Odor representations in the rat olfactory bulb change smoothly with morphing stimuli

Abstract

Many species of mammals are very good at categorizing odors. One model for how this is achieved involves the formation of "attractor" states in the olfactory processing pathway, which converge to stable representations for the odor. We analyzed the responses of rat olfactory bulb mitral/tufted (M/T) cells using stimuli "morphing" from one odor to another through intermediate mixtures. We then developed a phenomenological model for the representation of odors and mixtures by M/T cells and show that >80% of odorant responses to different concentrations and mixtures can be expressed in terms of smoothly summing responses to air and the two pure odorants. Furthermore, the model successfully predicts M/T cell responses to odor mixtures when respiration dependence is eliminated. Thus, odor mixtures are represented in the bulb through summation of components, rather than distinct attractor states. We suggest that our olfactory coding model captures many aspects of single and mixed odor representation in M/T cells.

Figure 1

Recording Procedures and Data Representation (A) Extracellular single-unit recordings were made using tetrodes, and the signal was amplified and filtered and acquired on a computer. The respiration of the rat was typically steady at 1 Hz and was monitored with a thermocouple placed in front of its nostril. The odor presentation protocol is shown below. (B) A schematic of the construction of a respiration raster that shows the respiration-locked firing pattern of a cell. The spike train is divided into each respiration cycle, and each spike is replotted with the respiration phase on the y axis and time of respiration cycle start (or simply time) on the x axis, aligned to the odor valve onset. (C) Data from a cell with five trials of an odor presentation superimposed. Each + sign represents an action potential. The color plot to the right is the same data after smoothing and color coding. The red bar indicates the duration of the odor stimulus here and in subsequent figures. This cell responds to the odor by changing its respiration tuning, but not its firing rate. The frequency shown on the side of the plot is the maximum firing rate on this figure here and in subsequent plots.

Figure 2

Odor Responses Pass through Intermediates During Exposure to the Morph Sequence (A)–(D) show cells from naive rats. (E)–(H) are from rats that were familiarized with the odors for 5–8 days. Each panel is from a cell that responded to two odors differently, and these two responses are shown on the top of each panel. Below these are the responses to the mixtures of the two odors in the morph sequence, which can be seen to pass through intermediate forms of responses. In a few particularly stable recordings, morph sequences were recorded in both directions as in (A), (B), (E), and (F). Arrows indicate temporal order of recordings. The color coding is the same for all plots in each panel. Numbers in brackets are the highest firing rate in each panel.

Figure 3

Simple Analysis of Morphing Responses (A) Estimating peak firing phase using Gaussian fit. (B) Firing rate buildup in a defined range of respiration phase. Rates were calculated by summing all spikes within the selected respiration phase range, shown as a box on the raster plot. (C) Example of change of response as a function of composition of the mixture fitting a straight line. (D) Sigmoid response. (E) Log response. (C) and (D) are from cells with firing rate buildup and (E) is from a cell with a shifting band. (F) The distribution of the 41 morphs from 32 cells between firing phase and firing rate calculations. (G) The distribution of cells between straight line, log, sigmoid, and other categories.

Figure 4

Schematic of Model (A) Example of a cell's response to an odor shown in three dimensions. (B) The air input strength function of the cell (left) is a function of the respiration cycle during air presentation. When passed through a sigmoid, the air input function results in the firing rate over the respiration cycle for the air period. (C) The odor input strength function (black) is added to the air input strength function (red) to give the function AIR + ODOR (blue). This AIR + ODOR function, when passed through the same sigmoid, will result in the AIR + ODOR firing rate function (right). (D) All possible mixture responses are obtained by scaling each odor input strength function and adding them to the air function. This is passed through the sigmoid to obtain the response of the cell to the mixture.

