M Sautreuil
email: sautreuil@g2elab.inpg.fr

N Retière
email: retiere@g2elab.inpg.fr

D Riu
email: riu@g2elab.inpg.fr

O Sename

A Generic Method for Robust Performance Analysis of Aircraft DC Power Systems

The recent evolution of aircraft power networks makes new design study necessary for solving key issues such as optimal efficiency, reliability, adaptability and performances. Indeed, DC power systems are subject to strong dynamic interactions between the source and the loads. In this paper, the need for a new design method of the power network is explained, and the authors propose to use a robust performance analysis method. The first main result concerns the analysis of the robustness of a classical aircraft DC source where the parameters of the DC bus are unknown. The second one shows the efficiency of the method to evaluate the potential gain in weight from a change in the performance specifications at the system level.

I. INTRODUCTION

At the end of the 19 th century, DC electrical systems were progressively replaced by AC distribution for flexibility reasons. With the development of power electronics and the generalization of electricity as an energetic vector, DC power systems are getting more and more used. Then, reactive energy management is not anymore necessary and AC/DC conversion stages are suppressed. This allows improvements in system efficiency, reliability and maintenance costs [START_REF] Ciezki | Selection and Stability issues Associated with a Navy Shipboard DC Zonal Electric Distribution System[END_REF][START_REF] Emadi | Aircraft Power systems: Technology, State of the Art, and Future Trends[END_REF]. Typical applications of DC systems include telecommunications, ships, spacecrafts and "More Electric" vehicles [START_REF] Ciezki | Selection and Stability issues Associated with a Navy Shipboard DC Zonal Electric Distribution System[END_REF][START_REF] Ehsani | On board Power Management[END_REF][START_REF] Nord | Voltage Stability in an Electric Propulsion for Ships[END_REF][START_REF] Suntio | Input Invariance as a Method to Reduce EMI Filter Interactions in Telecom DPS Systems[END_REF]. For aircraft applications, the power distribution is moving from 400Hz/115VAC to HVDC. European aircraft manufacturers initiated this change with the "Power Optimized Aircraft" European project [START_REF] Barruel | Stability Approach for Vehicles DC Power Network: Application to Aircraft On-board System[END_REF] followed by the current "More Open Electrical Technologies" project. The work presented in this paper is part of the latter.

MOET project [START_REF]More Open Electrical Technologies (MOET) project web site[END_REF] is focused on several aspects. One is the standardization of power electronics devices for aircraft applications. A second one is the integration of these devices in the power system. A classical approach for subsystems integration is to impose strict standards to the devices suppliers in order to guarantee that performance requirements will be met at the system level. The standards at the system level for aircraft DC networks are given in Fig. 1. They are generally defined by the aircraft manufacturer. If these standards are not respected when the integration is carried out, some of the devices should be re-designed by their suppliers. This may lead to a long design process, especially for a DC network design where dynamic interactions between the source and the loads may be strong [START_REF] Emadi | Aircraft Power systems: Technology, State of the Art, and Future Trends[END_REF]. It is a crucial point because the aircraft development program can be delayed, which could be very costly for the aircraft manufacturer. The authors propose to solve this point by a new approach based on robustness. It means that the devices will be designed so that they could withstand changes in their operating environment once integrated with minimal loss of performance. Only dynamic performances will be addressed in this paper even if energetic or harmonic issues could certainly be included in a general robustness approach. .

Another key design issue is that devices are designed for given performance requirements at the system level (Fig. 1). The question is then to know if the standards are suitable for the system optimization. In the case of "More Electric" aircrafts, the optimization addresses the issue of reducing the weight. The authors will show that the robustness indicators could be used for that purpose.

The robust performance analysis performed in this article will be applied to a DC power channel described in section II. In section III, the linear models necessary for the analysis are developed using a simple identification-based approach. Section IV explains the robust performance analysis from a theoretical point of view and its application to the studied power channel [START_REF] Doyle | Feedback Control Theory[END_REF]. In section V, the authors focus on the design results which can be achieved by the analysis. A particular attention will be paid to the influence of the source control. In section VI, the robust performance analysis is shown to be efficient for giving indicators to the network designer for the optimization of the system weight.

II. POWER CHANNEL DESCRIPTION

The DC power channel is constituted by (Fig. 2):

-a wounded rotor alternator which provides the energy to the power channel. The speed loop is The alternator excitation voltage is regulated through a PI controller (Fig. 3) and the stator frequency is assumed to be maintained at 400Hz. The generator supplies a nine phase autotransformer connected to three diode bridges. It is a classical structure for aircraft applications. The interphase inductors limit circulation currents between the rectifiers. The nominal voltage on the DC side is 540Vdc for a 60kW load. The speed control loop of the PMSM (Fig. 4) is assumed to be ideal. Then, the AC side variables have a constant frequency (1000Hz) and the machine can be modeled by its equivalent (R,L,E) model (constant flux and electrical pulsation). The measured currents (Fig. 4) are controlled with a PI resonant controller, tuned at 1000Hz. A 20 kHz -Pulse Width Modulator delivers the commutation orders to the switches of the inverter.

III. SMALL SIGNAL MODELING OF THE POWER CHANNEL

A Saber model of the power channel has been implemented. It will be used as a reference, in particular to obtain and validate the small-signal modeling required by the robust performance analysis.

A. Source and load modeling

Source and load are modeled using a frequency domain identification approach. The main advantage of this approach is its simplicity. It enables to identify the average behavior of the state variables. The models are then valid only for frequencies lower than half of the switching frequencies of the power electronic converters. To perform this frequency domain identification, a variable-frequency and small-signal sinus excitation is injected at the input of the load and at the output of the source. Before this injection, both load and source were operating at their steady-state nominal point. Resulting current and voltage are finally measured to compute the impedance over a large range of frequencies.

Load modeling

Fig. 5 shows that the MCU input gain and phase are constant for frequencies lower than half of the PWM frequency (10 kHz). Because phase is -180deg, it is a negative resistance behavior. For small-signal excitation the MCU load can then be identified as a constant power load.

Source modeling

The source (alternator + ATRU) is identified in two cases:

-case 1: the alternator is assumed to be ideally controlled. It means the AC voltage is assumed to be maintained at its nominal value. This case gives then the best performances achievable by any AC source control. In the next sections, this study case is called "ideal control" case. -case 2: the generator PI control is taken into account. Fig. 6 shows the identification results when an ideal AC source is considered (case 1). The ATRU is fed by a 400Hz source, then the switching frequency of the diodes is fc = 18*400 = 7,2kHz. For frequencies lower than fc/2, Fig. 3 clearly shows that the model of the ATRU can be identified by a (Rs,Ls) impedance:

ω ω jLs Rs j Z + = ) ( (1)
Fig. 6: Frequency domain identification of the ATRU output impedance when supplied by an ideal AC source Fig. 7 shows the identification results when the control loop is taken into account (case 2). It is shown that the source output impedance can be identified by:

ω ω ω ω ω ξ ω j T j j K j Z ⋅ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + ⋅ = 1 2 1 ) ( 2 0 0 ( 2 )

B. Power channel modeling

The small-signal equivalent network is then found to be: The model parameters are summed up in Table I.

C. Validation by time domain simulation

To validate the small-signal modeling and the identification procedure, a power step is applied to the mechanical load driven by the MCU. Results given by the small signal model and SABER time-domain simulations of the power channel are compared. In Fig. 9, the voltage at Point of Regulation (POR) after a +5% load step is plotted when the alternator is assumed to be an ideal AC source. The same comparison is shown in Fig. 10 when the control loop of the generator is taken into account. In both cases, the small signal models exhibit a good approximation of the time domain simulation. IV. ROBUST PERFORMANCE ANALYSIS

A. Background

Robustness methods allow the analysis of stability and performance of uncertain systems [START_REF] Skogestad | Multivariable Feedback Control: Analysis and Design[END_REF]. The first step is the uncertainties description. Uncertainties are assumed to be norm-bounded around their nominal values and can be classified into two main categories: structured and unstructured uncertainties. Unstructured uncertainties are used to represent unmodeled or neglected dynamics, highfrequency dynamics or time delays for example. Structured uncertainties are parametric uncertainties. They are either complex or real.

An uncertain parameter U is written by: ( )

U unc nom p U U δ + ⋅ = 1 (3)
with: U nom the nominal value of U p unc the relative uncertainty on U

δ U such that 1 ≤ U δ .
For a MIMO system, a block-diagonal matrix diagram is used for the system representation as shown in Fig. 11. The block diagonal matrix Δi includes the uncertainties. Parametric uncertainties are given by the terms {δ n+1 ;… ; δ n+m }. Unstructured ones are the p independent full-blocks matrices {Δ n+m+1 , Δ n+m+2 ,…Δ n+m+p }. The following matrix representation is then obtained. P CL is the system closed-loop matrix (Fig. 11): Once the uncertainties are modeled, the desired performance levels have to be fixed. This is done using weighting functions, for example defined as [START_REF] Skogestad | Multivariable Feedback Control: Analysis and Design[END_REF]:

k b b w s w Ms s s Wperf ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ + + = ε . ) ( (4)
with: ε low frequency performance specification Ms high frequency performance specification w b desired cut-off frequency.

