Conditions for wave trains in spiking neural networks

Spatiotemporal patterns such as traveling waves are frequently observed in recordings of neural activity. The mechanisms underlying the generation of such patterns are largely unknown. Previous studies have investigated the existence and uniqueness of different types of waves or bumps of activity using neural-field models, phenomenological coarse-grained descriptions of neural-network dynamics. But it remains unclear how these insights can be transferred to more biologically realistic networks of spiking neurons, where individual neurons fire irregularly. Here, we employ mean-field theory to reduce a microscopic model of leaky integrate-and-fire (LIF) neurons with distance-dependent connectivity to an effective neural-field model. In contrast to existing phenomenological descriptions, the dynamics in this neural-field model depends on the mean and the variance in the synaptic input, both determining the amplitude and the temporal structure of the resulting effective coupling kernel. For the neural-field model we employ liner stability analysis to derive conditions for the existence of spatial and temporal oscillations and wave trains, that is, temporally and spatially periodic traveling waves. We first prove that wave trains cannot occur in a single homogeneous population of neurons, irrespective of the form of distance dependence of the connection probability. Compatible with the architecture of cortical neural networks, wave trains emerge in two-population networks of excitatory and inhibitory neurons as a combination of delay-induced temporal oscillations and spatial oscillations due to distance-dependent connectivity profiles. Finally, we demonstrate quantitative agreement between predictions of the analytically tractable neural-field model and numerical simulations of both networks of nonlinear rate-based units and networks of LIF neurons.Comment: 36 pages, 8 figures, 4 table

Modelling human choices: MADeM and decision‑making

Research supported by FAPESP 2015/50122-0 and DFG-GRTK 1740/2. RP and AR are also part of the Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant (2013/07699-0). RP is supported by a FAPESP scholarship (2013/25667-8). ACR is partially supported by a CNPq fellowship (grant 306251/2014-0)

Persistent firing and oscillations in the septo-hippocampal system and their relation to locomotion

The medial septum, diagonal band of Broca has received most attention as a putative pacemaker of the hippocampal theta rhythm. However, due to its high interconnectivity with various cortical and subcortical regions, the medial septum is involved in a variety of neural processes. This thesis focuses on the relation between medial septal spiking activity, hippocampal theta rhythm and locomotion. It was previously demonstrated that theta-periodic optogenetic activation of medial septal glutamatergic neurons entrains hippocampal theta oscillation and initiates persistentlocomotion of the animal. We showed that hippocampal theta oscillation and locomotion, both persisting after the stimulus offset, can be induced by a brief continuous light stimulation of medial septal glutamatergic neurons. The hippocampal theta rhythm is not necessary for inducing persistent locomotion, as locomotion initiation is not affected by blocking synaptic transmission in the medial septum that abolishes the hippocampal theta. Furthermore, we observed persistent spiking activity of the medial septal neurons, lasting for many seconds after the stimulus offset.To test whether the persistent activity is generated locally in the medial septum, we repeated the stimulation experiment in an acute medial septal slice preparation. The persistent activity had a shorter duration than in vivo, but was present both in the intact slice and with blocked synaptic transmission, indicating that the persistent firing is a result of intrinsic dynamics of medial septal glutamatergic neurons. Further analysis of spontaneous spiking activity of neurons in the acute medial septal slice preparation revealed the existence of theta-rhythmic neurons that synchronizetheir firing, suggesting that the medial septum can generate the theta oscillation independently of external feedforward and feedback input. Even though medial septal synaptic connectivity is necessary for the hippocampal theta rhythm, our results suggest that the theta-rhythmic firing is a result of intrinsic cellular dynamics and a low level of synchrony can be achieved without synaptic coupling. It remains an open question how the septal theta-rhythmic input is transformed into a travelling theta wave observed in the hippocampus. The last part of the thesis offers a framework for studying the generation of periodic travelling waves in spiking neural networks. We developed a parameter mapping between a discrete network of neurons and apopulation model that describes the spatio-temporal spread of activity as a continuousprocess. Using this mapping, we derived conditions for the existence of periodictravelling waves in the spiking neural network

