protein, age of the target population, adjuvant used. The present study analyzes the memory B cell (MBC) response to the polysaccharide and to the carrier protein following vaccination with a glycoconjugate vaccine for the prevention of Group B streptococcus (GBS) infection. Not much is known about the role of adjuvants in the development of immunological memory raised against GBS polysaccharides, as well as about the influence of having a pre-existing immunity against the carrier protein on the B cell response raised against the polysaccharide component of the vaccine. We demonstrate in the mouse model that adjuvants can increase the antibody and memory B cell response to the carrier protein and to the conjugated polysaccharide. We also demonstrate that a pre-existing immunity to the carrier protein favors the development of the antibody and memory B cell response to subsequent vaccinations with a glycoconjugate, even in absence of adjuvants. These data provide a useful insight for a better understanding of the mechanism of action of this class of vaccines and for designing the best vaccine that could result in a productive and long lasting memory response.

Nonverbal emotional regulation in psychotherapy process according to an intersubjective perspective

In recent decades fascinating studies in developmental psychology, especially in infant research (for review see Lavelli, 2007) and recent discoveries in neuroscience (Welsh, et al, 2007; Siegel, 2001; Pally, 2007) have brought great interest to study the mode of sharing subjective experiences (affective states, intentions and attentional focus) in children and adults.It therefore appears today in the clinic is a growing consensus about the fact that the psychological disorder can be read as a deficit in intersubjective processes of affect regulation (see Benecke C. et al 2005; psychodynamic Diagnostic Manual-PDM, 2006) leading many authors to assume the centrality of affect regulation in the construction of the psychotherapeutic process of change (just to name a few Tronick, Greenberg, Stern, Sander, Fonagy, Beebe, Philippot, Rimé etc..). As previously stated, this study has led us to hypothesize that the long process of therapy is to assist with the sessions continue, a growing "emotional attunement" between the communication styles of both patient and therapist. And also to speculate that this synchronization can represent the existence of a significant positive correlation between the increased level of "emotional synchronization" and increased capacity for regulation of emotions by the patient.The research results despite the limitations of small sample showed encouraging results about the verification of the existence of an increasing degree of attunement between therapist and patient long psychotherapy sessions and also showed a good degree of positive correlation between the increase the latter construct and emotional regulation through the implicit mode of expression and nonverbal communication.

Sviluppo di un approccio congiunto fuzzy-Bayesiano per l'analisi e la modellizzazione degli ecosistemi: applicazione ad ecosistemi marini costieri.

Nell’attuale contesto di aumento degli impatti antropici e di “Global Climate Change” emerge la necessità di comprenderne i possibili effetti di questi sugli ecosistemi inquadrati come fruitori di servizi e funzioni imprescindibili sui quali si basano intere tessiture economiche e sociali. Lo studio previsionale degli ecosistemi si scontra con l’elevata complessità di questi ultimi in luogo di una altrettanto elevata scarsità di osservazioni integrate. L’approccio modellistico appare il più adatto all’analisi delle dinamiche complesse degli ecosistemi ed alla contestualizzazione complessa di risultati sperimentali ed osservazioni empiriche. L’approccio riduzionista-deterministico solitamente utilizzato nell’implementazione di modelli non si è però sin qui dimostrato in grado di raggiungere i livelli di complessità più elevati all’interno della struttura eco sistemica. La componente che meglio descrive la complessità ecosistemica è quella biotica in virtù dell’elevata dipendenza dalle altre componenti e dalle loro interazioni. In questo lavoro di tesi viene proposto un approccio modellistico stocastico basato sull’utilizzo di un compilatore naive Bayes operante in ambiente fuzzy. L’utilizzo congiunto di logica fuzzy e approccio naive Bayes è utile al processa mento del livello di complessità e conseguentemente incertezza insito negli ecosistemi. I modelli generativi ottenuti, chiamati Fuzzy Bayesian Ecological Model(FBEM) appaiono in grado di modellizare gli stati eco sistemici in funzione dell’ elevato numero di interazioni che entrano in gioco nella determinazione degli stati degli ecosistemi. Modelli FBEM sono stati utilizzati per comprendere il rischio ambientale per habitat intertidale di spiagge sabbiose in caso di eventi di flooding costiero previsti nell’arco di tempo 2010-2100. L’applicazione è stata effettuata all’interno del progetto EU “Theseus” per il quale i modelli FBEM sono stati utilizzati anche per una simulazione a lungo termine e per il calcolo dei tipping point specifici dell’habitat secondo eventi di flooding di diversa intensità.