The n weighting functions are defined for each of the input/output pairs and are linked to n complex fictive uncertainties {Δf 1 , Δf 2 ,… Δf n } (Fig. 12). This Δf block is connected to the Δi one to build the Δ matrix. The so-called (N, Δ) representation of the uncertain system is finally obtained, in which the outputs o wj of the system are the outputs of Fig. 11, weighted by the Wperf functions. The structured singular value μ Δ (M(jw) defined below allows evaluating the nominal stability (NS), nominal performance (NP), robust stability (RS) and robust performance (RP) of the closed-loop system [START_REF] Skogestad | Multivariable Feedback Control: Analysis and Design[END_REF][START_REF] Doyle | Feedback Control Theory[END_REF]:

( ) ( ) ( ) ( ) (
)

0 det / min 1 max = Δ - Δ = Δ Δ M I jw M σ μ (5)
Δ is a stable LTI block-diagonal matrix and σ max the maximum singular value. NS, NP, RS and RP are then solved following the conditions listed below:

⇔ NS N(s) is internally stable (6) ⇔ NP ( ) ( ) 1 22 < ∀ Δ ω μ ω j N f and NS (7) ⇔ RS ( ) ( ) 1 11 < ∀ Δ ω μ ω j N i and NS (8) ⇔ RP ( ) ( ) 1 < ∀ Δ ω μ ω j N
and NS [START_REF] Doyle | Feedback Control Theory[END_REF] Note that for a given Δ structure, exact μ calculation is not possible and a classical approach consists in approximating μ by lower and upper bounds [START_REF] Skogestad | Multivariable Feedback Control: Analysis and Design[END_REF].

B. Application to the power channel

In the following sections, the robust performance analysis is applied to the power channel. Before presenting the applications developed in section V and VI, the input/output pairs of the system are chosen, the uncertainties are detailed, and the performance specification is explained.

Selection of the Input / Output pairs

The main objective is to respect the transient envelop given in Fig. 2. It means that the DC voltage should not exceed the

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ Δ Δ = Δ + + + + + + p m n m n m n n s i 1 1 ) ( δ δ PCL(s) uΔ yΔ i 1 i n o 1 o n ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ Δ Δ Δ Δ = Δ + + + + + + p m n m n m n n n f f s 1 1 1 ) ( δ δ uΔ yΔ i 1 i n o 1 o n Wperf 1 Wperf n Δf Δi P CL (s) N(s) N 11 (s) i 1 i n N 12 (s) N 21 (s) N 22 (s) o w1 o wn Δ(s)= Δf(s) Δi(s)
o wn o w1 yΔ uΔ limits given by the standards during load steps. For that purpose and using the notations of Fig. 11 and Fig. 12, only one input i 1 (the load power step ΔP) and one output o 1 (the resulting voltage response ΔV dc,por ) are considered.

Uncertainties description

In the next sections, only real parametric uncertainties on the DC filter parameters are studied. The supposed nominal values are given in Table I. As shown in section V the uncertainties will be fixed to 40% on all the DC filter parameters.

Performance specification

In the time domain, the system performances can be assessed in terms of response time, static error, overshoot and damping. By limiting the maximal gain in the frequency domain, the damping of the time response is improved. The cut-off frequency in the frequency domain tunes the desired response time. This way, equivalencies between desired time domain performances and frequency domain specifications are made (Fig. 13). But this is just an approximation because it is not possible to translate exactly the performances given in Fig. 2, defined for any load step value, into small-signal frequency performances. However, by imposing suitable small-signal performances, large-signal standards can be guaranteed.

V. PERFORMANCE ANALYSIS OF A DEVICE CONNECTED TO AN UNKNOWN NETWORK

The connection of the source to an unknown network is studied in this section. When designing the source, the supplier does not know the exact values of the power channel parameters. He only knows a supposed nominal value and the parametric uncertainty bounds around this value for all the power channel parameters (DC filter, cables and loads). Similarly, load suppliers do not know the power channel. We will show that a robust performance analysis will enable the designers to respect the standards imposed at the system level by the aircraft manufacturer whatever the power channel parameters values are. Robust performance is first studied when the AC source is assumed to be ideally regulated. Then, the influence of the control loops on devices interactions will be investigated. In this paper, the uncertainties are related to the DC filter. The nominal values are given in Table I and the uncertainty value is 40% for each parameter.

A. Performance analysis with ideal control loops

The question is to know whether the system is robust (from a performance point of view) to the modelled parametric uncertainties or not. When the generator is considered as being an ideal 3-phase source (Fig. 6 and (1)), the structured singular value bounds are given in Fig. 14: At low frequencies, the μ calculation is independent of the parametric uncertainty level because the filter parameters are influent only about the cut-off frequency of the filter. That means that any parametric uncertainty value would lead to the same value of μ <1 at low frequencies. Then, only the frequency domain defined by w>100rad/s will be studied (non shaded zone in Fig. 14). Outside this domain, the maximum value of the μ upper bound is 0,86. This ensures that the condition of ( 9) is verified and the system performances are guaranteed for any combination of the parameters values inside the parameter space defined by the 40% uncertainty set.

B. Performance analysis with non-ideal control loops

The same procedure is now applied to the case of non-ideal voltage control loops. That means that the generator is no more considered as being an ideal voltage source and the source model is given by (2) and Fig. 7. A deterioration of the system performances is expected because the generator voltage is no more ideally controlled. The maximum value of the μ upper bound is 0,94>0,86 outside the shaded zone. This means that the performances may be deteriorated, by comparison with the ideal control loop case. But it is not as critical as it could have been expected. Indeed, couplings between the AC source control and the DC bus dynamics are not strong. This can be explained by the presence of the ATRU which decouples the AC source and the DC bus. Indeed, this device is highly inductive because of the autotransformer. If the system was not found to be robust in this study case, it would have been necessary to come back over the source control and calculate a more robust controller. As a conclusion, these results show the effectiveness of the method for analysis and design of a source feeding an unknown network.

VI. INFLUENCE OF REQUIRED PERFORMANCES ON WEIGHT

The influence of the standard on the acceptable uncertainty size is now studied. This size is now considered as being a design margin. The higher this design margin is, the higher the margins are for optimizing the system weight. For illustrating the links between standards and design margins, the non-ideal source model will be considered.

A. Influence of the required response time

The required response time is tuned by the cut-off frequency of the weighting function. The higher it is, the faster the time-domain response is. Hence, a constant Ms' factor is considered and wc is variable (Fig. 13). For each wc value, the design margin is calculated. The results are given in Fig. 16. It clearly shows that requiring a cut-off frequency of more than wcm = 2*24840 rad/s (time faster than 20ms) leads to a decrease in design margin. But for wc<wcm the design margins are not increased, which means that degrading the performances of the system may not lead to a gain in weight. These results show that there exists a optimal compromise between response time of the system and its design margins.

B. Influence of the required overshoot factor

A similar compromise can be seen from Fig. 17 for the overshoot factor. It is tuned by the Ms' factor and the lower Ms' is, the lower the design margins are. It means that a system with low overshoots is potentially heavier than a system which tolerates high overshoots.

C. Conclusion: influence of required performance on weight

Both previous analyses show that a compromise has to be made between potential weight decrease and performances: deteriorating the required performances does not always mean a gain in the electrical system weight. Even if this study can not be directly used for the definition of HVDC systems standards, it proves the efficiency of robust performance analysis to help the designer for a system level optimization.

VII. CONCLUSION

In this paper, a robust performance analysis method was described and applied to an aircraft DC power channel. This method was shown to be efficient to solve two key design issues of HVDC networks. The first one was to estimate the robustness of a device before its integration in the network. This integration should be made easier by imposing the source and loads suppliers to be robust to DC network parametric uncertainties. This solution should improve the pre-design phase. Second, the same tool can be used to estimate the design margins towards the required performances. High design margins may allow the designer to optimize the system in terms of weight. The first main prospect of this paper is a method to design and optimize the devices and their control loops to guarantee robust performances while minimizing weight. The authors will focus on optimal robust control techniques in future publications. The second one is to use "robust" standards. This may mean less restrictive norms from a nominal performance point of view, to get larger margins for the system optimization. The standards should also impose "robust" criteria specified by the aircraft manufacturer to guarantee an adequate dynamical behavior at the system level.

Fig. 1 :

 1 Fig. 1: Assigned transient envelop after a load step at Point Of Regulation (POR)

Fig. 2 :

 2 Fig. 2: Power channel description

Fig. 3 :

 3 Fig. 3: Detailed source structure

Fig. 4 :

 4 Fig. 4: Detailed load structure

Fig. 5 :

 5 Fig. 5: Frequency domain identification of the 60kW MCU

Fig. 7 :

 7 Fig. 7: Frequency domain identification for the ATRU output impedance with non-ideal control loop for the alternator

Fig. 8 :

 8 Fig. 8: Small Signal model of the power channel

Fig. 9 :

 9 Fig. 9: Time domain validation of the small signal model (Ideal AC source)

Fig. 11 :

 11 Fig. 11: Matrix representation of the uncertain system

Fig. 12 :

 12 Fig. 12: Matrix representation for Robust Performance Analysis

Fig. 13 :

 13 Fig. 13: Template for the transfer function ΔVdc/ΔP 1/Wperf

Fig. 14 :

 14 Fig. 14: μ lower and upper bounds for ideal AC source control

Fig. 15 :

 15 Fig. 15: μ lower and upper bounds for non-ideal AC source control

Fig. 16 :

 16 Fig. 16: design margin vs. cut-off frequency of the weighting function

Fig. 17 :

 17 Fig. 17: design margins vs. Ms' factor of the weighting function

  24840 rad/s)

ACKNOWLEDGMENT

This research is being conducted in the frame of the MOET project, a FP6 European Integrated Project. The authors would like to thank MOET partners for model parameters and on board structure definition.


