Signal transmission in stochastic neuron models with non-white or non-Gaussian noise

This thesis is concerned with the effect of non-white or non-Gaussian synaptic noise on the information transmission properties of single neurons. Synaptic noise subsumes the massive input that a cell receives from thousands of other neurons. In the framework of stochastic neuron models, this input is described by a stochastic process with suitably chosen statistics. If the overall arrival rate of presynaptic action potentials is high and constant in time and if each individual incoming spike has only a small effect on the dynamics of the cell, the massive synaptic input can be modeled as a Gaussian process. For mathematical tractability, one often assumes that furthermore, the input is devoid of temporal structure, i.e. that it is well described by a Gaussian white noise. This is the so-called diffusion approximation (DA). The present thesis explores neuronal signal transmission when the conditions that underlie the DA are no longer met, i.e. when one must describe the synaptic background activity by a stochastic process that is not white, not Gaussian, or neither. We explore three distinct scenarios by means of simulations and analytical calculations: First, we study a cell that receives not one but two signals, additionally filtered by synaptic short-term plasticity (STP), so that the background has to be described by a colored noise. The second scenario deals with synaptic weights that cannot be considered small; here, the effective noise is no longer Gaussian and the shot-noise nature of the input has to be taken into account. Finally, we study the effect of a presynaptic population that does not fire at a rate which is constant in time but instead undergoes transitions between states of high and low activity, so-called up and down states. In all cases, we are interested in the information transmission properties of the neuron, which we quantify using a frequency-resolved measure, the spectral coherence between a signal and the cell’s output spike train. This allows to assess how different frequency components of the signal are encoded in the output spike train. It also provides a lower bound on the total rate of information transmission about the signal and allows to explore how this rate depends on the properties of the synaptic noise. In a first part, we study a neuron that simultaneously receives two signals. We assume that synapses differ in the kind of STP they exhibit: One signal is encoded in spike trains impinging on the neuron through facilitating synapses, the other through depressing synapses. Here, either signal can be considered a source of noise with respect to the transmission of the other signal. As signals are temporally structured and additionally filtered by STP, this noise is not white but colored. We find that the presence of a second signal can switch the coherence from broadband to frequency selective and that a second signal may help the transmission of the first, a novel form of stochastic resonance (SR). Subsequently, we derive analytical results for integrate-and-fire (IF) neurons driven by Markovian dichotomous noise, a two-state process and the rare case of a nonGaussian colored noise that allows exact solution. Specifically, we derive expressions for the stationary voltage density, the moments of the interspike interval density, and, in the case of leaky IF neurons, for the power spectrum and the susceptibility, two spectral measures that allow to study information transmission using the coherence. These results form the basis for the theoretical study of the two remaining scenarios. We exploit a limit case of dichotomous noise to derive exact expressions for an IF neuron driven by excitatory shot noise (SN) with exponentially distributed weights. These expressions are then used to investigate how finite spike weights change information transmission properties compared to the DA. We find that SN input leads to firing rates that are increased when the mean input is low, but decreased when it is high. Additionally, the response to high frequency components of a current-