Lernassoziierte Genexpression im murinen Hippokampus

Die bei Lern- und Gedächtnisvorgängen ablaufenden neurobiologischen Prozesse sind in ihrer Funktion bis heute nur unzureichend verstanden, wobei besonders die Rolle der lernabhängigen Genexpression unklar ist. Wiederholungen im Lernprozess fördern die Bildung von stabilen Gedächtnisinhalten. Die Lerneffiktivität kann hierbei durch lernfreie Zeitintervalle, insbesondere durch eingeschobene Schalfperioden, zusätzlich gesteigert werden. Entsprechend kann man den mehrtägigen Morris Water Maze (MWM)-Test mit einer verborgenen Plattform als einen mehrstufigen räumlichen Lernprozess bezeichnen. Dieser Test ist Hippokampus-abhängig und produziert Langzeitgedächtnisspuren in Nagern. Für diese Studie wurden FVB/NxC57Bl/6-Mäuse der F1-Generation über vier Tage in der MWM trainiert, das Erlernte in einem Probe Trial an Tag 5 überprüft und die Tiere gemäß ihrer Lernleistung in die beiden Gruppen „gute“ und „schlechte Lerner“ eingeteilt. Eine Analyse der hippokampalen Expression von Kandidatengenen per Microarray und Real-Time PCR erfolgte eine, sechs beziehungsweise 24 Stunden nach dem jeweils letzten Trainingslauf eines Tages. Durch den Vergleich von Schwimmkontrollen mit Test-naiven Mäusen wurde eine gleichgeschaltete, mit dem impliziten Lernen der MWM-Erfahrung der Tiere assoziierte unspezifische Genexpression festgestellt. Beim Vergleich der Schwimmkontrollen (ohne Plattform) mit den trainierten Tieren (verborgene Plattform mit konstanter Lokalisation) wurde in guten Lernern zu bestimmten Zeitpunkten eine Hochregulation von Genen, die mit Lernen und Gedächtnis (PP1, Kibra), neuronaler Aktivität (mt-CO1), Epigenetik (Dnmt3a, Dnmt3b) und neurodegenerativen Erkrankungen (Mapt, Sorl1) assoziiert sind, gefunden. Im Hippokampus der schlechten Lerner wurde eine im Vergleich zu den guten Lernern gesteigerte Synthese der mRNA von Genen festgestellt, die mit Lernen und Gedächtnis (Reelin, PP1, Kibra), Epigenetik (Dnmt1, Dnmt3a, Dnmt3b) und neurodegenerativen Erkrankungen (Mapt, Sorl1, APP) in Zusammenhang stehen. Diese Studie liefert somit den bisher ersten Hinweis, dass während eines mehrtägigen MWM-Lernprozesses eine abnormal erhöhte de novo-mRNA-Synthese mit verminderter Lernleistung in Zusammenhang steht.

Stimulus-induced gamma activity in the electrocorticogram of freely moving telemetric implanted rats: the neuronal signature of novelty detection

During this thesis a new telemetric recording system has been developed allowing ECoG/EEG recordings in freely behaving rodents (Lapray et al., 2008; Lapray et al., in press). This unit has been shown to not generate any discomfort in the implanted animals and to allow recordings in a wide range of environments. In the second part of this work the developed technique has been used to investigate what cortical activity was related to the process of novelty detection in rats’ barrel cortex. We showed that the detection of a novel object is accompanied in the barrel cortex by a transient burst of activity in the γ frequency range (40-47 Hz) around 200 ms after the whiskers contact with the object (Lapray et al., accepted). This activity was associated to a decrease in the lower range of γ frequencies (30-37 Hz). This network activity may represent the optimal oscillatory pattern for the propagation and storage of new information in memory related structures. The frequency as well as the timing of appearance correspond well with other studies concerning novelty detection related burst of activity in other sensory systems (Barcelo et al., 2006; Haenschel et al., 2000; Ranganath & Rainer, 2003). Here, the burst of activity is well suited to induce plastic and long-lasting modifications in neuronal circuits (Harris et al., 2003). The debate is still open whether synchronised activity in the brain is a part of information processing or an epiphenomenon (Shadlen & Movshon, 1999; Singer, 1999). The present work provides further evidence that neuronal network activity in the γ frequency range plays an important role in the neocortical processing of sensory stimuli and in higher cognitive functions.

