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Conceived and designed the experiments: CA MS MB. Performed the experiments: CA MB. Analyzed the data: CA MB. Wrote the paper: CA MS MB.

The authors have declared that no competing interests exist.

Neurons in the insect antennal lobe represent odors as spatiotemporal patterns of activity that unfold over multiple time scales. As these patterns unspool they decrease the overlap between odor representations and thereby increase the ability of the olfactory system to discriminate odors. Using a realistic model of the insect antennal lobe we examined two competing components of this process –lateral excitation from local excitatory interneurons, and slow inhibition from local inhibitory interneurons. We found that lateral excitation amplified differences between representations of similar odors by recruiting projection neurons that did not receive direct input from olfactory receptors. However, this increased sensitivity also amplified noisy variations in input and compromised the ability of the system to respond reliably to multiple presentations of the same odor. Slow inhibition curtailed the spread of projection neuron activity and increased response reliability. These competing influences must be finely balanced in order to decorrelate odor representations.

The antennal lobe of insects and the olfactory bulb of vertebrates represent the first centers of the olfactory system where information about odor properties can be reorganized and optimized for further processing. Complex excitatory and inhibitory synaptic interactions within the antennal lobe and the olfactory bulb alter the responses of the principal neurons throughout the duration of the odor stimulation. These dynamic changes progressively increase the difference between firing patterns evoked by structurally similar odors, potentially helping the animal distinguish one odor from another. However, this process, called odor decorrelation, appears to oppose another important goal of olfactory processing, to minimize the inevitable noisy variations in representations of the same odor encountered under different environmental conditions; such variations could potentially lead to misclassification. It remains an interesting mystery how olfactory circuitry can solve these two seemingly contradictory goals as they process olfactory stimuli: first, separating different but chemically similar odors (sensitivity, capacity); and second, identifying representations of the same odor in a noisy environment (reliability). Our results suggest a balance between inhibitory and excitatory connections mediated by local antennal lobe interneurons enhances the decorrelation of similar odors while keeping the representation robust in the presence of noise.

The olfactory system must accomplish two seemingly conflicting goals —generate distinct representations of different odors, yet maintain stable representations of a repeated odor despite variability introduced by noise. These conflicting ends, separability and reliability, are met as information about odors traverses multiple levels of the olfactory system.

Odor detection begins when odorant molecules bind to olfactory receptor neurons (ORNs) and initiate cellular mechanisms leading to the opening of ion channels, the depolarization of the receptor neuron cell membrane, and the generation of action potentials

Antennal lobe neurons respond to odor-elicited input with a rich variety of spatiotemporal patterns

What network interactions shape spatio temporal patterning in the AL to accomplish essentially opposed information processing goals: that representations of different odors may be rapidly distinguished; yet the same odor presented under changing environmental circumstances is reliably identified? To address this question we examined the contributions of two factors in a realistic model of the locust AL

In the insect olfactory system input from ORNs converges into PNs and LNs of the AL. With a model of the AL network we sought to test the complementary effects of fast lateral excitation and slow inhibition, both of which have been observed

To test the network's responses to external input we simulated two classes of odor stimuli: odors represented by blue traces in

We reasoned that unrestricted lateral excitation within the AL could potentially recruit neurons explosively, and we hypothesized that slow inhibition (mediated by GABA_{B} receptors) could provide both a suitable counterbalance to this, and an ability to generate broadly distributed, temporally structured responses in the PN ensemble. Indeed, our simulations showed that a balance of lateral excitation and slow inhibition prevented cascading excitation that could recruit all neurons in the network, and at the same time allowed some neurons that receive sub–threshold input directly from ORNs to become activated (_{A} receptors was present in all the simulations including those in which slow inhibition was removed (_{B} mediated slow inhibition. To visualize these population-wide responses, we calculated the peri–stimulus time histogram (PSTH) for each PN and projected the collective dynamics of the model's three hundred PNs onto the first three principal components (

Next, to characterize each PN's tuning properties we simulated a broad range of odors by successively displacing the Gaussian input (

Further, we analyzed the roles lateral excitation and slow inhibition play to shape the complexity of spatiotemporal responses of PNs to an odor presentation. We first determined each PN's response to a panel of 21 odors (similar to each panel in

Decorrelation of odor representations, a process that reduces the overlap between odors, occurs over the duration of the stimulus presentation. Network interactions between PNs and LNs likely play a crucial role in this process. In this study AL neurons received a stable pattern of input from the ORNs. If the AL neurons respond to this input by generating a spatially distributed but static pattern of activation, then the pattern should not decorrelate over time. Decorrelation over time is only possible if the odor representation is transformed either by network interactions or by temporally varying noise.