Figure 5

Model Validation and Predictions (A) Above is the original data showing odor responses to the morph sequence, and below is the model prediction. This is the same example from Figure 2A, reverse morph. Cineole is odor A and iso amyl acetate is odor B. (B) Alternate representation of data in (A) and its comparison with the model. Odor periods are placed alongside for each mixture of the morph sequence. The model representation is very close to the experiment. (C) Overlaid respiration phase versus firing rate plots for the data (with error bars) and the model. Curves are shown for air, 1%A, and 1%B. (D) Input strength functions for odors A and B, showing scaling with different odor concentrations. (E) Coefficients for odors A and B as a function of odor mixture. In this example the coefficients fit a straight line. (F) An illustration of the process of obtaining the mixture response of .4A + .6B. The two respective curves from (D) of .4A and .6B are added to obtain the purple curve (left). The air baseline is shown in green. The two horizontal lines correspond to the approximate lower and upper cutoffs imposed by the sigmoid, of zero and saturated firing, respectively. Adding the three curves gives the brown Air + .4A + .6B curve (center). This is passed through the sigmoid to give the red curve (right) showing the response for this particular mixture. It is a good fit to the experimental data, in black. Error bars indicate SEM.

Figure 6

Population Data and Validation of the Model A distribution of simulated chi-square scores was calculated for each morph experiment in a Monte Carlo manner (n = 41 morphs). The difference between the mean of the simulated scores and the score from fitting the data, normalized by the standard deviation of the simulated score distribution, was found. The histograms of these values are plotted. The two vertical lines are at ±3.29. Eighty percent of morphs (33/41) were within this range. The arrowhead indicates the bin in which the example from Figure 5 belongs.

Figure 7

The Model in the Single-Odor Case (A) Two examples of the effect of increasing the concentration of a single odor on a cell's response, comparing data and model. A(i) is a primarily inhibitory response and A(ii) is primarily excitatory. Here the effect is an increase in the width and/or amplitude of the response. This contrasts with the shift in the tuning pattern seen in some of the mixture results. Example A(i) is explored in detail in the rest of the figure. (B) Comparing the entire concentration series and the average air period for the data and model for the cell shown in A(i), as in Figure 5B. (C) The 1% odor case and the air period overlaid for odor and model. Error bars indicate SEM. (D) The input strength functions for the odor at different concentrations. The large inhibitory component is evident, and the asymmetry in its shape explains why the inhibitory “gap” in the data increases in one direction more than the other (toward later respiration phases). (E) The plot of the coefficients against the externally applied odor concentration is shown overlaid with the best fit; in this case, a sigmoid. (F) The population analysis (akin to Figure 6), showing that 91% (32/35) of the experiments validate the model. Arrowhead indicates the bin in which example A(i) belongs. Vertical red lines are at ±3.29. (G and H) Distributions of coefficient plots across straight line, log, and sigmoid categories for the morph and single-odor experiments, respectively. These two distributions were not different as shown by a chi-square test (p < 0.05).

Figure 8

Validation of Scaling and Additivity (A) Diagram showing the double tracheotomy preparation and the odor presentation protocol. As earlier, an air stream was always blowing at the rat's nose and this was switched to an air + odor stream in the period shown (100, 200, or 500 ms). (B) Raster showing a cell with a flat baseline responding to a 500 ms odor pulse. Below is the PSTH of same cell binned at 125 ms. Black bar: odor duration; blue bar: suction duration; gray bar: 2 s period used for determining baseline firing rate. Both transient and stable firing rate changes from suction alone can be seen. (C and D) Two examples of cells showing the same-shaped response scaling in amplitude with odor concentration. Shown are 200 ms and 100 ms odor pulses [(C) and (D), respectively]; spikes are binned at 50 ms, and odor was iso-amyl acetate in both. Error bars indicating SEM have been removed for clarity. (E) Predicted versus observed firing rate; baseline is plotted for the 12/17 cells that were consistent with a single-shape scaling (Q value > 0.001). (F and G) Two examples of cells that showed that the response to the mixture was a direct summation of the responses to the components. A and B are the components and M is the mixture. The dashed green line shows what the mixture would be if there were perfect addition. The odor pairs in (F) and (G) are iso-amyl acetate/(+) limonene and methyl amyl ketone/iso-amyl acetate, respectively. Error bars indicate SEM. (H) Histogram of the values of R. Perfect addition would cause these values to be 0.5 (red line).