Natural environments feature mixtures of odorants of diverse quantities, qualities and complexities. Olfactory receptor neurons (ORNs) are the first layer in the sensory pathway and transmit the olfactory signal to higher regions of the brain. Yet, the response of ORNs to mixtures is strongly non-additive, and exhibits antagonistic interactions among odorants. Here, we model the processing of mixtures by mammalian ORNs, focusing on the role of inhibitory mechanisms. We show how antagonism leads to an effective ‘normalization’ of the ensemble ORN response, that is, the distribution of responses of the ORN population induced by any mixture is largely independent of the number of components in the mixture. This property arises from a novel mechanism involving the distinct statistical properties of receptor binding and activation, without any recurrent neuronal circuitry. Normalization allows our encoding model to outperform non-interacting models in odor discrimination tasks, leads to experimentally testable predictions and explains several psychophysical experiments in humans.https://doi.org/10.7554/eLife.34958.001
When ordering in a coffee shop, you probably recognize and enjoy the aroma of freshly roasted coffee beans. But as well as coffee, you can also smell the croissants behind the counter and maybe even the perfume or cologne of the person next to you. Each of these scents consists of a collection of chemicals, or odorants. To distinguish between the aroma of coffee and that of croissants, your brain must group the odorants appropriately and then keep the groups separate from each other.
This is not a trivial task. Odorants bind to proteins called odorant receptors found on the surface of cells in the nose called olfactory receptor neurons. But each odorant does not have its own dedicated receptor. Instead, a single odorant will bind to multiple types of odorant receptors, and thus, each olfactory receptor neuron may respond to multiple odorants. So how does the brain encode mixtures of odorants in a way that allows us to distinguish one aroma from another?
Reddy, Zak et al. have developed a computational model to explain how this process works. The model assumes that an odorant triggers a response in an olfactory receptor neuron via two steps. First, the odorant binds to an odorant receptor. Second, the bound odorant activates the receptor. But the odorant that binds most strongly to a receptor will not necessarily be the odorant that is best at activating that receptor.
This allows a phenomenon called competitive antagonism to occur. This is when one odorant in a mixture binds more strongly to a receptor than the other odorants, but only weakly activates that receptor. In so doing, the strongly bound odorant prevents the other odorants from binding to and activating the receptor. This helps tame the dominating influence of background odors, which might otherwise saturate the responses of individual olfactory receptor neurons.
Reddy, Zak et al. show that processes such as competitive antagonism enable olfactory receptor neurons to encode all of the odors within a mixture. The model can explain various phenomena observed in experiments and it adds to our understanding of how the brain generates our sense of smell. The model may also be relevant to other biological systems that must filter weak signals from a dominant background. These include the immune system, which must distinguish a small set of foreign proteins from the much larger number of proteins that make up our bodies.https://doi.org/10.7554/eLife.34958.002
The olfactory system, like other sensory modalities, is entrusted to perform certain basic computational tasks. Of primary importance is the specific identification of odors and the recognition of isolated sources or objects in an olfactory scene. A typical scene in a natural environment is complex: the olfactory landscape is determined by the chemical composition of odorants released by the objects, the stoichiometry of the mixture and the physical location of the objects relative to the observer. An efficient olfactory system is expected to eliminate irrelevant background components and de-mix contextually relevant components received as a blend (Ache et al., 2016; Cardé and Willis, 2008; Gottfried, 2010; Hopfield, 1999; Howard and Gottfried, 2014; Jinks and Laing, 1999; Knudsen et al., 1993; Pentzek et al., 2007; Raguso, 2008; Riffell, 2012; Riffell et al., 2008; Riffell et al., 2014; Rokni et al., 2014; Stevenson and Wilson, 2007; Szyszka and Stierle, 2014; Thomas-Danguin et al., 2014).
The importance of filtering a complex background is shared by the olfactory and the adaptive immune systems. In the latter, lymphocytes must quickly and accurately identify a small fraction of foreign ligands in a sea of native ligands (Abbas et al., 2014). Inhibitory feedback plays a key role in meeting the challenge of a proper combination of rapidity, sensitivity and specificity (François et al., 2013). Inhibitory interactions in the form of receptor antagonism have indeed been observed in experiments with olfactory receptor neurons (ORNs) (Oka et al., 2004; Takeuchi et al., 2009; Kurahashi et al., 1994), although it has not been quantified systematically. For instance, the response of cells expressing the mOR-EG receptor is strongly suppressed when methyl isoeugenol is delivered together with the receptor’s cognate ligand, eugenol, at equal concentrations (Oka et al., 2004). Further evidence of intensity suppression and overshadowing (i.e. when one odorant makes another indiscernible) in the perception of odorant mixtures comes from psychophysical observations (Lawless, 1997; Keller and Vosshall, 2004; Doty and Laing, 2015; Thomas-Danguin et al., 2014). The importance of peripheral interactions in shaping mixture perception has been directly shown by electrophysiological and psychophysical measurements (Bell et al., 1987; Laing and Willcox, 1987; Chaput et al., 2012). However, the functional role, if any, of inhibition at the ORN level remains unknown.
Each ORN expresses receptors of a particular type, which typically display broad sensitivities to different odorants, whereas each odorant binds promiscuously to receptors of many types. The axons of ORNs of a common type converge onto glomeruli, where the axon terminals form synaptic contacts with mitral and tufted (M/T) projection neurons leading to the cortex, as well as local periglomerular (PG) interneurons. The activation of an individual glomerulus therefore represents the activation of a single ORN type. Discriminatory computations are carried out by brain regions such as the olfactory cortex, which receive combinatorial information from the entire ORN ensemble. To achieve a quantitative description of ORN inhibitory effects, it is then imperative to take their global nature into account. In other words, it is necessary to address the knowledge gap between the mixture response properties of a single ORN, the ensemble glomerular response, and ultimately its influence on odor discrimination and perception, which constitutes the goal of the present work.
Previous computational models that examined discrimination tasks have, for simplicity, assumed a linear summation model of mixture response at the ORN level (Hopfield, 1999; Koulakov et al., 2007; Zhang and Sharpee, 2016; Zwicker et al., 2016; Mathis et al., 2016; Grabska-Barwińska et al., 2017). Conversely, our emphasis is on explicitly characterizing the ORNs’ biophysical attributes, with a focus on mixture response properties. A key aspect of the model is that odorant-receptor interactions depend on two distinct features: the sensitivity to binding and the efficiency of activation after binding, respectively. Competitive antagonism occurs when a component in a mixture that binds strongly, activates the downstream transduction pathway less effectively compared to other components. While this might naively seem disadvantageous, we show how an antagonistic encoding model has inherent normalization properties, leading to superior performance in odor discrimination and identification tasks. Finally, we make an explicit connection between a variety of psychophysical observations related to the perception of odorant mixtures and inhibitory effects at the single ORN level, providing a potential neurobiological basis to perceptual phenomena.
Odorants in the nasal cavity are captured by G-protein-coupled-receptors located on the cilia of ORNs. The conversion of chemical binding events into transduction currents in the cilia leads to spike signals transmitted to the brain (see Refs. [Pifferi et al., 2010; Kleene, 2008] for reviews). The signal transduction pathway is complex; here, we build a chemical rate model of the mammalian ORN meant to capture its major response properties. The model complements and extends previous work on mixture interactions (Rospars et al., 2008; Cruz and Lowe, 2013). In Figure 1A, we illustrate the transduction pathway as modeled, and present a summarized version below (see Materials and methods for details).
