Abstract
Significant insights into the dynamics of neuronal populations have been gained in the olfactory system where rich spatio-temporal dynamics is observed during, and following, exposure to odours. It is now widely accepted that odour identity is represented in terms of stimulus-specific rate patterning observed in the cells of the antennal lobe (AL). Here we describe a nonlinear dynamical framework inspired by recent experimental findings which provides a compelling account of both the origin and the function of these dynamics. We start by analytically reducing a biologically plausible conductance based model of the AL to a quantitatively equivalent rate model and construct conditions such that the rate dynamics are well described by a single globally stable fixed point (FP). We then describe the AL's response to an odour stimulus as rich transient trajectories between this stable baseline state (the single FP in absence of odour stimulation) and the odour-specific position of the single FP during odour stimulation. We show how this framework can account for three phenomena that are observed experimentally. First, for an inhibitory period often observed immediately after an odour stimulus is removed. Second, for the qualitative differences between the dynamics in the presence and the absence of odour. Lastly, we show how it can account for the invariance of a representation of odour identity to both the duration and intensity of an odour stimulus. We compare and contrast this framework with the currently prevalent nonlinear dynamical framework of 'winnerless competition' which describes AL dynamics in terms of heteroclinic orbits. This article is part of a Special Issue entitled "Neural Coding".
Highlights
It is widely accepted that insects encode odor identity in terms of the stimulus specific rate patterning observed in the projection neurons of the antennal lobe (AL)
The heteroclinic orbit (HO) framework assumes that the presence of an odor re-parameterises the connectivity of the AL through input to local neurons (LNs)
The mathematical image of this change is a bifurcation from a regime with a single stable fixed point (FP) to a regime with a stable HO
Summary
It is widely accepted that insects encode odor identity in terms of the stimulus specific rate patterning observed in the projection neurons of the antennal lobe (AL). Despite its obvious appeal there has been little work on applying the HO framework to more detailed conductance based models of olfactory dynamics even though it is in principle possible to obtain HO dynamics from biologically plausible neurons [5]. Obtaining proper HO dynamics with conductance based Hodgkin-Huxley neurons in this work required non-standard assumptions for the synapses [5].
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