Non-synaptic interactions between olfactory receptor neurons, a possible key feature of odor processing in insects

When flies explore their environment, they encounter odors in complex, highly intermittent plumes. To navigate a plume and, for example, find food, flies must solve several tasks, including reliably identifying mixtures of odorants and discriminating odorant mixtures emanating from a single source from odorants emitted from separate sources and mixing in the air. Lateral inhibition in the antennal lobe is commonly understood to help solving these two tasks. With a computational model of the Drosophila olfactory system, we analyze the utility of an alternative mechanism for solving them: Non-synaptic (“ephaptic”) interactions (NSIs) between olfactory receptor neurons that are stereotypically co-housed in the same sensilla. For both tasks, NSIs improve the insect olfactory system and outperform the standard lateral inhibition mechanism in the antennal lobe. These results shed light, from an evolutionary perspective, on the role of NSIs, which are normally avoided between neurons, for instance by myelination.


Introduction
. a) NSI interaction Theoretical and experimental studies have proposed that the non-synaptic interaction (NSI) between ORNs is mediated by a direct electrical field interaction between such closely apposed neurons. b) Hypothesis n.1: An inhibitory mechanism can increase the dynamic range of the ORNs and help to correctly encode the ratio between odorants even at high concentration. At low concentration, the ratio of two odorants (A1 and B1) can be encoded by ORNs, with and w/o NSI; when concentration is high (A2 and B2), the ORNs response without NSI is flatted on similar values and the ratio cannot be encoded. Hypothesis n.2: If a single source emits an odorant mixture (c), odorants will arrive in close synchronization, NSIs will take effect and the response in both ORNs is affected. If separate sources emit the odorants (d), they will arrive in a less correlated way (Erskine, 2018), and NSIs have almost no effect, resulting in larger ORN responses. ORN response data shown is based on a preliminary model.  Here, we present a network model with two groups of ORNs, each tuned to a specific set of 108 odorants, connected to their corresponding glomeruli, formed by lateral neurons (LNs) and PNs, 109 following the path started by Av-Ron and Rospars (1995); Av-Ron and Vibert (1996), and subse-  For maximum clarity, we here focus on only one type of sensillum and hence two types of ORNs 129 that we denote as ORN and ORN . We further assume that odorants labeled A and B selectively 130 activate ORN and ORN , respectively (see Figure 2 and Figure 1a). This assumption is not only 131 sensible for a reductionist analysis of the role of NSIs, but it is also based on experimental obser-   i.e. series of input pulses which durations and inter-stimulus-intervals were drawn from a Gaussian 143 distribution. We found that our model reproduces the data to a similar quality (relative error of  Figure 3). 146 To further constrain the model, we compared its results to electrophysiological recordings from   where max is the maximum firing rate of ORNs, is a fitted constant representing the level of ORN 164 input that drives half-maximum response, and ORN and PN , are the average firing rates of the ORNs 165 and the PN over the stimulation period (500 ms), respectively. Our model reproduces this behavior 166 as a direct consequence of the model structure without any further parameter tuning (Figure 4). 167 LNs follow the same behavior (see Figure 4f). Note that this result, i.e. the sigmoidal behavior,  With a model in place that demonstrates the correct response dynamics for a variety of stimuli, 172 we then analysed its predictions on whether NSIs can be beneficial for odor mixture processing. In 173 particular, we tested the following two hypotheses: 1. Do NSIs improve the encoding of concentra-   Table 1) in such a 196 way that the average PN responses to a synchronous mixture pulse were matched across the two 197 models. While the stimulus lasts only 50 ms, the effect on ORNs, PNs and LNs lasts more than twice 198 as long. We observed the same behavior for other stimulus durations (tested from 10 to 500 ms). In that the response of the PNs for both models is of similar magnitude (peak response for PNs for 208 independent glomeruli ∼110Hz, for AL lateral inhibition and NSI mechanism ∼70 Hz).

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To investigate the effectiveness of the two mechanisms for ensuring faithful odorant ratio en-210 coding more systematically, we tested the three models with synchronous triangular odor pulses  (Figure 6f). 233 The results in Figure 6 are all based on the ratio of peak activity = ∕ (see Model   234 and methods) during the first 100ms after the stimulus onset. We also tested the ratio of average  In the next section we will explore the effectiveness of the different models when the whiffs 256 arrive asynchronously.    of odorants is released from a single source they form a plume where the odorants typically ar-261 rive together (Figure 7-Figure Supplement 1). We hypothesise that if lateral inhibition (via LNs or 262 NSIs) only takes effect in the synchronous case but not in asynchronous case, it will help distin-263 guishing single source and multi-source plumes. For instance, in the case of pheromone receptor 264 neurons that are co-housed with receptor neurons for an antagonist odorant, the response to the 265 pheromone would be suppressed by NSI when both odorants arrive in synchrony (same source) 266 and not when arriving with delays (the pheromone source is separate from the antagonistic source).

