Attractors of neural network dynamics

in an insect's olfactory system

To investigate the neural representation of odors we analyzed the neural dynamics recorded with calcium-imaging in the olfactory system of an insect, the honeybee Apis Mellifera (data provided by Dr. Silke Sachse). In particular, we focused on the antennal lobe, the analogue of the olfactory bulb in vertebrates, and on the interaction between the antennal lobe and the mushroom body, an immediate downstream network. The antennal lobe is a prototypical system in neuroscience because it is a highly structured neural network that allows one to uniquely identify its functional neural units: the glomeruli.

Using a multidimensional representation of the network in which each dimension corresponds to the activity of one glomerulus, we first showed that the neural dynamics in the antennal lobe, the primary processing network in the olfactory system, converge to stable odor-specific patterns of neural activity within approximately 800 ms, regardless of odor identity and intensity. The odor-specific patterns are reproducible across trials and individual bees (Fig. 1). Details of these studies are provided in my doctoral dissertation, as well as in R.F.Galán et al. (2004) Neural Computation 16(5), p.999-1012 [PDF].

Trajectories

Figure 1: Multidimensional representation of the antennal lobe dynamics during stimulation. Several odors were presented twice to the same bee and the neural activity of the antennal lobe was recorded with calcium imaging at fixed time intervals (167 ms). Thus, the distance between successive data points represents the speed of activity changes. The trajectories depart rapidly from the origin and slow down when they approach odor-specific regions. To aid visualization, the original 21-dimensional space (corresponding to the 21 recorded glomeruli) has been projected down onto the three first principal components (PC). These three components account for more than 58% of the variance of the trajectories.


Interestingly, the connectivity between the antennal lobe and the immediate downstream network -the mushroom body- resembles the architecture of the simplest artificial neural network: the perceptron (Fig. 2). This analogy suggested that the olfactory system may encode, classify and recognize odors in a manner similar to a perceptron network. To test this idea, for each odor dataset a perceptron was implemented and trained to discriminate an odor-specific stable pattern of neural activity in the antennal lobe. This half biological, half computational olfactory system presented properties of a fully biological one: 1) the system could discriminate very similar odors that bees can discriminate; 2) the minimal time required for recognition was below 300 ms; the median “reaction time” for bees is 290 ms; 3) for some odors a generalization effect was observed: odors learned at low concentrations were recognized at higher concentrations but not vice versa. Further details are provided in my doctoral dissertation, as well as in R.F.Galán et al. (2004) Neural Computation 16(5), p.999-1012 [PDF]

Perceptron

Figure 2: Perceptron-like architecture of the olfactory network in the honeybee. The algorithm used to analyze the imaging data can be implemented as a simple neural network, the perceptron, whose architecture is compatible with the anatomy of the bee brain. The units in the lower layer represent individual glomeruli in the antennal lobe. The unit in the upper layer represents a neuron of a downstream network (mushroom body). This unit responds to a given odor A only if the whole activity of the lower units weighed by their synaptic strength exceeds a given threshold.

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Last update: May 2009