Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities

Abstract

We investigate how synchrony can be generated or induced in networks of electrically coupled integrate-and-fire neurons subject to noisy and heterogeneous inputs. Using analytical tools, we find that in a network under constant external inputs, synchrony can appear via a Hopf bifurcation from the asynchronous state to an oscillatory state. In a homogeneous net work, in the oscillatory state all neurons fire in synchrony, while in a heterogeneous network synchrony is looser, many neurons skipping cycles of the oscillation. If the transmission of action potentials via the electrical synapses is effectively excitatory, the Hopf bifurcation is supercritical, while effectively inhibitory transmission due to pronounced hyperpolarization leads to a subcritical bifurcation. In the latter case, the network exhibits bistability between an asynchronous state and an oscillatory state where all the neurons fire in synchrony. Finally we show that for time-varying external inputs, electrical coupling enhances the synchronization in an asynchronous network via a resonance at the firing-rate frequency.

Morphologically mixed chemical–electrical synapses formed by primary afferents in rodent vestibular nuclei as revealed by immunofluorescence detection of connexin36 and vesicular glutamate transporter-1

“…While the importance of faster electrical transmission is understood in many electrically coupled systems in cold-blooded species, it has been repeatedly emphasized that there is little such advantage in mammals, where body temperature shortens chemical synaptic delay to speeds sometimes approaching or overlapping that of electrical synapses (Bennett, 1972, 1977, 1997, 2000; Bennett and Goodenough, 1978; see however Ostojic et al, 2009). Even with a shorter latency of transmission at electrical synapses, it has been noted that speed of motor responses triggered by vestibular activity would be more limited by physical constraints of movement imposed by body size (Korn et al, 1977).…”

Effect of Phase Response Curve Skewness on Synchronization of Electrically Coupled Neuronal Oscillators

“…Finally the interactions are assumed to be weak, and thus the results reported here cannot explain effects due to strong coupling. We have also not considered the role of heterogeneities and noise (for such studies in LIF models see (Ostojic et al, 2009)) on the phase-locked states. In fact the synchronous state considered here is a perfect synchronous state where the spikes align with no phase difference.…”

“…When the neurons are in oscillatory state either autonomously or in response to external stimuli a synchronous state may emerge in the connected network (Kepler, Marder, & Abbott, 1990; Traub et al, 2003; Fuentealba et al, 2004; Hestrin & Galarreta, 2005; Mancilla et al, 2007) (also see simulations in (Gao & Holmes, 2007; Ostojic, Brunel, & Hakim, 2009)). Electrical coupling has also been found to result in a failure of synchrony (Bou-Flores & Berger, 2001).…”

Emergence of local synchronization in neuronal networks with adaptive couplings

“…The coupled system of neurons is described by the following equations: Here x i ( t ), y i ( t ) and z i ( t ) denote the x ( t ), y ( t ) and z ( t ) variables of the i th neuron, respectively, k ij ( t ) (where k ij ( t ) ≥ 0, for all i , j and t ) represents the coupling between neurons i and j at time t , and A = ( A ij ) is the adjacency matrix of the network Γ (i.e., A ij = 1 if neurons i and j are connected by an edge in Γ, and A ij = 0 otherwise). For k ij ( t ) = k , for all i , j , and Γ the complete network, Eqs (4)–(6) describes N Hindmarsh-Rose neurons, each of which is coupled to all others with common, fixed, coupling strength k [27, 39–41]. …”