Maintaining phase of the crustacean tri-phasic pyloric rhythm

Abstract

We construct and analyze a model network of the pyloric rhythm of the crustacean stomatogastric ganglion consisting of an oscillator neuron that inhibits two reciprocally inhibitory follower neurons. We derive analytic expressions that determine the phase of firing of the follower neurons with respect to the oscillator. An important aspect of the model is the inclusion of synapses that exhibit shortterm synaptic depression. We show that these type of synapses allow there to be a complicated relationship between the intrinsic properties of the neurons and the synapses between them in determining phase relationships. Our analysis reveals the circumstances and ranges of cycle periods under which these properties work in concert with or independently from one another. In particular, we show that phase maintenance over a range of oscillator periods can be enhanced through the interplay of the two follower neurons if the synapses between these neurons are depressing. Since our model represents the core of the oscillatory pyloric network, the results of our analysis can be compared to experimental data and used to make predictions about the biological network.

Co-existent activity patterns in inhibitory neuronal networks with short-term synaptic depression

“…The effect of synaptic depression on network behavior depends, in some measure, on network structure, particularly whether a network is generally feedforward in design or includes feedback projections among its constituent neurons (see Grande and Spain, 2005 for a review). In reciprocally connected networks, depression has been shown to broaden network dynamics in a variety of ways, such as by generating rhythmic spontaneous activity (Rubin et al, 2009;Tabak et al, 2000), regulating the relative timing of firing of network components (Manor et al, 2003;Mouser et al, 2008), supporting persistent activity (Barbieri and Brunel, 2007) and introducing co-existing stable firing patterns (Bose et al, 2001;Chandrasekaran et al, 2009;Jalil et al, 2004;Manor and Nadim, 2001;Nadim et al, 1999). Understanding the contributions of synaptic depression to the generation of such diverse patterns of activity is often best achieved by studying small, idealized networks of model neurons.…”

The complexity of small circuits: the stomatogastric nervous system

“…The pyloric rhythm is based on intrinsic oscillatory properties of a pacemaker kernel, and follower neurons burst in rebound from inhibition by the pacemaker [8] (Fig. 1B&C).…”

“…The pyloric pacemaker neuron AB is shown as a reference for pyloric timing. A , B , & D are modified from reference [9]; C is modified from reference [8]. …”

A Codimension-2 Bifurcation Controlling Endogenous Bursting Activity and Pulse-Triggered Responses of a Neuron Model

“…A variety of network mechanisms producing specific temporal patterns of activity have been previously studied [1], [10], [18], [31], [34], [41], [52]–[60].…”