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Asymmetric ephaptic inhibition between compartmentalized olfactory receptor neurons

Abstract

In the Drosophila antenna, different subtypes of olfactory receptor neurons (ORNs) housed in the same sensory hair (sensillum) can inhibit each other non-synaptically. However, the mechanisms underlying this underexplored form of lateral inhibition remain unclear. Here we use recordings from pairs of sensilla impaled by the same tungsten electrode to demonstrate that direct electrical (“ephaptic”) interactions mediate lateral inhibition between ORNs. Intriguingly, within individual sensilla, we find that ephaptic lateral inhibition is asymmetric such that one ORN exerts greater influence onto its neighbor. Serial block-face scanning electron microscopy of genetically identified ORNs and circuit modeling indicate that asymmetric lateral inhibition reflects a surprisingly simple mechanism: the physically larger ORN in a pair corresponds to the dominant neuron in ephaptic interactions. Thus, morphometric differences between compartmentalized ORNs account for highly specialized inhibitory interactions that govern information processing at the earliest stages of olfactory coding.

Introduction

Ionic fluxes from neuronal activity lead to changes in the extracellular potential1, which can influence the excitability of adjacent neurons by electrical field effects, known as ephaptic interaction2,3. First observed between two axons brought together experimentally4,5, ephaptic interaction takes place between uninsulated neuronal processes packed into an electrically isolated microenvironment2,3. Such an arrangement commonly occurs in fascicles containing bundles of unmyelinated axons, such as the mammalian olfactory nerve6 and the interoceptive sensory system7, as well as in regions of the nervous system including the fish hindbrain, mammalian cerebellum, hippocampus, and retina1,2,3,8,9. Despite their likely prevalence, field effects have long been considered nebulous10, as most neurons that are known to interact ephaptically also communicate via chemical synapses or gap junctions2,3,8. In addition, ephaptic interaction is notoriously difficult to study because it is enabled by high extracellular resistance and density of neural membranes2,3, none of which are amenable to in vivo experimental manipulation. Therefore, it remains unclear whether and how ephaptic interaction by itself is sufficient to influence circuit function.

Taking advantage of the powerful genetic toolkit of Drosophila melanogaster, we showed that olfactory receptor neurons (ORNs) housed in the same sensory hair, or sensillum, can inhibit each other, and that such lateral inhibition can modulate odor-guided behavior11. Despite the lack of direct synaptic connections, transient activation of one ORN rapidly suppresses the ongoing activity of its neighbor11. Electric circuit modeling suggested a potential mechanism for this nonsynaptic signaling11,12: in the restrictive space of a sensillum lumen, the high resistance of the lymph13 favors the generation of field effects between compartmentalized ORNs2,3. However, whether ephaptic interaction underlies the inhibition between ORNs has not been directly demonstrated.

In addition, outstanding questions remain about the peripheral organization of ORNs. Most insect ORNs housed in the same sensillum exhibit distinct and characteristic extracellular spike amplitudes. Grouped ORNs are thus named “A”, “B” or “C” based on their relative spike amplitudes in descending order14. In fruitflies, olfactory sensilla contain up to four neurons, with the majority of them housing two ORNs14,15. Intriguingly, certain odorant receptors are exclusively expressed in the large-spike “A” neurons, whereas others in the small-spike ORNs. For instance, in D. melanogaster, the Or22a receptor is expressed in the large-spike “A” neuron in the antennal basiconic sensilla of type 3 (ab3A), which is paired with a small-spike neighbor expressing Or85b (ab3B)16,17,18. The ab3A(Or22a)-ab3B(Or85b) arrangement is also observed in other Drosophila species19,20. These evolutionarily conserved patterns of ORN arrangement point to functional constraints in neuronal organization. They also imply that grouped ORNs have distinguishable functional characteristics. However, beyond ligand specificity21, little is known about whether and how the large-spike “A” ORN functionally differs from its small-spike neighbor.

In this study, we use a novel experimental approach to provide direct experimental evidence that ephaptic coupling alone is sufficient to drive lateral inhibition between ORNs. In addition, combining electrophysiological recordings, morphometric analysis based on serial block-face scanning electron microscopy (SBEM)22 and circuit modeling, we uncover a surprising functional disparity between compartmentalized ORNs in ephaptic inhibition and elucidate the underlying mechanism. Our study thus establishes the peripheral olfactory system of Drosophila as an ideal model to illuminate the impact of ephaptic interaction on circuit function and to determine its general operating principle.

Results

Direct evidence of ephaptic inhibition between ORNs

How does one prove that ORNs inhibit each other ephaptically if the inhibition is not mediated by any manipulatable target? We addressed this question by testing whether direct electrical interaction is sufficient to cause inhibition between ORNs. If lateral inhibition proceeds electrically in a sensillum, by means of experimental manipulation, we expect to observe similar cross inhibition between ORNs housed in different yet electrically coupled sensilla. We therefore performed extracellular recordings using a metal electrode to connect the electric fields of two adjacent sensilla, a manipulation that allows for direct demonstration of the impact of electrical interaction23.

In the control experiment examining an individual ab1 sensillum, the sustained spike responses of ab1A and ab1B to a prolonged dose of vinegar (large spikes in Fig. 1a, top panel, ab1A and ab1B spikes could not be sorted reliably and were thus grouped) were markedly reduced by a pulse of superimposed CO2 that activated ab1C (small spikes). The inhibition of ab1A/B by CO2 was abolished in mutant flies lacking functional CO2 receptors24 (Fig. 1a, bottom panel), indicating that the inhibition of ab1A/B depends on the excitation of ab1C, consistent with our earlier results by genetic ablation of ab1C11.

Next we used a tungsten electrode to impale two adjacent sensilla, ab1 and ab3, in order to connect their electric fields so that the field changes in one sensillum can be detected by ORNs in the other sensillum23. This approach eliminates the influence of other possible nonsynaptic mechanisms, such as inhibition mediated by shared odorant binding proteins25. Using this paradigm, we recorded ORN activity from both ab1 and ab3 sensilla simultaneously (Fig. 1b, top panel). As predicted, the sustained responses of ab1A/B were similarly inhibited by a superimposed pulse of E2-hexenol that excited the electrically coupled ab3B. The cross-inhibition depended on the electric coupling because withdrawing the tungsten electrode from the ab3 sensillum also abolished the inhibition of ab1A/B by E2-hexenol (Fig. 1b, middle panel, from the same group of ab1A/B neurons). We note that vinegar did not elicit significant sustained responses in ab3A (Fig. 1b, bottom panel). Therefore, the inhibition observed in the bridged configuration (Fig. 1b, top panel) was driven by the activation of electrically coupled ab3B. In control experiments, we showed that the bridged configuration did not cause any change in the responses of individual ORNs (Supplementary Fig. 1).

Furthermore, when ab3A was chronically activated by optogenetic stimulation, the sustained response could also be inhibited by a pulse of CO2, which excited ab1C housed in the electrically coupled sensillum (Fig. 1c). Together, these results provide direct evidence that the sustained response of one ORN was cross-inhibited by the excitation of another ORN via the interconnected electric fields. In other words, direct electrical interaction, or ephaptic coupling, is sufficient to drive lateral inhibition between ORNs that share the same electric field.

Field response and ephaptic inhibition

We next asked whether the large-spike “A” ORNs are functionally distinguishable from their small-spike neighbors in ephaptic interaction. In earlier work, we showed that lateral inhibition between ORNs is bidirectional: Transient activation of the “B” ORN inhibits the sustained response of the “A” neuron and vice versa11. However, it is unclear whether the bidirectional inhibition is equal in strength. To compare directly the strength of A-to-B and B-to-A inhibition is technically challenging because high frequency firing of the large-spike “A” neuron occludes spike activity of the “B” neuron. In addition, the degree of inhibition is influenced by the activity level of both ORNs11. To overcome these limitations, we sought to define the strength of ephaptic inhibition by other means.

