Original ResearchDynamics of excitable neural networks with heterogeneous connectivity
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 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 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.
References (37)
- et al.
Complex networks: structure and dynamics
Phys. Rep.
(2006) - et al.
Interneuron diversity series: circuit complexity and axon wiring economy of cortical interneurons
Trends Neurosci.
(2004) - et al.
The effects of physiologically plausible connectivity structure on local and global dynamics in large scale brain models
J. Neurosci. Methods
(2009) - et al.
Intraglomerular dendritic link connected by gap junctions and chemical synapses in the mouse main olfactory bulb: electron microscopic serial section analyses
Neuroscience
(2005) - et al.
The organizing principles of neuronal avalanches: cell assemblies in the cortex?
Trends Neurosci.
(2007) - et al.
Organization, development and function of complex brain networks
Trends Cogn. Sci.
(2004) - et al.
High-frequency population oscillations are predicted to occur in hippocampal pyramidal neuronal networks interconnected by axoaxonal gap junctions
Neuroscience
(1999) - et al.
Statistical mechanics of complex networks
Rev. Mod. Phys.
(2002) - et al.
The architecture of complex weighted networks
Proc. Natl. Acad. Sci. USA
(2004) - et al.
Neuronal avalanches in neocortical circuits
J. Neurosci.
(2003)
Ephaptic interactions in the mammalian olfactory system
J. Neurosci.
Auditory sensitivity provided by self-tuned critical oscillations of hair cells
Proc. Natl. Acad. Sci. USA
Synchronization is enhanced in weighted complex networks
Phys. Rev. Lett.
Excitable scale free networks
Eur. Phys. J. B.
Spectra of Graphs: Theory and Applications
Self-organized criticality model for brain plasticity
Phys. Rev. Lett.
Spatial patterns for discrete models of diffusion in excitable media
SIAM J. Appl. Math.
Synchronous neural activity in scale-free network models versus random network models
Proc. Natl. Acad. Sci. USA
Cited by (5)
Brain synchronizability, a false friend
2019, NeuroImageCitation Excerpt :In the remainder, we argue that some essential characteristics of the brain render the MSF framework difficult to apply to neuroscience, review some misunderstandings about the synchronizability construct, and propose alternative ways to understand synchronization in brain networks. The use of synchronizability, initially designed to study theoretical models, rapidly extended to the analysis of real datasets and, in the context of neuroscience, to quantify the ability of anatomical (Chavez et al., 2011; Zhao et al., 2011; Ton et al., 2014; Phillips et al., 2015; Tang et al., 2017) and functional (de Haan et al., 2012; Bassett et al., 2006; Reijneveld et al., 2007; Stam and Reijneveld, 2007; Schindler et al., 2008; Deuker et al., 2009; van Wijk et al., 2010; Jalili and Knyazeva, 2011; van Dellen et al., 2012; Tahaei et al., 2012; Bialonski and Lehnertz, 2013; Lehnertz et al., 2014; Niso et al., 2015; Khambhati et al., 2016) brain networks to synchronize. For example, Tang and co-workers (Tang et al., 2017) investigated how the human brain's anatomical organization evolves from childhood to adulthood by measuring changes in the synchronizability parameter, and proposed that during the course of development human brain anatomy evolves towards an organization that limits synchronizability (Tang et al., 2017).
BrainModes: The role of neuronal oscillations in health and disease
2011, Progress in Biophysics and Molecular BiologyBrain synchronizability, a false friend
2018, arXivEpilepsies in the elderly
2014, Zeitschrift fur EpileptologieOptimal channel efficiency in a sensory network
2013, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics