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Impact of adaptation and synaptic plasticity on synchronization of coupled oscillating neurons

Josef Ladenbauer:

 

Synchronized oscillating activity in cortical circuits is considered to be fundamental to cognitive function, selective attention and consciousness. In the present study we describe how threshold-dependent adaptation currents affect the synchronization properties of coupled neurons driven to repetitive spiking, in presence of conduction delays and synaptic strengths that are modified by spike-timing-dependent plasticity (STDP).

We analyze networks of adaptive exponential leaky integrate-and-fire (aELIF) neurons [1], which involve subthreshold as well as spike-triggered adaptation components, by applying phase reduction theory based on the assumption of weak coupling [2]. We calculate phase response curves (PRCs) to obtain interaction functions which determine the dynamics of the reduced phase networks. In these networks, each phase difference is described by a scalar differential equation. We identify stable phase locked states of coupled pairs of neurons for synaptic strengths that are either fixed, or changed by STDP [3].

We find that subthreshold adaptation causes a transition of the PRC from type I (only advancing) to type II (advancing and delaying) whereas spike-triggered adaptation determines its skewness. Both adaptation mechanisms synchronize spiking of coupled excitatory pairs as long as conduction delays are negligible. With increasing delays, the stable states shift from in-phase towards anti-phase locking. Inhibitory neurons without adaptation on the other hand synchronize, unaffected by conduction delays. Spike-triggered adaptation in these cells causes bistability of in-phase and anti-phase locking for coupled pairs. Our analysis reveals that pairs of neurons with type II PRCs have stable phase locked states even for highly heterogeneous synaptic strengths. When the (excitatory) synapses are modified by STDP, such pairs phase lock with a phase difference slightly above the conduction delay. Larger delays lead to anti-phase locking; intermediate delays cause bistability of anti-phase and out-of-phase locking. We complement these results on pairs by numerical simulations of phase networks as well as aELIF networks, respectively, demonstrating that STDP promotes clustering, where the number of clusters largely depends on the conduction delay.

[1] R. Brette, W. Gerstner (2005) Adaptive Exponential Integrate-and-Fire model as an effective description of neuronal activity. J Neurophysiol 94: 3637-42.

[2] B. Ermentrout, D. Terman (2010) Mathematical Foundations of Neuroscience. Springer: New York.

[3] A. Morrison, M. Diesmann, W. Gerstner (2008) Phenomenological models of synaptic plasticity based on spike timing. Biol Cybern 98: 459-78.

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