Claire Meissner-Bernard

Yulia Dembitskaya

Laurent Venance

Alexander Fleischmann
email: alexander_fleischmann@brown.edu

Encoding of odor fear memories in the mouse olfactory cortex

Odor memories are exceptionally robust and essential for animal survival. The olfactory (piriform) cortex has long been hypothesized to encode odor memories, yet the cellular substrates for olfactory learning and memory remain unknown. Here, using intersectional, cFos-based genetic manipulations ("Fos-tagging"), we show that olfactory fear conditioning activates sparse and distributed ensembles of neurons in mouse piriform cortex. We demonstrate that chemogenetic silencing of these Fostagged piriform ensembles selectively interferes with odor fear memory retrieval, but does not compromise basic odor detection and discrimination. Furthermore, chemogenetic reactivation of piriform neurons that were Fos-tagged during olfactory fear conditioning causes a decrease in exploratory behavior, mimicking odor-evoked fear memory recall. Together, our experiments identify specific ensembles of piriform neurons as critical components of an olfactory fear memory trace.

Introduction

Odor perception and behavioral responses to odors strongly depend on experience, and learned odor-context associations often last for the lifetime of an animal [START_REF] Mouly | Memory and Plasticity in the Olfactory System: From Infancy to Adulthood[END_REF]. The cellular and neural circuit mechanisms underlying olfactory learning and memory, however, remain poorly understood. Recent studies on episodic and contextual learning in hippocampus and cortex have suggested that memories are encoded in distributed ensembles of neurons, often referred to as a 'memory trace' or 'engram' [START_REF] Mayford | Exploring Memory Representations with Activity-Based Genetics[END_REF][START_REF] Tonegawa | Memory engram storage and retrieval[END_REF]. These engram cells are thought to store information about the environmental context and associated emotions of past experiences, and their activity is necessary and sufficient for memory recall [START_REF] Liu | Optogenetic stimulation of a hippocampal engram activates fear memory recall[END_REF][START_REF] Reijmers | Localization of a Stable Neural Correlate of Associative Memory[END_REF][START_REF] Tanaka | Cortical representations are reinstated by the hippocampus during memory retrieval[END_REF].

Here, we investigate the organization of odor memories in the olfactory (piriform) cortex of mice. The piriform cortex (PCx), a trilaminar paleocortical structure, is the largest cortical area receiving direct afferent inputs from the olfactory bulb, which, in turn, receives topographically organized inputs from olfactory sensory neurons in the nose. Individual piriform neurons respond to combinatorial inputs from multiple olfactory bulb projection neurons [START_REF] Apicella | Pyramidal cells in piriform cortex receive convergent input from distinct olfactory bulb glomeruli[END_REF][START_REF] Davison | Neural circuit mechanisms for pattern detection and feature combination in olfactory cortex[END_REF], suggesting that odor objects are constructed in PCx from the molecular features of odorants extracted in the periphery [START_REF] Wilson | Cortical processing of odor objects[END_REF]. PCx has long been hypothesized to support auto-associative network functions that can retrieve previously learned information from partial or degraded sensory inputs [START_REF] Haberly | Parallel-distributed processing in olfactory cortex: new insights from morphological and physiological analysis of neuronal circuitry[END_REF][START_REF] Wilson | Cortical processing of odor objects[END_REF]. Piriform pyramidal cells form a large recurrent network, which is reciprocally connected with high-order associative areas including the prefrontal, entorhinal and perirhinal cortex, and the amygdala [START_REF] Johnson | New features of connectivity in piriform cortex visualized by intracellular injection of pyramidal cells suggest that "primary" olfactory cortex functions like "association" cortex in other sensory systems[END_REF][START_REF] Sadrian | Optogenetic Stimulation of Lateral Amygdala Input to Posterior Piriform Cortex Modulates Single-Unit and Ensemble Odor Processing[END_REF]. Storage of information is made possible by NMDA-dependent, associative plasticity of connections [START_REF] Johenning | Dendritic compartment and neuronal output mode determine pathway-specific long-term potentiation in the piriform cortex[END_REF][START_REF] Kanter | NMDA-dependent induction of long-term potentiation in afferent and association fiber systems of piriform cortex in vitro[END_REF][START_REF] Quinlan | A molecular mechanism for stabilization of learning-induced synaptic modifications[END_REF]. Furthermore, changes in piriform network activity [START_REF] Chapuis | Bidirectional plasticity of cortical pattern recognition and behavioral sensory acuity[END_REF][START_REF] Chen | Generalized vs. stimulusspecific learned fear differentially modifies stimulus encoding in primary sensory cortex of awake rats[END_REF][START_REF] Sevelinges | Olfactory fear conditioning induces field potential potentiation in rat olfactory cortex and amygdala[END_REF] and stabilization of odor representations [START_REF] Shakhawat | Arc-Expressing Neuronal Ensembles Supporting Pattern Separation Require Adrenergic Activity in Anterior Piriform Cortex: An Exploration of Neural Constraints on Learning[END_REF] have been observed after associative olfactory learning. Finally, excitotoxic lesions of the posterior PCx in rats perturb odor fear memories [START_REF] Sacco | Role of secondary sensory cortices in emotional memory storage and retrieval in rats[END_REF], and optogenetic stimulation of artificial piriform ensembles is sufficient to drive learned behaviors [START_REF] Choi | Driving opposing behaviors with ensembles of piriform neurons[END_REF].

Taken together, these studies have led to the hypothesis that piriform neural ensembles encode olfactory memory traces.

We have adapted an intersectional genetic strategy to target components of odor fear memories in the PCx. We combined cFos-tTA transgenic mice [START_REF] Garner | Generation of a synthetic memory trace[END_REF], in which the tTA transcription factor is expressed under the promoter of the immediate early gene cFos, with virally targeted expression of tTA-responsive fluorescent reporters and regulators of neural activity [START_REF] Alexander | Remote Control of Neuronal Activity in Transgenic Mice Expressing Evolved G Protein-Coupled Receptors[END_REF][START_REF] Ferguson | Transient neuronal inhibition reveals opposing roles of indirect and direct pathways in sensitization[END_REF][START_REF] Zhang | Neuronal ensembles sufficient for recovery sleep and the sedative actions of α2 adrenergic agonists[END_REF]. This approach allows us to selectively and persistently "Fos-tag" piriform neurons that were activated during olfactory fear conditioning. We then tested the behavioral consequences of manipulating such Fostagged piriform ensembles during memory recall. We find that chemogenetic silencing of Fos-tagged piriform ensembles interferes with a learned odor escape behavior. In contrast, silencing piriform neurons Fos-tagged during presentation of a neutral odor only partially attenuates odor fear memory recall, suggesting that memory impairments are largely specific to the piriform ensemble that is Fos-tagged during learning. Finally, artificial reactivation of Fos-tagged piriform neurons elicits behavioral changes consistent with memory recall. Together, our results suggest that piriform neural ensembles encode an essential component of olfactory fear memories.

Results

Behavioral expression of odor fear memory depends on the retrieval context

We used classical conditioning to train mice to associate an odor with foot shock (the reinforced conditioned stimulus, CS+) [START_REF] Choi | Driving opposing behaviors with ensembles of piriform neurons[END_REF]. Training occurred in a rectangular box with odor ports at each extremity. Brief odor stimuli (7 s) were presented on randomly alternating sides when mice were close to the odor port. The CS+ (ethyl acetate) was paired with a foot shock, applied to the side of the box where the odor was delivered.

Mice escaped from the foot shock by running towards the opposite side of the box (see Methods and Figure 1A). Two control odors, whose presentation was not paired with foot shock (non-reinforced stimuli, CS-), were used to entrain specific as opposed to generalized fear responses to odors [START_REF] Chen | Generalized vs. stimulusspecific learned fear differentially modifies stimulus encoding in primary sensory cortex of awake rats[END_REF]. Memory retrieval of cFos-tTA transgenic mice (n=9) was first tested by presenting the odors alone in a similar context as during conditioning: same stimulus duration and a testing box with the same dimensions as the training box but with a different texture and color (see Methods). We combined two parameters to quantify the learned escape behavior: the position of the mouse in the box and the increase in its maximum velocity after odor presentation (Figure 1B). These parameters were chosen because they described well the behavioral response of mice to the odor-foot shock pairing during training (Figure S1). The median position of the mice in the box at the end of stimulus delivery was 0.71 (with 0 defined as the site of odor presentation and 1 as the opposite end of the box), and mice exhibited a 1.8-fold increase of their maximum velocity. Importantly, the escape behavior was specific to the CS+, as none of the mice ran away from the CS-(Figure 1C, D andE). We then subtracted the position after CS-presentation from the one after CS+ presentation and the CS-maximum velocity ratio (after/before presentation) from the CS+ one. A value of 0 would indicate a generalized learned response to odors (escape from the CS+ and the CS-) or no learning. Here, the differences were significantly different from 0 (Wilcoxon Signed-Rank Test (WSRT), W=45, p=0.0039 for both the position and velocity ratio,

Figure 1F and G).

During both training and testing, odors were presented at the extremities of the box, and the training and testing box have the same shape and dimensions. Therefore, contextual features (visual and/or tactile) could be an important determinant for successful memory retrieval. To assess the context-dependence of the memory, we tested memory retrieval in a different context. We monitored mouse behavior in an open field during ambient and prolonged odor exposure, where the odor does not originate from a spatially defined odor source as during training (Figure 1A). We fear conditioned mice to ethyl acetate as described above (n=6). Mice exposed to ethyl acetate without foot shock served as a control (n=5). Diffusion of ethyl acetate above the open field caused a significant decrease in exploratory behavior of fearconditioned mice compared to control mice (Mann-Whitney test (MWT), U=0, p=0.0043, Figure 1H andI). Baseline exploratory behavior measured one day earlier did not differ between fear-conditioned and control mice (MWT, U=11, p=0.5368).