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This is thought to underlie the ability of male moths to identify a compatible female, where the an-       , 2007; Lin et al., 2007, 2014), could be present in higher brain 314 areas to interpret them. However, as before, we applied the simple measure of peak PN activity in 315 terms of the total firing rate above a given threshold to analyze the quality of the encoding.

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In order to analyze the discrimination of plumes with odorants coming from a single source 317 -highly correlated stimuli -from separate sources -poorly correlated stimuli -we developed a  (Figure 8a-b), while the average ORN activity for the NSI model is lower and depends on the 326 correlation between odor signals (Figure 8a-b). These effects are approximately the same for the 327 whole range of the tested NSI strengths (data not shown).

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The situation is different for the average PN activity. The average PN response in the NSI model 329 is almost the same as in the control model and only weakly, if at all, dependent on input correlation 330 (see Figure 8c). It, therefore, does not encode input correlation well. To the contrary, the average 331 PN responses in the LN inhibition network are lower than in the control model, and a bit more 332 clearly dependent on input correlation (Figure 8c). Hence, LN inhibition is useful for encoding 333 input correlation with the average PN activity. All reported effects remain approximately the same 334 for the entire range of explored parameters ( and ) (data not shown). 335 We next analysed instead of the average PN response the "peak PN" response, defined as the 336 integrated PN activity over time windows where the PN firing rate is above a given threshold (e.g. 50, 337 100, or 150 ms). ideally we would like the PN responses to differ maximally between highly correlated plumes and 359 independent plumes in order to discern the two conditions.

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To quantify these effects we measured the following distances: 1. The distance between peak   Furthermore, using a model variant with no NSIs but LN inhibition between glomeruli in the 391 AL we found that 1. For synchronous individual whiffs, both models, the one with NSI mechanism 392 and the one with LN inhibition, are better than the control model in several conditions (Figure 6 393 g); moreover, the NSI mechanism is typically more effective than LN inhibition. This is especially 394 true for very short stimuli (<100ms These results further support the hypothesis that the NSI mechanism offers an evolutionary In conclusion, we have demonstrated in a model of the early olfactory system that NSIs have ad-526 vantages over LN inhibition in the AL with respect to faithful mixture ratio recognition and plume 527 separation. In our future work we seek to confirm the behavioral relevance of NSIs in Drosophila. 528 Other interesting future directions include the relationship of NSIs and syntopic effects/masking, 529 as well as the differential roles of NSIs and LN inhibition when both are present at the same time. To simulate experimentally observed NSIs, we assume a simple linear model with respect to the 572 output variable of the transduction model, as the exact biochemical mechanism for NSIs is of yet 573 unclear. We do this with a multiplicative term (x x ) to reflect that presumably the driving force 574 for x (x ) is removed, rather than ORN (ORN ) being directly hyperpolarized.
The full set of parameters used for the simulations are reported in Table1.

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The antennal lobe 577 We here reduce the antennal lobe (AL) to two glomeruli, a and b (see where V is the LN membrane potential, s represents the synaptic input, and reflects the rate where t1= 0.5s, t2=2.5s, and = 0.1s (see Figure 3- Figure Supplement 1).  Figure 7-Figure Supplement 1). To test the function of NSIs for odor source separa-618 tion, we adopted long stimuli (>3 s), with statistical properties that resemble the filaments observed  (Jacob et al., 2017)) 630 and the correct correlation between odorants. We achieved this by the following procedure: 631 1. We drew two correlated pseudo random numbers from a Gaussian distribution, with a given 632 correlation 633 2. We mapped the two numbers into two uniform random variables

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Analysis and simulation 638 We used the PNs spiking activity as the output of the networks and we analysed it to estimate 639 the ability of the three networks to encode odorants mixture ratio and spatio-temporal analysis. 640 We assumed for simplicity that the relevant information is present in the firing rate and therefore 641 analyse the average activity and peak activity, defined below and in the main text.

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For the analysis of the ratio encoding (see Figure 6), The concentration ratio is ratio between 643 the weak and the strong concentration values, = ∕ ; while the PN ratio is = ∕ .

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We defined the coding error as the square relative distance between the ratio of the PN activity 645 and the ratio of the odorant concentrations. The relative distance is therefore: (( − )∕( + )) 2 .

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Spike density function Firing rates were obtained from the convolution of the spike trains with . 650 The model was simulated with custom Python code, as well as the analysis of the simulations.

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All code is publicly available on github, https://github.com/mariopan/flynose. Linster C, Smith BH. A computational model of the response of honey bee antennal lobe circuitry to odor mix-