Spike-triggered averages for passive and resonant neurons receiving filtered excitatory and inhibitory synaptic drive

A path-integral approach is developed for the analysis of spike-triggered-average quantities in neurons with voltage-gated subthreshold currents. Using a linearization procedure to reduce the models to the generalized integrate-and-fire form, analytical expressions are obtained in an experimentally relevant limit of fluctuation-driven firing. The influences of voltage-gated channels as well as excitatory and inhibitory synaptic filtering are shown to affect significantly the neuronal dynamics prior to the spike. Analytical forms are given for all relevant physiological quantities, such as the mean voltage triggered to the spike, mean current flowing through voltage-gated channels and the mean excitatory and inhibitory conductance wave forms prior to a spike. The mathematical results are shown to be in good agreement with numerical simulations of the underlying non-linear conductance-based models. The method promises to provide a useful analytical tool for the prediction and interpretation of the temporal structure of spike-triggered averages measured experimentally.

Microcircuits of excitatory and inhibitory neurons in layer 2/3 of mouse barrel cortex

Michael Avermann, Wulfram Gerstner, Céline Matéo, Carl Petersen, Christian Tomm

Avermann M, Tomm C, Mateo C, Gerstner W, Petersen CC. Microcircuits of excitatory and inhibitory neurons in layer 2/3 of mouse barrel cortex. J Neurophysiol 107: 3116-3134, 2012. First published March 7, 2012; doi:10.1152/jn.00917.2011.-Synaptic interactions between nearby excitatory and inhibitory neurons in the neocortex are thought to play fundamental roles in sensory processing. Here, we have combined optogenetic stimulation, whole cell recordings, and computational modeling to define key functional microcircuits within layer 2/3 of mouse primary somatosensory barrel cortex. In vitro optogenetic stimulation of excitatory layer 2/3 neurons expressing channelrhodopsin-2 evoked a rapid sequence of excitation followed by inhibition. Fast-spiking (FS) GABAergic neurons received large-amplitude, fast-rising depolarizing postsynaptic potentials, often driving action potentials. In contrast, the same optogenetic stimulus evoked small-amplitude, subthreshold postsynaptic potentials in excitatory and non-fast-spiking (NFS) GABAergic neurons. To understand the synaptic mechanisms underlying this network activity, we investigated unitary synaptic connectivity through multiple simultaneous whole cell recordings. FS GABAergic neurons received unitary excitatory postsynaptic potentials with higher probability, larger amplitudes, and faster kinetics compared with NFS GABAergic neurons and other excitatory neurons. Both FS and NFS GABAergic neurons evoked robust inhibition on postsynaptic layer 2/3 neurons. A simple computational model based on the experimentally determined electrophysiological properties of the different classes of layer 2/3 neurons and their unitary synaptic connectivity accounted for key aspects of the network activity evoked by optogenetic stimulation, including the strong recruitment of FS GABAergic neurons acting to suppress firing of excitatory neurons. We conclude that FS GABAergic neurons play an important role in neocortical microcircuit function through their strong local synaptic connectivity, which might contribute to driving sparse coding in excitatory layer 2/3 neurons of mouse barrel cortex in vivo.

American Physiological Society2012

What matters in neuronal locking?

Wulfram Gerstner

Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of {\em spiking/} neurons. Under standard conditions, a necessary and in the limit of a large number of interacting neighbors also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is a kind of locking theorem and boils down to a subtle interplay of axonal delays, postsynaptic potentials, and refractory behavior. The theorem also allows for mixtures of excitatory and inhibitory interactions. On the basis of the locking theorem we present a simple geometric method to verify existence and local stability of a coherent oscillation.

Massachusetts Institute of Technology Press1996

Connectivity reflects coding: a model of voltage-based STDP with homeostasis

Claudia Clopath, Wulfram Gerstner, Eleni Vasilaki

Electrophysiological connectivity patterns in cortex often have a few strong connections, which are sometimes bidirectional, among a lot of weak connections. To explain these connectivity patterns, we created a model of spike timing–dependent plasticity (STDP) in which synaptic changes depend on presynaptic spike arrival and the postsynaptic membrane potential, filtered with two different time constants. Our model describes several nonlinear effects that are observed in STDP experiments, as well as the voltage dependence of plasticity. We found that, in a simulated recurrent network of spiking neurons, our plasticity rule led not only to development of localized receptive fields but also to connectivity patterns that reflect the neural code. For temporal coding procedures with spatio-temporal input correlations, strong connections were predominantly unidirectional, whereas they were bidirectional under rate-coded input with spatial correlations only. Thus, variable connectivity patterns in the brain could reflect different coding principles across brain areas; moreover, our simulations suggested that plasticity is fast.

Nature Publishing Group2010

Microcircuits of excitatory and inhibitory neurons in layer 2/3 of mouse barrel cortex

Michael Avermann, Wulfram Gerstner, Céline Matéo, Carl Petersen, Christian Tomm

American Physiological Society2012