These data suggest that re-exposure of mice to the CS+ induced memory recall, expressed as a decrease in exploratory behavior in the open field test. Similar results were obtained when mice where trained only with a CS+ and no CS-(MWT, U=2, p=0.0173 for ratio, Figure 1J andK). The differences in behavioral responses we observe in the two contexts (escape versus decreased exploratory behavior) likely reflects the adaptivity of fear [START_REF] Adolphs | The biology of fear[END_REF].

Fos-expressing piriform neurons can be tagged and functionally manipulated

If piriform neurons that were activated during olfactory learning encode an essential component of olfactory memories, then manipulating the activity of these neurons should impact memory recall.

As the PCx is a large area, we used Designer Receptors Exclusively Activated by Designer Drugs (DREADDs) [START_REF] Alexander | Remote Control of Neuronal Activity in Transgenic Mice Expressing Evolved G Protein-Coupled Receptors[END_REF][START_REF] Ferguson | Transient neuronal inhibition reveals opposing roles of indirect and direct pathways in sensitization[END_REF] to manipulate its activity. DREADDs increase (hM3Dq:mCherry) or decrease (HA:hM4Di-IRES-mCitrine) the excitability of neurons upon activation by their ligand clozapine N-oxide (CNO). To selectively label piriform neurons that were activated during odor exposure, we used cFos-tTA transgenic mice [START_REF] Reijmers | Localization of a Stable Neural Correlate of Associative Memory[END_REF] in which the activity-dependent cFos promoter drives expression of the tTA transcription factor, and we stereotaxically injected in PCx Adeno-Associated Viruses (AAVs) expressing DREADDs under the control of the tTA-responsive promoter tetO (Figure 2A). Temporal control of DREADD expression is provided by doxycycline, which interferes with the binding of tTA to tetO and thus suppresses transgene expression [START_REF] Gossen | Transcriptional activation by tetracyclines in mammalian cells[END_REF]. Mice maintained in their home cage on a doxycycline-containing diet showed low basal DREADD expression, detected by anti-HA immunohistochemistry and native mCherry fluorescence (Supplementary Figure 3C). To induce DREADD expression, mice were taken off doxycycline five days before odor presentation.

Previous studies have shown that cFos-tTA-dependent-dependent expression of regulators of neural activity lasts for at least five days [START_REF] Liu | Optogenetic stimulation of a hippocampal engram activates fear memory recall[END_REF][START_REF] Zhang | Neuronal ensembles sufficient for recovery sleep and the sedative actions of α2 adrenergic agonists[END_REF][START_REF] Cowansage | Direct reactivation of a coherent neocortical memory of context[END_REF]. We therefore restricted our manipulations of neural activity to a three-day time window after Fostagging. Exposure to odor followed by foot shock resulted in the Fos-tagging of sparse neural ensembles (median (interquartile range): 1.6 (0.3) % of piriform neurons, n=2 for hM4Di; 2.2 (0.5) % of piriform neurons, n=3 for hM3Dq). Fos-tagged neurons were broadly dispersed throughout the anterior and posterior PCx (Figure 2C and D and Figure S3). The number and distribution of Fos-tagged cells were similar to endogenous Fos expression (2.9 (0.2) %, n=2, Figure 2B and [START_REF] Datiche | Expression of Fos in the piriform cortex after acquisition of olfactory learning: an immunohistochemical study in the rat[END_REF][START_REF] Illig | Odor-evoked activity is spatially distributed in piriform cortex[END_REF]).

To test whether CNO-mediated activation of DREADDs in Fos-tagged piriform neurons alters their excitability, we performed whole-cell recordings in acute brain slices. DREADD-expressing neurons were identified based on mCitrine (HA:hM4Di-IRES-mCitrine) or mCherry (hM3Dq:mCherry) fluorescence. Fos-tagged neurons displayed diverse morphologies and electrophysiological properties and included both excitatory (pyramidal-like neurons, PN; semilunar-like neurons, SL) and inhibitory neurons (fast-spiking interneurons, FS, Figure S2). In the absence of CNO, the resting membrane potential of DREADD-negative neurons was indistinguishable from DREADD-expressing neurons (-72.14 (2.96) mV in DREADD-negative neurons, n=17; -71.58 (4.50) mV in hM4Di-expressing neurons, n=12; -72.56 (4.18) mV in hM3Dq-expressing neurons, n=12; p=0.819, Kruskal-Wallis ANOVA, Figure 2E).

After bath application of CNO (5 µM), the resting membrane potential of DREADDnegative cells remained unchanged (WSRT, -72.27 (3.72) mV, n=17, p=0.818), whereas it changed in DREADD-expressing cells: hM4Di-expressing cells hyperpolarized and hM3Dq-expressing cells depolarized (WSRTs, -74.51 (5.17) mV, n=12, p=0.011 and -66.95 (5.29) mV, n=12, p=0.005, respectively; Figure 2E). To determine the impact of CNO treatment on neuronal excitability, we delivered depolarizing current steps and compared the number of action potentials triggered by 60 pA step current above action potential threshold (see Methods and Figure 2G).

We found that in hM4Di-expressing cells, the number of evoked action potentials significantly decreased after CNO application, whereas in hM3Dq-expressing cells, it significantly increased (WSRTs: 3.75 (1.59) vs. 0.30 (3.48), n=10, p=0.010 and 8.67 Taken together, these experiments show that Fos-tagging during olfactory fear conditioning marks a sparse and dispersed subpopulation of piriform neurons, and that CNO-mediated activation of hM4Di or hM3Dq expressed in Fos-tagged neurons selectively decreases or increases their excitability.

Silencing Fos-tagged piriform ensembles impairs odor fear memory recall

To test the effects of Fos-tagged ensemble manipulation on memory recall, we Fostagged piriform neurons during olfactory fear conditioning, and then chemogenetically silenced them during memory recall. cFos-tTA male mice ("experimental group", n=8) were bilaterally injected in PCx with the AAV-tetO-hM4Di vector. Wild-type male mice injected with the same virus served as a control ("control group", n=8). Doxycycline was removed from the diet of mice prior to training, to permit the induction of hM4Di expression in Fos-expressing piriform neurons of mice of the experimental group.

Mice were returned to doxycycline-containing diet immediately after odor fear conditioning, and memory recall of the odor-foot shock association was tested three days later in the rectangular testing box after intraperitoneal injection of CNO.

(Figure 3A). Mice from the control group also received CNO injection, to control for behavioral changes caused by potential off-target CNO effects [START_REF] Gomez | Chemogenetics revealed: DREADD occupancy and activation via converted clozapine[END_REF]. For all mice, we verified viral gene expression by post hoc histological examination. Previous studies have suggested that the posterior PCx is important for associative memory encoding [START_REF] Haberly | Parallel-distributed processing in olfactory cortex: new insights from morphological and physiological analysis of neuronal circuitry[END_REF][START_REF] Sacco | Role of secondary sensory cortices in emotional memory storage and retrieval in rats[END_REF][START_REF] Calu | Associative encoding in posterior piriform cortex during odor discrimination and reversal learning[END_REF]. We therefore excluded from our analysis mice in which parts of the posterior PCx were spared from viral infection (Figures S3 andS4A).

As expected, control mice exhibited robust escape behavior upon CS+ presentation (median position in the box at the end of CS+ delivery:0.74; increase in maximum velocity:1.9-fold, Figure 3B, C andE). In contrast, escape behavior was significantly reduced in mice in which Fos-tagged neurons were silenced. Their median position in the box at the end of stimulus delivery (0.42) and their increase in maximum velocity (1.1-fold) were significantly lower than in the control group (MWT, U=7, p=0.007 for both position and velocity, Figure 3B, C andE). Subtracting the CS-position and maximum velocity ratio from the CS+ ones also lead to significant differences between the control and experimental groups (MWT, U=13, p=0.0499 for position and U=11, p=0.0281 for maximum velocity ratio, Figure 3D andG). Differences in behavioral responses of cFos-tTA mice were specifically due to hM4Di activation, as escape behavior after CNO injection was unaffected in cFos-tTA mice injected with AAVs expressing the calcium indicator GCaMP (Figure 1C, D, E andF).

Furthermore, all mice were similarly close to the odor port at the onset of CS+ odor presentation (MWT, U=28, p=0.7209, Figure 3B), and had similar maximum velocities during the 7 s time period that preceded CS+ presentation (MWT, U=24, p=0.4418, Figure 3E). These observations exclude any inherent differences between groups due to how the CS+ was presented. Finally, we did not observe any differences in the overall mobility of mice throughout the entire testing session. The median speed of mice was not significantly different between the control and experimental group (0.68 (0.28) cm/s and 0.46 (0.14) cm/s respectively, MWT, U=22, p=0.3282), nor did mice show a bias for the left or right side of the testing box (time spent on the left side divided by time spent on the right side: 1.36 (0.72) and 1.51 (0.52) for the control and experimental groups respectively, MWT, U=27, p=0.6454).

Together, these data suggest that Fos-tagged piriform ensembles that were activated during olfactory fear conditioning are necessary for robust odor fear memory recall.

