Jiameng Wu: The Effect of the Phase-Response Curve on Synchronization in the Presence of Synaptic Plasticity

BCCN Berlin / HU Berlin

 

Abstract

Synchronization is an emergent phenomenon in the brain and in neuronal networks, and is believed to play a central role in physiological and pathological brain activities. It has been shown that under the assumption of weak coupling, the synchronization properties of tonically spiking neurons are defined by their phase-response curves - a cell-intrinsic property that depends on the bifurcations of the spiking limit cycle. However, it is unclear how synchronization depends on the phase-response curve when the coupling is subject to activity-dependent plasticity. In the present thesis, we study this question in two mutually coupled quadratic integrate-and- fire neurons with spike-timing dependent plasticity of either excitatory or inhibitory synapses. The phase-response curve of the neurons is systematically varied and its effect on the asymptotic behaviour of the system is observed. The synchronous state and its stability are analytically predicted using phase reduction and linear stability analysis. Our results show that both the excitatory and the inhibitory system exhibit a rich repertoire of dynamical behaviours. For excitatory coupling, phase-locked synchronization is observed for all phase-response curves considered, whereas only highly asymmetric phase-response curves can lead to a near-synchronous state in the inhibitory system. Both systems also exhibit various asynchronous states in dependence on the shape of the phase-response curve: Asymmetric phase-response curves seem to facilitate synaptic competition induced by spike-timing dependent plasticity and lead to asymmetric weights; Symmetric phase-response curves tend to balance potentiation and depression experienced by each synapse and often lead to symmetric weights. We conclude that the shape of the phase-response curve crucially affects the collective behaviour of the neurons, e.g. synchronization, in the presence of synaptic plasticity. Its interaction with the spike-timing dependent plasticity rule creates complex co-evolving dynamics of the phases of the neurons and the strengths of their coupling, and leads to various distinct qualitative states. These states may have distinct functional implications in larger networks and may offer new mechanisms for poising the network on the border between synchrony and randomness.

 

 

Additional Information

Master thesis defense

Organized by

Prof. Dr. Susanne Schreiber & Prof. Dr. Henning Sprekeler