A Mathematical Model of the Olfactory Bulb for the Selective Adaptation Mechanism in the Rodent Olfactory System

Abstract

To predict the odor quality of an odorant mixture, the interaction between odorants must be taken into account. Previously, an experiment in which mice discriminated between odorant mixtures identified a selective adaptation mechanism in the olfactory system. This paper proposes an olfactory model for odorant mixtures that can account for selective adaptation in terms of neural activity. The proposed model uses the spatial activity pattern of the mitral layer obtained from model simulations to predict the perceptual similarity between odors. Measured glomerular activity patterns are used as input to the model. The neural interaction between mitral cells and granular cells is then simulated, and a dissimilarity index between odors is defined using the activity patterns of the mitral layer. An odor set composed of three odorants is used to test the ability of the model. Simulations are performed based on the odor discrimination experiment on mice. As a result, we observe that part of the neural activity in the glomerular layer is enhanced in the mitral layer, whereas another part is suppressed. We find that the dissimilarity index strongly correlates with the odor discrimination rate of mice: r = 0.88 (p = 0.019). We conclude that our model has the ability to predict the perceptual similarity of odorant mixtures. In addition, the model also accounts for selective adaptation via the odor discrimination rate, and the enhancement and inhibition in the mitral layer may be related to this selective adaptation.

Fig 1. Schematic diagram of the proposed olfactory model.

The model consists of a glomerular layer, mitral and granular layer, and a dissimilarity evaluation module. The model takes the glomerular activity patterns of odorants composing an odor as input, and considers respiration cycles to simulate the glomerular response to odorant mixture. The neural activity in mitral and granular cells is simulated based on the models proposed in a previous study [20, 21]. The dissimilarity evaluation module defines a dissimilarity index E and compares the activity patterns evoked in the mitral layer by different input odorant mixtures.

Fig 2. Method of generating the model input from measured glomerular activity patterns provided by a web database (http://gara.bio.uci.edu/) (adapted from [5]).

The original image of the glomerular activity pattern (left) is composed of 357 × 197 pixels, and the grayscale of each pixel corresponds to the activity strength. The original image is divided into 1805 lattices, approximately equal to the actual number of glomeruli distributed on the olfactory bulb. The average activity strength is calculated for each pixel and converted into a vector representing an activity pattern.

Fig 3. Configuration of synapse connections.

The figure represents the connection range of a mitral or a granular unit. A unit at the center of the grey circle is connected to all units within a range of the circle. If the connection range exceeds the limit, it is folded back to the other end, considering the bulbous shape of the olfactory bulb, using Eqs (7)–(12).

Fig 4. Prediction of perceptual similarity for odors composed of IA, EB, and Ci.

(a) Output from the glomerular layer for odorant input [IA, Ci, EB]. The figure shows the steps taken to generate output for the glomerular layer. The activity strength is represented in grayscale, where whiter pixels correspond to higher activity. The uppermost row shows the glomerular activity pattern for the odorant composing odor [IA, EB, Ci] obtained from Johnson et al. [–31]. The middle row shows the binarized activity patterns given by adapting Eq (2) after dividing the pixels into 1805 lattices and generalizing the activity strength into the range [0, 1]. The third row shows the output from the glomerular layer, and the bottom row shows that from the mitral layer generated by the procedure described in Section 2. (b) Comparison between discrimination rates of mice obtained from experiments and dissimilarity obtained from simulations (ζ_m = 4, ζ_g = 15). The figure compares the dissimilarity index E obtained from the simulation and discrimination rate for each odor. The orange bars denote simulation results and the blue bars represent the experimental results. The error bars added to the experimental results address the standard deviation in 10 mice, and the error bars added to the simulation results correspond to the standard deviation of 20 sets of synapse connection parameters. Orange and blue lines above the bars denote a significant difference of p<0.01 between odor pairs. Orange lines represent multiple comparison results from the simulation, and blue lines represent that of experiments on mice. (c) Scatter plot between discrimination rates of mice obtained from experiments and dissimilarity index E obtained from simulations. The figure shows a scatter plot between the dissimilarity index and discrimination rate. The error bars correspond to those in (b).

Fig 5. Results of Hebbian learning.

(a) Convergence of the synapse connection strength of H. (b) Changes of activity patterns in mitral layer. The deep red parts are the most activated and blue parts are least activated.

Fig 6. Parameter set ζ_m, ζ_g and prediction accuracy.

Pearson correlations between dissimilarity index E and discrimination rate of the mice obtained from experiments are plotted with different ζ_g and ζ_m.