Optical stimulation evokes sustained activity in the isolated medial septum

The processing of spatially related input during locomotion involves oscillatory hippocampal (HPC) activity in the theta band. It is known that the medial septum (MS) plays a central role in the generation of HPC theta activity, but the underlying mechanisms have not yet been described. Fuhrmann et al. [1] have shown that a brief stimulation of glutamatergic (VGluT2) neurons in the mouse MS in vivo evokes sustained theta activity in the HPC local-field potential (LFP), lasting for at least 10 seconds and preceding the onset of locomotion. Blocking of glutamatergic synapses in the MS suppresses sustained theta activity.Here, we investigate to what extent the MS alone can generate sustained activity. To this end, we study responses of individual MS neurons to optical stimulation in acute mouse MS slices recorded by microelectrode arrays (MEAs). MS slices exhibit spontaneous activity, with a fraction of neurons being active at rates of 5-15 spikes/s. Brief 1-second optical stimulation of VGluT2 neurons consistently leads to a sustained increase in the activity in some of the MS neurons, lasting for several, sometimes more than 10 seconds. The same effect is observed in slices with blocked glutamatergic and/or GABAergic connections (see Figure 1). Irrespective of the blocking condition, we do not detect any signs of spike-train synchronization or spatial clustering of stimulus evoked sustained activity. Stimulation of parvalbumin-expressing (PV) neurons does not lead to any significant firing rate modulation after stimulus offset.We conclude that the isolated MS is capable of generating sustained activity at time scales comparable to those found in the HPC [1]. The generation of this sustained activity seems to be the result of a bistable dynamics of individual VGluT2 neurons, and does not rely on synaptic interactions within the MS network. Single neurons exhibiting bistable dynamics have been described in earlier studies [2,3].It remains to be shown how coherent HPC theta activity can emerge from asynchronous sustained activation of MS neurons, and to what extent the stimulus-evoked generation of sustained HPC theta activity relies on direct projections from VGluT2 neurons to the HPC. Future work is further dedicated to a systematic comparison between the characteristics (duration, stimulus efficiency) of sustained spiking activity in the MS, sustained theta activity in HPC LFPs, and behavioral responses

Neural Network Mean-Field Analysis Toolbox

In recent years, a lot of mean-field methods for calculating properties of commonly used random network models have been developed [1,2,3,4,5]. But, implementing them accurately can cause substantial work, just as it is to develop them. The availability of an easy-to-use implementation will foster the wide use of these methods by a broad range of scientists, beyond the fraction of people who initially developed these method. The employed coarse-grained reductions enable insights into the mechanistic origin of network phenomena, they allow for targeted manipulations, and they enable the formulation of parameter constraints based on empirically observed activity; calculating network properties analytically is also often way faster than retrieving them from simulations. To support the widespread use of mean-field methods, we started collecting these implementations in an unified and easy-to-use framework of a python package. Currently, the focus is on random networks of leaky integrate-and-fire model neurons. In the future, we are planning to extend this package to include more tools and to support more neuron and network types

Conditions for traveling waves in spiking neural networks

Spatiotemporal patterns such as traveling waves are frequently observed in recordings of neural activity. The mechanisms underlying the generation of such patterns are largely unknown. Previous studies have investigated the existence and uniqueness of different types of waves or bumps of activity using neural-field models, phenomenological coarse-grained descriptions of neural-network dynamics. But it remains unclear how these insights can be transferred to more biologically realistic networks of spiking neurons, where individual neurons fire irregularly. Here, we employ mean-field theory to reduce a microscopic model of leaky integrate-and-fire (LIF) neurons with distance-dependent connectivity to an effective neural-field model. In contrast to existing phenomenological descriptions, the dynamics in this neural-field model depends on the mean and the variance in the synaptic input, both determining the amplitude and the temporal structure of the resulting effective coupling kernel. For the neural-field model we derive conditions for the existence of spatial and temporal oscillations and periodic traveling waves using linear stability analysis. We first prove that periodic traveling waves cannot occur in a single homogeneous population of neurons, irrespective of the form of distance dependence of the connection probability. Compatible with the architecture of cortical neural networks, traveling waves emerge in two-population networks of excitatory and inhibitory neurons as a combination of delay-induced temporal oscillations and spatial oscillations due to distance-dependent connectivity profiles. Finally, we demonstrate quantitative agreement between predictions of the analytically tractable neural-field model and numerical simulations of both networks of nonlinear rate-based units and networks of LIF neurons