Ruolo della Interleuchina-6 nella colite ulcerosa long-standing: regolazione della p53 ed induzione delle cellule mesenchimali epiteliali

L’infiammazione cronica è un fattore di rischio di insorgenza del cancro, e la citochina infiammatoria IL-6 gioca un ruolo importante nella tumorigenesi. In questo studio abbiamo dimostrato che L’IL-6 down-regola l'espressione e l'attività di p53. In linee cellulari umane, IL-6 stimola la trascrizione dell’rRNA mediante espressione della proteina c-myc a livello post-trascrizionale in un meccanismo p38MAPK-dipendente. L'up-regolazione della biogenesi ribosomiale riduce l'espressione di p53 attraverso l'attivazione della via della proteina ribosomale-MDM2. La down-regolazione di p53 produce l’acquisizione di modifiche fenotipiche e funzionali caratteristiche della epitelio mesenchimale di transizione, un processo associato a trasformazione maligna e progressione tumorale. I nostri dati mostrano che questi cambiamenti avvengono anche nelle cellule epiteliali del colon di pazienti affetti da colite ulcerosa, un esempio rappresentativo di una infiammazione cronica soggetta a trasformazione neoplastica, che scompaiono dopo trattamento con farmaci antinfiammatori. Questi risultati svelano un nuovo effetto oncogenico indotto dall’IL-6 che può contribuire notevolmente ad aumentare il rischio di sviluppare il cancro non solo in pazienti con infiammazioni croniche, ma anche in quei pazienti con condizioni patologiche caratterizzate da elevato livello di IL-6 nel plasma, quali l'obesità e e il diabete mellito di tipo 2.

Nonlinear Characterization and Modelling of GaN HEMTs for Microwave Power Amplifier Applications

Semiconductors technologies are rapidly evolving driven by the need for higher performance demanded by applications. Thanks to the numerous advantages that it offers, gallium nitride (GaN) is quickly becoming the technology of reference in the field of power amplification at high frequency. The RF power density of AlGaN/GaN HEMTs (High Electron Mobility Transistor) is an order of magnitude higher than the one of gallium arsenide (GaAs) transistors. The first demonstration of GaN devices dates back only to 1993. Although over the past few years some commercial products have started to be available, the development of a new technology is a long process. The technology of AlGaN/GaN HEMT is not yet fully mature, some issues related to dispersive phenomena and also to reliability are still present. Dispersive phenomena, also referred as long-term memory effects, have a detrimental impact on RF performances and are due both to the presence of traps in the device structure and to self-heating effects. A better understanding of these problems is needed to further improve the obtainable performances. Moreover, new models of devices that take into consideration these effects are necessary for accurate circuit designs. New characterization techniques are thus needed both to gain insight into these problems and improve the technology and to develop more accurate device models. This thesis presents the research conducted on the development of new charac- terization and modelling methodologies for GaN-based devices and on the use of this technology for high frequency power amplifier applications.

Emotional engagement and brain potentials: repetition in affective picture processing

The present thesis addresses several experimental questions regarding the nature of the processes underlying the larger centro-parietal Late Positive Potential (LPP) measured during the viewing of emotional(both pleasant and unpleasant) compared to neutral pictures. During a passive viewing condition, this modulatory difference is significantly reduced with picture repetition, but it does not completely habituate even after a massive repetition of the same picture exemplar. In order to investigate the obligatory nature of the affective modulation of the LPP, in Study 1 we introduced a competing task during repetitive exposure of affective pictures. Picture repetition occurred in a passive viewing context or during a categorization task, in which pictures depicting any mean of transportation were presented as targets, and repeated pictures (affectively engaging images) served as distractor stimuli. Results indicated that the impact of repetition on the LPP affective modulation was very similar between the passive and the task contexts, indicating that the affective processing of visual stimuli reflects an obligatory process that occurs despite participants were engaged in a categorization task. In study 2 we assessed whether the decrease of the LPP affective modulation persists over time, by presenting in day 2 the same set of pictures that were massively repeated in day 1. Results indicated that the reduction of the emotional modulation of the LPP to repeated pictures persisted even after 1-day interval, suggesting a contribution of long-term memory processes on the affective habituation of the LPP. Taken together, the data provide new information regarding the processes underlying the affective modulation of the late positive potential.