The binding of an odorant to a receptor induces the activation of the odor-receptor complex via a two-step process. For an odorant , its interactions at the receptor level are then represented by a two-step process:
where and are the ratios of backward to forward rates for the binding and the activation steps. R, RX and RX represent unbound, bound inactive and bound activated receptors, respectively. Activated complexes convert ATP into cAMP molecules via adenylyl cyclase III. The rate of production of cAMP is assumed independent of the available ATP (which is in excess), and is therefore proportional only to the number of activated receptors. The cAMP molecules diffuse locally and cooperatively open nearby cyclic-nucleotide-gated (CNG) channels permeable to Ca and Na ions. Since CNG channels are distributed uniformly along the cilia (Flannery et al., 2006; Takeuchi and Kurahashi, 2005), we ignore the time required for cAMP to diffuse from its production site to the CNG channel. CNG channels have four binding sites for cAMP that exhibit allosteric cooperativity, which leads to nonlinear response functions of the Hill form (Segel, 1993) and constitutes the first stage of signal amplification in the ORN. The generated Ca current is then proportional to the number of fully bound CNG channels and is exchanged out of the cell at a constant rate through Na/Ca exchangers. Ca ions open Cl channels further downstream, which produces an outward amplifying Cl current (Boccaccio and Menini, 2007). Spike firing, in proportion to the current, follows. Lastly, ORN adaptation occurs due to the subsequent blocking of the CNG channels by a Ca-calmodulin complex.
Despite the complexity of the transduction model, the specific identity of odorants plays a role only at the level of receptors (except for masking agents, described below). Odorants are characterized by two parameters (mathematically defined by (Equation 15) in the Materials and methods): the sensitivity, , which controls the affinity of to the receptor, and the activation efficacy, , which combines with parameters of downstream reaction steps to measure the current produced by once bound. Numerically integrating the set of coupled rate equations presented in the Methods yields the temporal firing rate response of the ORN to pulses of odorant molecules and their mixtures at various concentrations (Figure 1B–D). For single odorants, the model successfully captures the strongly non-linear peak response for different concentrations of the odorant, the latency in response (Rospars et al., 2003), the quadratic rate of cAMP production (Takeuchi and Kurahashi, 2017), and calcium-based adaptation (Kurahashi and Menini, 1997) (Figure 1E–G). Since our focus in subsequent analysis will be on the peak response, its form is reproduced here (see Materials and methods for details) for a monomolecular odorant delivered at a concentration for a fixed, short duration:
Here, is the Hill coefficient and is the maximum physiologically possible firing rate, which depends on parameters related to the transduction pathway downstream of receptor activation and can be rescaled to unity. The maximal response at saturating concentrations, is truncated below by , which controls the equilibrium level of activated receptors.
On stimulation with more than one chemical species, the different species bind and activate the ORN in distinct ways. Its peak response to a pair of odorant molecules and is a special case of the general formula (Equation 14) derived in the Materials and methods, and reads:
Strong amplification by the ion channels render the mixture response hyper-additive at concentrations close to the sensitivity threshold; at higher concentrations, as the receptors become saturated and the odorants compete for limited binding sites, the response turns hypo-additive. The reduction in response due to competitive antagonism is determined by the binding affinity of the weaker odorant (with lower activation efficacy) relative to the stronger one.
Before further theoretical analysis, it is worth clarifying a few points. One may question the relevance of introducing a separate parameter, since the saturating ORN response could instead be due to limiting factors downstream of receptor activation. Our assumption is motivated by observations made from spike recordings of single rat ORNs to odorant mixtures, where the responses of the same ORN to saturating concentrations of different odorants yield very different firing rates (Rospars et al., 2008). Since odorant-ORN specific interactions occur only at the receptor, the differences at saturation must be due to differences in receptor activation efficacy. Further evidence comes from examining the minimum latency of spiking response to different odorants at saturating concentrations (Figure 1E), which can range from a few hundred milliseconds to a few seconds depending on the odorant-ORN pair (Rospars et al., 2003). The lifetime of odorants bound to a receptor is short (of a few milliseconds) and the probability of activation of a particular G-protein in a 50 ms interval at saturating concentrations is low (Bhandawat et al., 2005). These observations strongly suggest that the latency arises due to a relatively slow build-up of cAMP over many low-probability activation events. The differences in latency at saturating concentrations, when all receptors are bound, is therefore most likely due to differing activation probabilities, in line with our assumptions on . Note that even though both the sensitivity and the activation efficacy depend on (Equation 15), the low probability of activation, which is reflected in the limit , implies and depend separately on and .
While a purely competitive model of mixture interactions captured many cases from previous experiments on ORN mixture responses, a significant fraction showed discrepancies (Rospars et al., 2008). Non-competitive interactions are particularly manifest in synergy or suppression, which correspond to the mixture response curve lying above or below the individual response curves for each odorant, respectively, neither of which is possible with pure competition. Below, we show how non-competitive antagonistic effects, namely masking, can generate those effects. Non-competitive inhibition due to PI3K-dependent antagonism (Ukhanov et al., 2010) is beyond the scope of this paper.
Masking is the phenomenon of non-specific suppression of CNG channel currents (Kurahashi et al., 1994; Takeuchi and Kurahashi, 2017). Experimental evidence suggests that masking agents disrupt the lipid bilayer on the cell membrane, and thereby alter the binding affinity of cAMP to the CNG channels (Takeuchi et al., 2009). Masking agents can also be odorants (like amyl acetate), that is, they also bind to receptors and excite the transduction pathway. We suppose that the agents bind to sites on the lipid bilayer, and that multiple masking agents compete for the available sites. Similar to (Equation 1), the effects of a masking agent are determined by its affinity for the masking binding sites, and a masking coefficient (lying between 0 and 1), which measures its inhibitory effects once bound (see Materials and methods). The latter quantifies the lowered affinity of cAMP for the CNG channels when a masking agent is bound in the vicinity of the channel. Since the activation efficacy that appears in (Equation 2) quantifies the effective rate of signal transduction, the effect of a lowered affinity appears as a lowered value for . Specifically, we show that , where is the fraction of masking sites occupied by the masking agent. It follows that the firing rate at saturating concentrations, which depends on , is reduced (see [Equation 19] in Materials and methods).
The model above (and detailed in the Materials and methods) reproduces qualitative features of odorant suppression observed in experiments (Kurahashi et al., 1994; Takeuchi et al., 2013) (Figure 2A,B). We stress that the presented fits serve as qualitative consistency checks; more experimental data on masking agents is required to verify the specifics of the model. Importantly, we show that both suppression and, counterintuitively, synergy are possible mixture interactions that could arise due to masking (Figure 2C,D), both of which have been observed in experiments with single ORNs (Rospars et al., 2008). To define suppression and synergy, we remark that the response curve of the mixture, taking into account competitive binding alone, always lies between the response curves of the individual components. This property is a simple consequence of the fact that the number of activated receptors for a mixture (at a particular total concentration) can never be larger/smaller than the most/least effective odorant delivered alone at the same total concentration. Suppression can then be defined as the situation when the mixture response curve is lower than the lowest response curves among the components while synergy occurs when the mixture response is higher than the highest response curve. In our model, synergy is qualitatively due to the taming of suppressive effects: for instance, let us consider a component that binds masking sites more weakly than , yet it is a stronger suppressor. If binds and activates the ORN more strongly than , the net effect of mixing and is to reduce the suppressive masking effect of and unmask its strong activation properties, which can exceed the individual response curves as in Figure 2C.
Equipped with the biophysical model above, we now proceed to investigate the functional consequences of antagonism. To this end, we first define a model of olfactory encoding that focuses on competitive antagonism and introduce simplifying assumptions to highlight the main ideas.
