Robust encoding of sub-sniﬀ temporal informa6on in the mouse olfactory bulb

Summary The sensory world is highly dynamic, and the temporal structure of s7muli contains rich informa7on about the environment. Odour plumes are shaped by complex airﬂow that imprint informa7on about the nature and spa7al organisa7on of the olfactory environment onto their temporal dynamics. Whilst insects and mammals alike can discern high-frequency informa7on, how temporal proper7es of the olfactory environment are represented in the brain remains largely unknown. Here, we presented temporally rich and systema7cally varying odour s7muli whilst electrically recording from the output neurons of the mouse olfactory bulb, mitral and tuCed cells (MTC). We found that temporal aspects of odour s7muli could readily be read out from MTC responses, with a temporal resolu7on of up to 20 ms. Remarkably, temporal representa7on was virtually iden7cal across three diﬀerent odours. To understand which temporal features are encoded, we developed a single-cell model accurately describing both single-cell and popula7on responses. Temporal recep7ve ﬁelds of MTCs translated between diﬀerent odours, indica7ng that MTC tuning to odour quality and dynamics are par7ally separable. Together, this suggests a stereotypical representa7on of odour dynamics across projec7on neurons and can serve as an entry point into dissec7ng mechanisms underlying how informa7on about the environment is extracted from temporally ﬂuctua7ng odour plumes.


Introduc.on
Pauses shaping syllables of speech, a growing spot on the reAna suggesAng a nearing predator, the wobbling electric fields indicaAng the proximity of a predatory fish, whiskers vibraAng when palpaAng a new-born pup -dynamics are a key aspect of sensory sAmuli, oMen encoding features criAcal for an animals' survival.Yet, in the realm of olfacAon, the significance of temporal dynamics is frequently underesAmated.Odours, transported by complex and oMen turbulent airflow, form rich temporal structures in their instantaneous concentraAon [1][2][3][4] .The resulAng concentraAon fluctuaAons are known to contain informaAon about the nature of odour sources, such as their distance or direcAon 2,5,6 .In insects, it has been well established that this informaAon can be used to guide behavioural decisions such as odour source localisaAon 7,8 .Further, both odour idenAty and turbulence have been reported to be essenAal for some insect behaviours 9 .More recently, similar temporal acuity has been demonstrated for mammals, suggesAng that even high-frequency (>10 Hz) odour dynamics can be exploited for behavioural decisions 5 .
How such temporal dynamics shape neuronal acAvity and how the brain might extract informaAon from it is sAll poorly understood.In insects, subpopulaAons of neurons in the olfactory processing pathway have been found to couple to select temporal features 10,11 .In lobsters, for example, olfactory receptor neurons were shown to implement specific temporal filters 12,13 .
In mice, olfactory sensory neurons (OSNs) in the nasal cavity transform chemical informaAon into electrical impulses 14,15 .OSNs in turn project their axons to the first processing stage of the olfactory system, the olfactory bulb (OB).There, they establish synapses not only onto projecAon neurons (mitral and tuMed cells, MTCs) that extend their axons into diverse corAcal areas such as entorhinal cortex, piriform cortex or corAcal amygdala 16,17 .They also connect to periglomerular neurons that -together with a variety of superficial and deep interneuron populaAons 18 -shape the output of the OB [19][20][21][22] .
While individual OSNs generally show slow kineAcs 15 , the enAre populaAon of OSNs readily represents inter-pulse intervals down to ~10 ms 5 .Similarly, MTCs were shown to respond disAnctly to e.g.correlated or anAcorrelated sAmuli and the populaAon reflected -in both sub-and suprathreshold acAvity -the frequency of modulated odour concentraAon faithfully 5,23 .Moreover, when presenAng intermi^ent or pa^erned sAmuli, MTCs show diverse responses, suggesAng that MTCs may differently encode temporal features present in odour sAmuli [24][25][26] .There are both experimental and theoreAcal suggesAons that a combinaAon of cellular biophysics and network computaAon underlies these temporal filter properAes 22,27 .However, central quesAons remain unanswered.For example, how do the recepAve fields of individual neurons contribute to the global populaAon representaAon of select temporal features?Or, how does the preference for specific temporal structures manifest in single-cell properAes?Further, how separable are responses to temporal dynamics and odour idenAty at both the individual and populaAon levels?
Thus, here we systemaAcally assess the representaAon of sub-sniff temporal structure in the output of the OB.We find that 20ms pa^erns are faithfully separated by populaAons of OB projecAon neurons.Moreover, we find that the response properAes of individual neurons could be parametrized along a 2-dimensional manifold and fall into ~5 different archetypes.Importantly, not only were temporal structures for different odours represented near-indisAnguishably, but on an individual cell level, responses to the dynamically varying intensity fluctuaAons of one odour strongly predicted the temporal recepAve fields to other odours.Thus, not only do we find a robust representaAon of sAmuli on 20 ms Ame scales but we do provide evidence that temporal and chemical responses are parAally separable.

Individual cells respond consistently to s2mulus subsets with single feature variability
To probe the response of the olfactory system to temporally complex sAmuli we designed a panel of systemaAcally varying, temporally structured sAmuli and delivered them triggered on onset of inhalaAon using a recently developed high-speed odour delivery device 5,23  Assuming a temporal resoluAon of ~50 Hz (20 ms 5 ), a mouse inhalaAon duraAon of ~100 ms, and a single sniff as a key unit of olfacAon [28][29][30] resulted in 5 "Ame bins" andignoring concentraAon variaAons within each bin -32 (2 5 ) disAnct sAmuli for each odour (Fig 1B).Whilst presenAng these temporally rich odour sAmuli, we recorded the acAvity of in total 130 putaAve projecAon neurons of the olfactory bulb (OB) (from here on referred to as mitral/tuMed cells or MTCs) using extracellular silicon probes (Fig 1A, Supp Fig 1 .2;n=8 mice anaestheAsed with a ketamine/xylazine mixture (Methods)).The odour pulses in these sAmuli pa^erns were presented along with pulses of odourless "blank" air.We found that the total flow over each sAmulus presentaAon did not vary (Fig 1C What odour features do MTCs respond to?A natural possibility is that neurons in the OB encode the total amount of odour (i.e.concentraAon) during a sniff.To invesAgate this, we examined responses to a subset of 5 sAmulus pa^erns which varied only by the total odour presented (Fig 1Di).Indeed, as previously described 31 , we could idenAfy MTCs responding in a graded fashion to the sAmulus subset of increased total odour (Fig 1D).19/130 MTCs showed a significant correlaAon in response with increased total odour (Pearson R correlaAon coefficient, p < 0.05).Latency or phase during sniff cycle has also been proposed as a key feature for odour encoding in the OB 32 .By latency, we refer to Aming of odour presentaAon relaAve to the onset of inhalaAon.A small latency refers to an odour presentaAon with a short delay between the onset of inhalaAon whilst a larger latency would refer to an odour presented later into inhalaAon.Thus, we invesAgated whether MTCs showed a systemaAc change in acAvity following latency changes in a selected subset of 5 sAmuli (Fig 1Ei).Again, 35/130 MTCs showed a significant correlaAon between response and odour latency (Fig 1E) (Pearsons R correlaAon coefficient, p < 0.05).Across the enAre populaAon of cells, we were able to discern changes in cell firing following small changes in either of these two features (Fig 1F).
Total odour and latency are sAmulus features that are frequently suggested as important properAes the OB might represent.Our comprehensive set of sAmuli, however, offers us the opportunity to invesAgate the representaAon of other and more general temporal properAes.
For example, we find that intermi^ency -the delay between subsequent odour pulses -is reflected accurately in some MTC units as well (Fig 1G), suggesAng that even more complex temporal odour plume characterisAcs might shape mouse OB acAvity.

