We performed psychophysical experiments on rats using a binary odor mixture discrimination task (Uchida and Mainen, 2003
) (Figure ). Subjects were first trained on binary mixtures of two odorants (“A” and “B”) delivered in eight different ratios (Figure A) produced by independently varying the flow rates of odor streams fA
in a carrier stream of fixed rate (see Materials and methods
section). In the first experiment, two alternative responses (left vs. right nose poke) were differentially rewarded according on which of the two mixture components had the higher concentration. These training procedures left open a variety of strategies for subjects to solve the problem. In particular, correct responses to the training stimuli could be obtained by ignoring one component and responding according to whether the other component had a high or low concentration. Alternatively, responses could be based on both components.
To test what kind of chemical information subjects based their decisions, subjects were tested by interleaving probe stimuli at 1/2 the training concentration (i.e., 50% of the flow rate; Figure A, red circles). Probe trials were randomly rewarded so that subjects received no feedback as to a “correct” strategy and comprised <20% of trials to discourage rats from learning the lower reward rate associated with these stimuli. We analyzed the data by plotting choice functions using different independent variables corresponding to different types of extracted information. When the ratio fA/fB was used as the independent variable, responses to the probe stimuli fell on the same line as the training stimuli (Figure B). That is, the fraction of left vs. right choices to a given probe could be accurately predicted by the performance with a training stimulus of the same component ratios. In contrast, when a single component was the independent variable, responses to the probe stimuli no longer match the line fitted to the training data (fA, Figure C; fB not shown). This result supports the idea that when encountering mixture stimuli rats naturally tend to base their decisions on information extracted about the ratio of mixture components.
Across the population, a similar pattern was obtained, with left/right choices on probe trials being closely predicted by choices on training stimuli of the same mixture ratio. We quantified these results by testing how well a sigmoid function fit to the training stimuli predicted choices on the probe stimuli (see Materials and methods
section). For 4 out of 4 rats tested using 1-hexanol vs. caproic acid and 3 out of 4 rats tested with R(+)-2-octanol vs. S(−)-2-octanol, choices on probe stimuli (twofold diluted) were significantly better fit when the mixture ratio as opposed to either single component was used as the independent variable (criterion p
0.05 for each subject, bootstrap test). To examine whether these results would generalize to a wider concentration range, we tested an additional set of rats with more diluted probe stimuli (tenfold dilution in mineral oil, 1-hexanol vs. caproic acid) (Figure D). In this condition, rats continued to generalize according to mixture ratio (Figure E and F). Although choice functions were less exactly matched by the predictions based on the training set, possibly because the difference in intensity between probe and test stimuli was more salient, 3 out of 3 subjects tested showed a better fit with a ratio-based function than a function of either component (p
0.05 for each subject, bootstrap test).
Concentration-invariant odor classification based on extraction of ratio information could explain how rats could generalize from training stimuli to probe stimuli at concentrations they have not experienced. However, while training odors were delivered at a fixed concentration in the odor stream, it is possible that subjects were inadvertently exposed to diluted concentrations of the training stimuli outside the direct odor stream. Therefore, we ran additional subjects using probe stimuli with higher rather than lower concentration than the training stimuli (Figure A). Since subjects would have no way to experience concentrations higher than the source, generalization in this case could not arise from inadvertent training with diluted odors. In this experiment, choices on higher-concentration probe stimuli (1.5-fold) were also closely predicted using the ratios of components as the independent variable (Figure B) and not well using either single component (Figure C). This difference was significant in 3 out of 3 rats tested (criterion p
0.05, bootstrap test). This result suggests that generalization across concentrations may be based on an intrinsic computation rather than requiring experience with different concentrations.
The preceding experiments show that the ratio of mixture components is a good predictor of choice behavior. But could a similar choice pattern also be obtained by a different computation such as the difference of mixture components? Choices based on the ratio of mixture components correspond to a discrimination boundary of fA
, indicated by the yellow line in Figures A, D, 2A and 3A. When mixture components have equal intensity and the training category boundary is half way between the two components, the ratio discrimination boundary, fA
1, is equivalent to one based on the difference of mixture components, fA
0 (yellow line in Figure A) and could therefore yield a similar pattern of behavior. However, this is a very special case. In general, if the mixture components have unequal intensity or the training category boundary is shifted toward one component, the boundaries diverge and the two discrimination strategies will yield very different choice patterns. Therefore, to better distinguish behavior based on ratios vs. differences of chemical components, in the next experiment, rats were trained with a shifted category boundary, i.e., fA
3 (Figure A), where the ratio boundary (yellow line) and difference boundary (blue line) were well separated. When tested in these conditions, subjects' behavior was significantly better predicted by a ratio computation, fA
, than the difference fA
(Figure B and C) (2
out of 2 rats at twofold dilution; 1 out of 2
rats at tenfold dilution; criterion of p
0.05, bootstrap test).