Collective oscillations in disordered neural networks

Olmi, Simona; Livi, Roberto; Politi, Antonio; Torcini, Alessandro

doi:10.1103/physreve.81.046119

Cited by 68 publications

(71 citation statements)

References 18 publications

(45 reference statements)

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“…This difference is actually the strongest one in our view: while increasing the number of neighbors in astrocyte networks dilutes away IP 3 and decreases ICW propagation, increasing the number of neighbors in neuronal networks only implies the addition of new synapses and can thus only increase the network excitability. In agreement with this view, increased connectivity (i.e., mean degree) has been shown to promote synchronization in model networks of excitable neurons (Wang et al, 1995; Golomb and Hansel, 2000) and to control the switch between asynchronized states and partially synchronized (or coherent) states (Olmi et al, 2010; Luccioli et al, 2012; Tattini et al, 2012). In the present study, the presence of hubs and long range connections between astrocytes impaired ICW extent.…”

Section: Discussionmentioning

confidence: 78%

Sparse short-distance connections enhance calcium wave propagation in a 3D model of astrocyte networks

Lallouette

Pittà

Ben‐Jacob

et al. 2014

Front. Comput. Neurosci.

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Traditionally, astrocytes have been considered to couple via gap-junctions into a syncytium with only rudimentary spatial organization. However, this view is challenged by growing experimental evidence that astrocytes organize as a proper gap-junction mediated network with more complex region-dependent properties. On the other hand, the propagation range of intercellular calcium waves (ICW) within astrocyte populations is as well highly variable, depending on the brain region considered. This suggests that the variability of the topology of gap-junction couplings could play a role in the variability of the ICW propagation range. Since this hypothesis is very difficult to investigate with current experimental approaches, we explore it here using a biophysically realistic model of three-dimensional astrocyte networks in which we varied the topology of the astrocyte network, while keeping intracellular properties and spatial cell distribution and density constant. Computer simulations of the model suggest that changing the topology of the network is indeed sufficient to reproduce the distinct ranges of ICW propagation reported experimentally. Unexpectedly, our simulations also predict that sparse connectivity and restriction of gap-junction couplings to short distances should favor propagation while long–distance or dense connectivity should impair it. Altogether, our results provide support to recent experimental findings that point toward a significant functional role of the organization of gap-junction couplings into proper astroglial networks. Dynamic control of this topology by neurons and signaling molecules could thus constitute a new type of regulation of neuron-glia and glia-glia interactions.

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Section: Discussionmentioning

confidence: 78%

Sparse short-distance connections enhance calcium wave propagation in a 3D model of astrocyte networks

Lallouette

Pittà

Ben‐Jacob

et al. 2014

Front. Comput. Neurosci.

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“…Indeed, there are many potential biophysical sources of heterogeneity in neural systems, both at the network level (i.e., heterogeneity in the network connectivity, as in Olmi et al, 2010) and at the neuron level. In this second group, possible heterogeneity sources can be defined in terms of anatomical and morphological properties, or also at a functional level, including neuronal excitability (Tessone et al, 2006; Perez et al, 2010), different degrees of spike frequency adaptation (Hemond et al, 2008; Nicola and Campbell, 2013), or other biophysical properties (Padmanabhan and Urban, 2010; Tripathy et al, 2013), to name a few.…”

Section: Discussionmentioning

confidence: 99%

“…In particular, the role of heterogeneity on synchronization has been extensively studied (Golomb and Rinzel, 1993; White et al, 1998; Neltner et al, 2000; Golomb et al, 2001; Denker et al, 2004; Talathi et al, 2008, 2009; Luccioli and Politi, 2010; Olmi et al, 2010; Brette, 2012; Mejias and Longtin, 2012). More recently, the effect of neural heterogeneities on neuronal correlations (Chelaru and Dragoi, 2008; Yim et al, 2013), detection of weak signals (Tessone et al, 2006; Perez et al, 2010) and different types of neural coding (Chelaru and Dragoi, 2008; Savard et al, 2011; Mejias and Longtin, 2012; Hunsberger et al, 2014) have drawn special attention as well.…”

Section: Introductionmentioning

confidence: 99%

Differential effects of excitatory and inhibitory heterogeneity on the gain and asynchronous state of sparse cortical networks

Mejías¹,

Longtin²

2014

Front. Comput. Neurosci.