Temporal features are robustly encoded in neuronal popula2on ac2vity
Based on our analysis above we conclude that individual MTCs can have recepAve fields for features like latency or intermi^ency.How does this translate to sAmulus encoding in the MTC populaAon?The recorded responses of cells might not be uniformly distributed in relaAon to the variaAons in the sAmulus set.For instance, in Fig 1Dii-iv, the responses elicited by sAmuli with higher total odour concentraAon are more alike than those triggered by sAmuli with lower total odour concentraAons.The extent to which these features are separable is not clearly determinable by examining the PSTHs of example cells alone.Therefore, we trained linear classifiers on the responses of random subsamples of MTCs to the total odour sAmuli subset (as shown in Fig 1Di).We found that total odour could be reliably disAnguished by the MTC populaAon at accuracies of up to 57 % (Odour 1 (O1) -57%, O2 -50%, O3 -52%), well above chance (17%; Fig 2Ai).InteresAngly, some pa^erns were easier to disAnguish than others as illustrated by the confusion matrix (Fig 2Bi).When we examined classifier performance, we found that classifiers could readily discriminate both the "no odour" sAmulus and the single 20 ms pulse of odour from all others.However, accuracy declined as the amount of total odour was further increased so that odour sAmuli of intermediate and high total odour were much less discriminable (Fig 2Bi).We repeated this classifier analysis with the latency to odour arrival subset (Fig 1E) and again found that latency trials were disAnguishable from each other at accuracies well above chance (O1 -63%, O2 -59%, O3 -54%, chance 17% Fig 2Aii).However, as apparent from the confusion matrix, the misclassificaAon between these trials was more uniform than between the total odour trials in 2Bi (Fig 2Bii).The trials were more uniformly disAnguishable, with an increase in confusion between trials with long latencies, later during the inhalaAon, i.e., the top 3 rows of the matrix, consistent with recent behavioural observaAons 33 .What about more complex pa^erns?To this end, we invesAgated the "intermi^ency" sAmulus subset (Fig 1G) on a populaAon level where both total odour and latency were held fixed but the Ame between two odour pulses varied between 0 and 60 ms.The populaAon again faithfully classified these sAmuli with all trials similarly separable from one another (O1 -71%, O2 -67%, O3 -54%, chance 25%) (Fig

Select temporal features are encoded independently of one another
Having established that addiAonal temporal features are indeed encoded in the neural acAvity, we moved on to consider the implicaAons of this finding in a real-world context.In a naturalisAc serng, an olfactory-reliant animal may be required to extract temporal features containing informaAon from noisy uninformaAve features i.e. group together different sAmuli depending on a single feature and ignore uninformaAve features.For example, different temporal features are thought to encode the distance between odour sources 5 than are thought to encode the distance between a source and a sampler 34 .It is beneficial to be able to robustly determine if two sources are disAnct irrespecAve of the distance between a sampler and source.RelaAve to the previous paragraph, if the latency of an odour sAmulus is informaAve then it should be extractable irrespecAve of the total odour present in the sAmulus.In general, select features should be disAnguishable despite variaAons in other uninformaAve features.To test this, we repeated our analysis but used all 32 sAmuli.We grouped sAmuli by the total odour present in each sAmulus, defined as the number of 20 ms pulses each contains.For example, a sAmulus of odour-blank-blank-odour-odour would be labelled as '3' as it contains three odour pulses.We found again that classifiers were able to disAnguish trials from each other well above chance (O1 -47%, O2 -42%, O3 -46%, chance 17%,

Rela2ve separability of temporal pa<erns is conserved across odour iden2ty
Our results thus far reveal that features on sub-sniff Amescales such as latency or total odour within a single sniff are represented across the MTC populaAon.Furthermore, specific, more complex temporal pa^erns such as intermi^ency (for sAmuli with idenAcal latency and total odour) can be separated linearly.To extend this analysis to arbitrary (50 Hz) temporal pa^erns we invesAgated the representaAon of all binary pa^erns within a 100 ms inhalaAon.A compact visualisaAon of neural representaAon of the enAre pa^ern is the confusion matrix for a linear classifier (Fig 3Ai Notably, the overall structure of representaAon is largely diagonal, implying that across the 32 sAmuli, representaAons are separable well above chance (O1 -25%, chance 3%).There are, however, disAnct off-diagonal elements, indicaAng parAal generalisaAon across specific different sAmuli.Is this pa^ern random and odour-specific or a general feature of the representaAon of dynamic sAmuli?To answer this quesAon, we repeated the same experiment and analysis for two addiAonal odours (O2 -20%, O3 -21%).Remarkably, the pa^ern of generalisaAon and misclassificaAon was highly similar between odours (Fig 3Ai .Thus, we can conclude that sub-sniff temporal structure of the odour environment is represented across the OB output in a largely odour-invariant manner, reliably represenAng differences between some and generalising across other dynamical pa^erns.