An odorant is defined by two -dimensional vectors of sensitivities and activation efficacies across distinct ORN receptor types. We take , which is large enough to generalize our results across species. Parameters for different odorants are drawn independently from log-normal probability distributions (see Materials and methods), although our main conclusions below do not depend on their specific form. The width of the distribution reflects the broad sensitivities of odorants, spanning about six orders of magnitude (Saito et al., 2009).
An odorant caught in a sniff elicits a response in the glomerular ensemble whose individual activations vary in magnitude and progress differently in time. We focus on the vector , which represents the peak responses (Equation 2) to the odorant for the different ORN types. The statistics of the glomerular response is encoded in the distribution of , which is directly related to the distribution of for saturating concentrations of the odorant.
A straightforward generalization of the expression for the binary mixture response from (Equation 3) allows us to write the mixture response for components in terms of effective mixture parameters and (which replace and in [Equation 2]):
where is the fraction of component in the mixture. We first consider for simplicity an equiproportionate mixture, and then show below that this is not a limitation. The key observation made here is that, since sensitivities are broadly distributed, we typically have one term dominating the sum in the expression for (see Figure 3B). If we suppose that this dominant term is , we may write:
for typical values of for . The expression for above follows from (Equation 4) when we approximate the sum in the expression for as ; multiplying this sum with the expression for in (Equation 5) then yields the approximation. Relation (Equation 5) still holds for complex mixtures as the broad width of the sensitivity distribution ensures the dominance of one of the ’s even for relatively large numbers of components. In Figure 3C, we show that the approximations in Equation 5 result in a relative error in and of about for equiproportionate mixtures with over a hundred components. In other words, it is highly likely that only one component in the mixture occupies the receptors of ORNs of a particular type, and thus the response from these ORNs is determined by the activation efficacy of that specific component.
In order to measure the strength of competitive antagonism, we introduce the antagonistic factor . To define , we note that an odorant competitively antagonizes odorant (at equal concentrations) when its sensitivity exceeds that of (), yet its activation efficacy is lower than (). A quantification of this relationship is the Pearson correlation coefficient between binding and activation strengths across the ORN ensemble:
where the logarithms conveniently account for the broad range of the two variables.
Let us first consider the extreme case of , when there is no antagonism as the odorant that binds best also has the strongest activation. This corresponds to an ORN behaving as a logical OR gate, a feature shared by any additive model of mixture response. From Equation 5, the consequence is that always takes the maximum value of in the mixture, which significantly biases toward higher values. To see this, we define the sparsity , that is, the fraction of glomerular responses above a certain threshold for an odorant at saturating concentrations; then, the fraction above for a mixture with components is given by . Thus, for any additive model of mixture response, the sparsity quickly saturates to one as increases and all information about individual components is lost.
On the contrary, when and are independent, that is, , is independent of the constraint () implicit in Equation 5 and the distribution of precisely matches the distribution of the single component . The condition of decorrelation between and is important for the argument since, even though Equation 5 holds generally, the constraint that is the most sensitive odorant biases the statistics of for . Since the entire distribution of activations across the ORN ensemble is invariant to the number of components in the mixture, we conclude that the statistics of activation is conserved as the complexity of the mixture increases, that is, the population response is ‘normalized’ (Figure 4A–C, Figure 4—figure supplement 1). Remarkably, such a normalization of the mixture response is a direct consequence of antagonism in receptor encoding, independent of any neural circuitry. The upshot is that a sparse representation for a single odorant typically remains sparse for a complex mixture, allowing for improved performance in the detection of individual components (as quantified in the next Section).
Notably, the above arguments rely solely on the broad distribution of the sensitivities, which enables the approximation in Equation 5. Despite the error in this approximation, our arguments for normalization presented above still hold for a mixture with over a hundred components, as shown in Figure 4A. An important consequence is that the approximation becomes even better when the concentrations of the components are allowed to be different, as any variation in the ’s makes the distribution of each term even broader. This is confirmed by the plots in Figure 3C. The result holds generally true for any distribution of and any broad distribution of ; their log-normal forms are used here only to simplify subsequent calculations (Figure 4C).
Structural constraints at the receptor level, however, are likely to hamper a perfect decorrelation . Nevertheless, normalization does not require an exact equality and its effects fade gradually as increases (see Figure 4A). The extent of the advantageous effects of normalization (and the value) depends on the sparsity of activation for single odorants, the number of components in the mixture and their properties. Indeed, the effect of normalization on the detection of an odorant in the presence of a large number of other odorants depends on the balance between two opposing factors. On the one hand, normalization induces an advantageous effect of maintaining sparsity and preventing saturation of the bulb, leading to easier segmentation. On the other hand, the number of active glomeruli corresponding to each odorant is greatly reduced, which makes detection harder.
To explore how our model performs in discrimination tasks, we next compute the performance of the antagonistic encoding model described above in detecting a known odorant from a large background of unknown odorants, that is, figure-ground segregation (Rokni et al., 2014). The capacity of an optimal Bayesian decoder in the task depends on the mutual information (in bits) that the glomerular pattern preserves about the presence () or absence () of the target. To simplify the calculation of , we convert the vector of continuous values into a binary vector by applying a threshold that partitions the glomeruli into two subsets, active and inactive glomeruli (see Figure 3A). In general, any continuous read-out is demarcated into a few discrete, distinguishable states depending on the level of intrinsic noise in the system. Taking more graded states into account will not change the qualitative result of our calculation. Specifically, as we show below, the relative performance between an antagonistic and a non-antagonistic model is still dominated by the loss of information due to glomerular saturation, which occurs independently of the number of gradations in our read-out.
Figure 5A demonstrates that an encoding model with significant antagonism () contains more information than a non-antagonistic model () as the background increases in complexity. The results are robust to the presence of significant internal variability in the transduction pathway of an ORN (Figure 5—figure supplement 1). When the number of odorants in the mixture is small, the glomerular pattern for the non-antagonistic model is not saturated and preserves information about the glomeruli activated by each component. For a specified sparsity (as defined in the previous section as the fraction of glomerular responses above the threshold at high concentrations), the non-antagonistic case is thus advantageous when the mixture complexity is less than . However, for mixtures of higher complexity, it is useful to introduce correspondingly higher levels of antagonism in order to prevent saturation and still maintain an ability to segment out different components. To further emphasize this point, for different values of , we compute the level of antagonism that maximizes information transmission when the background varies both in composition and complexity (see Materials and methods). We find that for experimentally observed levels (0.1–0.3) of sparsity (Saito et al., 2009; Lin et al., 2006; Soucy et al., 2009; Vincis et al., 2012), it is always advantageous to incorporate non-zero levels of antagonism into odorant encoding (Figure 5B).
We measure the performance of a linear classifier in component separation, the task of identifying several known components from a mixture, for different levels of antagonism. Component separation is qualitatively different as the information about the other known odorants can be recurrently exploited to extract more information about an odorant’s presence or absence (Grabska-Barwińska et al., 2017). First, a linear classifier is trained to individually identify 500 known odorants in the presence of other odorants from the set. In the test phase, a mixture which contains 1 to 20 known components, uniformly chosen, is delivered. The hit rate measures the fraction of odorants that were correctly identified, while the false positives (FPs) is the number of odorants out of the 500 that were not actually present but were declared to be present. Generalized Receiver Operating Characteristics (ROC) curves are drawn by varying the detection threshold of the linear classifier for each odorant (Figure 5C–D). We find again that antagonism in receptors yields superior performance, independent of sparsity.
