Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits

Abstract

The purpose of this paper is trifold -to serve as an instructive resource and a reference catalog for biologically plausible modeling with i) conductance-based models, coupled with ii) strength-varying slow synapse models, culminating in iii) two canonical pair-wise rhythm-generating networks. We document the properties of basic network components: cell models and synaptic models, which are prerequisites for proper network assembly. Using the slow-fast decomposition we present a detailed analysis of the cellular dynamics including a discussion of the most relevant bifurcations. Several approaches to model synaptic coupling are also discussed, and a new logistic model of slow synapses is introduced. Finally, we describe and examine two types of bicellular rhythm-generating networks: i) half-center oscillators ii) excitatory-inhibitory pairs and elucidate a key principle -the network hysteresis underlying the stable onset of emergent slow bursting in these neural building blocks. These two cell networks are a basis for more complicated neural circuits of rhythmogensis and feature in our models of swim central pattern generators. II. CONDUCTANCE-BASED MODEL OF SWIM CPG INTERNEURONSOur objective in choosing a neuron model was its biological plausibility, even though cellular currents in swim CPG

Error Function Optimization to Compare Neural Activity and Train Blended Rhythmic Networks

“…A detailed analysis of the Si model and the pairing of matching synaptic properties to build pairwise rhythm-generating circuits can be found in Ref. [53].…”

“…The outcome is contingent on the ∆ Ca parameter. Further information on the dynamical and bifurcation characteristics can be found in a recent study [53]. In this study, a value of the parameter ∆ x = −3.5 mV was fixed to ensure that the Si model bursts endogenously.…”