Generalised linear models can be used to capture single-cell temporal tuning How does this populaAon representaAon arise from the contribuAons of individual neurons?
To address this, we first tested whether the populaAon representaAon could be directly reconstructed from basic sAmulus features.This would be the case if neural acAvity reflected e.g. the total odour in a sAmulus.In that situaAon, the representaAonal similarity of a pair of sAmuli would reflect the similarity of their total odour concentraAons.However, we found that neither total odour nor latency nor a combinaAon of both accurately recapitulated the conserved structure of the representaAon (Supp Fig 3 .2).
The sAmulus features driving the acAvity of single neurons, and thereby determining the populaAon representaAon, may be more complex than total odour or latency.Therefore, we next a^empted to determine these features by firng neural acAvity directly.We would then be able to a^ribute the populaAon representaAon to the sAmulus features encoded by the neurons consAtuAng the populaAon.Therefore, we searched for a parameterisaAon of single neuron responses that was sufficiently complete to allow simulated populaAon responses to reconsAtute the confusion matrix, but simple enough that we could directly examine which odour features were encoded by individual neurons.To this end, we constructed generalised linear models (GLM), inspired by linear non-linear Poisson (LNP) models which have been successfully used to model the acAvity of sensory neurons in other sensory modaliAes of the mammalian brain 35 and provide a tractable model of non-linear responses to sAmuli.Our GLMs consist of three steps.First, a filter computes a weighted sum of the inputs.This weighted sum is passed through a non-linearity (chosen to be an exponenAal to preserve convexity), yielding the average firing rate of a Poisson process (Fig 4A).Whilst individual spike counts are not inherently generated during this modelling, the Poisson process alters the form of the loss funcAon used in the firng procedure by assuming that the spike count from repeated presentaAons of a given sAmulus pa^ern follows a Poisson distribuAon.AddiAonally, like LNP models, our GLMs contain no hyper-parameters, simplifying the firng procedure.We chose for our GLM filters to be computed across Ame rather than space, as we were focused on the temporal aspect of the sAmuli.As such, some assumpAons about GLMs used in other studies may not hold here, such as temporal invariance.

Select filters can capture single cell and popula2on ac2vity
In a first step, we assessed which filter could recapitulate single-neuron responses.Consistent with our prior findings (Fig 1), filters that compute latency or total odour accurately capture cellular responses for a large proporAon of neurons (O1 -61%, O2 -53%, O3 -47%, sMAPE score < 0.1, Supp Fig 4 .1).However, even filters combining both features were unable to capture the unique pa^ern of misclassificaAon which was previously found (Fig 3) (Supp Fig 4 .1).Therefore, we constructed an alternaAve filter which weighted each of the five windows present in each sAmulus pa^ern.Whilst this filter was able to capture the acAvity of some neurons, select cells showed changes in their cellular responses which could not be simply a^ributed to a summaAon of the sAmulus pa^ern (O1 -37%, O2 -38%, O3 -40%, sMAPE score < 0.1, Fig 4B).This prompted us to invesAgate filters which were sensiAve to both the presence of odour and rising edges across the enAre sAmulus pa^ern, resulAng in a 9parameter filter (Supp Fig 4 .1).These model weighAngs can be split into two groupings, the base odour sAmuli bins and the first differenAal of these pa^erns.We will refer to this filter in general as the DifferenAal filter.The first five bins encode the presence of odour at a given Ame point in a trial.For example, bin 2 was acAvated when odour was present in the 20-40 ms sAmulus window.The differenAal bins were acAvated when a rising edge was present at a select latency.Bin 6, for example, was acAvated when a rising edge was present at 20ms.The differenAal bins only required 4 parameters because by construcAon bin 1 was always presented with a rising edge.Therefore, bin 1 encoded both odour presence at 0-20 ms and a rising edge at 0 ms.Modelled responses using this filter accurately recapitulated acAvity pa^erns for the majority of cells (O1 -64%, O2 -55%, O3 -51%, sMAPE score < 0.

1, Fig 4B).
To assess whether these single cell models were sufficiently complex to accurately describe populaAon representaAon, we generated confusion matrices based on populaAons of modelled cells.While representaAon generated from latency, total-odour or mixed models failed to recapitulate the experimentally measured representaAon (Supp

GLMs fit to cell responses can be expressed with only 2 features
Having idenAfied a compact descripAon that accurately describes not only populaAon but also single-cell responses, we now set out to interrogate the parametrisaAon to further understand which odour features are encoded by the individual cells.Performing principal component analysis on all parameters across the 130 MTCs showed that more than 84 % of variance is already explained by the first two principal components and relaAve fit error plateaus thereaMer (Fig 5A,B).InteresAngly, these first two PCs were virtually idenAcal between odours (Fig 5Ci,ii, Supp Fig 5 .1).This is consistent with the noAon that representaAon of temporally complex sAmuli is stereotypical across odours.We can therefore describe the populaAon of temporal response profiles of MTCs as a conAnuous, two-dimensional filter manifold (Fig 5D).
Cell responses are generated from these filters through the non-lineariAes of the GLM.How does this filter parameter distribuAon translate to actual temporal recepAve fields?GeneraAng populaAons of model neurons along the filter manifold reproduced the zoo of temporal responses (Supp  5E).Despite the mulAtude of different cellular responses, we found that all cells were tuned towards odours arriving earlier in the trial and therefore earlier in the respiraAon cycle (Supp Fig. 5.3).We found no evidence for cell tuning spanning the enAre respiraAon cycle.However, not all cells were found to be uniformly excited/inhibited by both odour presence and rising edges arriving earlier in the respiraAon cycle.For example, cells in region 2 had a posiAve weighAng for odour presence and a negaAve weighAng for rising edges (Supp Fig. 5.3B).We found that cells from certain regions encoded select temporal features be^er than cells from other regions (Supp Fig. 5

Temporal tuning is odour independent
We have shown that representaAon and the nature of the temporal filters is highly consistent between different odours (e.g.Fig 3 , Fig 5).While this points towards a consistent, chemicalindependent representaAon of temporal informaAon, it does not directly address the quesAon whether there is such thing as an odour-independent "temporal recepAve field" of a neuron.2).Consistent with that, a GLM trained on odour 1 reliably predicted responses to odour 2 (again except for scaling and offset, Supp Fig 6 .4).Together this suggests that MTC responses are shaped by the temporal structure of odour input, parAally independent of the chemical nature of the presented odour.

Discussion
The olfactory bulb encodes select temporal features Whilst it has been speculated that the complex shape of the nasal cavity and the diffusion of odour molecules through the mucus layer in the nasal cavity may impose a low pass filtering effect on incoming odour sAmuli 36 , we have shown here that the mammalian olfactory system readily encodes fast sub-sniff temporal informaAon, further expanding on results found previously 5,23 .We found that select properAes, such as the latency to odour onset, were readily decodable from a small number of neurons (Fig 2Ai-iii).Further, we found that these features were sAll readily accessible even when the whole sAmulus set was used (Fig 2Aiv,v).In addiAon to these simplisAc features, general 20ms pa^erns could be reconstructed from populaAon acAvity well above chance (Fig 3A).Intriguingly, the pa^ern of misclassificaAon between the responses was highly conserved across the three odours used here, indicaAng that the OB has the capacity to represent temporal structure uncoupled from its be^er-known capacity to represent odour idenAty (Fig 3A).