Psychophysical observations related to odor perception were the primary investigative tools before neurobiological studies became prominent in the last few decades. Formulating an explicit connection between the vast body of literature on olfactory psychophysics and recent discoveries in neurobiology remains a challenge, particularly since perception is influenced by interactions throughout the olfactory sensory pathway (Jinks and Laing, 1999; Su et al., 2009; Grossman et al., 2008; Wilson and Sullivan, 2011). Various direct and indirect measurements (Bell et al., 1987; Laing and Willcox, 1987; Chaput et al., 2012) strongly hint at the role of receptor-level interactions, although a mechanistic explanation for how these effects may arise has not been proposed. Here, we examine the possible relation between antagonism and observations from psychophysical experiments on the perception of odor mixtures. The upshot is that the combination of competitive antagonism and masking supports the diverse range of well-established psychophysical effects enumerated hereafter.
Specifically, the list of psychophysical effects relevant here is as follows (see (Lawless, 1997; Keller and Vosshall, 2004; Doty and Laing, 2015; Thomas-Danguin et al., 2014; Takeuchi et al., 2013)). (1) Inhibition and synergy: The former is the strong reduction of perceived intensities when two odorants are mixed, usually at high concentrations; synergy is occasionally observed, namely at low concentrations. (2) Masking: When the concentration of a masking agent, such as 2,4,6- trichloroanisole (called cork taint), is increased, the perceived intensity of the odorant decreases. (3) Symmetric and asymmetric suppression: When two odorants of equal perceived intensities are added, they typically suppress each other in a striking reciprocal fashion so that the perceived intensity of both odorants is still equal but sharply lowered. Asymmetric suppression (sometimes called counteracting), where the intensity of one of the odorant is lowered more than the other, is observed occasionally. (4) Overshadowing: The loss of perception of a less intense odorant when a more intense odorant is present in a mixture.
To examine the prevalence of inhibition and synergy, we estimate the inferred concentration (or perceived intensity) of a component in the mixture as the concentration at which those precise number of glomeruli corresponding to the odorant would have been activated (i.e. above a fixed threshold) had that odorant been delivered alone. In Figure 6A, we show that this simple algorithm leads to an unbiased estimate of the concentration over a broad range of concentrations. Figure 6A further demonstrates that inhibition and synergy naturally arise from competitive antagonism. Stronger inhibition arises at higher concentrations as the glomeruli that are otherwise activated by an odorant when delivered alone are antagonized by the second odorant, leading to lower perceived intensity. At lower concentrations, competitive antagonism plays a limited role; instead, cooperative effects in the ORN transduction pathway result in hyper-additivity, which pushes a few glomeruli above the activation threshold and gives rise to a small synergistic effect. Masking is also readily explained by our model, where the inferred concentration (based on the activated glomeruli) is below the actual concentration as the masking agent’s concentration increases (Figure 6B).
To quantify suppression, we use the fraction of suppressed glomeruli, defined as the fraction of glomeruli which are inactive in the mixture of and , yet are activated in isolation by odorant () and not activated in isolation by odorant (). Figure 6C shows that the reciprocal suppression of intense binary mixtures is conspicuously absent for a non-antagonistic model. To see this, let us suppose that each odorant individually activates half of all glomeruli (i.e. the sparsity = 0.5). Note, is more sensitive than to half (on average) of all the glomeruli that activates. Then, for , when they are delivered together at equal concentrations, binds better to half the otherwise active receptors of , activating half of them and suppressing the other half. Since has precisely the same effect on , each odorant reciprocally suppresses the other. On the other hand, when there is no antagonism, still binds better to half the active receptors of , but now activates all of them, resulting in no suppression. A strong asymmetric suppressive effect is observed when one of the odorants has a capacity for masking.
Finally, to quantify overshadowing, we train a logistic regressor to identify a set of known odorants as in Figure 5C–D. A weak odorant is delivered along with a stronger odorant at varying concentration ratios. The probability of presence of ascomputed by the regressor is compared against the the ratio of concentrations of and . When the probability of presence goes below the detection threshold (set at 0.5), is no longer detected and is ‘overshadowed’. Figure 6D demonstrates that overshadowing for binary mixtures is intensified by antagonism, in spite of its superior discriminatory performance for more complex mixtures.
Natural smells are due to mixtures of many chemicals, yet the need for tight stimulus control in experiments often leads to a focus on individual molecular entities. In this paper, we have characterized mixture interactions with a realistic biophysical model. Importantly, we explored how these interactions can naturally lead to ‘normalization’ of the glomerular responses, improve the coding capacity of the olfactory system, and account for many observed perceptual phenomena.
The odorant receptor dynamics in our model is based on a two-step activation process analogous to previous works in vertebrates (Rospars et al., 2008; Cruz and Lowe, 2013) and the fly (Nagel and Wilson, 2011). A key aspect of two-step activation is that it separates sensitivity of ligand binding from activation efficacy (del Castillo and Katz, 1954). At the structural level, this distinction is consistent with observations on the binding and activation of GPCRs (Strange, 2008). The common and parsimonious approximation of a single step (parametrized by a for affinity) in binding models, appears too drastic. In contrast to earlier work, we explicitly model the pathway downstream of receptor activation (Pifferi et al., 2010; Kleene, 2008), which features the successive steps of cAMP production, allosteric opening of CNG channels, and ultimately current fluxes. This provides a biophysical basis to the cooperativity effects that were previously introduced ad hoc. Moreover, this explicit formulation allows us to go beyond pure competitive antagonism, which was reported to explain about half the cases and thus requires generalizations (Rospars et al., 2008). In particular, non-competitive antagonistic effects, such as our masking model for the non-specific suppression of the cyclic nucleotide-gated channels permit us to account for synergy and inhibition effects that are impossible for competitive antagonism.
A major focus of our work is the functional role of antagonistic interactions. Antagonistic reduction of glomerular activation can be seen as a form of ‘normalization of activity’. Normalization with increasing stimulus intensity or complexity is common in neural systems (Carandini and Heeger, 2011) and has been thought of as a circuit property that involves inhibitory synaptic interactions (Wachowiak et al., 2002; Cleland et al., 2007). In the olfactory system, this was elegantly demonstrated in the Drosophila antennal lobe, where activation of increasing number of receptors (or glomeruli) proportionally increases inhibition provided to any one glomerular channel (Olsen et al., 2010). Similarly, in fish and mouse olfactory bulbs, increasing stimulus intensity is thought to recruit populations of interneurons (namely, short axon cells) that inhibit principal cells, leading to blunted activity for higher stimulus intensities. In an extreme example of this, a mouse with a particular receptor forcibly expressed widely has remarkably similar activation of the mitral cell population despite the massive increase in the input when the cognate odorant is presented (Roland et al., 2016).
The key insight from our model is that normalization is granted at the level of receptors by purely statistical reasons, without any additional circuit burden. In the limit of full statistical decorrelation between ligands’ binding affinity and activation efficacy, the distribution of activations across the ORN ensemble for a mixture coincides with that of a single monomolecular odorant, a property which has been confirmed in the fly (Stevens, 2016). Why would we need normalization if the optimal way to preserve information is to simply copy the input signal, i.e. have ORNs functioning as pure relays? Copying however requires an unrealistically broad dynamic range, especially for the processing of natural mixtures, where the concentration and the number of components can fluctuate wildly. Normalization at the first layer in the sensory pathway helps avoid early saturation effects that would confound the entire processing pathway. However, nonlinear distortions of the signal do lead to loss of information, and the balance between the two effects calls for their quantification. Our information theoretic calculations demonstrate that detection of a target odorant within a complex mixture is enhanced by antagonistic interactions, and that holds for a wide range of receptor tuning widths, that is, the average number of activated glomeruli per odorant.