According to an electric circuit model, neighboring ORNs shared the same electric field, also known as the transepithelial potential, which provides the driving force for odor-induced transduction currents12. As such, activation of one ORN reduces the transepithelial potential, thereby shunting currents away from its neighbor to cause ephaptic inhibition11. Thus, the degree to which activation of one ORN reduces the transepithelial potential, which can be measured as a change in the local field potential (LFP), indicates the magnitude of its ephaptic influence. The larger the LFP responses of one ORN, the more it can inhibit its neighbor.

To determine the relationship between ephaptic inhibition and LFP responses, we first identified odorants that strongly and selectively activate only one of the grouped ORNs (henceforth referred to as “private odorants”, Supplementary Fig. 2 and Supplementary Table 1). Using private odorants for the ab2 ORNs (ab2A: methyl acetate; ab2B: ethyl 3-hydroxy butyrate), we recorded LFP responses to 0.5-s pulses of the private odorants, delivered either as individuals or as concurrent binary odor mixtures (Supplementary Figure 3a). If there is no ephaptic inhibition, the LFP response to a binary odor mixture is expected to be the linear sum of the responses to its constituents. Thus, the difference between the linear sum and the measured LFP response indicates the magnitude of ephaptic inhibition.

As expected, we observed bidirectional inhibition using binary odor mixtures. Concurrent activation of ab2B by ethyl 3-hydroxy butyrate attenuated the LFP responses of ab2A to methyl acetate, and so did activation of ab2A to ab2B responses (Supplementary Fig. 3b). Importantly, the degree of inhibition increased with higher LFP responses (Supplementary Fig. 3c). Henceforth, we measured the LFP responses of an ORN to evaluate its ephaptic influence on its neighbor.

Grouped ORNs have different maximal field responses

To compare the LFP responses, we first focused on the ab2 ORNs, for which multiple private odorants are available (Supplementary Table 1). When ab2A was stimulated by increasing concentrations of methyl acetate, its LFP responses plateaued at ~23 mV. In comparison, the near-saturated LFP responses elicited by ethyl 3-hydroxy butyrate, a private odorant for ab2B, were markedly smaller, only ~10 mV (Fig. 2a, top panel). Importantly, the LFP amplitudes were characteristics of the ORNs, regardless of the position of the electrode along the sensillum. We note that ethyl 3-hydroxy butyrate activates ab2B strongly and effectively; at 3×10−4 dilution, the odorant elicited a high spike response in ab2B (~250 spikes s−1), comparable to the spike responses of ab2A to methyl acetate (Supplementary Fig. 4 and Supplementary Table 1). Thus, the difference in the ab2A and ab2B LFP responses is unlikely to have originated from different efficacies of the odorants. To verify this interpretation, we tested another pair of private odorants for the ab2 ORNs (ab2A: ethyl acetate; ab2B: E3-hexenol). We found that the near-saturated LFP response of ab2A remained markedly larger than that of ab2B (Fig. 2a, bottom panel). These results indicate that strong activation of ab2A can reduce the shared electric field more than that of ab2B. In this context, ab2A is the dominant ORN in the pair.

To test whether other large-spike “A” neurons also exert greater ephaptic influence upon their neighbors, we extended our analysis to additional sensillum types, selected on the basis of whether private odorants are available (Supplementary Table 1). In total, our analysis included eight sensilla covering the major sensillum classes in the antenna and maxillary palp: large basiconic (ab2 and ab3), small basiconic (ab4 and ab5), coeloconic (ac3I and ac3II), trichoid (at4), and palp basiconic (pb1)14,26,27.

In five out of the eight sensillum types examined, grouped ORNs exhibited notably different maximal LFP responses, including ORNs housed in the ab2, ab3, ab4, pb1, and ac3II sensilla. In each case where near-saturated responses were observed, the “A” neuron showed greater maximal LFP responses than its small-spike neighbor (Fig. 2a–e). Analysis of the at4 ORNs could not be completed because their private odorants failed to elicit near-saturated LFP responses even at a high concentration (10−1) (Fig. 2f; see Methods for details).

We note that a small minority of Drosophila olfactory sensilla contain ORNs of similar spike amplitudes, such as the ab5 and ac3I sensilla (Supplementary Fig. 5). In both cases, the near-saturated LFP responses of the grouped ORNs were nearly indistinguishable (Fig. 2g, h), suggesting that these neurons exert comparable ephaptic influence upon each other.

Overall, our results indicate that grouped ORNs exhibiting markedly different spike amplitudes likely exert unequal ephaptic influence upon each other, and most large-spike “A” neurons are the dominant neurons in this context. The relative spike amplitudes of grouped ORNs thus indicate the rank order of their ephaptic influence. In agreement with this notion, we found that transient activation of ab1C was more effective than ab1D in inhibiting the sustained response of ab1A ORNs (Supplementary Fig. 6).

Grouped ORNs have different tendencies to change spike rates

Next we compared the susceptibility of grouped ORNs to ephaptic influence. Using single-sensillum recordings, we simultaneously recorded the LFP responses, which originate in the sensory cilia and reflect transduction currents28,29, as well as the spike responses, which result from depolarization of the ORN soma. We used the spike/LFP ratio to evaluate the degree to which the neuron alters its spiking rate in relation to changes in its LFP response. For an ORN with a higher spike/LFP ratio, the neuron will experience a greater reduction in its spike response when the shared driving force is diminished by the activation of its neighbor. The ORN will therefore be more susceptible to ephaptic influence.

Upon stimulation, the frequency of ORN spiking is determined by depolarization of the soma, which is the product of the transduction current and somatic input resistance (see Methods). Although the transduction current cannot be measured directly in an in vivo preparation, it is thought to give rise to the LFP responses28,30,31. Hence, we used the LFP responses as a proxy for transduction currents in the following analysis.

We first stimulated ab3A and ab3B with 0.5-s pulses of their respective private odorants at increasing concentrations (Fig. 3a). By plotting the peak spike rate as a function of the peak LFP amplitude (absolute value), we found that the spike/LFP ratio was significantly higher for ab3B (Fig. 3b), indicating that ab3B is more susceptible to ephaptic influence than ab3A. However, the spiking rate of an insect ORN is determined not only by the amplitude but also by the kinetics of the LFP28. Thus, the variability in LFP kinetics introduced by differing transduction kinetics or odorant dynamics28,32 may confound our spike/LFP analysis.

To address this concern, we used an optogenetics approach so that identical stimuli can be used to activate grouped ORNs. When light activated either ab3A or ab3B expressing Channelrhodopsin2 (H134R-ChR2)33, the LFP responses increased with stimulus intensity (Fig. 3c). Consistent with our earlier analysis with odor stimulation, the spike/LFP ratio was also significantly higher for ab3B in the optogenetic assay (Fig. 3d). Of note, a similar spike/LFP relationship was observed even with a lower level of functional H134R-ChR2, achieved by lowering the concentration of retinal fed to flies (Supplementary Fig. 7). Therefore, the difference in the spike/LFP ratios between ab3A and ab3B was unlikely to have been affected by the exact expression level of H134R-ChR2.

We note that direct activation of H134R-ChR2 in the soma could in principle also contribute to ORN spike responses. To evaluate the impact of this possibility, we performed additional control experiments. We ectopically expressed Or83c, an odorant receptor tuned to farnesol34, in either ab3A or ab3B to allow for direct comparison of their responses to identical odor stimuli. Farnesol (≤2×10−2 dilutions) did not activate the cognate receptors of the ab3 ORNs (Supplementary Fig. 8a). Analyses of farnesol-induced responses in the Or83c-expressing ab3 ORNs indicated that the spike/LFP ratio was also significantly higher for ab3B (Supplementary Fig. 8b, c). This result suggests that somatic activation of H134R-ChR2, if any, is unlikely to have altered the relative spike/LFP relationship between neighboring ORNs.