Single cell responses are explainable with a small number of components
To uncover the structure of temporal representaAon in the OB, we explored what single neuron tuning could generate such misclassificaAon pa^erns and found that we were able to capture single cell acAvity using GLMs and recapitulate populaAon representaAon (Fig 4E).The weighAngs extracted from these models were found to exist predominantly in a small number of PCs (Fig 5A,B).Therefore, the apparent rich temporal responses previously observed could be expressed by a combinaAon of these two PCs.Further, these PCs were highly conserved across the three odours (Fig 5C).We found that these PCs both had larger weighAngs for odour presence and edges which arrived earlier in a sAmulus, consistent with the noAon that the OB is tuned to odours arriving earlier in inhalaAon 37 .This tuning may derive enArely from the physics of airflow during an inhalaAon cycle with peak airflow occurring shortly aMer the onset of inhalaAon 38 .Increasing the inhalaAon rate may increase the sensiAvity of the olfactory system and allow for greater disAnguishability between similar odour sAmuli 39,40 .

Cell responses dras2cally vary across the PC space
CombinaAons of these two principal components were found to generate the wide range of responses we observed iniAally (Fig 5E).All resultant combinaAons of the two PCs showed consistent excitaAon/inhibiAon to odour presence or rising edges.Whilst the presence of odour and the rising edges are not mutually exclusive it may be easy to assume that a cell which was excited by the presence of odour would also have had a posiAve change to firing following a rising edge.This was not inherently the case.Cells in region 2 and 3 (Supp Fig 5 .3B,  D) showed inverted excitaAon/inhibiAon between edges and odour presence.Cells in region 2 were excited by odour presence but were inhibited by rising odour edges whilst cells in region 3 showed the opposite, increasing their firing when rising edges were present but decreasing it as total odour presented increased.

What circuitry generate the response pa<erns?
The origin of the 'inverse' temporal tuning (e.g., excited by odour presence but inhibited by rising edges) of some of the MTCs may arise from a variety of sources.It is unlikely that single OSNs are able to couple directly to the fluctuaAng odour presented here 41 but it has been previously speculated on how OSNs may transmit fast temporal informaAon despite not consistently encoding it 5 .Instead, this behaviour may be due to long range inhibiAon from other glomeruli, in which case the inhibiAon/excitaAon balance would be driven largely by receptor dynamics.Neurons which sample from a fast receptor may be excited iniAally, then when slower or lower affinity receptors increase their acAvity to other glomeruli, may increase lateral inhibiAon to the recorded cell.This could be explored by blocking local inhibiAon in the glomeruli layer, as done previously 22,42 during recording.If the same inverted behaviour is observed then this acAvity is likely driven by far reaching lateral inhibiAon in the granule cell layer.AlternaAvely, this behaviour may be primarily due to the local inhibitory circuitry in the OB.Both projecAon neurons and local interneurons receive direct input from ORNs.Therefore, for example, an iniAal rising edge of odour may drive a projecAon neuron to a greater extent than the inhibiAon generated via local interneurons and produce an increase in firing, whilst conAnual odour presentaAon ramps up the acAvity of the local inhibitory circuitry and dominates over the excitatory input to a projecAon neuron.In fact, the consistent temporal tuning of individual cells across odours (Fig 6, Supp Fig 6 .1)supports the noAon that the underlying mechanism is largely feedforward.If this effect was driven by lateral inhibiAon from other glomeruli, we would expect the inhibiAon to vary between odour idenAAes, as different glomeruli would be acAvated.This variaAon in inhibiAon would be expected to differently inhibit the recorded MTCs and generate variaAons in their temporal tuning.Further, whilst the MTCs receive their input from OSNs, it is unlikely that the output of the OSNs alone is able to robustly encode the complex temporal fluctuaAons presented here.

Single cell responses are odour independent
Finally, we asked if these temporal responses were cell specific.We found that cells were able to be^er fit their response to another odour than any random cell could.We found that many cells produced highly correlated responses across odours (

2).
Numerous of these alternaAve responses were also flipped from excitaAon to inhibiAon or inhibiAon to excitaAon.Despite this inversion of response sign, the relaAve change in firing between these sAmuli were highly conserved.Cells which were poorly fit typically showed a weak response to one of the odours in quesAon.Therefore, the responses of these cells to temporal fluctuaAons might derive from feedforward circuitry (that will influence MTC responses similarly if the parent glomerulus is excited) rather than either feedback or lateral inhibiAon from other glomeruli columns.

Separability of odour iden2ty and temporal features
How are both temporal and odour idenAty informaAon encoded by the same populaAon of cells?It is well known that different odours evoke different pa^erns of glomerular acAvaAon across the OB, encoding odour idenAty spaAally.As MTCs receive direct input from a single glomerulus, odour idenAty can be enArely encoded in the index of each acAvated MTC without considering the relaAve change in firing rate over shorter Ame scales.Therefore, as shown here, the temporal aspects of sAmuli may be encoded in the relaAve firing rate of acAvated neurons, fully separaAng odour idenAty and temporal encoding.Whilst this is an oversimplificaAon, and the inclusion of addiAonal odours presented during sAmuli would likely alter the relaAve firing of individual MTCs, the general concept outlines how temporal informaAon may be encoded without encroaching on odour idenAty.Further, due to the blind extracellular recordings done here, it is difficult to accurately separate mitral cell from tuMed cell responses.As tuMed cells receive more direct input from OSNs they may preferenAally encode odour idenAty whilst mitral cells may play a larger role in encoding other, possibly temporal, features.Further, mitral cells are known to respond with a delay relaAve to TCs, due to the inhibitory network in the OB 43 .This inhibiAon may be encoding the mitral cells with informaAon extracted over the enAre sniff, whilst the tuMed cells deliver iniAal odour idenAty informaAon to downstream regions.If this is true then silencing of the local inhibitory connecAons to mitral cells should prevent the extracAon of temporal informaAon.

Final thoughts
We have shown here that the early olfactory system has a high temporal bandwidth enabling it to discriminate small differences between olfactory sAmuli based enArely on their temporal profiles.Further, we have shown that the projecAon neurons of the OB are tuned towards both the presence of odour, and rising edges, but not inherently with the same response sign.These responses are likely generated by local circuitry and may be of importance for discriminaAng fast temporal fluctuaAons of naturalisAc odour sAmuli.

Materials availability
This study did not generate new unique reagents.