Some of the predictions from our analysis can be tested experimentally. Direct measurements from mammalian ORNs have been obtained in vitro in many biophysical studies studying signal transduction (Lowe and Gold, 1995; Bhandawat et al., 2005). Although such preparations offer excellent access for measurement, there is significant uncertainty about mimicking the native conditions in terms of delivery of odors (airborne vs solution) as well as the ionic composition of the perfusion medium, which will affect response amplitudes. Electrical recordings from individual ORNs are difficult and have low yield, but have offered tantalizing hints on different nonlinear interactions (Rospars et al., 2008). More extensive data will likely have to rely on glomerular imaging methods (Bozza et al., 2004; Rokni et al., 2014; Mathis et al., 2016), which offer robust signals and extended recording times to obtain measurements at different concentrations and mixture ratios (Soucy et al., 2009). Here too, there are some concerns including potential effects of feedback mediated by olfactory bulb neurons on ORN axon terminals, particularly through GABAb receptors (McGann et al., 2005; McGann, 2013). Carefully controlled experiments that isolate feedforward sensory signals could reveal the prevalence of antagonistic interactions in mammalian ORNs.
Extensive measurements at a large range of concentrations and mixture ratios will allow robust fitting of our model to obtain accurate estimates of the two key parameters, and . A key empirical test of our theory will then rest on the relation between and for each glomerulus (or ORN). If these two parameters are highly correlated most of the time, then antagonistic interactions of the sort described in our theory will likely have only weak impact on olfaction. Even a modest decorrelation, on the other hand, will give rise to important effects on ensemble coding of odor mixtures even at the front end of the olfactory system.
In addition to functional advantages, we showed that antagonistic effects are consistent with psychophysical effects observed in mixture perception. Experiments show that the perceived intensity level of an odorant is empirically related to the true concentration of the odorant as a power function, reflecting their proportional relationship on a single logarithmic scale (Lawless, 1997; Wojcik and Sirotin, 2014). The intensity level for binary mixtures perception is commonly described via a vector sum of the intensities of each component (Berglund et al., 1973; Laing et al., 1984; Berglund and Olsson, 1993). The vector model captures the level independent, symmetric nature of mixture suppression. The biophysical model presented here is consistent with an even broader range of perceptual phenomena, including level independency, synergy, symmetric and asymmetric suppression, masking and overshadowing. The bottomline is that global antagonistic interactions at the ORN level may play a major role in non-trivial perceptual phenomena.
In conclusion, ORNs are far from simple relays, and their strong nonlinear interactions crucially affect olfactory processing. Non-competitive antagonistic mechanisms, such as masking effects discussed here, have not been widely studied in mice and they may only occur for selected odorants. While this experimentally necessitates an extensive experimental dataset, the non-competitive effects presented here make their future investigation particularly relevant. Finally, the generality of the potential relations highlighted here between ORN antagonism and psychophysical phenomena motivates their exploration in mice, where a broader arsenal of experimental techniques and manipulations can be leveraged.
When a mixture of monomolecular odorants at concentrations is presented to an ORN, the odorants compete for the finite number of receptors available on the olfactory cilia. In this Section, we derive the response of the ORN in such a case of competitive binding under the assumptions stated below.
The binding of an odorant to a receptor induces the activation of the odor-receptor complex, via a two-step GTP-mediated phosphorylation process (Pifferi et al., 2010). For a mixture of odorants, the binding dynamics reads:
where and symbolize the bound and activated complexes (), while , and denote the number of unbound receptors, receptors bound by odorant but inactive, and receptors activated by odorant , respectively. The concentration of the various odorants is supposed to be in excess for the total number of receptors . The parameters and are the ratio of the backward rates tothe forward rates for the two reaction steps involving odorant . We introduce only the ratio of the rates because the time scale of the slowest step, the activation of the odor-receptor complex, is estimated to be a few hundred milliseconds (Rospars et al., 2003). For delivery times of a few seconds or longer, we then assume equilibrium (see below). By using the steady-state relations , , and the above equation for , we obtain that the number ofactivated receptors bound to odorant at equilibrium is
with and . Since a sniff typically lasts only for about a hundred milliseconds, the activation profile of the receptors depends on the full kinetics of sniffing, receptor binding and receptor activation. However, the number of activated receptors after a sniff of 100 ms is still proportional to those at equilibrium. Since our main conclusions below, that is, the importance of the two-step activation step and different saturation levels for different odorants, still hold, we have assumed equilibrium for simplicity and clarity of the presentation.
A chain of steps follows receptors’ activation in the transduction pathway. First, activated receptors convert ATP into cAMP molecules via adenylyl cyclase III. Then, the cAMP molecules diffuse locally and open nearby cyclic-nucleotide-gated (CNG) ion channels. The open CNG channels are permeable to Ca (and Na) ions, which are crucial in regulating further downstream processes and for adaptation (Kurahashi and Menini, 1997). Finally, Ca ions bind to calmodulin (CaM) and the formed complex (Ca-CaM) inhibits the CNG channels, leading to adaptation and, possibly, the termination of the response. The primary depolarizing current is carried by an Cl efflux out of the cell through Ca regulated Cl channels. We now proceed to model these various steps.
First, since CNG channels are spread out along the cilia membrane and cAMP diffusion is restricted to the site of its production (Flannery et al., 2006; Takeuchi and Kurahashi, 2005), successful receptor activation events are largely independent. Indeed, the electrical response is consistent with Poisson statistics, and the voltage-clamped current response close to the threshold is linear (Bhandawat et al., 2010). At concentrations much larger than the threshold, the production of cAMP is linearly proportional to the number of activated receptors, as evidenced by the linear increase of the rate of production of cAMP with time. The degradation of cAMP occurs on a single time scale of a few hundred milliseconds (Takeuchi and Kurahashi, 2005). The effective cAMP dynamics is then succinctly written as:
where is the rate of production of cAMP (and implicitly includes the concentration of the converted ATP, which is supposed to be in excess and thereby treated as fixed), is the rate of degradation, and the index runs over the set of rate equations. Since the production of cAMP occurs immediately downstream of activation and is independent of the activating odorant, the rate of production is simply proportional to the total number of activated receptors. If is the intracellular cAMP concentration, we conclude that the steady state cAMP concentration is
Here, is an overall rate, is the number of allosteric binding sites for cAMP, and modulate the various steps of the reactions. For allosteric cooperativity, , which reflects the fact that the binding of one cAMP molecule promotes the binding of further cAMP molecules. Here, we have ignored the inhibitory effect of Ca-CaM, which will be introduced below. Allosteric cooperativity leads to response functions of the Hill form (Segel, 1993). In the limit of strong cooperativity, most of the CNG channels are expected to be either unbound or fully bound, and the steady state number of fully bound CNG channels reduces then to
Here, is the expression (Equation 9), and is the total number of CNG channels. The Ca current is directly proportional to the number of fully bound CNG channels and decreases at a constant rate (Boccaccio and Menini, 2007):
Third, the production of the CaCaM complex by Ca and CaM is described as:
where is the ratio of the forward and backward rates. The effect of calmodulin-mediated feedback inhibition is accounted by assuming CaCaM modulates the CNG opening rate as . The previous form is empirical, yet we verified that its precise shape and the value of the Hill coefficient do not modify numerical results below as long as a steep sigmoidal shape holds. With the values of the parameters used in our model (given below), CaCaM acts on the CNG channel before the cAMP and the activated receptors reach steady state and terminates the response. The resulting set of differential equations does not lend to analytical treatment but can be numerically integrated to give a time series of the ORN response, as shown in Figure 1B. Numerical curves indicate (data not shown) that the Ca peak response terminated by CaM is roughly proportional to the steady state Ca response without CaM, that is, , which is the approximation that we shall use hereafter.