Even though cFos-tTA transgenic mice expressing hM4Di failed to robustly escape from the CS+, it should be noted that they behaved differently after CS+ and CSpresentation. They were further away from the odor port after CS+ presentation than after CS-presentation (WSRT, W=-36, p=0.0078, Figure 3C), and their maximum velocity ratio was significantly higher (after/before odor presentation, WSRT, W=-36, p=0.0078, Figure 3E, F andG). This could indicate a partial memory of the learned association, possibly due to incomplete silencing of functionally relevant neurons in PCx, or the existence of parallel neural pathways that partially compensate for the loss of PCx functions.

Memory impairments are specific to the piriform ensemble Fos-tagged during learning

Silencing the PCx in only one brain hemisphere did not abolish the learned escape behavior to the conditioned odor (Figure S5). Furthermore, memory impairments were not related to the bilateral or unilateral infection of brain regions adjacent to PCx due to spillover of the virus (parts of cortical and basolateral amygdala, and insular cortex; Figure S5). Therefore, memory impairments are most likely specific to PCx.

We next wanted to determine if the memory deficits were specific to the neurons that were Fos-tagged during learning. Odors activate unique yet overlapping ensembles of piriform neurons [START_REF] Bolding | Complementary codes for odor identity and intensity in olfactory cortex[END_REF][START_REF] Roland | Odor identity coding by distributed ensembles of neurons in the mouse olfactory cortex[END_REF][START_REF] Stettler | Representations of Odor in the Piriform Cortex[END_REF]. Therefore, silencing neurons that respond to one odor could partially interfere with the retrieval of information associated with other odors.

To test this, we modified the behavioral protocol to separate Fos-tagging from fear conditioning. cFos-tTA transgenic and wild-type control mice were injected with AAV-tetO-hM4Di, and expression of hM4Di in piriform neurons was induced while mice were exposed to eugenol or beta-citronellol in a neutral environment, without subsequent foot shock. Mice were returned to doxycycline-containing diet and fearconditioned two days later to ethyl acetate (CS+). Behavioral testing of memory recall was performed one day later, after intraperitoneal injection of CNO (Figure 4A). Fostagging resulted in the labeling of sparse neural ensembles, similar in numbers to those tagged during olfactory fear conditioning (1.1 (0.3) % of piriform neurons, n=3,

Figure S3E and S4B

). We found that learned escape behavior of cFos-tTA mice (experimental group, n=12) was similar but somewhat attenuated compared to controls (n=10). Both groups exhibited an escape behavior after CS+ presentation, indicated by the significant increase in the maximum velocity (WSRT, W=55, p=0.0020 and W=54, p=0.0342 for the control and experimental groups respectively; no difference in the maximum velocity ratio after/before between groups, MWT, U=35, p=0.1072, Figure 4E, F andG). The difference in the position of mice after CS+ and CS-presentation was also similar between groups (MWT, U=37, p=0.1402, Figure 4D). However, we observed that silencing neutral odor representations somewhat dampened the behavioral response to the CS+, as behavioral responses were less robust compared to controls when quantifying the position of mice in the box after CS+ presentation (MWT, U=22, p=0.0112, Figure 4B andC). The attenuated behavioral responses we observe likely reflect the partial degradation of odor information as a result of the silencing of piriform neurons responsive to both the CS+ and the neutral odor.

Silencing Fos-tagged piriform ensembles does not alter odor detection and discrimination

Chemogenetic silencing of piriform ensembles Fos-tagged during olfactory fear conditioning could disrupt odor detection and discrimination rather than selectively affecting odor fear memory recall. To test this possibility, we monitored sniffing behavior of mice during an olfactory habituation assay (Figure 5A), a wellestablished test for odor detection and discrimination [START_REF] Coronas-Samano | The Habituation/Cross-Habituation Test Revisited: Guidance from Sniffing and Video Tracking[END_REF][START_REF] Wesson | Sniffing behavior of mice during performance in odor-guided tasks[END_REF]. Fos-tagging of piriform neurons during olfactory fear conditioning was performed as described in Figure 3A.

Three days later, changes in sniffing behavior in response to odor exposure were tested in a plethysmograph, while Fos-tagged neurons were silenced with CNO (see Figure S5C and Methods). We observed that mice of both experimental (n=8) and control (n=6) groups increased their sniff frequency upon the first presentation of pinene, a novel and neutral odor (1.6-fold increase relative to pre-odor baseline frequency; Figure 5B andD). Repeated exposure to the same odor (pinene or CS-) resulted in a decrease in the sniff frequency, reflecting habituation after 4 consecutive exposures (WSRT for the neutral odor, W=-21, p=0.0312 for the control and W=-36, p=0.0078 for the experimental group; Figure 5D). Subsequent presentation of the CS+ increased the sniff frequency (1.4-fold increase; WSRT, W=21, p=0.0312 for the control and W=34, p=0.0156 for the experimental group, Figure 5E). Such changes in odor sampling behavior have been shown to report the detection and discrimination of different odor stimuli [START_REF] Coronas-Samano | The Habituation/Cross-Habituation Test Revisited: Guidance from Sniffing and Video Tracking[END_REF][START_REF] Wesson | Sniffing behavior of mice during performance in odor-guided tasks[END_REF][START_REF] Verhagen | Sniffing controls an adaptive filter of sensory input to the olfactory bulb[END_REF].

Furthermore, the baseline sniff frequency, the difference in sniff frequency between the first and fourth exposures of the same odor, and the difference in sniff frequency between the CS-after habituation and the CS+ were similar between control and experimental groups (MWTs, U=12.5, p=0.1512 for baseline; U=22, p=0.8228 for pin4-pin1 and U=24, p>0.9999 for CS+-CS-4, Figure 5C). These data suggest that basic behaviors characteristic of odor sampling, detection and discrimination were unaffected by the silencing of piriform ensembles that were Fos-tagged during olfactory fear conditioning.

Reactivation of Fos-tagged piriform ensembles mimics odor-evoked fear memory recall

If piriform neural ensembles that were activated during olfactory fear conditioning encode an essential component of odor fear memories, then reactivation of these neurons may be sufficient to trigger memory recall.

To test this, we infected the PCx of cFos-tTA female mice with the activating DREADD AAV-tetO-hM3Dq (Figure S4D). We first trained mice to associate ethyl acetate with foot-shock, without CS-presentation. We then intraperitoneally injected CNO to reactivate hM3Dq-expressing piriform neurons that were Fos-tagged during learning (Figure 6A). Chemogenetics does not provide precise temporal control of neuronal activity, and CNO binding leads to a prolonged modulation of neuronal activation [START_REF] Alexander | Remote control of neuronal activity in transgenic mice expressing evolved G proteincoupled receptors[END_REF]. We therefore tested artificial memory retrieval in the open field box (see Figure 1H-K for memory retrieval tested with prolonged odor exposure). 11.7 (1.7) % of hM3Dq-expressing cells were reactivated upon CNO injection. As a point of comparison, 1.8 (1.4) % of neurons were reactivated during olfactory memory retrieval (Supplementary Figure 6). CNO-mediated reactivation, similar to CS+ exposure, caused a significant decrease in exploratory behavior of fearconditioned mice (n=7), compared to baseline exploratory behavior measured one day earlier (WSRT, W=-26, p=0.0312, Figure 6B). In contrast, reactivation of piriform neurons that were Fos-tagged during ethyl acetate exposure without foot shock (n=7) did not affect exploratory behavior (WSRT, W=-10, p=0.4688, Figure 6B).

Exploratory behavior after CNO injection normalized to baseline was significantly different between control and experimental groups (Mann Whitney test, U=8, p=0.0379, Figure 6C). These data suggest that chemogenetic reactivation of piriform neurons that were active during odor-foot shock exposure is sufficient to trigger fear memory recall.

We next asked whether artificial memory recall depends on the specificity of the Fostagged neural ensemble: is piriform reactivation sufficient to trigger fear memory recall, as long as it includes the CS+-tagged ensemble? For this purpose, we generated a synthetic Fos-tagged ensemble, by alternating exposure to the CS+ odor paired with foot-shock with exposure to CS-neutral odors. We found that artificial reactivation of synthetic Fos-tagged ensemble did not result in changes in exploratory behavior indicative of memory recall (WSRT, n=8, W=-4, p=0.8438, Figure 6B). These data suggest that during artificial reactivation, PCx cannot extract meaningful information from the synthetic representation generated by the sequential presentation of CS+ and CS-odors.

Discussion

The PCx has long been thought to provide the substrate for storing associative olfactory memories, yet the cellular substrates for olfactory learning and memory remain unknown. Using a cFos-dependent, intersectional genetic approach to visualize and manipulate piriform neurons activated during olfactory fear conditioning, we found that chemogenetic silencing of Fos-tagged ensembles robustly diminished a learned odor escape behavior without altering basic odor detection and discrimination. Furthermore, chemogenetic reactivation of Fos-tagged piriform ensembles resulted in reduced exploratory behavior in an open field assay, an effect that was similarly observed when exposing mice to the conditioned odor stimulus.

Together, our experiments identify piriform neurons expressing Fos during learning as an essential neural circuit component for triggering odor fear memory recall.