Animals:
All mice used for recordings were C57BL/6 male mice aged between 5-8 weeks old.All experiments were conducted in line with the Animals (ScienAfic Procedures) Act 1986 (2013 revision) and EU direcAve 2010/63/EU.All surgeries followed the protocol outlined below.

Surgery:
All surfaces were sterilised with 1% trigene.5-8 week old C57BL/6Jax mice were anaestheAsed using a mixture of ketamine/xyazline (100mg/kg and 10mg/kg respecAvely) by intraperitoneal (IP) injecAon.An IP line was inserted aMer the iniAal injecAon to allow for easier and more regular subsequent injecAons of anaestheAcs.During surgery and recordings, the toe-pinch reflex of the mice was measured rouAnely roughly every 15-20 mins to monitor the level of anaesthesia.Fur from the Ap of the nose to the base of the neck was shaved over, and the skin cleaned with 1\% chlorhexidine.A rectal probe was inserted into the mice and their temperature fed into a thermoregulator (DC Temperature Controller, FHC, ME USA) which was used to set the temperature of a heat mat to ensure that the mouse's internal body temperature did not drop during the recording in a closed loop manner.The head of the animal was placed into custom made ear-bars.A scalpel was used to make an incision along the midline of the head, from just in-front of the eyes, to just between the ears.Springsteel scissors were used to make small cuts horizontally at both end of the main iniAal incision to make two flaps.These were pulled back using four arterial clamps, two at the front, and two at the back.The skull was then cleaned of connecAve Assue using a bone-scraper.A custom head-fixaAon implant was a^ached to the base of the skull using medial super glue (Vetbond, 3M, Maplewood MN, USA), with its most anterior point resAng approximately 0.5 mm posterior of bregma.Dental cement (Paladur, Heraeus Kulzer GmbH, Hanau, Germany; Simplex Rapid Liquid, Associated Dental Products Ltd., Swindon, UK) was then applied around the edges of the implant to fix it securely in place.A well was built out of quick drying silicon (Kwik-Cast, WPI, Sarasota, FL, USA) to a height of approximately 5 mm around the edge of the cleared skull.A craniotomy roughly 2 mm x 2 mm was opened over the mouse's leM olfactory bulb hemisphere by gently drilling a 2 x 2 mm hole over the hemisphere.Once the drill had broken through the bone the silicon well was filled with ACSF (NaCl (125 mM), KCl (5 mM), HEPES (10 mM), pH adjusted to 7.4 with NaOH, MgSO4.7H2O(2 mM), CaCl2.2H2O(2 mM), glucose (10 mM)) to cover the skull.The bone fragment was removed with fine forceps.The dura was removed with a bent high gauge needle to expose the brain.Following surgery, mice and custom pla€orm were transferred to the extracellular recording set up.A flow sensor (A3100, Honeywell, NC, USA) was placed in front of the contralateral nostril whilst an output from the temporal olfactometer was posiAoned in front of the ipsilateral nostril.The respiraAon was conAnuously monitored through this flow sensor, and the onset of inhalaAon was used as a trigger to iniAate odour presentaAon.An Ag/Ag+Cl-reference coil was immersed in the well, over the right hemisphere of the skull.The reference wire was connected to both the reference and ground of the amplifier board (RHD2132, intan, CA, USA), which was connected (OmneAcs, MN, USA) to a head-stage adapter (A32-OM32, NeuroNexus, MI, USA).A 32-channel probe (A32-Poly3/A32-Buzsaki, NeuroNexus, MI, USA)/(H6b, Cambridge Neurotech, Cambridge, UK) was connected to the adapter, and the Ap of the probe was manoeuvred to be posiAoned 1-2 cm above the craniotomy.The adapter and probe were held above the craniotomy using a micromanipulator (PatchStar, ScienAfica, UK) set at 90 degrees to the surface of the brain.The probe was moved towards the surface of the OB, whilst being observed through a surgical microscope.Once the probe was in contact with the surface, but had not entered the brain, the manipulator's Z posiAon was set to zero.The signal from the probe was streamed through an OpenEphys acquisiAon board and soMware (OpenEphys, RI, USA).The probe was inserted at < 4 µm/s unAl the number and amplitudes of spikes began to decrease on deeper channels, indicaAng the Ap of the probe was exiAng the MC layer.This was found to be between 400-600 µm from the surface of the OB.From here, the probe was leM for 10 minutes for neural acAvity to stabilise before recording began.
All temporal sAmuli were delivered using a custom odour delivery device.This device is briefly outlined in both 5,23 .The device consists of two sets of four odour channels, with each channel individually controllable.The device itself consisted of two manifolds, the odour bo^le manifold, and the high-speed valve manifold.First, the odour bo^le manifold was constructed out of a custom milled steel block.The block contained 4 circular indentaAons approximately 1 cm in radius, and 1 cm in depth.In each of these indentaAons two threaded holes were drilled through to the top of the manifold.One was used to install an input flow controller (AS1211F-M5-04, SMC, Tokyo, Japan) and the other a filter (INMX0350000A, The Lee Company, West-brook CT, USA).Inside each indentaAon, the cap of a 15 ml glass vial (27160-U, Sigma-Aldrich, St. Louis MO, USA) with a hole drilled in its centre was stuck, and sealed with epoxy resin (Araldite Rapid, Hunstman Advanced Materials, Basel, Switzerland).The epoxy was used both to hold the cap, and to create an airAght seal when a glass bo^le was screwed into the lid.Once the epoxy was set, the filter and flow controller were installed.Each flow controller was fed an individual airflow which could be adjusted via the flow controller.The accompanying glass bo^les from which the lids had been taken were screwed back into the now fixed lids.These bo^les were filled with odour diluted in mineral or pure mineral oil, as outlined in the secAon Odour sAmulaAon.The filter output from each odour channel connected to a single very high speed (VHS) valve (INKX0514750A, The Lee Company, Westbrook CT, USA).Each valve was fit into a four-posiAon manifold (INMA0601340B, The Lee Company, Westbrook CT, USA).The valves were connected to the odour bo^les with a short length of Teflon coated tubing (TUTC3216905L, The Lee Company, Westbrook CT, USA).The valves were controlled using a custom-built spike-and-hold driver.Each driver could provide a 0.5 ms 24 V pulse to open the valve and maintain its opened posiAon with a 3.