We then extended the optogenetic analysis to five additional sensillum types, including ab1, ab2, ab4, pb1, and at4. In each case, the small-spike ORNs exhibited significantly higher spike/LFP ratios than the neighboring “A” ORNs (Fig. 3e), except for the at4 ORNs of which the spike amplitudes were the least distinct (Supplementary Fig. 5g). Notably, even in the ab1 sensillum that houses four ORNs, the relative spike amplitudes of the neurons (ab1A ≥ ab1B > ab1C > ab1D) remained indicative of the rank order of the spike/LFP ratios (ab1A ≤ ab1B < ab1C < ab1D) (Fig. 3e).

To test whether grouped ORNs with similar spike amplitudes have similar spike/LFP ratios, we examined ab5 and ac3I, the two sensilla which house ORNs of similar spike amplitudes (Supplementary Fig. 5h, i). For technical reasons, we could not perform the optogenetic analysis in these sensilla (see Methods for details). Therefore, we ectopically expressed Or83c in either ab5A or ab5B to compare their responses to the same odorant, farnesol. Analyses of farnesol-induced responses indicated that ab5A and ab5B indeed have similar spike/LFP relationships (Fig. 4a, b). Consistent with this result, analyses with private odorants for ab5 and ac3I ORNs also suggested that these neighboring neurons exhibit similar spike/LFP relationships (Fig. 4c–f).

Taken together, our odorant and optogenetic analyses show that in most sensilla, ephaptic interactions are asymmetric in that the large-spike “A” neuron is dominant. This dominance is due to (1) the “A” neuron’s greater ability to reduce the shared driving force (measured as LFP responses, Fig. 2), and (2) its lower susceptibility to ephaptic influence, evaluated by its lower propensity to change spiking rate in response to changes in LFP (Fig. 3).

Overexpression of odorant receptors

What determines the difference in the maximal LFP responses of the “A” and “B” ORNs? One possibility is that the density of odorant receptors expressed in the “B” ORNs is typically lower than in the “A” ORNs. As such, fewer receptors in the “B” neuron can be activated by odor stimulation, resulting in a smaller increase in conductance and subsequently a smaller LFP response. To test this possibility, we overexpressed the cognate receptor, Or85a, together with its obligatory coreceptor Orco35, in the ab2B ORNs. Immunostaining of the epitope-tagged odorant receptors indicated successful dendritic targeting (Supplementary Fig. 9).

In the wild-type control, strong activation of ab2A resulted in a large LFP response (~28 mV), markedly higher than the near-saturated LFP response of ab2B (~12 mV) (Fig. 5a, left panel). Interestingly, in the ab2B overexpressing Or85a, the maximal LFP response remained similar to that of the control, well below the ab2A counterpart (Fig. 5a, right panel). That is, overexpression of Or85a did not increase the LFP responses of ab2B. A plausible scenario is that the expression level of endogenous Or85a is already high, likely close to saturation, such that overexpressed Or85a only replaces the endogenous receptor in the sensory dendrite without further increasing its receptor density. Thus, the smaller LFP response of a “B” ORN is unlikely to have arisen from a lower receptor density.

Swapping odorant receptors does not alter the LFP response

Next, we examined the contribution of receptor identity to the maximal LFP responses. In a sensillum, neighboring ORNs express different odorant receptors17,18,36. Given that Drosophila odorant receptors are ligand-gated cation channels37,38,39, it is possible that the conductance of the receptors expressed in the “A” ORNs is typically larger than in the “B” neurons. If so, when the cognate receptor of an “A” ORN is replaced by a “B” neuron receptor, one would expect a marked reduction in the maximal LFP response of the neuron.

To test this possibility, we performed receptor-swap experiments in ab4A, of which the cognate receptor is Or7a16. We chose ab4A because Or7a receptor mutants (ΔOr7aGAL4) are readily available40, and because its small-spike neighbor, ab4B, is narrowly tuned to geosmin41. In ΔOr7aGAL4 mutants, the response of ab4A (Δab4A) to an Or7a ligand, E2-hexenol, is completely abolished. Genetic rescue of Or7a in Δab4A (Δab4A:Or7a) restored the response; the restored LFP dosage curve was similar to that of the wild-type ab4A (Figs. 5b and 2c). When a “B” neuron receptor (Or85a/ab2B) was expressed in ab4A instead (Δab4A:Or85a), the LFP dosage curve to an Or85a ligand, ethyl 3-hydroxy butyrate (Fig. 5b, left panel), was remarkably similar to that of Δab4A:Or7a to E2-hexenol (Fig. 5b, right panel). These results suggest that the characteristic near-saturated LFP responses of an ORN are not influenced by receptor density or identity but likely by other ORN features.

Morphometric analysis of grouped ORNs

What then underlies the asymmetry in ephaptic interactions? The size difference between grouped ORNs is likely a key. In most sensilla, grouped ORNs have differing sizes42, and the large-spike “A” neurons were postulated to have larger dendritic calibers43,44,45. However, without a genetically encoded EM marker, it was impossible to assign ORN identity. Notably, the ORN with a larger soma would have a smaller input resistance, which could account for the smaller spike/LFP ratio of the “A” neurons. In addition, a larger surface area of the sensory dendrites could give rise to a larger maximal LFP response, also characteristic of the “A” neurons. Therefore, we hypothesized that the dominant “A” neuron is larger than its neighbor.

To test this hypothesis, we endeavored to measure the morphometric features of genetically identified ORNs using electron microscopy (EM). To this end, we developed a method termed CryoChem, which allows for optimal morphological preservation of genetically labeled structures for EM imaging46. With OR-specific drivers, we expressed an EM marker, APEX2 (enhanced ascorbate peroxidase 2)47, in select ORNs to render them electron dense through diaminobenzidine (DAB) labeling. As a proof of principle, we first generated 3D volumes of at4A (Or47b > APEX2) and at4C (Or88a > APEX2) using SBEM (Supplementary Fig. 10a, b). Among the three at4 ORNs, we identified at4A and at4C as the largest and intermediate-sized neurons in the group, respectively, and used this information to assign neuronal identity to the unlabeled ORNs. By comparing the APEX2-labeled and unlabeled ORNs, we verified that APEX2/DAB labeling does not significantly alter the morphometric features of ORNs (Supplementary Fig. 10c).

Dominant “A” ORNs are physically larger than their neighbors

Next, we expanded our morphometric analysis to a total of five sensillum types (ab3, ab4, ac3II, at4, and ab5). In the sensilla where grouped ORNs exhibit distinct spike amplitudes (ab3, ab4, ac3II, and at4), the “A” ORNs were significantly larger than their small-spike neighbors with respect to the soma, inner and outer (sensory) dendrites (Fig. 6a–d, Supplementary Table 2; the inner and outer dendrites are defined based on the location of cilium base). Notably, ephaptic interactions were also asymmetric in these sensilla (with the exception of at4 where the dose−response analysis was incomplete), supporting our hypothesis that morphometric disparity between grouped ORNs underlies their asymmetrical ephaptic interactions. To further test this hypothesis, we examined the ab5 ORNs, which exert equal ephaptic influence onto each other (Figs. 2 and 4) and would thus be predicted to be of similar size. Indeed, in ab5A and ab5B we found that their somata, and likely also the sensory dendrites, were similar in size (Fig. 6e, Supplementary Table 2, see below for disparity in inner dendritic volumes).

