Sequential mechanisms underlying concentration invariance in biological olfaction

Abstract

Concentration invariance-the capacity to recognize a given odorant (analyte) across a range of concentrations-is an unusually difficult problem in the olfactory modality. Nevertheless, humans and other animals are able to recognize known odors across substantial concentration ranges, and this concentration invariance is a highly desirable property for artificial systems as well. Several properties of olfactory systems have been proposed to contribute to concentration invariance, but none of these alone can plausibly achieve full concentration invariance. We here propose that the mammalian olfactory system uses at least six computational mechanisms in series to reduce the concentration-dependent variance in odor representations to a level at which different concentrations of odors evoke reasonably similar representations, while preserving variance arising from differences in odor quality. We suggest that the residual variance then is treated like any other source of stimulus variance, and categorized appropriately into "odors" via perceptual learning. We further show that naïve mice respond to different concentrations of an odorant just as if they were differences in quality, suggesting that, prior to odor categorization, the learning-independent compensatory mechanisms are limited in their capacity to achieve concentration invariance.

Keywords: categorization; computational neuroscience; concentration invariance; generalization; learning; mice; odor representations; olfactory bulb.

Figure 1

Depiction of the problem of concentration invariance. (A) Simple models of concentration invariance are predicated upon the principle that increases in concentration generate predictably monotonic increases in the activation levels of all sensitive receptors. The broad aggregate dose-response curves of glomeruli, hypothesized to combine inputs from similarly tuned OSNs that exhibit different half-activation concentrations owing to differences in receptor reserve, can in principle extend this quasi-linear range and thereby improve the similarity of relational representations of odorants across concentrations. Top panel. In a computational model of ligand-receptor interactions, three ORs are activated by three odotopes of an odorant presented at a range of concentrations (five of which are labeled: [1]–[5]). Dose-response curves that do not rise to a maximum value of 1 connote odotopes that are partial agonists for their cognate ORs. Ligand-receptor interaction i exhibits a glomerular Hill equivalent [exponent of the population dose-response function; (Cleland and Linster, 1999)] of 0.2, yielding a quasi-linear dose-response range extending across roughly five orders of magnitude in concentration. Interactions ii and iii exhibit somewhat higher—i.e., less extreme—Hill equivalents in this example and hence have steeper, narrower dose-response curves. As a result of these broadened curves, the relational representation of the odorant across concentrations is recognizable to some degree across modest concentration ranges. Middle panel. Primary odor representations at five concentrations, directly read as activation levels at each of the three OR interactions depicted (identified on graph of concentration [5]). Lower panel. Data from the middle panel, divisively normalized so that the activity resulting from each odor presentation sums to a constant. Odor representations at concentrations [4] and [5], and to some extent [3], are reasonably similar. This similarity across concentrations will improve if the quasi-linear ranges of OR interactions ii and iii are extended to resemble that of interaction i. (B) Top panel. Allosteric and other non-competitive interactions, even low-affinity interactions, can render dose-response profiles at individual ORs non-monotonic, generating variance that cannot be resolved by broadening glomerular intensity tuning ranges. Adding low-affinity non-competitive interactions to the model generated clearly non-monotonic dose-response profiles for odotopes i and iii. Middle panel. Primary odor representations at five concentrations, directly read as activation levels at each of the three OR interactions depicted (identified on graph of concentration [2]). Lower panel. Data from the middle panel, divisively normalized so that the activity resulting from each odor presentation sums to a constant. Odor representations are unrecognizable across even similar concentrations, even after normalization.

Figure 2

Circuit diagram of the mammalian olfactory bulb (two glomeruli shown, with corresponding postglomerular circuitry). The axons of olfactory sensory neurons (OSNs) expressing the same odorant receptor type (denoted by the shape and color of the receptor) converge together to form glomeruli (shaded ovals) on the surface of the olfactory bulb. Multiple classes of olfactory bulb neuron also innervate each glomerulus. Glomerular interneuron classes are heterogeneous, and include olfactory nerve-driven periglomerular cells (PGo), external tufted cell-driven periglomerular cells (PGe), and multiple subtypes of external tufted cells (ET). Superficial short-axon cells (sSA) are not associated with specific glomeruli but project broadly and laterally within the deep glomerular layer, interacting with glomerular interneurons. Principal neurons include mitral cells (Mi), which interact via reciprocal connections in the external plexiform layer (EPL) with the dendrites of inhibitory granule cells (Gr), thereby receiving recurrent and lateral inhibition. Middle/deep tufted cells, another class of olfactory bulb principal neurons, are not depicted. OE, olfactory epithelium (in the nasal cavity); GL, glomerular layer; EPL, external plexiform layer; MCL, mitral cell layer; IPL, internal plexiform layer; GCL, granule cell layer. Filled triangles denote excitatory (glutamatergic) synapses; open circles denote inhibitory (GABAergic) synapses. Speckles surrounding OSN terminals connote volume-released GABA and dopamine approaching presynaptic GABA_B and dopamine D2 receptors. Figure adapted from (Cleland, 2010).

Figure 3

Olfactory generalization gradients in mice. (A) Associative generalization from a conditioned odorant stimulus (CS) to a series of four sequentially similar odorants (S1-S4) plus one structurally and perceptually dissimilar control odorant (D). Presenting all odorants at a higher concentration (theoretical vapor-phase partial pressure of 1.0 Pa; black line) yielded a steeper, narrower generalization gradient than did identical training with low-concentration odorants (0.01 Pa; gray line), reflecting the learning-theoretic principle that higher CS salience supports greater learning. Twelve training trials were administered prior to testing. Figure adapted from Cleland et al., (2009). (B) Increasing the number of training trials (CS-reward pairings) prior to testing progressively increased perseverance and sharpened associative generalization gradients. 3×: three training trials; 6×: six training trials; 12×: 12 training trials. Figure adapted from Cleland et al., (2009). (C) Generalization gradients adapt to the variance of the conditioning odor. The high-variance conditioning group (see Methods) generalized fully across the range of CS variability (no difference in digging times between 50:50 and either C4 or C5; Welch test, t(46.36) = 0.444, p = 0.659; t(47.43) = 0.854, p = 0.398, respectively), whereas the low-variance group clearly distinguished both C4 and C5 from the 50:50 odor mixture CS (significant differences in digging times; Welch test, t(56.87) = 2.583, p = 0.012; t(43.45) = 3.314, p = 0.002, respectively). (D) Mice perceive sufficiently different concentrations of novel odorants as distinct odors. One group of mice was conditioned to an odorant CS at a high concentration (1.0 Pa; black line, test concentrations in Pa listed in Roman font on x-axis) and tested on two lower concentrations of that odorant as well as a dissimilar control odorant (D) at 1.0 Pa. A second group was conditioned to the same odorant CS at a low concentration (0.01 Pa; gray line, test concentrations in Pa listed in italic font on x-axis) and tested on two higher concentrations of that odorant as well as a dissimilar control odorant (D) at 0.01 Pa. Both groups treated the test odorant that was two orders of magnitude higher or lower in concentration as a distinct odor, roughly comparable in similarity to a structurally dissimilar odorant D. See the Learning-Dependent Construction of Odor Representations section for analysis details. Odor sets and vol/vol dilutions are detailed in Table 1. In all figures, error bars denote the standard error of the mean.