Circadian rhythms are periodic physiological cycles that recur about every 24 hours, by means of which organisms integrate their physiology and behavior to the daily cycle of light and temperature imposed by the rotation of the earth. Circadian derives from the Latin word circa "about" and dies "day". Circadian rhythms have three noteworthy properties. They are endogenous, that is, they persist in the absence of external cues (in an environment of constant light intensity, temperature, etc.). Secondly, they are temperature compensated, that is, the nearly 24 hour period of the endogenous oscillator is remarkably independent of ambient temperature. Finally, they are phase shifted by light. The circadian rhythm can be either advanced or delayed by applying a pulse of light in constant darkness. Consequently, the circadian rhythm will synchronize to a periodic light-dark cycle, provided the period of the driving stimulus is not too far from the period of the endogenous rhythm. A window on the molecular mechanism of 24-hour rhythms was opened by the identification of circadian rhythm mutants and their cognate genes in Drosophila, Neurospora, and now in other organisms. Since Konopka and Benzer first discovered the period mutant in Drosophila in 1971 (Konopka and Benzer, 1971), there have been remarkable developments. Currently, the consensus opinion of molecular geneticists is that the 24-hour period arises from a negative feedback loop controlling the transcription of clock genes. However, a better understanding of this mechanism requires an approach that integrates both mathematical and molecular biology. From the recent discoveries in molecular biology and through a mathematical approach, we propose that the mechanism of circadian rhythm is based upon the combination of both negative and positive feedback. / Master of Science

Sleep is essential for mammals and possibly for all animals. Advancing our knowledge of sleep regulation is crucial for the development of interventions in sleep-related health and social problems. With this aim, this study utilizes laboratory mice to explore sleep regulatory mechanisms at behavioral, molecular, and genetic levels. Sleep is regulated by the interaction of circadian and homeostatic processes. The circadian clock facilitates sleep to occur at a favorable time of the day. Normal mice, such as the C57BL/6J (B6) strain, sleep mostly during the day and initiate activities at dark onset. Here, I show mice of the CAST/EiJ (CAST) strain initiate activity unusually early (hours before dark). The circadian gating of photic phase-shifting responses was phase-lagged in the CAST mice relative to their activity rhythms, implying an altered coupling between the clock and its output. Light failed to suppress activity in the CAST mice, allowing full expression of the early activity. A previously identified quantitative trait locus that contributes to the advanced circadian phase was also confirmed and refined to a smaller genomic region. The circadian oscillation and light-induction of clock-genes Per1 and Per2 expression was not different between B6 and CAST mice in the suprachiasmatic nucleus (SCN) of the brain, where the mammalian master circadian clock is located. However, in the cerebral cortex and paraventricular hypothalamic nucleus of CAST mice, Per mRNA oscillations were phase-advanced coordinately with their advanced behavioral rhythms. These data thus provide direct evidence that the cause of the early runner phenotype is located downstream of the master circadian clock. The rhythms of cortical Per expression may not be a result of direct SCN effector mechanisms, but rather driven by activity-rest and sleep-wake. I further show that prolonged waking induces cortical Per expression, and this induction persisted in SCN-lesioned animals. SCN Per expression in intact animals was not affected. Thus, a homeostatic drive, independent of the SCN clock, regulates cortical Per expression, although a possible circadian influence in the intact animals was also suggested by detailed analyses. These data may suggest a molecular mechanism bridging the circadian and homeostatic processes for sleep regulation and functions.

There is a significant amount of computational literature on networks of neurons and their resulting behavior. This dissertation combines electrophysiology experiments with computational modeling to validate the assumptions and results found in this literature. First, we investigate the weak coupling assumption, which states that the phase response of a neuron to weak stimuli is separable from the stimulus waveform. For weak stimuli, there is an intrinsic neuronal property described by the infinitesimal phase response curve (IPRC) that will predict the phase response when convolved with the stimulus waveform. Here, we show that there is a linear relationship between the stimulus and phase response of the neuron, and that we are able to obtain IPRCs that successfully predict the neuronal phase response. Next, we use hybrid networks of neurons to study the phase locking behavior of networks as the synaptic time constant is changed. We verify that networks show anti-phase synchrony for fast time constants, and in-phase synchrony for slow time constants. We also show that phase models and phase response curves (PRCs) qualitatively predict phase locking observed in electrophysiology experiments. Finally, we investigate the stability of the dynamic clamp system. We determined that the maximal conductance of the current being simulated, the dynamic clamp sampling rate, the amount of electrode resistance compensation, and the amount of capacitance compensation all affect when the instability is present. There is a dramatic increase in stability when the electrode resistance and system capacitance are well compensated.

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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.