Beyond morphometric measurements, our SBEM experiments also revealed novel ORN morphological features. For example, in the basiconic sensilla, but not in other sensillum types, we noticed a marked enlargement of the inner dendrite in every “A” ORN (Fig. 6f). This feature explains why the inner dendrite of ab5A is significantly larger than that of ab5B, despite their otherwise similar sizes (Fig. 6e). In addition, in the ab4 sensilla, we observed bending or looping of the unbranched outer dendrite around the base of the sensillum (Fig. 6g). These observations further highlight the diversity of ORN morphology among different sensillum types.

An electric circuit model predicts asymmetric interactions

We used mathematical modeling to explain how the morphometric disparity between ORNs contributes to their asymmetric ephaptic interactions. The existing electric circuit model of a sensillum assumes that neighboring ORNs have identical passive electrotonic properties12. However, our morphometric analysis suggests otherwise. We therefore took into account that the input resistance of an ORN is inversely proportional to the surface area of the soma, and that the conductance change upon odor stimulation scales with the surface area of the sensory dendrite (Fig. 7a, see Methods for details).

In our circuit model, the ORN-specific parameters are the odorant sensitivity and the surface areas of soma and sensory dendrite. For other modeling parameters, such as the resting membrane potential and membrane resistivity, identical values were assumed for all ORNs. First we evaluated our model by fitting the peak LFP responses of the ORNs housed in the ab3, ab4 and ab5 sensilla, of which electrophysiology and morphometric data were both available. We fitted the responses from the three ORN pairs simultaneously with identical free parameters using the Data2dynamics framework with a nonlinear least-squares optimization algorithm48. The fitted dose−response curves indicated that our circuit model well describes the experimental data (Fig. 7b). They also confirmed that the larger sizes of the “A” neurons result in higher maximal LFP responses, as evidenced in the fittings of the ab3 and ab4 ORNs, which are of different sizes, but not the ab5 ORNs, which are of similar sizes (Fig. 7b). For the ab3 and ab4 sensilla, where measurements for the sensory dendrites were unavailable, the fitted parameters indicate that the dendritic surface areas of ab3A and ab4A are both larger than those of their respective neighbors (see Methods). The model also predicts the relationship between ORN depolarization (ΔVm) and LFP responses (Fig. 7c). Given that the peak spike response of an ORN is a function of ∆Vm28, the smaller ∆Vm/LFP slopes of the “A” neurons are consistent with their smaller spike/LFP ratios (Fig. 3).

Our experimental data indicate that ephaptic interaction is asymmetric between grouped ORNs in most sensilla (Figs. 2, 3). To test whether our model describes asymmetric inhibition, we simulated the transmembrane potential of ab4 ORNs when either ab4A or ab4B was activated by a private odorant at increasing concentrations. According to our model, depolarization of one ORN hyperpolarizes its neighbor (Eqs. 11 and 12, Methods). We observed this relationship when both ORNs were assumed to be initially inactive (Fig. 7d, e, 0% activation) and when one ORN was assumed to be chronically activated by a background odorant, a paradigm used in Fig. 1 and in our earlier work11 (Fig. 7d, e, 50% activation). We then evaluated the strength of ephaptic inhibition between neighboring ORNs by comparing the degree to which depolarization of one ORN hyperpolarizes its neighbor. A higher value of the ratio (hyperpolarization/depolarization) indicates stronger ephaptic inhibition. By comparing the absolute values of ΔVmBVmA (Fig. 7d) and ΔVmAVmB (Fig. 7e), we found that activation of ab4A was indeed more effective in inhibiting ab4B than the reverse situation, indicating that A-to-B ephaptic inhibition is stronger than B-to-A inhibition.

In our model focusing on the basiconic ORNs, the only parameters that are different between grouped ORNs are the neuronal size and odorant sensitivity, both of which can in principle contribute to asymmetric ephaptic interaction. To illustrate the impact of neuronal size, we simulated ab4 ORN responses in a hypothetical situation where both ORNs express the same odorant receptor, Or56a. Even with identical odorant sensitivity, the larger size of ab4A was sufficient to yield a larger maximal LFP response (Fig. 7f, top panel) and a smaller increase in the transmembrane potential (Fig. 7f, bottom panel). In other words, morphometric differences alone can account for the asymmetric ephaptic interactions between grouped ORNs.

Discussion

We demonstrate here that ephaptic interaction alone is sufficient to influence circuit function by driving lateral inhibition between compartmentalized ORNs. What benefits might this form of direct neuronal interaction provide for olfactory coding? Ephaptic interaction between ORNs shapes timing of spiking in ORNs11, thereby allowing for a more elaborately patterned neural code in higher processing centers49. In addition, the rapid kinetics afforded by ephaptic interaction likely permits fast processing of odor-mixture information in the pheriphery11.

Surprisingly, we find that across sensillum types, most large-spike “A” neurons can exert greater ephaptic influence onto their neighbors and are also less susceptible to ephaptic influence. Mechanistically, the functional disparity arises from morphometric differences between compartmentalized ORNs. Together, our study describes a highly specialized inhibitory interaction that governs information processing at the earliest stages of olfactory coding. It also establishes the peripheral olfactory system of Drosophila as a model to understand the impact of electric field effects on neural circuit function.

Ephaptic interactions are asymmetric between grouped ORNs with distinct spike amplitudes. Conversely, grouped ORNs exhibiting similar spike amplitudes exert similar ephaptic influence on each other (Figs. 2g, h and 4). This relationship suggests that the extracellular spike amplitude of an ORN and its ephaptic influence are regulated by a common factor. Indeed, as with ephaptic influence, the extracellular spike amplitude of a neuron also negatively correlates with its input resistance50. Thus, the larger ORN in a pair, which has the smaller input resistance, is expected to have larger spike amplitude as well as ephaptic dominance over its neighbor.

In addition to fly ORNs, there are reports of asymmetric inhibition between other primary sensory neurons. For example, in fly vision, R7 and R8 photoreceptors of the same ommatidium inhibit each other synaptically. Interestingly, the mutual inhibition between R7 and R8 is also asymmetric51. The asymmetry may have arisen from the unequal numbers of reciprocal synapses52. In the bumblebee galea sensilla, gap junction-mediated inhibitory coupling is unequal between compartmentalized gustatory receptor neurons53. Therefore, although the precise mechanisms may vary, asymmetric lateral inhibition between adjacent primary sensory neurons may represent a conserved computational motif whereby sensory inputs are unequally processed at the periphery before being transmitted to higher brain centers.

Ephaptic interactions between ORNs allow odor-mixture information to be processed by the first neurons of an olfactory circuit11. To evaluate the extent to which natural odors activate grouped ORNs simultaneously, we surveyed volatile compounds from several food sources for fruitflies (Supplementary Data 1). From 16 fruits and fermented foods, we identified 51 odorants that can excite at least one ORN with responses ≥50 spike s−1, based on published datasets15,21,41. Among them, 30 individual odorants were capable of coactivating neighboring ORNs. For instance, ethyl hexanoate elicited significant responses in both ab3A and ab3B ORNs (Supplementary Data 1). Strikingly, all of the analyzed odor sources contained volatiles that excited at least one pair of the grouped ORNs, suggesting that grouped fly ORNs are commonly coactivated by natural odors.

What then is the significance of asymmetric lateral inhibition between grouped ORNs? In such a situation, this operation may provide a peripheral mechanism for evaluating countervailing signals and favoring the propagation of the input carried by the large-spike ORNs. In a mixture, odorants that excite the small-spike ORNs are more likely to be masked by odorants activating their large-spike neighbors. In support of this idea, we previously found that this coupling effect is powerful enough to influence animal behavior and that activation of ab1A by vinegar odors attenuated the aversiveness of CO2 detected by ab1C11. In future studies, it will be important to determine how odorants that excite the large-spike ORNs qualitatively differ from those that excite the small-spike neurons.