Finally, the Cl current is the predominant component of the currents that depolarize ORNs (Li et al., 2016; Boccaccio and Menini, 2007) and is mediated by Ca-gated Cl ion channels. This current response induced due to Ca is again a Hill function of coefficient greater than one, suggesting further cooperativity (Reisert et al., 2005). We can formally write the steady state Cl current as , where is some unknown function. The firing rate response of the ORN is assumed to be proportional to the current, so that , where is a constant.
By combining all the equations above, we can write the firing rate as a function of the odorant concentrations :
where the odorant-receptor dependent parameters for the th odorant are written explicitly:
As mentioned in the main text, for each odorant , and carry the dependence on the odorants and control their interactions within mixtures. Conversely, the unknown function is related to downstream processes and therefore expected to not depend on the odorant and receptor type. This point, together with the reduction in the number of free parameters, was our rationale for using the approximation of a linear function . Then, the proportionality constant in is lumped together with and in (Equation 14) into a single parameter , which defines the maximum physiologically possible firing rate of the neuron. Both and are constants that do not depend on the odorant or the receptor type.
We can finally write a general expression for the ORN response to a mixture of odorants with concentrations . Denoting the total concentration by and the contribution of the th component by , it follows from (Equation 14) that the response reads
where the ‘effective’ mixture parameters and are
A complex odorant can therefore be treated in a manner similar to monomolecular odorants, namely, by specifying its effective sensitivity and activation efficacy to each receptor type. Note that this holds generally true, irrespective of the linear chosen in Equation 14 to limit the number of free parameters.
The parameters used in Figure 1 are as follows – we first define as the forward and backward rates for the binding step of Equation 1, and as the forward and backward rates for the activation step. For panels B,C and D, we use , , , for odorant A and , , , for odorant B. The concentration is unity in panels B, F and G. For panels E, F and G, the parameters for odorant A are used. In all panels, we use , , , , , , , , .
Here, we present a phenomenological description of non-competitive masking processes.
We suppose that masking agents bind sites on the lipid bilayer and compete for their limited number. The suppression timescale and off-timescale are smaller than a few hundred milliseconds (Kurahashi et al., 1994), justifying the assumption of steady state. In steady state, the occupancy fraction of the th masking agent with concentration and binding affinity is
The disruption of a CNG channel conformation due to agent is supposed to alter the affinity of cAMP to one of its binding sites on the channel in the reactions (9). The energy of the cAMP bound state is increased by and its probability is reduced by the corresponding Gibbs factor , where is the inverse temperature. The resulting reduction in the opening of the channels is most conveniently accounted for by a mean-field approach where the channel opening rate appearing in (10) is modified by the masking agents. In other words, with the suppression factor derived below. It follows from the definition (13) of that a modification of by carries over to as . Therefore, when saturating concentrations of excitatory odorants are presented together with masking agents that produce a masking coefficient , the maximal firing rate is reduced as
which reflects the masking effect.
The dependence of the suppression factor on the concentrations of the masking agents is estimated as follows. Let us denote the radius of disruption of the channels by a single masking molecule on the lipid bilayer by , and the surface density of masking binding sites by . The typical number of masking binding sites surrounding a given CNG channel is then . The number of masking binding sites within distance of a CNG channel is assumed to be Poisson distributed, that is . For a given number of sites , the vector of their occupancy numbers is distributed following a multinomial distribution with probabilities given by Equation 18, that is, . The index corresponds to unoccupancy, and . The probability of each is proportional to its Gibbs factor , where is the energy shift to the binding of masking agents.
We consider the first step in Equation 10; similar arguments hold for successive ones. The unmodified is the ratio between the probability for a channel to be cAMP bound or cAMP unbound, and is their energy difference. In the presence of masking, there are multiple cAMP bound and unbound states, which differ in their occupancy of the masking binding sites. The sum over all those states defines the probabilities and of cAMP bound and unbound, respectively. The suppression factor that modifies is obtained as the ratio , where the power stems from the definition of in (10). The sum is obtained by combining all the previous factors:
where is a normalization factor. Assuming the masking sites do not affect the energy of the channels when cAMP is unbound, the sum has a similar expression with . It is then verified that . As for , the simplest possible assumptions are that is additive, and the masking binding sites are dilute, that is, is small. Equation (20) reduces then to
where satisfy , and the same inequality holds for . In general, masking agents can affect multiple CNG channel subunits (Chen et al., 2006). If a masking agent affects the binding of cAMP to CNG subunits, the suppression effect is with .
The ratio in (Equation 19) is plotted in Figure 2B and compared to experimental data. In Figure 2C,D, the parameters for generating the response curves for odorants A and B are . For synergy (Figure 2C), the masking parameters are , while the corresponding parameters for inhibition (Figure 2D) are . The parameter is chosen to be unity in both cases.
Every odorant is defined by a vector of binding sensitivities and a vector of activation efficacies , each with dimensionality , where is the chosen number of receptor types. An odorant’s binding sensitivity to a particular receptor type is drawn independently from a log-normal distribution , where its standard deviation is set to to obtain a six orders of magnitude separation between the most sensitive and least sensitive receptor types (Saito et al., 2009). The activation efficacies are similarly drawn independently for each receptor type such that . The measure of antagonism, , is defined as the Pearson correlation coefficient between and :
where denotes the variance of the random variables and the angular brackets denote expectation values. To generate an odorant-receptor pair, first is drawn from the standard normal distribution. Then, is generated with correlation as , where is drawn from a standard normal distribution. At saturating concentrations of an odorant, the peak firing rate it elicits for a receptor type with activation efficacy is (see (Equation 16), where can be chosen to be unity). The rescaled glomerular activation vector (each component is rescaled between 0 and 1) is given by , where the transformation is performed on each component of the vector. The probability that each component exceed a threshold is given by the probability that a random variable drawn from a standard normal distribution exceed . This probability represents the sparsity of the glomerular activations at saturating concentrations after thresholding. The sparsity is set by selecting , where is the cumulative distribution function for a standard normal random variable.
To quantify the performance of the encoding model in figure-ground segregation, we compute the mutual information between the absence () or presence () of the target odorant and the glomerular activation pattern . Noise is introduced due to the presence of background odorants of unknown sensitivities and activation efficacies. The mutual information controls the performance of an optimal Bayesian decoder in detecting a target odorant in a background by using the glomerular activation pattern as input. The mutual information is defined as
where is the entropy of target presence or absence, which equals one bit (since the target is present in half the trials). The second term on the right hand side (in bits) is given by
where Bayes’ formula yields , and , where is the distribution of the number of background odorants. is estimated numerically by using Monte Carlo sampling. The quantities and are also computed numerically by observing that . Due to the independence of the receptor types and since the background odorants are independently drawn, the probability factorizes into multiplicative terms, each of which can be pre-computed prior to Monte Carlo sampling. To obtain the results in Figure 5A, we choose . When the number of background odorants fluctuate (as in Figure 5B), we draw from a truncated exponential distribution with a mean of 32 and truncated at a maximum of 128 background odorants.
