While motor neuron activity has been studied for many decades, the relative contribution of synaptic and non-synaptic mechanisms underlying this activity during natural behaviors is not well understood. Thus, the goal of this dissertation was to further understand the role of non-synaptic properties of motor neurons during voluntary activity. In particular, I considered three non-synaptic properties: persistent inward currents (PICs) that boost synaptic inputs, spike-threshold accommodation that affects recruitment threshold as excitation rates of rise slow, and spike-frequency adaptation that leads to a decrease in firing rate despite constant excitation levels. Computer simulations were employed to understand the potential effect that these properties could have on firing rate behavior. In particular, the focus was on paired motor unit recordings where a lower threshold motor unit’s firing rate served as a proxy for synaptic drive, and differences in firing rate (ΔF) were compared at a higher threshold unit’s recruitment and derecruitment. While ΔF has been used by others to estimate PIC activation, the simulation results indicated that each of these non-synaptic mechanisms could lead to positive ΔF. Furthermore, by varying contraction speed and duration it seemed possible to determine which property contributes to ΔF in vivo. The results from human experiments indicated that adaptation is most likely the predominant contributor to ΔF during natural behaviors. Additionally, positive ΔF was even observed in the genioglossus muscle of the tongue, where the role of PICs has been debated. These results suggested that ΔF may not the best method to detect PICs during natural behaviors. As such, I also considered whether there might be another metric to infer PIC activation during natural behaviors. Motor unit firing rates tend to plateau, or saturate, despite continued force increase, and one hypothesis is that PICs contribute to this behavior. Indeed, motor unit firing rate saturation was diminished by the addition of inhibition, which should have limited PIC activation. Therefore, this final study provided possible evidence for PIC activation during natural behaviors. Overall, this dissertation highlights that non-synaptic properties of motor neurons are activated during natural behaviors and that they contribute significantly to firing rate output.

Das Neuron ist das zentrale Element in der Informationsverarbeitung im Nervensystem. In dieser Arbeit werden verschiedene Aspekte der Spikegenerierung sowohl theoretisch als auch experimentell untersucht. Phasen-Rotatoren verschiedener Komplexität werden zur Vorhersage von Spikezeitpunkten vorgestellt. Die Kennlinie eines Neurons wird dabei als wichtiger Parameter für diese Modelle verwendet, damit diese leicht auf echte Neurone anwendbar sind. Die Phasenantwortkurve als ein zweiter wichtiger Aspekt der Spikedynamik wird zur Erweiterung der Modelle verwendet. Solange ein Neuron in seinem überschwelligen Bereich gereizt wird, erweisen sich die Phasenrotatoren als gute Beschreibung des Spikeverhaltens. Es wird jedoch gezeigt, daß bei einer Stimulierung mit Strömen, die um die Schwelle des Neurons herum fluktuieren, diese Modelle, genauso wie alle anderen eindimensionalen Modelle einschließlich des Intergrate-and-fire Neurons, versagen. Feuerraten Adaptation kann in vielen Neuronen beobachtet werden. Es wird ein allgemeines phänomenologisches Modell für die Feuerrate adaptierender Neurone aus den Eigenschaften verschiedene Ionenströme, die Adaptation verursachen, hergeleitet. Dieses Modell ist durch die Kennlinien und einer Adaptations-Zeitkonstanten vollständig definiert. Mit Hilfe des Modells können die Eigenschaften der Adaptation als Hochpassfilter quantifiziert werden. Weiterhin wird die Rolle der Adaptation bei der Unterdrückung von Hintergrundrauschen diskutiert. Sowohl die Phasenrotatoren als auch das Adaptationsmodell werden an auditorischen Rezeptorzellen der Wanderheuschrecke und dem AN1, ein primäres auditorisches Interneuron der Grille {Teleogryllus oceanicus}, getestet. In beiden Fällen stimmen die Modelle gut mit den experimentelle Daten überein. Es wird mit Hilfe der Modelle gezeigt, daß Adaptation in den Rezeptorzellen durch Ionenströme des Spikegenerators verursacht wird, während in dem Interneuron der Eingang schon adaptatiert. Zusätzlich wird der Einfluß der Feuerraten-Adaptation auf die Gesangserkennung analysiert. / The single neuron is the basic element of information processing in nervous systems. In this thesis several properties of the dynamics of the generation of spikes are investigated theoretically as well as experimentally. Phase oscillators of different complexity are introduced as models to predict the timing of spikes. The neuron's intensity-response curve is used as a basic parameter in these models to make them easily applicable to real neurons. As a second important aspect of the spiking dynamics, the neuron's phase-resetting curve is used to extend the models. The phase oscillators turn out to be a good approximation of the spiking behavior of a neuron as long as it is stimulated in its super-threshold regime. However, it is shown by comparison with conductance-based models that these models, as well as all other one-dimensional models including the common integrate-and-fire model, fail, if the neuron is stimulated with currents fluctuating around its threshold. Spike-frequency adaptation is a common feature of many neurons. For various ionic currents, as a possible reason for adaptation, a general phenomenological model for the firing rate of adapting neurons is derived from their biophysical properties. This model is defined by the neuron's intensity-response curves and an adaptation time-constant. By means of this model the high-pass properties of spike-frequency adaptation can be quantified. Also the role of adaptation in supression of background noise is discussed. Both the phase oscillators and the adaptation-model are tested on auditory receptor neurons of locusts and the AN1, a primary auditory interneuron of the cricket {Teleogryllus oceanicus}. In both cases the models are in good agreement with the experimental data. By means of the models it is shown that adaptation in the receptor neurons is caused by ionic currents of the spike generator while in the interneuron it is the input which is already adapting. In addition, the influence of spike-frequency adaptation on the recognition of courtship songs is analysed.