Methods

Drosophila stocks

Flies were raised on standard cornmeal medium at 25 °C, ~60% relative humidity in an incubator with a 12-h light/dark cycle. Female CS flies 5–7 days post eclosion were used in all experiments unless noted otherwise. For the ablation (UAS-rpr) and optogenetic (UAS-H134R-ChR2) experiments, 5-day-old females were used; for the SBEM (UAS-APEX2) experiments, 6–8-day-old females were used. For further information on genotypes, refer to Supplementary Table 4.

Single-sensillum recordings

A fly was wedged into the narrow end of a truncated plastic 200-μl pipette tip to expose the antenna, which was subsequently stabilized between a tapered glass microcapillary tube and a coverslip covered with double-sided type54. Single-unit recordings were performed as follows. Briefly, electrical activity of the ORNs was recorded extracellularly by placing a sharp electrode filled with 0.6× sensillum lymph Ringer solution31 into a sensillum and the reference electrode filled with the same Ringer solution was placed in the eye or the clypeus (for at4 recordings). For recordings performed with a tungsten electrode, a tungsten rod (0.01 × 3 inch, 717000, A-M Systems) secured in an electrode holder (ST50-BNC, Syskiyou) was sharpened in 0.5 N NaOH with a microelectrode etcher (EE-1D, Bak Electronics) at 24 V for nine cycles. No more than three sensilla from the same antenna were recorded. All measurements were taken from distinct neurons except for recordings performed using the bridged configuration shown in Fig. 1b (top and middle panels) and Supplementary Fig. 1.

AC signals (100–20k Hz) and DC signals were simultaneously recorded on an NPI EXT-02F amplifier (ALA Scientific Instruments) and digitized at 5 kHz with Digidata 1550 (Molecular Devices). ORN spikes were detected and sorted using threshold search under Event Detection in Clampfit 10 (Molecular Devices). Spike timing data were exported and analyzed in Igor Pro 6.3 (Wavemetrics). Peri-stimulus time histograms were obtained by averaging spike activities in 50-ms bins and smoothed using a binomial filter (Igor Pro 6.3, Wavemetrics).

Sensillum types were identified based on their locations on the antenna or maxillary palp, and their characteristic odor response profiles15,21. For ac3I and ac3II sensilla, sensillum types were determined according to ORN-specific fluorescent labeling (ac3I: Ir75b-GAL4; ac3II: Ir75c-GAL4) because the response profiles for ac3I and ac3II in D. melanogaster are virtually indistinguishable27. Based on the location of the fluorescence signals, we recorded from ac3I with a medial mounting position and ac3II with a posterior mounting position55.

Odor stimuli

Chemicals were >99% pure or of the highest purity available at Sigma-Aldrich unless otherwise specified. Odorants were diluted in paraffin oil unless otherwise noted. Apple cider vinegar (Spectrum, naturals filtered apple cider vinegar) and geosmin were diluted in water, and trans-palmitoleic acid (Cayman Chemical) was diluted in ethanol. For odor mixture experiments, individual odorants (2× stock solutions) were mixed either with paraffin oil or with another odorant at 1:1 (v/v) ratio prior to experiments. For short odor pulses, odor stimuli (100 μl applied to a filter disc) were delivered from a Pasteur pipette via a pulse of air (200 ml min−1) into the main air stream (2000 ml min−1). A Pasteur pipette filled with pure (Fig. 1 and Supplementary Fig. 1) or diluted CO2 (5×10−2, v/v in air, Supplementary Fig. 6) was used to deliver CO2 stimuli into the main air stream. Background odor stimuli were delivered from a 125-ml flask containing 3 ml of odor dilutions directly downstream of the main air stream (2000 ml min−1).

For palmitoleic acid, 4.5 μl of the freshly diluted odorant was applied to filter paper inserted inside a truncated 200-µl pipette tip. Ethanol was allowed to evaporate for 1 h in a vacuum desiccator prior to experiments. The odor cartridge was positioned around 4 mm away from the antenna as described54. Odor stimulus was delivered via a 500-ms pulse of air (500 ml min−1) directly at the antenna in the presence of humidified air flow at 2000 mlmin−1 from a different direction. Of note, female at4A does not respond to palmitoleic acid as strongly as male at4A in 7-day-old flies (Ng et al., unpublished data).

Optogenetic stimulation

Newly eclosed female flies expressing the H134R-ChR2 transgene in target ORNs were reared in constant darkness for 5 days on fly food supplemented with 100 μM all trans-retinal (Sigma) unless otherwise specified. Flies were transferred to fresh retinal food 1 day prior to experiments. A light stimulus was generated via a blue LED (470 nm, Universal LED Illumination System, pE-4000, Cool LED). Light pulses (500-ms duration) were controlled by a shutter (Vincent Associates) driven by Clampex 10.4 (Molecular Devices). Light output around the position of the recorded antenna was measured with an optical power meter (PMKIT-05-01, Newport Corporation) via a slim profile wand detector (818-ST2/DB, Newport Corporation).

The LFP light responses in the ac3 neurons expressing H134R-ChR2 were too small to be reliably analyzed. Attempts to express H134R-ChR2 in ab5A (Or82a-GAL4) or ab5B (Or47a-GAL4) failed to yield any light responses, despite the observation that the fluorescence of mCherry tag on H134-ChR2 was visible in the target ORNs. Aging the transgenic flies to 14 days old or increasing retinal concentrations in the food did not improve the situation.

Immunohistochemistry

Seven-day-old female files expressing myc-tagged Orco and/or Or85a odorant receptors in the ab2B ORNs were anesthetized on ice, with their heads aligned in a collar, covered with Cryo-OCT (Tissue-Tek, Fisher Scientific), and frozen on dry ice56. Cryosections (14μm) were fixed with 4% paraformaldehyde in 1× phosphate-buffered saline and stained with rabbit anti-myc antibody (1:250, 71D10, Cell Signaling Technology) and 21A6 (ciliary base marker, 1:200, DSHB), followed by goat anti-rabbit Alexa 647 secondary antibody (1:250, A21236, Life Technologies) and goat anti-mouse Alexa 568 (1:200, A11019, Life Technologies). Confocal microscopy was performed with a Zeiss 880 Airyscan Microscope, and images were processed with ImageJ software.

Sample preparation for SBEM

Target expression of APEX2 in ORNs for SBEM was performed as follows46. Briefly, transgenic Drosophila lines (10xUAS-myc-APEX2-Orco or 10xUAS-mCD8GF-APEX2) were generated to facilitate dendritic targeting of APEX2 46. Expression of APEX2 in select ORNs was driven by OrX-GAL4 drivers (Supplementary Data 1). Six- to eight-day-old female flies were cold anesthetized prior to the dissection of their antennae. The antennae were processed with the CryoChem method46, which involves cryofixation by high-pressure freezing, freeze-substitution, rehydration, DAB labeling reaction, en bloc heavy metal staining, dehydration, and resin infiltration.

Microcomputed X-ray tomography was performed on resin-embedded specimens using a Versa 510 X-ray microscope (Zeiss) to determine DAB-labeled region of interest. The specimens were then mounted on aluminum pins with conductive silver epoxy (Ted Pella) and sputter coated with gold-palladium for SBEM imaging. The ab3, ab4, ac3II, at4 datasets were collected with a Gemini SEM (Zeiss) equipped with a 3View block-face unit (Gatan); the ab5 dataset was collected with a Merlin scanning electron microscope (Zeiss) equipped with a 3View2XP and OnPoint backscatter detector (Gatan). Parameters for SBEM image acquisition are listed in Supplementary Table 5.

Segmentation of DAB-labeled Drosophila ORNs

The DAB-labeled Drosophila ORN was segmented in a semi-automated fashion using the IMOD software57 to generate a 3D model46. The IMOD command line “imodauto” was used for the auto-segmentation by setting thresholds to isolate the labeled neuron of interest. Auto-segmentation was followed by manual proofreading and correction of errors by two independent proofreaders. The neighboring, unlabeled ORN was manually segmented using the same software. Due to insufficient DAB labeling, the fine outer dendritic branches of most basiconic ORNs could not be reliably identified for segmentation.

