Complex dynamics in recurrent cortical networks based on spatially realistic connectivities

Abstract

Most studies on the dynamics of recurrent cortical networks are either based on purely random wiring or neighborhood couplings. Neuronal cortical connectivity, however, shows a complex spatial pattern composed of local and remote patchy connections. We ask to what extent such geometric traits influence the “idle” dynamics of two-dimensional (2d) cortical network models composed of conductance-based integrate-and-fire (iaf) neurons. In contrast to the typical 1 mm2 used in most studies, we employ an enlarged spatial set-up of 25 mm2 to provide for long-range connections. Our models range from purely random to distance-dependent connectivities including patchy projections, i.e., spatially clustered synapses. Analyzing the characteristic measures for synchronicity and regularity in neuronal spiking, we explore and compare the phase spaces and activity patterns of our simulation results. Depending on the input parameters, different dynamical states appear, similar to the known synchronous regular “SR” or asynchronous irregular “AI” firing in random networks. Our structured networks, however, exhibit shifted and sharper transitions, as well as more complex activity patterns. Distance-dependent connectivity structures induce a spatio-temporal spread of activity, e.g., propagating waves, that random networks cannot account for. Spatially and temporally restricted activity injections reveal that a high amount of local coupling induces rather unstable AI dynamics. We find that the amount of local versus long-range connections is an important parameter, whereas the structurally advantageous wiring cost optimization of patchy networks has little bearing on the phase space.

Testing the odds of inherent vs. observed overdispersion in neural spike counts

“…3). Thus reflects the amount of convergence to a neuron, which is, for instance, consistent with a model of the convergent connectivity from V1 to area V5/MT (Simoncelli and Heeger 1998;Rust et al 2006;Wang et al 2012). In addition, it was observed that the simulation of networks based on biologically realistic parameters (Voges and Perrinet 2010) A: correlation between an noisy Gabor image (input) and a population of Gabor filters at different orientations models the linear processing in the receptive field (RF) of a visual neuron.…”

“…could lead to complex dynamics, showing in particular an excess of variability (Voges and Perrinet 2012). Thus we could expect an overdispersion in V5/MT resulting from dimensionality reduction [i.e., projecting inputs from a high-dimensional space to a lower dimensional one (Haykin 1999)].…”

Stable learning of functional maps in self-organizing spiking neural networks with continuous synaptic plasticity

“…In general, neurons in the cerebral cortex are densely connected to neurons close to it and sparsely connected to neurons far away from it (Schummers et al, 2004; Song et al, 2005; Perin et al, 2011; Voges and Perrinet, 2012). In particular, models of cortical function often assume that cortical circuitry acts in a center–surround fashion, whereas separated pairs of cells have a mutually suppressive influence.…”

Emergence of Metastable State Dynamics in Interconnected Cortical Networks with Propagation Delays

“…The network topology is a key determinant of the types of macroscopic activity patterns a network can generate [4]–[11]. Understanding this structure-function relationship provides important insight not only into normal brain function but also into the mechanistic basis of psychiatric illnesses such as schizophrenia and autism that likely represent “connectivity disorders” [12]–[15].…”