Connectivity concepts in neuronal network modeling.

Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic implementations, or parameterizations hinder progress. Such flaws are unfortunately frequent and one reason is a lack of readily applicable standards and tools for model description.

Parvalbumin interneuron dendrites enhance gamma oscillations.

Dendrites are essential determinants of the input-output relationship of single neurons, but their role in network computations is not well understood. Here, we use a combination of dendritic patch-clamp recordings and in silico modeling to determine how dendrites of parvalbumin (PV)-expressing basket cells contribute to network oscillations in the gamma frequency band. Simultaneous soma-dendrite recordings from PV basket cells in the dentate gyrus reveal that the slope, or gain, of the dendritic input-output relationship is exceptionally low, thereby reducing the cell's sensitivity to changes in its input.

Robust parallel decision-making in neural circuits with nonlinear inhibition.

An elemental computation in the brain is to identify the best in a set of options and report its value. It is required for inference, decision-making, optimization, action selection, consensus, and foraging. Neural computing is considered powerful because of its parallelism; however, it is unclear whether neurons can perform this max-finding operation in a way that improves upon the prohibitively slow optimal serial max-finding computation (which takes [Formula: see text] time for N noisy candidate options) by a factor of N, the benchmark for parallel computation.

Firing-rate models for neurons with a broad repertoire of spiking behaviors.

Capturing the response behavior of spiking neuron models with rate-based models facilitates the investigation of neuronal networks using powerful methods for rate-based network dynamics. To this end, we investigate the responses of two widely used neuron model types, the Izhikevich and augmented multi-adapative threshold (AMAT) models, to a range of spiking inputs ranging from step responses to natural spike data. We find (i) that linear-nonlinear firing rate models fitted to test data can be used to describe the firing-rate responses of AMAT and Izhikevich spiking neuron models in many cases; (ii) that firing-rate responses are generally too complex to be captured by first-order low-pass filters but require bandpass filters instead; (iii) that linear-nonlinear models capture the response of AMAT models better than of Izhikevich models; (iv) that the wide range of response types evoked by current-injection experiments collapses to few response types when neurons are driven by stationary or sinusoidally modulated Poisson input; and (v) that AMAT and Izhikevich models show different responses to spike input despite identical responses to current injections.

Dynamics of self-sustained asynchronous-irregular activity in random networks of spiking neurons with strong synapses.

Random networks of integrate-and-fire neurons with strong current-based synapses can, unlike previously believed, assume stable states of sustained asynchronous and irregular firing, even without external random background or pacemaker neurons. We analyze the mechanisms underlying the emergence, lifetime and irregularity of such self-sustained activity states. We first demonstrate how the competition between the mean and the variance of the synaptic input leads to a non-monotonic firing-rate transfer in the network.

How pattern formation in ring networks of excitatory and inhibitory spiking neurons depends on the input current regime.

Pattern formation, i.e., the generation of an inhomogeneous spatial activity distribution in a dynamical system with translation invariant structure, is a well-studied phenomenon in neuronal network dynamics, specifically in neural field models.

Firing-rate models capture essential response dynamics of LGN relay cells.

Firing-rate models provide a practical tool for studying signal processing in the early visual system, permitting more thorough mathematical analysis than spike-based models. We show here that essential response properties of relay cells in the lateral geniculate nucleus (LGN) can be captured by surprisingly simple firing-rate models consisting of a low-pass filter and a nonlinear activation function. The starting point for our analysis are two spiking neuron models based on experimental data: a spike-response model fitted to data from macaque (Carandini et al.

How synaptic weights determine stability of synchrony in networks of pulse-coupled excitatory and inhibitory oscillators.

Under which conditions can a network of pulse-coupled oscillators sustain stable collective activity states? Previously, it was shown that stability of the simplest pattern conceivable, i.e., global synchrony, in networks of symmetrically pulse-coupled oscillators can be decided in a rigorous mathematical fashion, if interactions either all advance or all retard oscillation phases ("mono-interaction network").

Creating, documenting and sharing network models.

As computational neuroscience matures, many simulation environments are available that are useful for neuronal network modeling. However, methods for successfully documenting models for publication and for exchanging models and model components among these projects are still under development. Here we briefly review existing software and applications for network model creation, documentation and exchange.

Inferring synaptic connectivity from spatio-temporal spike patterns.

Networks of well-known dynamical units but unknown interaction topology arise across various fields of biology, including genetics, ecology, and neuroscience. The collective dynamics of such networks is often sensitive to the presence (or absence) of individual interactions, but there is usually no direct way to probe for their existence. Here we present an explicit method for reconstructing interaction networks of leaky integrate-and-fire neurons from the spike patterns they exhibit in response to external driving.

Correlations in spiking neuronal networks with distance dependent connections.

Can the topology of a recurrent spiking network be inferred from observed activity dynamics? Which statistical parameters of network connectivity can be extracted from firing rates, correlations and related measurable quantities? To approach these questions, we analyze distance dependent correlations of the activity in small-world networks of neurons with current-based synapses derived from a simple ring topology. We find that in particular the distribution of correlation coefficients of subthreshold activity can tell apart random networks from networks with distance dependent connectivity. Such distributions can be estimated by sampling from random pairs.

Correlations and population dynamics in cortical networks.

The function of cortical networks depends on the collective interplay between neurons and neuronal populations, which is reflected in the correlation of signals that can be recorded at different levels. To correctly interpret these observations it is important to understand the origin of neuronal correlations. Here we study how cells in large recurrent networks of excitatory and inhibitory neurons interact and how the associated correlations affect stationary states of idle network activity.