Morphometric analysis

The 3D model of each ORN was first separated into cell body, inner dendrite and outer (sensory) dendrite models. The inner and outer dendrites were separated at the cilium base, a notably constricted dendritic region42. The volume measurements of ORNs were then obtained with the “imodinfo” function in IMOD based on the 3D models.

The lengths of most inner and outer dendrites were determined by first converting the 3D models into binary image files using the IMOD command “imodmop”. Then the skeletons of the 3D images were extracted using Skeletonize3D (https://imagej.net/Skeletonize3D) plugin in Fiji (NIH). The lengths of the resulting skeletons were obtained by the Fiji “Analyze Skeleton” function. For the ab3A, ab4A and ab5A ORNs, which exhibit significant dendritic enlargements (Fig. 6f), their inner dendritic lengths were determined by first visually identifying the center point in every ninth contour of the 3D models (300~400 nm z-step), then manually measuring and summing the distances between those points. The inner dendritic lengths of the ab3B, ab4B, and ab5B ORNs were determined in the same way. The outer dendritic lengths reported in Supplementary Table 2 are the distances between the cilium bases and the tips of the longest dendritic branch.

The outer dendrites of ORNs were assumed to be cylindrical and their surface areas were calculated based on the measured volumes and lengths accordingly. The surface areas of cell bodies were measured with the “imodinfo” function in IMOD.

Statistics

All data presented as mean ± s.e.m. were analyzed using Igor Pro 6.3 or SigmaPlot 13.0. Coefficients and the standard deviations of the linear fits were generated in Igor Pro 6.3. Unpaired two-tailed t test was performed in Supplementary Fig. 8 for single variable comparison between two groups. Paired two-tailed t test was performed in Fig. 6 for the morphological comparison between grouped ORNs. Data are presented as mean ± s.e.m. P < 0.05 was considered to be statistically significant and is presented as P < 0.05, P < 0.01, or P < 0.001. Statistical significance for linear coefficients was determined by analysis of covariance (ANCOVA) in RStudio using functions within the car package (version3.0-0). Data are presented as coefficient ± s.d. P < 0.05 was considered to be statistically significant and the differences are denoted by different letters.

Modeling

We consider the passive electric circuit model containing an auxiliary cell (denoted “A”) and two ORNs (ORN1 and ORN2) (Fig. 7a). Each cell is modeled as an effective Thevenin circuit with battery and resistances. The auxiliary cell is modeled as a battery EA in line with an input resistance RA. The soma of ORN1 is modeled as a battery E1 with input resistance Rin1, and the sensory dendrite is modeled as an odorant stimulation-dependent resistance Rd1 (similar for ORN2). The driving forces for the currents are the batteries EA, E1 and E2. The voltage VA is the transepithelium potential, and Vm1 and Vm2 are the neuronal transmembrane potentials that control spike firing. Changes in VA are recorded as changes in the local field potential, LFP. Of note, this passive electric circuit model concerns voltage changes resulting from constant odor stimulation. Therefore, all capacitive currents are considered zero in this model.

The system of equations for the currents IA, I1 and I2 reads

$${V_{\mathrm{{A}}}} = {E_{\mathrm{{A}}} + I_{\mathrm{{A}}}R_{\mathrm{{A}}}},\\ {V_{\mathrm{{A}}}} = {E_1 + I_1R_1},\\ {V_{\mathrm{{A}}}} = {E_2 + I_2R_2},\\ 0 = {I_{\mathrm{{A}}} + I_1 + I_2},$$
(1)

where we introduce the total resistances R1 = Rin1 + Rd1 and R2 = Rin2 + Rd2. By solving these equations, we obtain the currents

$$\begin{array}{*{20}{c}} {I_{\mathrm{{A}}}} & = & {\frac{{E_1\frac{{R_2}}{{R_1 + R_2}} + E_2\frac{{R_1}}{{R_1 + R_2}} - E_{\mathrm{{A}}}}}{{\frac{{R_1R_2}}{{R_1 + R_2}} + R_{\mathrm{{A}}}}}}, \\ {I_1} & = & {\frac{{E_2 - E_1}}{{R_1 + R_2}} - I_{\mathrm{{A}}}\frac{{R_2}}{{R_1 + R_2}}}, \\ {I_2} & = & {\frac{{E_1 - E_2}}{{R_1 + R_2}} - I_{\mathrm{A}}\frac{{R_1}}{{R_1 + R_2}}}. \end{array}$$
(2)

The neuronal part is an effective Thevenin circuit with battery $$E_{\mathrm{T}} = E_1\frac{{R_2}}{{R_1 + R_2}} + E_2\frac{{R_1}}{{R_1 + R_2}}$$ and resistance $$R_{\mathrm{T}} = \frac{{R_1R_2}}{{R_1 + R_2}}$$. The neuronal membrane potentials are

$$\begin{array}{*{20}{r}} \hfill {V_{{\mathrm{m}}1}} & \hfill = & \hfill {E_1 + R_{{\mathrm{{in}}}1}I_1},\\ \hfill {} & \hfill {} & \hfill {}\\ \hfill {V_{{\mathrm{m}}2}} & \hfill = & \hfill {E_2 + R_{{\mathrm{{in}}}2}I_2}.\end{array}$$
(3)

To further simplify the analysis, we use RA to define dimensionless resistances $$\tilde R_{\mathrm{{A}}} = R_{\mathrm{{A}}}{\mathrm{/}}R_{\mathrm{{A}}} = 1$$, $$\tilde R_1 = R_1{\mathrm{/}}R_{\mathrm{{A}}}$$, $$\tilde R_2 = R_2{\mathrm{/}}R_{\mathrm{{A}}}$$ and rescale currents $$\widetilde I_{\mathrm{{A}}} = I_{\mathrm{{A}}}R_{\mathrm{{A}}}$$,$$\widetilde I_1 = I_1R_{\mathrm{{A}}}$$and $$\tilde I_{2} = I_{2}R_{\mathrm{A}}$$. This does not affect the voltages in Eqs. 1 and 3 and is formally equivalent to setting RA = 1. In the following, we therefore omit the tilde symbols and simply use RA = 1. As mentioned before, this does not affect the results and conclusions concerning voltages.

We next focus on the input and dendritic resistances. We are interested in how odorant stimulation and the morphometric properties of soma and sensory dendrites affect the transmembrane potentials Vm1 and Vm2. We assume that the input resistances Rin1 and Rin2 depend on the size of the soma and a smaller ORN has a higher input resistance compared to a larger ORN. Specifically, we assume that Rin1 and Rin2 are inversely proportional to the soma surfaces As1 and As2

$$R_{{\mathrm{{in}}}1} = \frac{{\rho _{\mathrm{{s}}}}}{{A_{{\mathrm{{s}}}1}}}\quad {\mathrm{and}}\quad R_{{\mathrm{{in}}}2} = \frac{{\rho _{\mathrm{{s}}}}}{{A_{{\mathrm{{s}}}2}}},$$
(4)

where ρs is the soma membrane resistivity.

