Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon’s implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike’s preceding ISI. As we show, the EIF’s exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron’s ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation.

Effects of oligotrophication on primary production in peri-alpine lakes

During the second half of the 20th century untreated sewage released from housing and industry into natural waters led to a degradation of many freshwater lakes and reservoirs worldwide. In order to mitigate eutrophication, wastewater treatment plants, including Fe-induced phosphorus precipitation, were implemented throughout the industrialized world, leading to reoligotrophication in many freshwater lakes. To understand and assess the effects of reoligotrophication on primary productivity, we analyzed 28 years of 14C assimilation rates, as well as other biotic and abiotic parameters, such as global radiation, nutrient concentrations and plankton densities in peri-alpine Lake Lucerne, Switzerland. Using a simple productivity-light relationship, we estimated continuous primary production and discussed the relation between productivity and observed limnological parameters. Furthermore, we assessed the uncertainty of our modeling approach based on monthly 14C assimilation measurements using Monte Carlo simulations. Results confirm that monthly sampling of productivity is sufficient for identifying long-term trends in productivity and that conservation management has successfully improved water quality during the past three decades via reducing nutrients and primary production in the lake. However, even though nutrient concentrations have remained constant in recent years, annual primary production varies significantly from year to year. Despite the fact that nutrient concentrations have decreased by more than an order of magnitude, primary production has decreased only slightly. These results suggest that primary production correlates well to nutrients availability but meteorological conditions lead to interannual variability regardless of the trophic status of the lake. Accordingly, in oligotrophic freshwaters meteorological forcing may reduce productivity impacting on the entire food chain of the ecosystem.