Mechanical microcontacts of powder particles studied with the quartz crystal microbalance

Within this work, a particle-polymer surface system is studied with respect to the particle-surface interactions. The latter are governed by micromechanics and are an important aspect for a wide range of industrial applications. Here, a new methodology is developed for understanding the adhesion process and measure the relevant forces, based on the quartz crystal microbalance, QCM. rnThe potential of the QCM technique for studying particle-surface interactions and reflect the adhesion process is evaluated by carrying out experiments with a custom-made setup, consisting of the QCM with a 160 nm thick film of polystyrene (PS) spin-coated onto the quartz and of glass particles, of different diameters (5-20µm), deposited onto the polymer surface. Shifts in the QCM resonance frequency are monitored as a function of the oscillation amplitude. The induced frequency shifts of the 3rd overtone are found to decrease or increase, depending on the particle-surface coupling type and the applied oscillation (frequency and amplitude). For strong coupling the 3rd harmonic decreased, corresponding to an “added mass” on the quartz surface. However, positive frequency shifts are observed in some cases and are attributed to weak-coupling between particle and surface. Higher overtones, i.e. the 5th and 7th, were utilized in order to derive additional information about the interactions taking place. For small particles, the shift for specific overtones can increase after annealing, while for large particle diameters annealing causes a negative frequency shift. The lower overtones correspond to a generally strong-coupling regime with mainly negative frequency shifts observed, while the 7th appears to be sensitive to the contact break-down and the recorded shifts are positive.rnDuring oscillation, the motion of the particles and the induced frequency shift of the QCM are governed by a balance between inertial forces and contact forces. The adherence of the particles can be increased by annealing the PS film at 150°C, which led to the formation of a PS meniscus. For the interpretation, the Hertz, Johnson-Kendall-Roberts, Derjaguin-Müller-Toporov and the Mindlin theory of partial slip are considered. The Mindlin approach is utilized to describe partial slip. When partial slip takes place induced by an oscillating load, a part of the contact ruptures. This results in a decrease of the effective contact stiffness. Additionally, there are long-term memory effects due to the consolidation which along with the QCM vibrations induce a coupling increase. However, the latter can also break the contact, lead to detachment and even surface damage and deformation due to inertia. For strong coupling the particles appear to move with the vibrations and simply act as added effective mass leading to a decrease of the resonance frequency, in agreement with the Sauerbrey equation that is commonly used to calculate the added mass on a QCM). When the system enters the weak-coupling regime the particles are not able to follow the fast movement of the QCM surface. Hence, they effectively act as adding a “spring” with an additional coupling constant and increase the resonance frequency. The frequency shift, however, is not a unique function of the coupling constant. Furthermore, the critical oscillation amplitude is determined, above which particle detach. No movement is detected at much lower amplitudes, while for intermediate values, lateral particle displacement is observed. rnIn order to validate the QCM results and study the particle effects on the surface, atomic force microscopy, AFM, is additionally utilized, to image surfaces and measure surface forces. By studying the surface of the polymer film after excitation and particle removal, AFM imaging helped in detecting three different meniscus types for the contact area: the “full contact”, the “asymmetrical” and a third one including a “homocentric smaller meniscus”. The different meniscus forms result in varying bond intensity between particles and polymer film, which could explain the deviation between number of particles per surface area measured by imaging and the values provided by the QCM - frequency shift analysis. The asymmetric and the homocentric contact types are suggested to be responsible for the positive frequency shifts observed for all three measured overtones, i.e. for the weak-coupling regime, while the “full contact” type resulted in a negative frequency shift, by effectively contributing to the mass increase of the quartz..rnThe interplay between inertia and contact forces for the particle-surface system leads to strong- or weak-coupling, with the particle affecting in three mentioned ways the polymer surface. This is manifested in the frequency shifts of the QCM system harmonics which are used to differentiate between the two interaction types and reflect the overall state of adhesion for particles of different size.rn

