Connection topology dependence of synchronization of neural assemblies on class 1 and 2 excitability

Lago-Fernández, Luis F.; Corbacho, Fernando J.; Huerta, Ramón

doi:10.1016/s0893-6080(01)00032-6

Cited by 29 publications

(22 citation statements)

References 18 publications

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“…Using a network of FitzHugh-Nagumo (FN) neurons [783,784], the frequency of the coherent oscillations was found to be highly modulated by the network topology [785]. In contrast with the HH model, the propagation speed in the FN network is not dependent of the wiring structure.…”

Section: Dynamicsmentioning

confidence: 99%

Complex networks: Structure and dynamics

et al. 2006

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Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the dynamical units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks' dynamics, such as learning how a large ensemble of dynamical systems that interact through a complex wiring topology can behave collectively. We review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

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Section: Dynamicsmentioning

confidence: 99%

Complex networks: Structure and dynamics

et al. 2006

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“…Possibilities include largely distributed changes in structural (Cohen-Cory et al, 2010) and functional connectivity (Thomason et al, 2009). As connectivity determines neural network synchronization and dynamics (Lago-Fernández et al, 2001;Kitano and Fukai, 2007), synchronization may constitute a relevant mechanism by which BDNF affects cognitive functions. Such possible mechanisms have until now not been investigated.…”

Section: Introductionmentioning

confidence: 99%

The Role of the BDNF Val66Met Polymorphism for the Synchronization of Error-Specific Neural Networks

Beste¹,

Kolev²,

Yordanova³

et al. 2010

J. Neurosci.

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Behavioral adaptation depends on the recognition of response errors and processing of this error-information. Error processing is a specific cognitive function crucial for behavioral adaptation. Neurophysiologically, these processes are reflected by an event-related potential (ERP), the error negativity (Ne/ERN). Even though synchronization processes are important in information processing, its role and neurobiological foundation in behavioral adaptation are not understood. The brain-derived neurotrophic factor (BDNF) strongly modulates the establishment of neural connectivity that determines neural network dynamics and synchronization properties. Therefore altered synchronization processes may constitute a mechanism via which BDNF affects processes of error-induced behavioral adaptation. We investigate how variants of the BDNF gene regulate EEG-synchronization processes underlying error processing. Subjects (n ϭ 65) were genotyped for the functional BDNF Val66Met polymorphism (rs6265). We show that Val/Val genotype is associated with stronger error-specific phase-locking, compared with Met allele carriers. Posterror behavioral adaptation seems to be strongly dependent on these phase-locking processes and efficacy of EEG-phase-locking-behavioral coupling was genotype dependent. After correct responses, neurophysiological processes were not modulated by the polymorphism, underlining that BDNF becomes especially necessary in situations requiring behavioral adaptation. The results suggest that alterations in neural synchronization processes modulated by the genetic variants of BDNF Val66Met may be the mechanism by which cognitive functions are affected.

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“…We find that even this simple model exhibits a rich repertoire of distinct dynamical behaviors as a function of the density p of added shortcuts: a low p regime characterized by persistent periodic activity that is bistable with the quiescent state, a transition to failure with increasing p, followed by a reemergence of long-lasting disordered activity. We note that a SWN with unidirectional shortcuts has been considered in a different regime by Lago-Fernández et al [14,15] to address the possibility of rapid synchronization among conductance-based neurons of the HodgkinHuxley type.The model considered here consists of a onedimensional array of N integrate-and-fire neurons (IFNs) in which a SWN topology is created through the addition of a density p of unidirectional long-range couplings. The membrane potential of the IFNs is determined by…”

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confidence: 99%

Self-Sustained Activity in a Small-World Network of Excitable Neurons

2004

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We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities p of directed random connections, a localized transient stimulus results in either selfsustained persistent activity or in a brief transient followed by failure. Averages over the quenched ensemble reveal that the probability of failure changes from 0 to 1 over a narrow range in p; this failure transition can be described analytically through an extension of an existing mean-field result. Exceedingly long transients emerge at higher densities p; their activity patterns are disordered, in contrast to the mostly periodic persistent patterns observed at low p. The times at which such patterns die out are consistent with a stretched-exponential distribution, which depends sensitively on the propagation velocity of the excitation.PACS numbers: 87.18.Sn,87.10.+e Recent research in complex networks has provided increasing evidence for their relevance to a variety of physical, biological, and social phenomena [1,2,3]. Two distinct types of topology have been particularly useful in providing insights into the implications of complex connectivity: scale-free networks [3], characterized by the existence of a small number of hubs with high coordination number, and small-world networks [1], characterized by the presence of shortcuts that link two randomly chosen sites regardless of the distance between them.So far, most work on complex networks has focused on their topological and geometrical properties; less attention has been given to the properties of dynamical systems defined on such networks. The interplay between the intrinsic dynamics of the constituent elements and their complex pattern of connectivity strongly affects the collective dynamics of the resulting system. For instance, the addition of shortcuts induces a finite-temperature phase transition even in the one-dimensional Ising model [4] and the introduction of unidirectional shortcuts can change the second-order phase transition in the twodimensional Ising model into a first-order one [5]. In a system of coupled oscillatory elements, the introduction of shortcuts enhances synchronization [6], while the introduction of hubs eliminates the threshold for epidemic propagation [7].The coexistence of shortcuts and regular local connections characteristic of small-world networks (SWNs) mimics a salient feature of the circuitry in the cortex [8,9,10,11,12,13], where experimental observations of excitatory traveling waves [11] provide evidence of some degree of local connectivity, while it is also recognized that long-range excitatory connections are present [10,12]. Our goal is to explore the influence of this complex connectivity on the dynamics of neuronal circuits; to this purpose, we choose a minimal model. The underlying network is modeled as a SWN with unidirectional shortcuts that reflect the nonreciprocal character of synaptic connections, and the excitable neurons are modeled as leaky integrate-and-fire units. We find that even this simple model exhibi...

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Connection topology dependence of synchronization of neural assemblies on class 1 and 2 excitability

Cited by 29 publications

References 18 publications

Complex networks: Structure and dynamics

Complex networks: Structure and dynamics

The Role of the BDNF Val66Met Polymorphism for the Synchronization of Error-Specific Neural Networks

Self-Sustained Activity in a Small-World Network of Excitable Neurons

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