Um die komplexe Dynamik von Neuronen und deren Informationsverarbeitung mittels Pulssequenzen zu verstehen, ist es wichtig, die stationäre Puls-Aktivität zu charakterisieren. Die statistischen Eigenschaften von Pulssequenzen können durch vereinfachte stochastische Neuronenmodelle verstanden werden. Eine gut ausgearbeitete Theorie existiert für die Klasse der Erneuerungsmodelle, welche die statistische Unabhängigkeit der Interspike-Intervalle (ISI) annimmt. Experimente haben jedoch gezeigt, dass viele Neuronen Korrelationen zwischen ISIs aufweisen und daher nicht gut durch einen Erneuerungsprozess beschrieben werden. Solche Korrelationen können durch Nichterneuerungs-Modelle erfasst werden, welche jedoch theoretisch schlecht verstanden sind. Diese Arbeit ist eine analytische Studie von Nichterneuerungs-Modellen, die zwei bedeutende Korrelationsmechanismen untersucht: farbiges Rauschen, welches zeitlich-korrelierten Input darstellt, und negative Puls-Rückkopplung, welche Feuerraten-Adaption realisiert. Für das "Perfect-Integrate-and-Fire" (PIF) Modell, welchen durch ein allgemeines Gauss''sches farbiges Rauschen getrieben ist, werden die Statistiken höherer Ordnung der Output-Pulssequenz hergeleitet, insbesondere der Koeffizient der Variation, der serielle Korrelationskoeffizient (SCC), die ISI-Dichte und der Fano-Faktor. Weiterhin wird die Dynamik des PIF Modells mit Puls-getriggertem Adaptionsstrom und weissem Stromrauschen im Detail analysiert. Die Theorie liefert einen Ausdruck für den SCC, der für schwaches Rauschen aber beliebige Adaptions-Stärke und Zeitskale gültig ist, sowie die lineare Antwortfunktion und das Leistungsspektrum der Pulssequenz. Ausserdem wird gezeigt, dass ein stochastischer Adaptionsstrom wie ein langsames farbiges Rauschen wirkt, was ermöglicht, die dominierende Quellen des Rauschen in einer auditorischen Rezeptorzelle zu bestimmen. Schliesslich wird der SCC für das fluktuations-getriebene Feuerregime berechnet. / To understand the complex dynamics of neurons and its ability to process information using a sequence of spikes, it is vital to characterize its stationary spontaneous spiking activity. The statistical properties of spike trains can be explained by reduced stochastic neuron models that account for various sources of noise. A well-developed theory exists for the class of renewal models, in which the interspike intervals (ISIs) are statistically independent. However, experimental studies show that many neurons are not well described by a renewal process because of correlations between ISIs. Such correlations can be captured by generalized, non-renewal models, which are, however, poorly understood theoretically. This thesis represents an analytical study of non-renewal models, focusing on two prominent correlation mechanisms: colored-noise driving representing temporally correlated inputs, and negative feedback currents realizing spike-frequency adaptation. For the perfect integrate-and-fire (PIF) model driven by a general Gaussian colored noise input, the higher-order statistics of the output spike train is derived using a weak-noise analysis of the Fokker-Planck equation. This includes formulas for the coefficient of variation, the serial correlation coefficient (SCC), the ISI density and the Fano factor. Then, the dynamics of a PIF model with a spike-triggered adaptation and a white-noise current is analyzed in detail. The theory yields an expression for the SCC valid for weak noise but arbitrary adaptation strengths and time scale, and also provides the linear response to time-dependent stimuli and the spike train power spectrum. Furthermore, it is shown that a stochastic adaptation current acts like a slow colored noise, which permits to determine the source of spiking variability observed in an auditory receptor neuron. Finally, the SCC is calculated for the fluctuation-driven spiking regime by assuming discrete states of colored noise or adaptation current.

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