Dielectrophoresis (dep) and electrowetting (ewod) as an anti-fouling process for antibacterial surfaces

Nowadays the medical field is struggling to decrease bacteria biofilm formation which leads to infection. Biomedical devices sterilization has not changed over a long period of time. This results in high costs for hospitals healthcare managements. The objective of this project is to investigate electric field effects and surface energy manipulation as solutions for preventing bacteria biofilm for future devices. Based on electrokinectic environments 2 different methods were tested: feasibility of electric gradient through mediums (DEP) reinforced by numerical simulations; and EWOD by the fabrication of golden interdigitated electrodes on silicon glass substrates, standard ~480 nm Teflon (PTFE) layer and polymeric gasket to contain the bacteria medium. In the first experiment quantitative analysis was carried out to achieve forces required to reject bacteria without considering dielectric environment limitations as bacteria and medium frequency dependence. In the second experiment applied voltages was characterized by droplets contact angle measurements and put to the live bacteria tests. The project resulted on promising results for DEP application due to its wide range of frequency that can be used to make a “general” bacteria rejecting; but in terms of practicality, EWOD probably have higher potential for success but more experiments are needed to verify if can prevent biofilm adhesion besides the Teflon non-adhesive properties (including limitations as Teflon breakthrough, layer sensitivity) at incubation times larger than 24 hours.

Hybrid inorganic-polymer coatings prepared via miniemulsion process

A synthetic route was designed for the incorporation of inorganic materials within water-based miniemulsions with a complex and adjustable polymer composition. This involved co-homogenization of two inverse miniemulsions constituting precursors of the desired inorganic salt dispersed within a polymerizable continuous phase, followed by transfer to a direct miniemulsion via addition to an o/w surfactant solution with subsequent homogenization and radical polymerization. To our knowledge, this is the first work done where a polymerizable continuous phase has been used in an inverse (mini)emulsion formation followed by transfer to a direct miniemulsion, followed by polymerization, so that the result is a water-based dispersion. The versatility of the process was demonstrated by the synthesis of different inorganic pigments, but also the use of unconventional mixture of vinylic monomers and epoxy resin as the polymerizable phase (unconventional as a miniemulsion continuous phase but typical combination for coating applications). Zinc phosphate, calcium carbonate and barium sulfate were all successfully incorporated in the polymer-epoxy matrix. The choice of the system was based on a typical functional coatings system, but is not limited to. This system can be extended to incorporate various inorganic and further materials as long as the starting materials are water-soluble or hydrophilic. rnThe hybrid zinc phosphate – polymer water-based miniemulsion prepared by the above route was then applied to steel panels using autodeposition process. This is considered the first autodeposition coatings process to be carried out from a miniemulsion system containing zinc phosphate particles. Those steel panels were then tested for corrosion protection using salt spray tests. Those corrosion tests showed that the hybrid particles can protect substrate from corrosion and even improve corrosion protection, compared to a control sample where corrosion protection was performed at a separate step. Last but not least, it is suggested that corrosion protection mechanism is related to zinc phosphate mobility across the coatings film, which was proven using electron microscopy techniques.

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.

Convergence results for stochastic particle systems with social interaction

We consider stochastic individual-based models for social behaviour of groups of animals. In these models the trajectory of each animal is given by a stochastic differential equation with interaction. The social interaction is contained in the drift term of the SDE. We consider a global aggregation force and a short-range repulsion force. The repulsion range and strength gets rescaled with the number of animals N. We show that for N tending to infinity stochastic fluctuations disappear and a smoothed version of the empirical process converges uniformly towards the solution of a nonlinear, nonlocal partial differential equation of advection-reaction-diffusion type. The rescaling of the repulsion in the individual-based model implies that the corresponding term in the limit equation is local while the aggregation term is non-local. Moreover, we discuss the effect of a predator on the system and derive an analogous convergence result. The predator acts as an repulsive force. Different laws of motion for the predator are considered.