Rich-club connectivity, diverse population coupling, and dynamical activity patterns emerging from local cortical circuits

Abstract

Experimental studies have begun revealing essential properties of the structural connectivity and the spatiotemporal activity dynamics of cortical circuits. To integrate these properties from anatomy and physiology, and to elucidate the links between them, we develop a novel cortical circuit model that captures a range of realistic features of synaptic connectivity. We show that the model accounts for the emergence of higher-order connectivity structures, including highly connected hub neurons that form an interconnected rich-club. The circuit model exhibits a rich repertoire of dynamical activity states, ranging from asynchronous to localized and global propagating wave states. We find that around the transition between asynchronous and localized propagating wave states, our model quantitatively reproduces a variety of major empirical findings regarding neural spatiotemporal dynamics, which otherwise remain disjointed in existing studies. These dynamics include diverse coupling (correlation) between spiking activity of individual neurons and the population, dynamical wave patterns with variable speeds and precise temporal structures of neural spikes. We further illustrate how these neural dynamics are related to the connectivity properties by analysing structural contributions to variable spiking dynamics and by showing that the rich-club structure is related to the diverse population coupling. These findings establish an integrated account of structural connectivity and activity dynamics of local cortical circuits, and provide new insights into understanding their working mechanisms.

Fractional diffusion theory of balanced heterogeneous neural networks

“…In the large network size limit, as a result of the generalized central limit theorem, this corresponds to heavy-tailed, power-law weights. This is, however, fundamentally different from recent studies of heterogeneous neural networks, in which heterogeneous connectivity has been interpreted in terms of heavy-tailed degree distributions with [18] and without [15] heavytailed synaptic strength distributions.…”

“…We thus expect that the fractional diffusion theory applies whenever the inputs have Lévy fluctuations, regardless of specific network structures. In addition, it should be noted that scale-free, Lévy-like fluctuations can emerge from neural networks with criticality [3,18,60,61]. In the future it would be interesting to apply our fractional framework for the formulation of critical neural dynamics, going beyond the demonstration of the presence of power-law distributions in some neural observables.…”

“…Occasional, large synaptic inputs which are the hallmark features of Lévy processes have been found in neural circuit models, due to a combination of heavy-tailed but non-power-law connectivity features along with a specific dynamical state of the circuit [18], e.g. near a transition regime between different circuit states.…”

“…As in the classical normal diffusion theory for homogeneous networks [8][9][10][11][13][14][15][16][17][18][19][20], we consider the dynamics of our heterogeneous network in the limit of large network size. By using the generalized central limit theorem [43], we rigorously prove that the total synaptic input I(t) to an individual neuron in the network has nonequilibrium Lévy fluctuations, in the limit of large network size, if and only if the distributions J r of synaptic strengths outgoing from population r ∈ {E, I, ext} have a power-law tail (see detailed derivation in Appendix A).…”

“…The standard Fokker-Planck formalism is then used in this theoretical framework to obtain the key statistical properties of complex neural dynamics. Virtually all existing balanced neural network models, including the classical ones [8][9][10] and their recent extensions incorporating heterogeneous degrees [13][14][15], distance-dependent connectivity [16][17][18], and alternative neuron models such as conductance-based neurons [19,20], have been studied by applying such normal diffusion-based formalisms.…”