Localization of the odor fear memory trace

The behavioral consequences of manipulating Fos-tagged piriform neurons suggest the formation of functional connections between piriform neurons and other association areas. Candidate target areas for the processing of odor-fear associations include the basolateral amygdala and the medial prefrontal cortex [START_REF] Dejean | Prefrontal neuronal assemblies temporally control fear behaviour[END_REF][START_REF] Gore | Neural Representations of Unconditioned Stimuli in Basolateral Amygdala Mediate Innate and Learned Responses[END_REF], however, the relevant neural circuit components remain to be identified. We propose that odor fear memories are encoded in distributed ensembles of neurons throughout the brain, with different regions contributing to different components of the overall memory. The PCx could store information about odor objects, while associated emotions of past olfactory experiences could be stored in the amygdala (see [START_REF] Mayford | Exploring Memory Representations with Activity-Based Genetics[END_REF][START_REF] Schoenenberger | Temporal control of immediate early gene induction by light[END_REF] for a similar model relative to contextual and auditory fear conditioning).

Several studies have shown that PCx cells can encode information that carries behavioral significance [START_REF] Sacco | Role of secondary sensory cortices in emotional memory storage and retrieval in rats[END_REF][START_REF] Calu | Associative encoding in posterior piriform cortex during odor discrimination and reversal learning[END_REF][START_REF] Mandairon | Context-driven activation of odor representations in the absence of olfactory stimuli in the olfactory bulb and piriform cortex[END_REF]. Future studies investigating learning-induced changes in cellular and network properties of Fos-tagged neurons will establish if their silencing modifies the perception of the CS+, and thus the reactivation of the memory linked to the CS+, or if a memory trace of the odor-foot shock association is also formed within the Fos-tagged piriform ensembles.

Technical limitations of Fos-tagging for studying odor fear memories

In this study, we used two different fear conditioning paradigms, and two different retrieval contexts. It has previously been shown that the absence or presence of odorants not paired with foot shock (CS-) lead to a more or less generalized fear to odors similar to the reinforced conditioned stimulus (CS+) and to differential changes in the responses of piriform neurons [START_REF] Chen | Generalized vs. stimulusspecific learned fear differentially modifies stimulus encoding in primary sensory cortex of awake rats[END_REF]. Thus, PCx might be differentially involved in the retrieval of olfactory memories, depending on the presence or absence of CS-.

In rats, PCx is not necessary three days after fear-conditioning to a CS+ odor without CS-, yet becomes indispensable when memory is tested one month after learning [START_REF] Sacco | Role of secondary sensory cortices in emotional memory storage and retrieval in rats[END_REF]. In our hands, Fos-tagged piriform ensembles are essential for odor fear memory retrieval three days after learning, when the CS+-shock presentation is coupled to the presentation of CS-.

A general limitation of the cFos-tTA system is that the tagging of neurons is transient.

The duration of the expression of tTA-dependent proteins is determined by the time course of induction and the stability of cFos-tTA-dependent transcripts and proteins.

Previous studies have shown that cFos-tTA-dependent expression of regulators of neural activity becomes undetectable by thirty days [START_REF] Liu | Optogenetic stimulation of a hippocampal engram activates fear memory recall[END_REF][START_REF] Zhang | Neuronal ensembles sufficient for recovery sleep and the sedative actions of α2 adrenergic agonists[END_REF][START_REF] Cowansage | Direct reactivation of a coherent neocortical memory of context[END_REF]. Therefore, the temporal involvement of PCx in memory retrieval cannot be addressed with Fostagging.

Another constraint of the Fos-tagging system is its slow temporal dynamics. As a consequence, when training included the presentation of CS-, neurons responding to the CS-were tagged in addition to neurons responding to the CS+. We showed that the additional CS-"background" neurons had no significant impact on the outcome of the silencing experiment, as chemogenetic silencing of neurons activated during presentation of a CS-only moderately attenuated odor fear memory recall.

Interestingly, the number of Fos-expressing and Fos-tagged piriform neurons we observe is significantly lower than the number of odor-responsive neurons detected in electrophysiological recordings in awake mice [START_REF] Bolding | Complementary codes for odor identity and intensity in olfactory cortex[END_REF][START_REF] Miura | Odor representations in olfactory cortex: distributed rate coding and decorrelated population activity[END_REF][START_REF] Zhan | Diverse patterns of odor representation by neurons in the anterior piriform cortex of awake mice[END_REF]. However, in these experiments, a large fraction of cells exhibited low firing rates. Therefore, the Fostagged population could represent a subpopulation of neurons that is strongly activated by odor [START_REF] Schoenenberger | Temporal control of immediate early gene induction by light[END_REF]. Fos-tagging could also mark plastic changes supporting memory formation [START_REF] Cole | Rapid increase of an immediate early gene messenger RNA in hippocampal neurons by synaptic NMDA receptor activation[END_REF][START_REF] Minatohara | Role of Immediate-Early Genes in Synaptic Plasticity and Neuronal Ensembles Underlying the Memory Trace[END_REF]. Indeed, cFos mRNA levels decrease after injection of an antagonist of the NMDA receptor, a key player in the induction of synaptic plasticity [START_REF] Tayler | Characterization of NMDAR-Independent Learning in the Hippocampus[END_REF], and long-term memory and synaptic plasticity are impaired when cFos production is perturbed in the central nervous system [START_REF] Fleischmann | Impaired longterm memory and NR2A-type NMDA receptor-dependent synaptic plasticity in mice lacking c-Fos in the CNS[END_REF].

Artificial reactivation of an olfactory memory trace

Reactivation of neurons by CNO-mediated activation of DREADD receptors does not recapitulate the temporal characteristics of piriform odor responses and their modulation by active sampling [START_REF] Bolding | Complementary codes for odor identity and intensity in olfactory cortex[END_REF][START_REF] Miura | Odor representations in olfactory cortex: distributed rate coding and decorrelated population activity[END_REF]. Despite this, reactivation of piriform ensembles Fos-tagged during odor-foot shock pairing was sufficient to elicit a behavioral response. How piriform neural circuits and downstream target regions process such artificial activity patterns remains to be determined. One possibility is that despite the temporal limitations of memory trace reactivation, piriform network mechanisms can retrieve the perception of the reinforced conditioned stimulus.

Consistent with this model, recent studies have shown that spatial patterns of odorevoked activity, in the absence of precise temporal information, are sufficient to decode odor identity [START_REF] Bolding | Complementary codes for odor identity and intensity in olfactory cortex[END_REF][START_REF] Roland | Odor identity coding by distributed ensembles of neurons in the mouse olfactory cortex[END_REF][START_REF] Miura | Odor representations in olfactory cortex: distributed rate coding and decorrelated population activity[END_REF]. Alternatively, it is possible that reactivation generates a state of fear, but without evoking the perception of the odor. Finally, reactivating a synthetic ensemble of neurons activated during exposure to both CS+ and CS-stimuli did not elicit a measurable behavioral response. This observation suggests that behaviorally relevant information cannot be extracted from a neural ensemble representing conflicting (aversive versus neutral) information and further supports the specificity of the Fos-tagged ensemble. This result is consistent with the finding that the reactivation of an artificial contextual memory in the hippocampus competes with the retrieval of a learned context-shock association [START_REF] Ramirez | Creating a false memory in the hippocampus[END_REF].

Memory traces in hippocampus and PCx

The hippocampus has been studied extensively for its role in spatial and contextual memory [START_REF] Basu | The Corticohippocampal Circuit, Synaptic Plasticity, and Memory[END_REF]. Recently, Fos-tagging of hippocampal neurons during contextual fear conditioning has provided important insight into the cellular and neural circuit mechanisms of learning and memory [START_REF] Liu | Optogenetic stimulation of a hippocampal engram activates fear memory recall[END_REF][START_REF] Garner | Generation of a synthetic memory trace[END_REF][START_REF] Ramirez | Creating a false memory in the hippocampus[END_REF][START_REF] Cai | A shared neural ensemble links distinct contextual memories encoded close in time[END_REF][START_REF] Roy | Distinct Neural Circuits for the Formation and Retrieval of Episodic Memories[END_REF][START_REF] Ryan | Memory. Engram cells retain memory under retrograde amnesia[END_REF]. However, if principles of memory formation and storage in hippocampus-related neural networks apply to other cortical structures remains largely unknown. Interestingly, PCx and hippocampus share a similar circuit organization and both have been modeled as auto-associative networks [START_REF] Haberly | Parallel-distributed processing in olfactory cortex: new insights from morphological and physiological analysis of neuronal circuitry[END_REF]. In both regions, learning marks sparse and distributed ensembles of neurons that appear to lack topographic organization. Furthermore, hippocampal neurons tagged during contextual fear conditioning, and piriform neurons tagged during olfactory fear conditioning were both necessary and sufficient for memory retrieval [START_REF] Liu | Optogenetic stimulation of a hippocampal engram activates fear memory recall[END_REF][START_REF] Tanaka | Cortical representations are reinstated by the hippocampus during memory retrieval[END_REF]. Our findings thus reveal striking similarities between memory traces of contextual fear in the hippocampus and olfactory memory traces in the PCx. (A) The "silencing" and "activating" TetTag system. AAVs (red) expressing DREADDs under the control of the tetO promoter were injected in the piriform cortex of cFos-tTA transgenic mice (see also Figure S3). hM4Di or hM3Dq are expressed in active Fos-expressing piriform neurons upon doxycycline removal. (E) Resting membrane potential in mV, before (baseline, BL) and after CNO application. The resting membrane potential does not differ between DREADDexpressing and non-expressing cells (Ctrl). After CNO application, it does not change in non-expressing cells (Ctrl), while hM4Di-expressing cells hyperpolarize and hM3Dq-expressing cells depolarize.