We model the sensory dendrite of an ORN as a uniform cylinder of length L with axial (cytoplasmic) resistivity ra and membrane resistivity rm, where rm depends on odor activation. From linear cable theory, the input resistance Rs of a uniform leaky cylinder with an open and a sealed end is

$$R_{\mathrm{{d}}} = \sqrt {r_{\mathrm{{m}}}r_{\mathrm{{a}}}} {\mathrm{coth}}\left( {L\sqrt {\frac{{r_{\mathrm{{a}}}}}{{r_{\mathrm{{m}}}}}} }, \right)$$
(5)

where $$l = L\sqrt {\frac{{r_{\mathrm{{a}}}}}{{r_{\mathrm{{m}}}}}}$$ is the electrotonic length of the cylinder and $$R_\infty = \sqrt {r_{\mathrm{{m}}}r_{\mathrm{{a}}}}$$ is the input resistance of an infinitely long cylinder. We further simplify Eq. 5 assuming that the cytoplasmic resistance is much smaller than the membrane resistance such that l 158. By expanding Eq. 5 for l 1 we get in first order

$$R_{\mathrm{{d}}} = \frac{{r_{\mathrm{{m}}}}}{L} = \frac{{\rho _{\mathrm{{d}}}}}{{A_{\mathrm{{d}}}}},$$
(6)

where ρd is the dendritic membrane resistivity and Ad is the dendritic surface.

The membrane resistivity ρd implicitly depends on odor activation because odorants activate receptors that increase the membrane conductivity. We simplify the transduction process and assume that for a given stimulation with odorant concentration “od”, the amount of activated receptors is given by the Hill function

$$R^ \ast = R_{\max}^ \ast \frac{{{\mathrm{{od}}}^n}}{{{\mathrm{{od}}}^n + K_{{\mathrm{{od}}}}^n}},$$
(7)

where n is the Hill-coefficient and Kod the odorant concentration that activates half of the receptors. Receptor activation induces the additional membrane conductivity $$\sigma _{\mathrm{{d}}} = \gamma R^ \ast = \sigma _{{\mathrm{{d}}},\max}\frac{{{\mathrm{{od}}}^n}}{{{\mathrm{{od}}}^n + K_{{\mathrm{{od}}}}^n}}$$. With the basal resistivity ρd,0, the overall conductivity is $$\frac{1}{{\rho _{\mathrm{{d}}}}} = \frac{1}{{\rho _{{\mathrm{{d}}},0}}} + \sigma _{\mathrm{{d}}} = \frac{{1 + \rho _{{\mathrm{{d}}},0}\sigma _{\mathrm{{d}}}}}{{\rho _{{\mathrm{{d}}},0}}}$$. This gives

$$\rho _{\mathrm{{d}}} = \frac{{\rho _{{\mathrm{{d}}},0}}}{{1 + g}}$$
(8)

with

$$g = g_{\max}\frac{{{\mathrm{{od}}}^n}}{{{\mathrm{{od}}}^n + K_{{\mathrm{{od}}}}^n}}$$
(9)

and $$g_{\max} = \rho _{{\mathrm{{d}}},0}\sigma _{{\mathrm{{d}}},\max}.$$

In summary, to model the dendritic resistances we use the formula

$$R_{\mathrm{{d}}} = \frac{{\rho _{{\mathrm{{d}}},0}}}{{A_{\mathrm{{d}}}(1 + g)}}.$$
(10)

We next address the changes in local field potential due to stimulation of ORN1 or ORN2. When the activation of ORN1 is altered due to odorant stimulation, the dendritic resistance Rd1 changes by ΔRd1 which alters the local field potential LFP by |ΔVA|. From Eqs. 1 to 3 we compute that the corresponding changes in the membrane potentials are $${\mathrm{\Delta }}V_{{\mathrm{{m}}}2} = {\mathrm{\Delta }}V_{\mathrm{{A}}}\frac{{R_{{\mathrm{{in}}}2}}}{{R_2}}$$ and

$${\mathrm{\Delta }}V_{{\mathrm{{m}}}1} = - {\mathrm{\Delta }}V_{\mathrm{{A}}}R_{{\mathrm{{in}}}1}\left( {1 + \frac{1}{{R_2}}} \right).$$
(11)

Similarly, when ORN2 is stimulated we have $${\mathrm{\Delta }}V_{{\mathrm{{m}}}1} = {\mathrm{\Delta }}V_{\mathrm{{A}}}\frac{{R_{{\mathrm{{in}}}1}}}{{R_1}}$$ and

$${\mathrm{\Delta }}V_{{\mathrm{{m}}}2} = - {\mathrm{\Delta }}V_{\mathrm{{A}}}R_{{\mathrm{{in}}}2}\left( {1 + \frac{1}{{R_1}}} \right).$$
(12)

Because R2 (R1) remains constant when ORN1 (ORN2) is stimulated12, it follows that ΔVm1 and ΔVm2 change linearly with ΔVA. Assume that ORN1 corresponds to the larger neuron A and ORN2 to the smaller neuron B such that Rin1 < Rin2 and R1 < R2. With this we have $$R_{{\mathrm{{in}}}1}( {1 + \frac{1}{{R_2}}} ) < R_{{\mathrm{{in}}}2}( {1 + \frac{1}{{R_1}}} )$$ which is in agreement with Fig. 3 showing that the slope of the spiking rate (which reflects ΔVm1 or ΔVm2) vs. LFP is smaller for ORNA compared to ORNB.

The following sections concern the fitting procedure. We are interested in whether the differences between our electrophysiological measurements can be explained by the morphometric differences among the grouped ORNs. To address this question, we focus on ab3, ab4 and ab5 sensilla for which we have electrophysiological and morphometric data. We simultaneously fitted the combined LFP data (Fig. 2) using a minimal model with a common set of basic parameters and ORN-specific parameters (surface area and odorant sensitivity). In the following, we derive the minimal model that we use for the fitting procedure. For values of fitting parameters, see Tables 13. The fitting and simulation results are presented in Fig. 7 of the main text.

We were able to fit the combined LFP measurements of ab3, ab4, and ab5 neurons by assuming a common set of parameters that differs only in the areas of soma and sensory dendrite. However, we could not adequately fit the combined LFP data of ac3II, ab3, ab4 and ab5 neurons by assuming such common set of parameters. We note that basiconic ORNs (ab3, ab4, ab5) have highly branched sensory dendrites, whereas coeloconic ORNs do not (ac3II). It is possible that the branching pattern of sensory dendrites or other unknown factors may have introduced additional parameters that affect the fitting results.

To estimate the batteries E1 and E2 using the resting membrane potential, we assume that the auxiliary cell is the same for all sensillum types, and therefore use a single value for EA. For E1 and E2, we do not assume that they are identical for all sensilla because ORN basal resistances differ depending on the morphometric feature of the neuron, and using the same E1 and E2 for all sensilla would lead to different resting membrane potentials for the ORNs (data not shown). This is problematic if one assumes that the mechanism of action potential generation is similar in all ORNs. Instead, we assume that at rest without odorant stimulation (basal condition) the membrane potentials of the ORNs are identical such that Vm1 = Vm2 = V0 with V0 = −60 mV. We used the conditions Vm1 = Vm2 = V0 to express the parameters E1 and E2 as a function of V0. With Eqs. 2 and 3 we find

$$\begin{array}{*{20}{c}} {E_1} & = & {E_{\mathrm{{A}}} - (E_{\mathrm{{A}}} - V_0){\mathrm{\Theta }}_0\left( {1 + \frac{{\xi _0}}{2}} \right)}, \\ {E_2} & = & {E_{\mathrm{{A}}} - (E_{\mathrm{{A}}} - V_0){\mathrm{\Theta }}_0\left( {1 - \frac{{\xi _0}}{2}} \right)} \end{array}$$
(13)

and

$${I_{\mathrm{{A}}}} = { - (E_{\mathrm{{A}}} - V_0){\mathrm{\Theta }}_0\left( {\xi _0(\alpha _1 - \alpha _2) + \beta _1 + \beta _2} \right)}, \\ {I_1} = {(E_{\mathrm{{A}}} - V_0){\mathrm{\Theta }}_0\left( {\xi _0\alpha _1 + \beta _1} \right)}, \\ {I_2} = {(E_{\mathrm{{A}}} - V_0){\mathrm{\Theta }}_0\left( { - \xi _0\alpha _2 + \beta _2} \right)}$$
(14)

