Theoretical mechanisms of information filtering in stochastic single neuron models

Neurons transmit information about time-dependent input signals via highly nonlinear responses, so-called action potentials or spikes. This type of information transmission can be frequency-dependent and allows for preferences for certain stimulus components. A single neuron can transmit either slow components (low pass filter), fast components (high pass filter), or intermediate components (band pass filter) of a time-dependent input signal. Using methods developed in theoretical physics (statistical physics) within the framework of information theory, in this thesis, cellintrinsic mechanisms are being investigated that can lead to frequency selectivity on the level of information transmission. Various stochastic single neuron models are examined numerically and, if tractable analytically. Ranging from simple spiking models to complex conductance-based models with and without nonlinearities, these models include integrator as well as resonator dynamics. First, spectral information filtering characteristics of different types of stochastic current-based integrator neuron models are being studied, including the perfect (PIF), leaky (LIF), and quadratic (QIF), as well as the exponential (EIF) integrateand-fire (IF) model. It will be numerically demonstrated that the previous mentioned IF models preferentially encode information about slow components of a time-dependent input signal and therefore act as low pass filters on information. Subsequently, the simple deterministic PIF model is being extended with a stochastic spiking rule, leading to positive correlations between successive interspike intervals (ISIs). In this simple model, the ISI distribution, as well as the strength of correlations between adjacent ISIs, can be controlled. It will be considered in two variants that solely differ in the presence of positive ISI correlations and therefore allow studying exclusively the effects of positive ISI correlations on the spectral information transmission characteristics. It will be shown that positive ISI correlations can alter the filtering properties of IF models from low to band pass filter. Thereafter, models are being examined which show subthreshold resonances (socalled resonator models) and their effects on the spectral information filtering characteristics are being investigated by using two distinct neuronal responses: i) the purely (linear) subthreshold response (without spikes), and ii) the (nonlinear) spiking response (resonate-and-fire model). It will be revealed that subthreshold resonances do not change the information filter characteristics of the purely subthreshold response, whereas their effects on the frequency-dependent information transmission of the spiking response become apparent. Finally, the spectral information filtering properties of stochastic linear-nonlinear cascade neuron models are being researched by employing different static nonlinearities (SNLs). The more ’nonlinear’ the transformation gets, the more pronounced the band-pass filtering effect in the presence of subthreshold resonances becomes. This work highlights the consequences of subthreshold resonances in conjunction with cell-intrinsic nonlinearities (fire-and-reset rule, biophysical spike mechanisms, and static nonlinearities), which generally can lead to shape the information transmission characteristics of the neuron model from low to band pass filtering. The trade-off between frequency-dependent signal transmission and the total amount of transmitted information will be demonstrated in all models and constitutes a direct consequence of the nonlinear formulation of the models.