Original Research
Dynamics of excitable neural networks with heterogeneous connectivity

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Abstract

A central issue of neuroscience is to understand how neural units integrates internal and external signals to create coherent states. Recently, it has been shown that the sensitivity and dynamic range of neural assemblies are optimal at a critical coupling among its elements. Complex architectures of connections seem to play a constructive role on the reliable coordination of neural units. Here we show that, the synchronizability and sensitivity of excitable neural networks can be tuned by diversity in the connections strengths. We illustrate our findings for weighted networks with regular, random and complex topologies. Additional comparisons of real brain networks support previous studies suggesting that heterogeneity in the connectivity may play a constructive role on information processing. These findings provide insights into the relationship between structure and function of neural circuits.

Introduction

Brain systems are sensitive to a large variety of stimuli, producing for a broad range of external conditions an appropriate neuronal response. Recent works have suggested that networks operating near a critical regime where one neuron activates, on the average, one other neuron, provide an optimal information transmission, memory capacity and computational power (Camalet et al., 2000, Beggs and Plenz, 2003, de Arcangelis et al., 2006, Haldeman and Beggs, 2005, Shew et al., 2009). Recently, theoretical models show that the dynamic range of excitable neural networks is optimal at this critical regime. Instead, a supercritical propagation regime saturates the system, whereas a subcritical setting results in a network where any input activity dies out (Kinouchi and Copelli, 2006, Copelli and Campos, 2007, Wu et al., 2007).

Empirical studies have shown that neural units interact with each other via a complex architecture that can be captured neither by regular connectivity models as lattices, nor by a random configuration (Watts and Strogatz, 1998, Sporns et al., 2004). Small world (SW) networks (Watts and Strogatz, 1998) are objects in between regular and random networks characterized by a small average distance between any two nodes (scaling logarithmically rather than linearly with the network size), while keeping a relatively highly clustered structure. Scale-free (SF) networks Networks (Albert and Barabási, 2002) are examples of SW networks displaying a power-law distribution p(k)kγ in the node connectivity k (degree).

Recent studies have revealed the strong interplay between the complexity in the overall topology and the emergence of collective (synchronized) behaviors (Boccaletti et al., 2006, Newman, 2003, Strogatz, 2001). A basic assumption characterizing most of the current neural models is that the local cells are symmetrically coupled with uniform coupling strengths (unweighted links) (Copelli and Campos, 2007, Grinstein and Linsker, 2005, Kinouchi and Copelli, 2006, Lago-Fernández et al., 2000, Wu et al., 2007). However, in many circumstances this simplification does not match satisfactorily the peculiarities of real networks. Indeed, the natural heterogeneity of neurons and their synaptic strength connections play an important role in the capabilities of transmission and information processing in neural networks (Buzsáki et al., 2004, Song et al., 2005).

In this work we mainly address the question of how a heterogeneous connectivity influences the dynamic range of excitable neurons embedded in complex networks. We show that, a heterogeneity in the connection strengths may tune the enhancement of the dynamic range. Additional analysis of neuroanatomical data sets (cortical circuits for the cat and macaque, and the brain structure of the Caenorhabditis elegans) suggest that the structure of neural connectivity may reach an optimal balance between sensitivity, synchronizability and wiring cost, promoting thus an efficient information transmission in brain systems.

Section snippets

Excitable neural model

In this work we consider an excitable neural model modified from early proposals by Greenberg–Hastings (Greenberg and Hastings, 1978). This model is a simple cellular automaton that captures the basic physical of coupled spiking neurons interconnected by strong and sparse connections (Copelli and Campos, 2007, Kinouchi and Copelli, 2006, Lewis and Rinzel, 2000, Traub et al., 1999; ; Wu et al., 2007). The model is formulated as follows. Each neuron i at time (t) is in one of the following

Sensitivity of complex networks

The behavior of the excitable neural model is evaluated by numerically determining the activity of different classes of networks for different values of θ1. Fig. 1 shows the response F as a function of the stimulus intensity r for a large class of networks

Conclusions

In conclusion, we address a fundamental problem in neural network research: whether the information processing is affected by the network architecture. We show that, for excitable neural systems, a heterogeneity of connection strengths may promote an efficient information transmission in neural systems. Our results provide further support to previous works suggesting that complex wirings of brain networks favor the emergence of coherent neural behaviors (Boccaletti et al., 2006, Grinstein and

Acknowledgements

The authors would like to thank H. Schuster for the many helpful discussions on the subject. This work was supported by the European Commission through project GABA (FP6-NEST), contract no. 043309.

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