Odour s2mula2on:
Odours were presented using an 8-channel version of the high-speed odour delivery device, which always contained 4 odours and 5 blank mineral oil channels, which were used to compensate flow during the recordings.Only 3 of the 4 odours were presented in these recordings.The odours were Odour 1 (O1): ethyl butyrate, O2: isoamyl acetate, O3: ethyl acetate.All odours were obtained at the highest purity available from Sigma-Aldrich.Onset of odour for all experiments was recorded using TTL (Transistor-transistor logic) pulses passed through addiAonal channels in the OpenEphys acquisiAon board.Trial starts were triggered on inhalaAon as detected by the flowmeter.
All odours presented were always `square' in shape, with instantaneous switching between odour off state, when the valve was closed, and the odour on state, when the valve was opened.Temporal fidelity was confirmed prior to neural recording using a PID (200B miniPID, Aurora ScienAfic) with the PID inlet posiAoned within 0.5 cm of the odour delivery port from the olfactory delivery device.For calibraAon trials ethyl butyrate was used as it elicited the strongest signal of the four odours.AMer confirming the stable presentaAon of the odour sAmuli, the PID was replaced with a flow sensor (AWM5101VN, Honeywell, USA).The flow sensor was used to ensure that airflow fluctuaAons during odour presentaAon were not present, and that the trial appeared as a single step funcAon.Odours were presented with the defined temporal pa^ern, with a 500Hz sha^ering convoluAon.This convoluAon oscillated the opened valve at 500 Hz.This stabilised the airflow through the valves and prevented a drop in odour delivery over extended trials.Further, the sha^ering improved both the rise Ame and the fall Ames of the square pulses.To ensure that the odour presentaAons did not decay at the end of the trial and therefore reduce the fidelity of the signal, all presentaAons were followed by an addiAonal 20 ms of odourless air.This was found to preserve the odour temporal pa^ern fidelity.

Trial randomisa2on:
The sAmuli were randomised between each repeAAon, and the number of repeAAons of the shuffled list varied between the experiments, from 3 to 15 Ames.The list itself contained different numbers of repeats of each trial type.No single trial type was presented less than 8 Ames to any animal in any of the experiments.

Analysis
Spike sor2ng: Spikes were extracted from the extracellular recordings using Kilosort3 (h^ps://github.com/MouseLand/Kilosort).Kilosort3 is a later iteraAon of the original Kilosort algorithm, which is outlined in 44 .For all recordings, units were isolated in the same manner.Units were classed as `good' if they displayed a strong refractory period, visible in their autocorrelogram, a typical waveform, and a stable firing rate throughout the majority of the recording.Units were classed as `MUA' (mulA-unit acAvity) if they presented a typical waveform, but a weak refractory period, and/or a variable firing rate.Lastly units were classed as `noise' if they showed no typical waveform and were suspected of being electrical or mechanical interference.All subsequent analysis was undertaken using custom Python code, accessible on github (h^ps://github.com/warnerwarner).

Responsive units:
Units were selected as responsive if they responded with at least 1 spike during a 500 ms window post sAmulus onset during every sAmulus presentaAon.

Bootstrapping datasets:
The number of repeats varied across mice and sAmulus type.In some instances, the experiment had to be concluded early due to faults with the acquisiAon system.Downstream analysis packages required a universal number of repeats for each sAmulus across all mice and experiments.To correct for the inconsistent number of repeats across pooled units in some of the datasets used, the data was bootstrapped such that the number of repeats for each unit and each trial type were idenAcal.As each recording in the dataset contained the same number of repeats for a given trial, all units were bootstrapped together, in an a^empt to preserve any co-fluctuaAons, present between cells in the dataset.For each recording, for each sAmuli type presented, the repeAAons from the recording's units were gathered, and sampled with replacement to increase the number of repeats arAficially.These resampled datasets were concatenated together and passed on for further analysis.To resample each recording's repeAAons numpy.random.sample was used.

Linear classifiers implementa2on:
All classifiers used were instances of sklearn.ensemble.RandomForestClassifier, a python implementaAon of a random forest classifier.In brief these classify labelled data by splirng data using random selecAons of parameters (in this case, the firing of individual cells) using decision trees.These decision trees are then grouped together (hence Forest) and used to idenAfy unseen data.

Classifica2on of bootstrapped data
Bootstrapped data cannot be thoroughly tested using a typical train/test split method as repeAAons of trials may be present in both the training and tesAng set of the data.Therefore, to avoid this, during the bootstrapping process outlined in Bootstrapping datasets secAon, one repeat was removed prior to the resample processes and preserved.The remaining repeats were bootstrapped as usual.The bootstrapped data was used to train Random Forest classifiers and was tested using the iniAal withheld trial.Unless reported otherwise this split, bootstrap, train, test procedure was repeated 100 Ames with a random withheld trial each Ame.

Neural response embedding:
Average responses were taken at each Ame point prior to, during, and post sAmulus.The responses were constructed of the average firing rate of each unit at each 10 ms Ame point for each sAmulus type presented (130 x 32).This matrix was used to calculate the distances between the neural response to each sAmulus to construct a distance matrix of size 32 x 32.A single dimensional vector was constructed with the same length as the number of sAmuli (32).The values in this vector were used to construct a second distance matrix also of size 32 x 32.The least squares error between these two distance matrices was used as the loss funcAon.DifferenAal evoluAon (scipy.opAmize.differenAal_evoluAon)was used to alter the posiAon of the 32 x 1 vector to minimise the difference between the two distance matrices.This was repeated for each Ame point individually.To align the reduced representaAons across Ame the least squares error was calculated between the reduced representaAon and the reduced representaAon from the previous Ame step.This was compared to the least squares error between the previous Ame step representaAon and the current Ame step inverted around 0 (i.e., mulAplied by -1).If the inverted error was less than the original, then the inverted version was used.If the original was smaller than the inverted version, then the inverted version was discarded.