To determine the degree to which noise can play a role in transforming the odor representation, we first calculated the correlation coefficient between the onset and subsequent epochs of the input vector provided to the PNs (

Next, we sought to characterize the ability of the population of PNs to differentiate among different odors. We presented a set of 21 odors and calculated the correlation between the responses of PNs to any two odors over time. Together, the correlation coefficients for each 50 ms time window formed a 21×21 matrix. To analyze the AL mechanism responsible for this decorrelation we then calculated the change over time in the correlation coefficient averaged for all similar and, separately, for all dissimilar odors, as a function of increasing amounts of lateral excitation and slow inhibition (

For similar odors we found that increasing the amount of lateral excitation lead to a decrease in the correlation between odor responses at a given time (

The correlation coefficient (see analysis in

To determine effect of the ratio of excitation to inhibition

To determine whether the correlation coefficient reflected a similar trend, for each value of lateral excitation and slow inhibition we calculated the correlation coefficient between 300–dimensional PN activity vectors generated as the network responded to the two similar odors independently. The correlation coefficients were determined during 50 ms epochs of time and the resulting time series were then plotted in increasing order of the E/I ratio (

Animals are able to recognize an odor reliably each time it is presented despite the inevitable small variations in each presentation. Thus, our model of the olfactory system should be robust enough to avoid classifying each encounter with a given odor as unique. Correlations between the activity of PNs generated by one odor and that of another odor provide a measure of how well their representations may be distinguished by follower neurons. The olfactory system should therefore maximize correlations between multiple presentations of an odor while simultaneously minimizing correlations between representations of different odors. We found this could be achieved in our model with a balance of lateral excitation and slow inhibition. In

We could readily achieve such a balance by maximizing the quantity (C_{trials}+(1−C_{odors})) where C_{trials} is the correlation between multiple presentations of the same odor and C_{odors} is the correlation between the representations of different odors (see _{trials} and C_{odors} differed in magnitude. These differences implied that the term (C_{trials}+(1−C_{odors})) was not uniform across the parameter space queried. Increasing the strength of both excitatory and slow inhibitory AL connections decreased correlations between trials (C_{trials}; _{odors}. The latter corresponded to a rapid increase in the “anti-correlation” parameter (1_{odors}; _{trials}+(1−C_{odors})) increased (_{trials} decreased faster than (1−C_{odors}) increased), so the term (C_{trials}+(1−C_{odors})) decreased (_{trials} is found for positive values of

The primary reason to compare the correlation between multiple presentations of the same odor versus correlations between similar odors was to understand the network mechanisms that enhance odor classification. In this section we examine how well a simple classification algorithm could differentiate similar odors despite realistic, noisy variations between multiple presentations of the same odor. The correlation between representations of the odor provides a useful metric of distance between representations. _{trials}+(1−C_{odors}) used in the previous section (see _{trials}+(1−C_{odors}) were high (_{trials}+(1−C_{odors}) was low. Consistent with the correlation analysis (_{trials}+(1−C_{odors}). However, a qualitative demarcation between regions of high and low error rates could be inferred from C_{trials}+(1−C_{odors}).

In insects, tens of thousands of ORNs converge onto a few hundred excitatory PNs and local inhibitory neurons in the AL

Excitatory interneurons (eLNs) have recently been described in the

We tested the hypothesis that both lateral excitatory and slow inhibitory connections, in proper balance, are required to achieve two apparently opposing goals during the processing the olfactory stimuli: to separate different but chemically similar odors (sensitivity, capacity) and to identify repeated instances of the same odor in a noisy environment (reliability).