To show that internal noise does not affect our results, we compare the performances of antagonistic and non-antagonistic models in figure-ground segregation by including an additional noise term in the expression for ORN response (Equation 16). Specifically, the response of an ORN to a mixture is modified as , where is an effective noise term that condenses the variability in signal transduction relative to the number of activated receptors. We train a linear classifier to identify a target odorant against a fixed number of background odors. The target odorant and background odorants (of varying composition) are delivered at concentrations drawn from a uniform distribution in the logscale over 3 orders of magnitude. The discrimination accuracy of the linear classifier is shown in Figure 5—figure supplement 1 for and and 0.4. The results show the superior performance of antagonism when the number of background odors is large even at noise levels of 40%. The higher performance for compared to for (at background odorants) occurs because the noise can desaturate glomeruli that are otherwise saturated.
For the component separation task, we use an ensemble of linear classifiers as our decoders. A linear classifier computes the probability of presence of an odorant from the glomerular activation pattern as , where and are the vector of learned weights and bias, respectively. First, linear classifiers are trained to identify odorants from a fixed set of 500 odorants. During the training phase, each classifier is trained to identify the presence of its target against a background of one to ten odorants also chosen from . In each trial of the test phase, 1 to 20 odorants are uniformly chosen from and the component separation performance is measured using the fraction of correct identifications (hit rate) and the number of false positives (FPs). An odorant is declared to be present if the probability of presence exceeds a detection threshold. The hit rate and the number of false positives are modulated by sliding the detection threshold of each linear classifier, yielding the generalized ROC curves in Figure 5C,D.
To infer the concentration based on the glomerular profile for a single odorant, we first note that glomeruli are progressively recruited as the concentration of the odorant increases depending on their sensitivity to that odorant. Suppose a glomerulus corresponding to this odorant is first recruited at concentration , where increases with the index . Then, the contribution of to the total inferred log concentration, , is taken to be for and for (here corresponds to the concentration at which the most sensitive receptor becomes active). This simple scheme to infer the concentration is accurate for a single odorant (Figure 6A) and can be easily shown to have a concentration invariant Weber ratio where is the number of receptor types, is the sparsity and is the saturating concentration (Koulakov et al., 2007). To obtain the results for mixtures when and 1, for each concentration of odorant , another odorant is delivered at an equal concentration. The log concentration of is then inferred by computing the sum of the contributions from the glomeruli corresponding to odorant as described above. The curve corresponding to the masking agent is obtained similarly as above for with having a masking coefficient .
To plot the curves in Figure 6B, odorant is delivered at a fixed concentration (red, dashed line) and a masking agent is applied at increasing concentrations (horizontal axis). Here, we use and we assume the masking agent does not bind to anyof the receptors.
To show symmetric and asymmetric suppression in Figure 6C, the concentration of is fixed at a saturating concentration and the concentration of is varied to get different concentration ratios (horizontal axis). We define a suppressed glomerulus as one that is active when an odorant is delivered individually yet is inactive when and are delivered together. The fraction of suppressed glomeruli for each concentration ratio is averaged over many samplings of the two odorants and .
To obtain the results for overshadowing, the different concentration ratios are generated similar to the method described above for Figure 6C. Logistic regressors that can detect odorants and are first trained to identify them when delivered alone at varying concentrations. A logistic regressor computes the probability of presence of an odorant given the glomerular pattern of activation. A detection threshold can then be applied on the probability of presence in order to declare the odorant present or absent. In Figure 6D, we show the probability of presence of odorant as determined by the logistic regressor corresponding to for different concentration ratios and values of (solid lines). Similar curves for odorant are shown as dashed lines.
Code for the modeling can be accessed at: https://github.com/greddy992/Odor-mixtures (Reddy, 2018); copy archived at https://github.com/elifesciences-publications/Odor-mixtures).
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Fred RiekeReviewing Editor; Howard Hughes Medical Institute, University of Washington, United States
In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.
[Editors’ note: a previous version of this study was rejected after peer review, but the authors submitted for reconsideration. The first decision letter after peer review is shown below.]
Thank you for submitting your work entitled "Antagonism in olfactory receptor neurons and its implications for the perception of odor mixtures" for consideration by eLife. Your article has been favorably evaluated by a Senior Editor and three reviewers, one of whom, Fred Rieke, is a member of our Board of Reviewing Editors. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Dmitry Rinberg (Reviewer #2); Tim Holy (Reviewer #3).
Our decision has been reached after consultation between the reviewers. Based on these discussions and the individual reviews below, we regret to inform you that your work will not be considered further for publication in eLife, at least in present form. We would be willing to consider a revised paper as a new submission if you think you can thoroughly address the issues raised in review.
The reviewers all recognized the importance and novelty of the proposed model, but were less enthusiastic about the experimental basis of the model. A particular area of concern was the lack of any evaluation of the goodness or uniqueness of the model fits. This results in concerns about the validity of the extracted parameters. These issues are detailed in the individual reviews below. Thus, the reviewers agreed that the paper either needed stronger experimental support, or perhaps alternatively the model could be developed more fully and could form the core of a purely theoretical paper.
This paper introduces a biophysical model for olfactory transduction, and then investigates the implications of this model for how mixtures of odors are encoded. I am not an expert in olfaction, so my comments are from the perspective of an interested outsider.
The paper makes a number of interesting points spanning a large range of olfactory phenomena. My primary concern is that the modeling approach does not seem sufficiently constrained by the data to draw strong conclusions. Examples of these and some smaller issues follow.
The experimental tests of the model are somewhat limited. The model is fit to measures of response vs. concentration for individual odors and odor pairs and to masking data. Given the number of free parameters in the model, it does not seem surprising that it is able to capture these data pretty well. But it is unclear whether the model architecture is unique or if the specific fit parameters are unique. This raises concerns about drawing specific mechanistic inferences from the model. For example, a major conclusion is that normalization comes about from the two-stage receptor activation rather than inhibition within the olfactory bulb. But a model incorporating inhibition and a single-stage receptor activation might explain the data well. It is also not clear whether the model will generalize outside of the data to which it is fit, and this limits the strength of the conclusions about perceptual phenomena. A couple specific points related to this:
- The evidence for different saturation levels for different odors in Figure 3 is not great. How badly do models that do not allow for different saturation levels fit the data? If possible, higher odor concentrations would be helpful here. Could the different saturation levels reflect different numbers of ORNs rather than different receptor activation levels? Could saturation reflect inhibitory input rather than receptor properties?
- Some aspects of the data are not particularly well fit – e.g. some of the masking data and Figure 3Bi bottom right. Some discussion of those discrepancies would be helpful.
In this manuscript, Reddy and colleagues investigate how antagonisms between different odors at ORNs shape odor perception using modeling and in-vivo Ca imaging. They proposed a novel computational model, which may explain multiple olfactory behavioral phenomena. The idea is novel and original. While the majority of previous works were focused on studying individual olfactory receptors and their interaction with one or a few ligands, the authors studied the statistics for multiple receptors and analyzed their role for such psychophysical phenomena as masking and figure-ground segregation.
It is very important and timely approach and I am looking forward to seeing this paper being published. However, my enthusiasm about experimental part of the paper is significantly lower.
1) The authors experimentally characterized ligand interactions for a few receptors in-vivo, on the level of glomerulus in a whole animal. This is definitely an important step forward. However, it is not clear how these experiments contribute to validation of the model. In a few presented cases, the authors demonstrated an existence of synergy and inhibition among ligands in-vivo, which may be important, but probably is incremental step compared to previous knowledge in the field. The main strength of the model is a prediction of collective phenomena for multiple receptors and psychophysical effects. No attempts were done to estimate relevant parameters from experimental data. Can, for example, an antagonism factor, ρ, be estimated based on current data?