Distance matrix es2ma2ons
Distances between trials were esAmated by assigning every sAmulus pa^ern a value dependent on either the total odour duraAon or the latency to the odour onset.For the total odour duraAon these values increased in increments of 1 (1 represenAng a trial with a single 20 ms window of odour) from 0 (no odour presented) to 5 (100 ms of odour presented).The latency was represented in a similar manner, with a latency of 0 represenAng 0 ms latency, increasing in increments of 1 (each represenAng a 20 ms increase to latency).The single conAnuously blank sAmulus (blank-blank-blank-blank-blank) was labelled as 5 despite it having no true latency.
Single unit Generalised linear models GLM (Generalised linear models) were constructed using custom Python classes.All instances of the model used the same exponenAal non-linearity and Poisson process and only varied their linear filters.The exponenAal used was the numpy.expfuncAon and the Poisson process the scipy.stats.poissonfuncAon.Models were fit by minimising the Poisson loss funcAon: where  is the loss that is to be minimised,  !& is the esAmated average firing rate of the unit to sAmuli ,  " is the true average firing rate of the unit to sAmuli , and  is the number of sAmuli to be considered, in the case of the single sniff temporal sAmuli  = 32.The fit score was then esAmated by the root mean squared difference between the predicted firing and the true firing, e.g.
where again  !& and  " are the predicted and true firing rates for a unit, σ " is the average standard deviaAon for this cell for trial .To prevent any division by zero if a cell had no variance in a set trial response (occurred with some of the low firing cells) the variance was set following Filters of GLMs Four filters were tested with the GLMs, the total odour, latency to iniAal odour onset, latency and total odour (L&T), and the DifferenAal filter.The total odour filter was constructed by iniAally taking the temporal pa^ern, e.g.blank-odour-blank-blank-blank and counAng the number of odour pulses within the trial.These were represented with a one-hot-encoding representaAon, such that instead of a single variable encoding the number of odour bins, 5 separate bins were used.The latency filter was constructed by taking the temporal pa^ern and selecAng the first index with odour, e.g.blank-odour-blank-blank-odour would have an onset representaAon of off-on-off-off-off.The L&T filter was a conjuncAon of the total odour and onset filters as they appear in Supp Fig 4 .1Aand contained 10 bin weights.The DifferenAal filter consisted of a one-hot-encoding representaAon of odour presence in each bin and rising edges in bins 2-5 (Supp Fig 4 .1F).All models also had an addiAonal bin weighAng that was set to 1 in all trials, which could be used as a threshold and allow the model to set the firing rate to a non-zero value even if all other inputs were 0.

GLM firng mechanism
The weighAngs for all filters were fit using the same firng process.The bin weights were iniAalised as all zeros, and no bounds were imposed.Firng was achieved by minimising the Poisson loss funcAon (Eq1) and used the scipy.opAmize.minimizefuncAon to do this.This funcAon uAlises the BFGS quasi-Newtonian opAmisaAon funcAon by default.Once the firng algorithm is completed it returns the bin weights and the fit error.
The predicted firing rate was generated by linearly projecAng the bin weighAngs with one of the filter pa^erns, and summing across the bins for each trial.This value was passed into an exponenAal funcAon, and the output was interpreted as the average predicted firing rate of the cell.As the exponenAal was strictly posiAve, whilst the bin weighAngs cannot be directly interpreted as firing rates, their relaAve values to one another do indicate which weighAngs cause a greater change in the predicted firing.

GLM Test train splirng
Data was split into two equally sized halves whilst the relaAve number of repeats of each sAmulus type was maintained.The training half was used to fit the model as outlined in GLM firng mechanism, and the tesAng half was preserved.The tesAng half was subsequently used to calculate the fit error using Eq2.Unless stated otherwise, this splirng was repeated 100 Ames with a random selecAon of training and tesAng trials on each iteraAon.

GLM modelled spike counts classificaAon
Predicted firing rates taken from fit GLMs were used to generate modelled repeats of trials via a Poisson process (scipy.stats.poisson)which takes a single value for the mean/variance of the Poisson process.The number of repeats generated was varied from 2 up to 10.For each number of repeAAons the same classifiers as outlined in (Linear classifiers implementaAon secAon) were used.The correlaAon between the resulAng confusion matrices from the predicted tesAng data and the true confusion matrix were compared.The matrix with the highest correlaAon was then selected.

GLM PCs fit error calculaAon
The weights from each fit GLM were conjoined together into a single 130 x 9 matrix.PCA was applied to this matrix, with the number of components varying between 0 and 9.The PCA coefficients were then inversely transformed back into weighAngs.These weighAngs were passed to the GLMs and the predicted firing calculated for each cell.The error was calculated as before following (Eq2).The fit errors were normalised across the different number of PC instances for each cell such that the maximum error was set to 1.
PC coefficient distribuAon PC1 and PC2 coefficients were modelled following Laplace distribuAons.The scale was esAmated and the fit was verified by comparing the distribuAons between the true and modelled coefficients using a Mann Whitney U test.
PC space sampling PC coefficients were sampled over 10 percenAle steps from the 10 th percenAle to the 90 th along both PC1 and PC2, generaAng 81 samples.The weighAngs at each sample were constructed by mulAplying the percenAle value with the associated PC.These weighAngs were then used to generate a modelled relaAve firing rate.The weighAngs were normalised such that their minimum response was 0 and their maximum was 1.
To generate the region clustering, the top 2 PC spaces were equally sampled in 0.05 steps from -2 to 2. The PC coefficients were then used to construct model weighAngs, which were in turn used to generate predicted responses to the 32 sAmuli pa^erns.The predicted responses were clustered together using K-means clustering.The number of clusters was determined by using both the silhoue^e score and the elbow rule, which jointly indicated 5 clusters as the opAmal number.Cells were assigned their region by passing the fit K-means clustering each cell's predicted response curve.
Inter-odour comparison Cells which were found to be responsive to all three odours (difference in response to 100 ms of odour and 100 ms of blank was larger than the standard deviaAon of their baseline) were selected for this analysis (66/130).Cell responses across mulAple odours were aligned by scaling the response of O2 to minimize the least squares difference between the two response curves.The correlaAons were measured by using numpy.corrcoefwhich calculated the Pearson correlaAon coefficient.The shuffled control was constructed by measuring the correlaAon between the response curve of all selected cells and a randomly selected cell's response to the secondary odour.This random selecAon was repeated 100 Ames.As some cells were found with highly anAcorrelated response curves, the magnitude of the correlaAon coefficients for both the same cell odour comparison and the shuffled control were also compared.

Figures:
Figure 1 Responses of OB units to rapid odour pulses (A) -SchemaAc of the experimental recording set up.An anestheAsed mouse was presented with short temporally complex odour sAmuli whilst OB projecAon neuron acAvity was recorded using silicon probes.(i).This subset contained sAmuli which varied only by the total amount of odour presented with the same latency to the iniAal odour onset.Each cell's response to 100 ms of blank odourless air is shown in each plot by the solid black line.An example respiraAon trace is shown above each PSTH plot.A downwards deflecAon in the respiraAon trace denotes exhalaAon and an upwards deflecAon denotes inhalaAon.SAmulus presentaAon is represented by the grey region in each plot.(E) -Same as in D but for a different sAmulus subset (i).This subset contained sAmuli with the same total odour but varied by their onset latency.As in D, the responses of 3 example cells to this sAmulus set.Note, that these are not the same cells as shown in Dii-iv.(Fi) -The responses of all 130 cells to the total odour varying sAmulus set in D. ii -Same as i but for responses to all cells to the sAmulus set with the same total odour but with a varying latency to odour presentaAon.The respecAve sAmuli are shown at the top of each column.Coloured arrows indicate cells which are displayed in D, E and G.The same colours are present in the box to the top leM of PSTHs in D, E and G. (G) -Same as D and E, but for a sAmulus set with the same total odour and latency to iniAal odour onset across all sAmuli in the set (i).As before the select cell responses (ii-iv) are coloured by the sAmulus pa^ern they are responding to.