(F) The normalized membrane potential in % to baseline in different cell types after CNO application. Pyramidal-like neurons (PN) are marked as circles, semilunar-like cells (SL) as triangles and fast-spiking interneurons (FS) as squares (see Figure S2). (A) Experimental design: cFos-tTA transgenic mice (experimental group, n=8) or wild-type mice (control group, n=8) are injected with AAV-tetO-hM4Di in both hemispheres of piriform cortex. Ten days later, mice are habituated to the training and testing boxes. Upon doxycycline (DOX) removal, mice are fear-conditioned, and hM4Di expression (green circles) is induced in Fos-tagged neurons (filled in blue and yellow, see Figure S4). Mice are returned to DOX-containing diet to avoid further expression of hM4Di. Three days later, all mice are intraperitoneally injected with CNO, which silences hM4Di-expressing neurons (black crosses), and memory retrieval is tested in the rectangular testing box (Figure 1B).

(B to G) Olfactory memory retrieval after CNO injection, assessed by the position of mice in the testing box and their maximum velocity upon odor exposure. Memory retrieval was significantly impaired in cFos-tTA mice in which piriform neurons that were active during learning were chemogenetically silenced during memory recall (experimental group). See Figure S5

Fos-tagged during learning

(A) Experimental design: dissociating Fos-tagging and fear conditioning. Upon doxycycline (DOX) removal, mice are presented with an odor in a neutral environment (C: eugenol, eug. or beta-citronellol, beta-cit.). hM4Di expression (green circles) is induced in Fos-tagged neurons (filled in orange, also see Figure S3 and S4). Two days later, mice are fear conditioned to ethyl-acetate (CS-: limonene and beta-cit. when Fos-tagged with eug., limonene and eug. when Fos-tagged with betacit.). One day later, memory retrieval is tested in the presence of CNO, which silences hM4Di-expressing neurons (black crosses).

(B-G) Olfactory memory retrieval after CNO injection, assessed by the position of mice in the testing box and their maximum velocity. Memory retrieval was moderately attenuated in cFos-tTA mice expressing hM4Di in neurons that were Fos-tagged during presentation of a neutral odor (experimental group, n=12), compared to WT mice (control group, n=10). (A) (Top) Experimental design: Fos-tagging during olfactory fear conditioning is performed as described in Figure 2 (see also Figure S4). Three days after fear conditioning, sniffing behavior is quantified in a plethysmograph. Mice are intraperitoneally injected with CNO, habituated to the plethysmograph for 15 min, and each odor is then presented for 8 s with a 2.5 min inter-trial interval. pin: pinene, CS-: beta-citronellol, CS+: ethyl-acetate.

(Bottom) Representative sniff recordings from one mouse when exposed to pinene (1st presentation) or the CS+ (ethyl-acetate). (C-E) For both the control (n=6) and experimental group (n=8), repeated exposure to the same odor resulted in a decrease in the sniff frequency (habituation), while presentation of a different odor resulted in an increase in the sniff frequency.

(C) The changes in sniff frequency after presentation of the same or a different odor are similar between the experimental and the control group. The sniff frequency during the fourth presentation of pinene is subtracted from its first presentation (pin4-pin1), or the sniff frequency during the fourth presentation of the CS-is subtracted from the sniff frequency during the CS+ presentation (CS+-CS-4). The recording solution also contained the morphological tracer Alexa Fluor 594 (5 µM, red channel) for non-expressing and hM4Di-positive cells or the Ca 2+ -sensitive dye Fura-2 (300 µM, replacing EGTA in the recording solution, green channel) for hM3Dq-positive cells, to enable identification of the patched cell and to visualize its morphology. The excitability of cells was measured in current-clamp mode by 500 ms steps of current injections from -300 to +500 pA with steps of 20 pA. We compared the number of action potentials triggered by equivalent depolarization at each step 60 pA above the action potential threshold before and after CNO (5 µM) application. The series resistance was usually <20 MΩ, and data were discarded if it changed by more than 20% during the recording. Signals were amplified using EPC10-2 amplifiers (HEKA Elektronik, Lambrecht, Germany). Voltage-clamp recordings were filtered at 5 kHz and sampled at 10 kHz, and current-clamp recordings were filtered at 10 kHz and sampled at 20 kHz, with the Patchmaster v2x32 program (HEKA Aldrich), at a concentration of 1% (vol/vol) in mineral oil were used: ethyl acetate, beta-citronellol, eugenol, limonene, and pinene.

Behavioral procedures

AAVs were stereotaxically injected in both hemispheres of PCx of cFos-tTA transgenic mice and littermate wild-type controls. Mice were given 10 days to recover, before being habituated on day 11 to the training and testing/open field/plethysmograph boxes (40 and 10 min each). 24 hours after habituation, doxycycline was removed and replaced by a regular diet. Five days later, mice were fear conditioned to ethyl acetate or exposed to an odor (odor "C") in a neutral environment. Immediately after fear conditioning or odor presentation, mice were put back on a diet containing doxycycline. During fear conditioning, mice were freely moving around the conditioning box. Ethyl acetate (the CS+) was presented when the mouse was located at one end of the box, and the corresponding half-side of the box' floor was electrified for 0.6 s (0.6 mA). The foot shock was delivered 4 seconds after CS+ presentation, and the CS+ lasted for an additional 2 seconds. Mice learned to escape to the opposite side when the CS+ was presented. The CS+ was presented 4 times, 2 times on each side of the box. When fear conditioning included presentation of two non-reinforced conditioned stimuli (CS-1 and CS-2), the choice between CS+ and CS-as well as the side of presentation was pseudo-randomized.

Training always started with one presentation of each CS-followed by the CS+. The two CS-odors were presented during 7 seconds, 3 times each, with a total presentation of 3 on the right side and 3 on the left side. The mean time interval between two odor presentations was 3 minutes.

In the rectangular testing box, the CS+ was presented 4 times (2 times on each side), and each CS-was presented once on each side, for 7 s each (mean time interval between two odors: 3 minutes). As for the training session, the order and side of odor presentations was pseudo-randomized: testing always started with one presentation of each CS-, followed by one CS+ presentation. In the open field, the olfactometer outputs were placed above the open field box. Mice were placed in the middle of the box at the start of each session.

Drugs

Clozapine-N-oxide (C0832, Sigma-Aldrich) was first dissolved in dimethylsulfoxide (DMSO, D2438, Sigma, final concentration of 1% vol/vol), then further diluted in 0.9% sterile saline solution to a final concentration of 0.2 mg/mL. Aliquots were stored for up to two months at -20°C and equilibrated to room temperature before injection. The solution was administered intraperitoneally (3 mg/kg). After injection, mice were left undisturbed for 25 minutes (Figure 2 and4) or 5 minutes (Figure 3 and5) in their home cage before the start of the experiment.

QUANTIFICATION AND STATISTICAL ANALYSIS

Cell counting

Z-stacks (7 µm step) were acquired with a Leica SP5 confocal microscope with a 20X objective and a resolution of 512x512 or 1024x1024 pixels (1 pixel: 0:72µm). First, the PCx was delineated on a maximum projection of each stack using a customwritten ImageJ macro. For each mouse, 2 to 4 sections (median volume 9.3e-2 (9.4e-3) mm 3 ) were analyzed, from one or both hemispheres, at Y=-0.8 and Y=-1.6mm relative to bregma.

( 9 .

 9 Figure 2H).

Figure 1 .

 1 Figure 1. Behavioral expression of odor fear memory depends on the retrieval

Figure 2 .

 2 Figure 2. Fos-expressing piriform neurons can be tagged and functionally

  (B-D) Mice were fear conditioned to ethyl acetate five days after doxycycline removal. Training includes the presentation of two other odors that are not paired with foot shock (CS-, eugenol and beta-citronellol). Mice were perfused one hour after the start of the experiment (B) or three days later (C-D). (B) Endogenous Fos expression. (C) Neurons expressing hM4Di were visualized using anti-HA immunohistochemistry. (D) Neurons expressing hM3Dq were visualized with mCherry fluorescence. Neurotrace counterstain in blue. Scale bars: 50 µm. The number below the coronal sections indicate the median percentage (interquartile range) of tagged neurons quantified in 2 or 3 mice. (E-I) Electrophysiological characterization of Fos-tagged piriform neurons.

(

  G-I) The excitability of DREADD-expressing cells is measured as the number of action potentials (APs) resulting from the third depolarizing current step, counting from the first step that elicits spiking (steps of 20 pA). (G) Representative traces before (baseline, BL) and after CNO application. (H) Number of APs before (baseline, BL) and after CNO application. After CNO application, the number of APs in DREADD-negative cells (Ctrl) does not change, significantly decreases in hM4Di-expressing cells and significantly increases in hM3Dq-expressing cells. (I) Normalized number of APs in % to baseline in different cell types after CNO application. Cell types are marked as in (F). Data are shown as individual data points, median and interquartile range, ** p<0.01.

Figure 3 .

 3 Figure 3. Silencing Fos-tagged piriform ensembles impairs odor fear memory

  for unilaterally infected mice. (B) Averaged position of mice in the testing box as a function of time after CS+ (black dashed line) and CS-(blue line) presentation. (C-G) Control group: color-coded black; experimental group: color-coded green. (C) Position in the testing box 7 s after CS+ or CS-presentation. (D) Position 7 s after CS-presentation subtracted from the position 7 s after CS+ presentation. (E) Maximum velocity during a 7 s time window before and after CS+ presentation. (F) Maximum velocity during a 7 s time window before and after CS-presentation.(G) Maximum velocity ratio after/before CS-subtracted from the maximum velocity

Figure 4 .