2) The presentation of the experimental data is very limited. The authors did not provide a quantitative analysis of the goodness of the model prediction. The figures present just a few examples, without any quantitative validation. What is the confidence interval for individual fit parameters? Visual observation of the glomerulus responses (Figure 3B) make me question an accuracy of estimation of the sensitivity κ_(-1) and activation efficacy η, because of the response curves sometime do not reach their plateaus at high concentrations. How inaccuracy in estimation of these parameters affect prediction of a mixture responses. The author should provide a quantitative analysis of discrepancies between model prediction and experimentally measured mixture responses.
3) The proposed model is a very important, and the paper is lacking experimental validation, which I would not strongly insist upon. The theoretical work is valuable by itself. However, I would strongly encourage authors to have a discussion about strategies for experimental validation. (The current session "Experimental validation of the model" is misleading). What features of the model can and should be tested in the future work? The authors should provide, if possible, an estimation of necessary amount of data for validation their main conclusions.
4) Approximation in relations (6) are non-trivial. However, if there are large number of components in the mixture (β_i for the most sensitive ligand is small), k_i^(-1)* β_i for the highest affinity odorant may not be larger than the sum of the rest. The authors should discuss the limitation of this assumption.
Reddy and colleagues explore olfactory coding both experimentally and theoretically. Consistent with previous studies, they find that some odorant receptors (as measured by imaging glomerular responses) appear to be poorly described by a simple single-state activation model. Experimentally using binary mixtures, they demonstrate competitive antagonism. The manuscript then turns to a theoretical analysis, demonstrating that competitive antagonism can act to normalize responses to large odorant mixtures, with advantageous consequences (in models) for foreground-background segmentation and at least qualitative alignment with previous psychophysical observations.
While antagonism has been known for many years, its potential role in normalizing odorant responses has not, to my knowledge, been noted. Previous work on this topic has explored the "obvious" mechanism for normalization, circuit inhibition. The mechanism explored here is less obvious, and its discovery counts as a genuinely creative contribution that could change how we think about important phenomena in olfaction.
However, the manuscript is not without its flaws:
- A conceptual understanding of how Figure 5C arises seems elusive. The logic and arguments surrounding Equation 6 are, in my opinion, either orthogonal or counterproductive to understanding the mechanism advanced by the authors. However, there appears to be a relatively satisfying argument based on the Holder inequality with p = 1 and q = infinity. In pseudo-LaTeX syntax, if we let s_i = C_i/κ_i, then η⋅s = \sum_i | η_i s_i| <= (\sum_i |s_i|) \max_i η_i where "max" is the infinity-norm, and thus (if we define S = \sum_i s_i) F = Fmax / (1 + ((1+S)/(η⋅s))^n) <= Fmax /(1 + ((1+S)/(S max_i η_i))^n) -> Fmax/(1 + (\max_i η_i)^(-n)) in the limit of large S. You will be closer this bound if η_i is correlated with s_i, and farther (i.e., smaller response) if it is uncorrelated. At least to this reviewer, this argument seems considerably more helpful in developing a conceptual understanding of Figure 5C.
- The experimental demonstration of competitive antagonism is a bit unsatisfying. Some of this may just be presentation (which glomeruli in Figure 3A correspond to the panels in Figure 3B? of the few glomeruli in 3A that visibly display mixture interactions, some are strikingly non-monotonic yet these do not seem to appear in 3B). Other concerns relate to the whole experimental strategy (the potential confound of presynaptic inhibition is treated too superficially, and Vucinic, Cohen, and Kosmidis should be cited in addition to McGann et al., 2005) or to the reliability of the extracted parameters (see below). Finally, one can't help but wish for some attempt to experimentally test whether the predictions of Figure 5C hold.
With regards to the "reliability of the extracted parameters" mentioned above, the main concern is whether the relatively uncorrelated nature of κ and η (Figure 3C) really reflects biology or whether this is a consequence of measurement noise. One could address this point and the previous one by showing the error bars for these fits of these parameters. From a technical standpoint, the fitting of the constants (κ and η being most important) should perhaps be viewed with some skepticism when κ gets near 1 or higher. In such circumstances, the data may not exist to accurately measure saturation, and hence the measurement of η may be unreliable. Some evidence for this can be found in Figure 3C, where there are a few "outliers" of very small η, but notably these occur pretty much only for κ near 1 or higher (log κ^(-1) near zero or lower).
[Editors’ note: what now follows is the decision letter after the authors submitted for further consideration.]
Thank you for resubmitting your work entitled "Antagonism in olfactory receptor neurons and its implications for the perception of odor mixtures" for further consideration at eLife. Your article has been favorably evaluated by Gary Westbrook (Senior Editor) and three reviewers, one of whom, Fred Rieke, is a member of our Board of Reviewing Editors. All of the reviewers felt the emphasis on the model and omission of the experimental data improved the paper. A few issues remain or were introduced in the revisions. These are clear in the individual reviews below. These issues need to be addressed before we can consider the paper further.
This is a resubmission of a paper on olfactory coding. Experimental data has been removed and the paper has been revised to focus on the model for coding of complex odor mixtures. This is a substantial improvement as the experimental data raised a number of questions, and the model itself is an interesting and important contribution. There are several areas in which I think the paper can be strengthened; these center around making the modeling assumptions and structure clearer to a general reader:
The main text would benefit from incorporation of some additional description of key properties of the model so that it can be read without continual reference to the Materials and methods. The description of the transduction model in the second paragraph of the subsection “Biophysics of mammalian olfactory receptor neurons” is one place that should be expanded. Similarly, the impact of masking in the subsection “Masking” should be expanded. Another example is the simplified model first introduced in the first paragraph of the subsection “Olfactory encoding and antagonism” (is there a schematic that could be added to illustrate the key points in Equation 5 – that might help quite a bit). The seventh paragraph of the aforementioned subsection is another place that could use expansion. The second paragraph of the subsection “Performance in discrimination and identification tasks” is another (give intuition for why antagonism can be bad, and point to range around 10 odors in 4A where this is true).
The results of the discrimination analysis are likely to depend strongly on the limiting source of noise. In the model, noise comes from randomness in the composition of the background odors. I suspect that noise originating after receptor binding, or after masking, could alter the results of this analysis. Ideally this would get explored in the model. At a minimum the paper should include some discussion of the assumption about where noise enters, and when this assumption is likely to hold.
This is the second submission of the paper by Reddy et.al, about a novel mechanism for normalization in olfactory processing. The authors took away some limited experimental data, which did not add much to the paper and improved a clarity of model presentation. This is a novel and original idea, which should be published.
The revised manuscript is greatly improved, particularly in the explanation of the mechanism by which decorrelated binding/efficacy generates "flat" responses as a function of number of odorants in the mixture. The removal of the experimental data is also a step forward, and I look forward to a more extensive test in a future publication. This is an important, insightful, and well-presented contribution.https://doi.org/10.7554/eLife.34958.014
- Gautam Reddy
- Massimo Vergassola
- Venkatesh N Murthy
- Joseph D Zak
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
We are grateful to JP Rospars for sharing the experimental dataset from Ref. (Rospars et al., 2008). We also thank Vikrant Kapoor for technical assistance and members of the Murthy Lab for helpful discussions. GR and MV were partially supported by the Simons Foundation Grant 340106. JZ and VNM were partly supported by a grant from the NIH (R01 DC014453); JZ was supported by NIH Fellowship F32 DC015938.
- Fred Rieke, Reviewing Editor, Howard Hughes Medical Institute, University of Washington, United States
- Received: January 10, 2018
- Accepted: March 30, 2018
- Version of Record published: April 24, 2018 (version 1)
© 2018, Reddy et al.
This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.