We found that lateral excitation improves the sensitivity of the olfactory system by recruiting additional PNs that do not receive direct input from ORNs, thereby amplifying differences between the representations of similar odors

ORNs are preferentially sensitive to some odors. This preference is manifest in the non-uniform firing rate distribution of ORNs with a high peak at low frequencies and a long tail over high frequencies

In our simulations we focused on the role network interactions play in decorrelating odor representations. Another contributor to the temporal patterning in the AL driving decorrelation appears to be the response dynamics of olfactory receptor neurons. Recent studies have characterized the temporal responses of ORNs by their response latency, rise time and adaptation to a prolonged odor presentation. Variations in these temporal properties, while not causing decorrelation in the responses of the ORNs themselves

Our study suggests local excitatory and inhibitory interneurons of the insect AL provide balanced, functional circuitry that significantly reformats and optimizes odor representations in the AL network. While the effects of excitation and inhibition would cancel each other if averaged across the entire population of AL neurons, heterogeneous interconnectivity among the lobe's neurons would allow a given receptor to trigger responses dominated by inhibition in some PNs and by excitation in others. The combined effect of excitation and inhibition may provide an improved representation of the identity of an odor by being both robust against noise and sensitive to relatively small variations in the identities of active ORNs.

The model network simulations were based on a realistic and robust model of the insect AL

Individual projection and local inhibitory interneurons were modeled by a single compartment that included voltage and Ca^{2+} dependent currents described by Hodgkin–Huxley kinetics. Consistent with locust physiology, isolated PNs displayed overshooting Na^{+} spikes at a fixed frequency throughout DC stimulation, and local inhibitory neurons, by contrast, fired low amplitude Ca^{2+} spikes and displayed spike frequency adaptation caused by Ca^{2+}–dependent potassium currents. A separate population of excitatory local interneurons with properties identical to the PNs was also simulated. The model AL network consisted of 300 PNs, 100 local inhibitory interneurons (LNs) and 50 local excitatory interneurons (eLNs) (

Fast GABAergic (LN–PN, LN–eLN, and LN–LN connections) and nicotinic cholinergic synaptic currents (PN–LN, PN–eLN, eLN–LN) were modeled by first order activation schemes. Connection probabilities were as follows. P(PN–eLN) = 0.5, P(eLN–PN) = 0.1, P(PN–LN) = 0.5, P(LN–LN) = 0.5, P(LN–PN) = 0.5, P(eLN–LN) = 0.5, P(LN–eLN) = 0.5. These probabilities are constrained by estimates made from locust AL circuits _{A} type and slow GABA_{B} type inhibitory lateral inputs from 25–50% of the remaining LNs _{A}type and slow GABA_{B}type inhibitory lateral inputs from 75% of the LNs (G.Laurent, personal communication). Probabilities of eLNs connections are presently unknown, however, varying their connection probability in our model produced effects similar to varying the number of eLNs (see above).

The AL network was simulated for a range of values of lateral excitation and slow inhibition. The maximal conductance denoting the total lateral excitation received by a given cell was set to a value ranging from _{B} type receptors was set to values ranging from

The distribution of intensities provided to the PNs followed a Gaussian profile (

The time course of the stimulus was modeled as a current pulse with a rise time constant of 100 ms and a decay time constant of 200 ms. This was scaled by the factor _{PN} and was used to drive individual PNs.

Different odors were generated by progressively shifting the Gaussian input profile by5 unit steps. Similar odors were defined as odors with input profiles shifted by 5 units; dissimilar odors were shifted by 40 units (

To calculate all measures of correlation we first generated a PSTH for individual neurons by determining the number of spikes produced by each neuron in consecutive 50 ms time bins that overlapped over 25 ms durations. The activity of the population of PNs (^{th}^{th}^{th}^{th}

We then evaluated the correlation between multiple trials (

For each (_{odors}. Similarly, we calculated a matrix for the mean correlation between multiple trials of the same odor C_{trials}. We then obtained the optimal value of _{trials}+(1−C_{odors}). The use of correlation coefficient over the Euclidean distance is preferred for this analysis as the correlation coefficient is already normalized between −1 and 1.

We performed the clustering analysis using the Matlab Statistics Toolbox. To cluster odor representations we first defined a distance between the spatiotemporal patterns generated in response to two odor stimulations. The two responses (_{ij} = 1−c_{ij}_{ij}_{ij}_{ij}_{err1}_{err2}_{err} = min(N_{err1}, N_{err2})_{err}/N_{total}_{total}

The authors would like to thank Prof. Gilles Laurent for many stimulating discussions and insightful suggestions.