 4 Figure 4. Memory impairments are specific to the piriform ensemble that is

(

  B) Averaged position of mice as a function of time after CS+ and CS-presentation. (C) Position of mice in the testing box 7 s after CS+ or CS-presentation. (D) Position 7 s after CS-presentation subtracted to the position 7 s after CS+ presentation. (E) Maximum velocity during the 7 s before and after CS+ presentation. (F) Maximum velocity during a 7 s time window before and after CS-presentation. (G) Maximum velocity ratio after/before CS-subtracted from the maximum velocity ratio after/before CS+ presentation. Dots represent individual mice, and averaged data are shown as median and interquartile range, * p<0.05; ** p<0.01; n.s. not significant.

Figure 5 .

 5 Figure 5. Silencing Fos-tagged piriform ensembles does not interfere with odor

  (B-C) Dots represent individual mice, and averaged data are shown as median and interquartile range. (D-E) Each thin line represents data of individual mice, the squares and thick lines represent averaged data (median and interquartile range). (B) Baseline sniff frequency, corresponding to the averaged sniff frequency 8 s before odor onset.

Figure 6 .

 6 Figure 6. Reactivation of Fos-tagged piriform ensembles mimicks odor-evoked

  rectangular testing box (Figure 1, 3 and 4). Statistics Statistical analysis was performed with Prism (GraphPad). Non-parametric tests were used: Mann-Whitney test (MWT) for between group comparison, and Wilcoxon matched-pairs signed rank test (WSRT) for within group comparison. Values are represented as median (interquartile range) unless otherwise stated. The n represents number of mice, or number of recorded neurons for the electrophysiology experiment. DATA AND SOFTWARE AVAILABILITY Data are available upon requests. t a z i r a l o p e D / n o i t a z i r a l o p r e p y

ratio after/before CS+ presentation. Dots represent individual mice, and averaged data are shown as median and interquartile range, * p<0.05; ** p<0.01; n.s. not significant.

Acknowledgements

We thank Mark Mayford for sharing the cFos-tTA transgenic mouse line, and Brian Roth and Susumu Tonegawa for sharing plasmids. We thank Yves Dupraz and Gérard Parésys for their work on the behavioral apparatuses, Agatha Anet for help with behavioral experiments, Tristan Piolot for help with image acquisition, Philippe Mailly for help with cell quantification and Marion Ruinart de Brimont for help with cloning. We thank Karim Benchenane and Sophie Bagur for sharing their plethysmograph. We thank Rainer Friedrich, Anne Didier, Kevin Franks, Boris Gourévitch, Andreas Schaefer, and Claire Zhang for careful reading and critical comments on the manuscript. This work was supported by the "Amorçage de jeunes équipes" program (AJE201106) of the Fondation pour la Recherche Médicale (to A.F.), and a postdoctoral fellowship by the LabEx "MemoLife" (to C.M.B.).

Author contributions

Conceptualization

Declaration of Interests

The authors declare no competing interests.

(D) Sniff frequency for the first to fourth presentation of pinene: control (left) and experimental group (right).

(E) Sniff frequency for the first to fourth presentation of the CS-, and subsequent presentation of the CS+: control (left) and experimental group (right). * p<0.05; ** p<0.01; n.s.: not significant.

STAR METHODS

CONTACT FOR REAGENT AND RESOURCE SHARING

Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Alexander Fleischmann (alexander_fleischmann@brown.edu).

EXPERIMENTAL MODEL AND SUBJECT DETAILS

Mice were housed at 24°C with a 12-hour light/12-hour dark cycle with standard food and water provided ad libitum. Mice were group-housed with littermates until the beginning of surgery and then single-housed in ventilated cages throughout the duration of the experiment. cFos-tTA mice [START_REF] Reijmers | Localization of a Stable Neural Correlate of Associative Memory[END_REF] were originally generated on a mixed C57BL/6 x DBA/2 genetic background and backcrossed for at least 6 generations into a pure C57BL/6N genetic background (Charles River). Wild-type control animals (n=46) were siblings that did not carry the cFos-tTA transgene. The age of mice at the time of behavioral testing ranged from 10 to 15 weeks. Male mice (n=48) were used for the hM4Di-mediated neural silencing, and littermate females (n=40) for the hM3Dq-mediated neural activation experiments. No differences in open field performance depending on the phase of the estrous cycle were found in female mice [START_REF] Meziane | Estrous cycle effects on behavior of C57BL/6J and BALB/cByJ female mice: implications for phenotyping strategies[END_REF], and CNO injection does not disrupt the estrous cycle [START_REF] Padilla | AgRP to Kiss1 neuron signaling links nutritional state and fertility[END_REF]. Mice were fed a diet containing 1g/kg doxycycline (SSNIFF) for a minimum of 4 days before surgery.

Experiments were carried out according to European and French national institutional animal care guidelines (protocol APAFIS#2016012909576100).

METHOD DETAILS

Constructs and viruses

The hSynapsin promoter of pAAV-hSyn-HA-hM4Di-IRES-mCitrine (kindly provided by Dr. B. Roth, University of North Carolina at Chapel Hill) was excised using the restriction enzyme XbaI (New England Biolabs) and replaced by the Tetracycline Response Element of a pAAV-TRE-EYFP (excised with Xba1 et Nhe1, plasmid kindly provided by Dr. S. Tonegawa, MIT, Cambridge). The pAAV-pTRE-tight-hM3Dq-mCherry [START_REF] Zhang | Neuronal ensembles sufficient for recovery sleep and the sedative actions of α2 adrenergic agonists[END_REF] was purchased from Addgene (#66795). Adeno-associated viruses (AAVs) were generated at Penn Vector Core, University of Pennsylvania (serotype 8, 10 13 genome copies/mL, 1:2 dilution with sterile PBS on the day of injection).

Stereotaxic injection

Mice were anaesthetized with ketamine/xylazine (100 mg/kg/10 mg/kg, Sigma-Aldrich) and AAV vectors were injected stereotaxically into the piriform cortex (PCx, coordinates relative to bregma: anterior-posterior, -0.6 mm; dorsal-ventral, -4.05 mm; lateral, 4.05 mm and -4.05 mm). Using a micromanipulator and injection assembly kit (Narishige; WPI), a pulled glass micropipette (Dutscher, 075054) was slowly lowered into the brain and left for 30 seconds in place before infusion of the virus at an injection rate of 0.2-0.3 µL per min. 0.8-1 µL of virus was sufficient to infect a large area of PCx. The micropipette was left in place for an additional 3-4 min and then slowly withdrawn to minimize diffusion along the injector tract.

Immunohistochemistry

Mice were deeply anesthetized with pentobarbital and perfused transcardially with phosphate-buffered saline (PBS) followed by 4% paraformaldehyde. Brains were Elektronik).

Behavioral apparatus

A training box was used to train mice to escape from an odor. The box was rectangular (L 57 cm, W 17 cm, H 64 cm), with a grid floor made of 72 stainless-steel rods (diameter=6 mm, space between rods=2 mm) and walls made of gray Altuglas Visio. Current was delivered by an aversive stimulator (MedAssociates, 115V, 60 Hz).

A custom-made switcher allowed an electric foot shock (0.6 mA, 0.6 ms) to be applied independently to either half of the box. A testing box was used to test Sniffing behavior was monitored in freely moving mice using a plethysmograph (Emka Technologies). Electrical signals were amplified using RHD 2132 amplifier boards (Intan Technologies) and band-pass filtered (1-30 Hz).

Odors were delivered using an 8 channels olfactometer (Automate Scientific). The olfactometer output was split into two channels downstream of the odor bottles, and controlled by independent valve controllers for left/right presentation. A continuous clean air stream and the output from the olfactometer valves converged into a custom-made manifold. To avoid pressure changes when presenting the odors, a valve connected to a bottle of mineral oil (Sigma-Aldrich) was opened when the valves connected to the odor bottles were closed. The following odors (Sigma-HA-stained neurons (hM4Di) were counted by hand. hM3Dq-mCherry and Fospositive neurons were counted using a custom-written ImageJ plugin. After preprocessing the image (Subtract Background, Remove Outliers and Median Filter), the z-stack is thresholded using the RenyiEntropy algorithm. On each slice of the stack, objects with an area smaller than 40µm 2 are removed using the Analyze Particle command in ImageJ. A mask of each slice from the stack is created containing the filled outline of the measured particles. The number of cells is the number of 3D objects detected in the stack. Automated cell detection can be prone to errors; thus, the detection efficiency was checked on a few pictures by two people blind to the experimental conditions. An estimate E TOT of the total number of neurons (counterstained with NeuroTrace) per cubic millimeter (7.1e4 mm -3 ) was obtained by counting neurons in representative volumes containing the three layers of PCx.

Numbers are consistent with those obtained by [START_REF] Srinivasan | A quantitative description of the mouse piriform cortex[END_REF]. The total number of neurons in each stack was calculated by multiplying E TOT by the volume of the stack.

Electrophysiology

Electrophysiological data were analyzed with custom-made software in Python 3.0 and averaged in MS Excel (Microsoft, USA). Cell types were classified based on their excitability, input resistance, the resting membrane potential, as described in [START_REF] Suzuki | Neural Coding by Two Classes of Principal Cells in the Mouse Piriform Cortex[END_REF] and morphology obtained from 2-photon images

Behavioral data

Behavioral sessions were video recorded and analyzed using custom-written Matlab programs (https://git.io/fxVeE). Parameters extracted from multiple CS+ (CS-) presentations were averaged for each mouse, when testing occurred in the