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Recent experimental and theoretical studies have highlighted the importance of cell-to-cell differences in the dynamics and functions of neural networks, such as in different types of neural coding or synchronization. It is still not known, however, how neural heterogeneity can affect cortical computations, or impact the dynamics of typical cortical circuits constituted of sparse excitatory and inhibitory networks. In this work, we analytically and numerically study the dynamics of a typical cortical circuit with a certain level of neural heterogeneity. Our circuit includes realistic features found in real cortical populations, such as network sparseness, excitatory, and inhibitory subpopulations of neurons, and different cell-to-cell heterogeneities for each type of population in the system. We find highly differentiated roles for heterogeneity, depending on the subpopulation in which it is found. In particular, while heterogeneity among excitatory neurons non-linearly increases the mean firing rate and linearizes the f-I curves, heterogeneity among inhibitory neurons may decrease the network activity level and induces divisive gain effects in the f-I curves of the excitatory cells, providing an effective gain control mechanism to influence information flow. In addition, we compute the conditions for stability of the network activity, finding that the synchronization onset is robust to inhibitory heterogeneity, but it shifts to lower input levels for higher excitatory heterogeneity. Finally, we provide an extension of recently reported heterogeneity-induced mechanisms for signal detection under rate coding, and we explore the validity of our findings when multiple sources of heterogeneity are present. These results allow for a detailed characterization of the role of neural heterogeneity in asynchronous cortical networks.

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“…This random dilution induces fluctuations in the evolution of the macroscopic variables and deterministic chaos at the microscopic level [1]. Our main aim is to mimic the effect of the dilution as a noise source acting on the dynamics of a globally coupled nonchaotic system.…”

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confidence: 99%

Stochastic mean-field formulation of the dynamics of diluted neural networks

Angulo-Garcia

Torcini

2015

Phys. Rev. E

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We consider pulse-coupled leaky integrate-and-fire neural networks with randomly distributed synaptic couplings. This random dilution induces fluctuations in the evolution of the macroscopic variables and deterministic chaos at the microscopic level [1]. Our main aim is to mimic the effect of the dilution as a noise source acting on the dynamics of a globally coupled nonchaotic system. We show that the evolution of a deterministic diluted neural network of any size can be well approximated by a much smaller fully coupled network, where each neuron is driven by a mean synaptic current plus additive noise. These terms represent the average and the fluctuations of the synaptic currents acting on the single neurons in the diluted system. The main microscopic and macroscopic dynamical features can be reproduced within this stochastic approximation. In order to illustrate the quality of this reconstruction, we compare the probability distribution function of the interspike intervals and the macroscopic attractor of the deterministic diluted system with those obtained by employing the mean-field stochastic model (see Figure 1A and 1B, respectively). Furthermore, the microscopic stability of the diluted network can be also reproduced, as demonstrated from the almost coincidence of the measured Lyapunov exponents in the deterministic and stochastic cases for an ample range of system sizes (see Figure 1C.). Our results strongly suggest that the fluctuations in the synaptic currents are responsible for the emergence of chaos in this class of pulse-coupled systems [2].

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Collective oscillations in disordered neural networks

Cited by 68 publications

References 18 publications

Sparse short-distance connections enhance calcium wave propagation in a 3D model of astrocyte networks

Sparse short-distance connections enhance calcium wave propagation in a 3D model of astrocyte networks

Differential effects of excitatory and inhibitory heterogeneity on the gain and asynchronous state of sparse cortical networks

Stochastic mean-field formulation of the dynamics of diluted neural networks

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