with

$$\begin{array}{*{20}{r}} \hfill {\alpha _1} & \hfill = & \hfill {\frac{{1 + \frac{{R_2}}{2}}}{{R_1R_2 + R_1 + R_2}}},\\ \hfill {} & \hfill {} & \hfill {}\\ \hfill {\beta _1} & \hfill = & \hfill {\frac{{R_2}}{{R_1R_2 + R_1 + R_2}}},\\ \hfill {} & \hfill {} & \hfill {}\\ \hfill {\alpha _2} & \hfill = & \hfill {\frac{{1 + \frac{{R_1}}{2}}}{{R_1R_2 + R_1 + R_2}}},\\ \hfill {} & \hfill {} & \hfill {}\\ \hfill {\beta _2} & \hfill = & \hfill {\frac{{R_1}}{{R_1R_2 + R_1 + R_2}}}\end{array}$$
(15)

and

$$\begin{array}{*{20}{r}} \hfill {\xi _0} & \hfill = & \hfill {\frac{{R_{{\mathrm{{in}}}1}\beta _{1,0} - R_{{\mathrm{{in}}}2}\beta _{2,0}}}{{1 - R_{{\mathrm{{in}}}1}\alpha _{1,0} - R_{{\mathrm{{in}}}2}\alpha _{2,0}}}},\\ \hfill {} & \hfill {} & \hfill {}\\ \hfill {{\mathrm{\Theta }}_0} & \hfill = & \hfill {\frac{1}{{1 - \frac{1}{2}(R_{{\mathrm{{in}}}1}\left( {\xi _0\alpha _{1,0} + \beta _{1,0}} \right) + R_{{\mathrm{{in}}}2}\left( { - \xi _0\alpha _{2,0} + \beta _{2,0}} \right))}}}.\end{array}$$
(16)

The values β1,0, β2,0, α1,0 and α2,0 are obtained from Eq. 15 by inserting basal dendritic resistances that depend on the neuronal morphometry. Equation 14 shows that the effective driving force for the currents is EA − V0.

Next we use the spike/LFP ratio to constrain the parameter space. For the ab5 sensilla, we use the measured values for the outer dendritic surfaces Ad1 and Ad2. In contrast, for ab3 and ab4, the surfaces Ad1 and Ad2 are unavailable and are therefore free fitting parameters. However, for these sensilla, we use the measured spike/LFP ratio r (Fig. 3) to further constrain the parameter space. Our passive electrical model does not predict spiking rates. However, we assume that ΔVm1VA or ΔVm2VA is correlated to the spike/LFP ratio shown in Fig. 3. Let r > 1 be the ratio of the spike/LFP slopes of ORNA to ORNB shown in Fig. 3. With the convention that ORN1 corresponds to ORNA and ORN2 to ORNB, we have

$$r = \frac{{R_{{\mathrm{{in}}}2}\left( {1 + \frac{1}{{R_{1,0}}}} \right)}}{{R_{{\mathrm{{in}}}1}\left( {1 + \frac{1}{{R_{2,0}}}} \right)}},$$
(17)

where R1,0 and R2,0 are basal resistances without odorant stimulation. We can use Eq. 17 to express R1,0 as a function of R2,0

$$R_{1,0} = \frac{{R_{2,0}}}{{r\kappa + R_{2,0}(r\kappa - 1)}},$$
(18)

where $$\kappa = \frac{{R_{{\mathrm{{in}}}1}}}{{R_{{\mathrm{{in}}}2}}}$$. With $$R_{1,0} = R_{{\mathrm{{d}}}1,0} + R_{{\mathrm{{in}}}1} = \frac{{\rho _{{\mathrm{{d}}},0}}}{{A_{{\mathrm{{d}}}1}}} + R_{{\mathrm{{in}}}1}$$ the dendritic surface of ORN1 is

$$A_{{\mathrm{{d}}}1} = \rho _{{\mathrm{{d}}},0}\left( {\frac{{R_{2,0}}}{{r\kappa + R_{2,0}(r\kappa - 1)}} - R_{{\mathrm{{in}}}1}} \right)^{ - 1}.$$
(19)

In summary, for ab3 and ab4, we use Ad2 and r as fitting parameters and Ad1 is computed with Eq. 19. The range for r is constrained by the values shown in Fig. 3. In contrast, for ab5 we use our measured values for Ad1 and Ad2.

For the odorant concentration, we write od = c010x, where x < 0 corresponds to the odorant dilution and c0 is the initial undiluted concentration. By writing $$K_{{\mathrm{{od}}}} = c_010^{k_{{\mathrm{{od}}}}}$$ we have

$$\frac{{{\mathrm{{od}}}^n}}{{{\mathrm{{od}}}^n + K_{{\mathrm{{od}}}}^n}} = \frac{1}{{1 + 10^{n(k_{{\mathrm{{od}}}} - x)}}}.$$
(20)

The parameter Kod (resp. kod) characterizes the sensitivity of the ORN to the odorant and is specific for each ORN. We therefore allow for each neuron a different parameter kod.

Tables 13 indicate the parameters for the electric circuit model.

Animal research

We have complied with all relevant ethical regulations for animal testing and research. No specific ethical approval is required for this study.

Data availability

The data that support the findings of this study are available from the corresponding author upon request. The source data underlying Figs. 2, 3, 4, 5, 6, and 7b–f and Supplementary Figs. 1, 3, 5, 6, 7, 8 and 10 are provided as a Source Data file.

Journal peer review information: Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Acknowledgements

We thank Jeffry Isaacson, Johannes Reisert, Jing Wang, Larry Squire, Gareth Thomas and Renny Ng for comments on the manuscript; Szu-Ying Chen, Vivian Nguyen, Renny Ng, Edie Zhang, Martin Orden, Uma Talagadadivi, Ben Damasco, Tiffany Tsai and Cesar Nava-gonzales for assistance in ORN segmentations; Cesar Nava-gonzales for assistance in the analysis of natural odors. This work was supported by Frontiers of Innovation Scholars Program and Croucher Foundation Scholarship to T.K.T.; Hellman Fellowship, the Ray Thomas Edwards Foundation Career Development Award, Kavli Institute for Brain and Mind Innovative Research Grant and NIH R01DC015519 to C.-Y.S. National Center for Microscopy and Imaging Research (NCMIR) technologies and instrumentation are supported by grant GM103412 from the National Institute of General Medical Sciences.

Author information

Author notes

1. These authors contributed equally: Ye Zhang, Tin Ki Tsang.

Affiliations

1. Neurobiology Section, Division of Biological Sciences, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA

• Ye Zhang
• , Tin Ki Tsang
•  & Chih-Ying Su
2. National Center for Microscopy and Imaging Research, Center for Research in Biological Systems, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA

• Eric A. Bushong
•  & Mark H. Ellisman
3. Brain Research Center, National Tsing Hua University, No. 101, Section 2, Kuang-Fu Road, Hsinchu, 30013, Taiwan

• Li-An Chu
•  & Ann-Shyn Chiang
4. Institut of Biology, École Normale Supérieure (IBENS), 46 rue d’Ulm, 75005, Paris, France

• Jürgen Reingruber
5. INSERM U1024, 75005, Paris, France

• Jürgen Reingruber

Contributions

Y.Z., T.K.T., and C.-Y.S. designed the experiments. Y.Z. performed sensillum recordings, data analysis, and natural odor analysis. T.K.T. and E.A.B. performed SBEM imaging with support from M.H.E. T.K.T. performed immunostaining and morphometric analysis. L.-A.C. conducted preliminary morphometric analysis using super-resolution confocal microscopy with support from A.-S.C. J.R. performed computational modeling. Y.Z., T.K.T., J.R., and C.-Y.S. wrote the manuscript with inputs from all authors.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Chih-Ying Su.