Figure 2 Accuracies of classifiers trained on responses to rapid odour pulses (A) -
The average and SEM accuracy for a series of Random Forest Classifiers in disAnguishing subsets or select features present in the sAmulus set against the number of randomly selected neurons.i -The accuracy for classifiers in disAnguishing the total odour variable subset of sAmuli, the same as presented in Fig 1D and 1F.ii -Accuracy in disAnguishing the latency variable subset of sAmuli, the same as presented in Fig 1E and 1F.iii -Accuracy in disAnguishing a subset of four sAmuli pa^erns which contain both the same latency to odour and same total odour present, the same as presented in Fig 1G .iv -Same as i-iii but instead of classifying subsets of the sAmuli set, all sAmuli were grouped by their total odour present.For example, a sAmulus which went odour-odour-blank-blank-blank would contain 2 odour windows, the same as a sAmulus which went odour-blank-blank-odour-blank.v -Same as iv but all sAmuli are grouped by the latency to the first odour window.Chance is shown in all subfigures by the dashed horizontal line.(B) -The confusion matrices for the classifier results show in A. Bv -Values represent the latency to the iniAal odour onset in ms.N/A represents the all blank trial as it does not have a latency value.representaAon which is condensed into a 1-dimensional value (a weighted sum of the 5 components).Second, this value is passed through a non-linearity, in this case an exponenAal funcAon.Third, the output of the exponenAal is used as an esAmate mean of a Poisson processes.(Bi) -An example cell response to all sAmuli (black) with a model firng using only 5 sAmuli bins (green), the same as shown in the schemaAc in A. ii -The same cell as in i, with   Both the full distribuAon and the absolute correlaAons were found to be significantly higher between same-cell response than from the shuffle (p < 0.0001, student t-test).was chosen as it was found to be the first confusion matrix which displayed any structure.Each window was constructed to end 20 ms aMer the previous to best capture the response to the sAmulus as each bin was presented).Responses to each of the three odours are organised in columns (column1 -O1; column2 -O2; column3 -O3).The confusion matrices are normalised across each row to have the same minimum and maximum, shown in the colour bars on each row.Supp Fig4.1 Alterna7ve GLM filters (A) -RepresentaAon of the input filters for the total odour (red) and latency filters (blue).Each filter represents the sequence of 5 blank or odourised pulses in a one-hot-encoding manner.The total odour filter represents how many pulses in each trial contain odour and the latency filter represents the Ame that the first odour pulse arrived.(B) -An example cell's firing response and the predicted firing based on the total odour (i), latency (ii), and a combinaAon of the total odour and latency.This cell was selected as it was captured well by the total odour predicAon.(C) -Same as B but for a cell's response   (B, C, D, E) -Same as A but for an example cell from region 2, 3, 4, and 5 respecAvely.(F) -The accuracies of classifiers trained on discriminaAng various combinaAons of sAmuli using only cells from a single region.Whilst these archetypes were not generated using informaAon about the discriminability of trials, some archetypes do perform be^er than others for given groups of sAmuli.For example, regions 1 and 5 outperform the other three in discriminaAng trials with variances in their latency but perform worse at discriminaAng trials varying by total odour.Chance levels are shown by the horizontal do^ed lines.Fit better than 94% of other units Fit better than 35% of other units the response of a cell to another odour response.The error between the true response and this seconday odour predicAon is measured.The weighAngs from every model is compared to the true response of every cell to the other odour.The posiAon of the fit generated by each cell's response to another odour is compared to the general distribuAon of fits (i.e. the score of the weighAng from cell n's response to O2 is compared to the score of the weighAng from all other cells) .(B) -The sorted fit fracAons from the comparison technique in A for O1 (i), O2 (ii), and O3 (iii).If there was no similarity then the sorted line would sit at x=y.For all 6 comparisons the true line sits below.
Fig 2Aiv).InteresAngly, the pa^ern of misclassificaAon was more closely aligned with the diagonal than in Fig 2Bi, despite the trials not outperforming the classifier analysis in Fig 2Ai (Fig 2Biv).We again repeated this analysis on all 32 sAmuli, but instead labelled each sAmulus by its latency to the first odour pulse.We found that the accuracy increased when compared to Fig 2Aii (O1 -73%, O2 -73%, O3 -68%, chance 17%, Fig 2Av).Further, the confusion between trials remained highly correlated with the matrix in Fig 2Bii (0.96 Pearson's R correlaAon coefficient, Fig 2Bv).Therefore, the addiAonal fluctuaAons in the sAmuli did not decrease separability.
, see Fig 2B for confusion matrices for select sAmulus subsets).

Fig 4 . 1
), the confusion matrix generated from the DifferenAal filter models mirrored the experimentally measured one (Fig 4C-F, Supp Fig 4.1).
3 V holding voltage.This iniAal high voltage spike caused the valve to open with very short delay, whilst the 3.3 V holding voltage allowed the valve to remain open indefinitely without causing overheaAng.The drivers themselves were passed valve opening Ames via a 5 V TTL pulse from digital I/O controls via a data acquisiAon (DAQ) device (PCI-6229, NaAonal Instruments, AusAn TX, USA).A schemaAc and example odour and flow recordings are shown in Fig 1A and 1C respecAvely.
of the 32 disAnct temporal pa^erns presented during these recordings.Each solid black box represents a 20 ms window which contained odour, each empty box represents a window with 20 ms of blank odourless air.The pa^erns are read from leM to right with the leM most window represenAng a window with 0ms latency.Each subsequent rectangle represents the following 20 ms window.Pa^erns presented in colours aside from black are presented in C. (C) -Odour and flow recordings from 3 of the 32 pa^erns show in B. The blank odourless pulses are used to maintain the same total flow across different pa^ern presentaAons.The corresponding representaAon in B is indicated by the colour of the square in the top leM of each plot.(D) -Example cells (ii-iv) responses to a subset of the sAmulus set

Figure 3
Figure 3 Confusion between all rapid odour pulse trials (A) -Confusion matrices generated by a series of Random Forest classifiers trained to disAnguish all 32 sAmulus pa^erns from each other.The classificaAon was repeated across responses to all three odours used in this study (i-iii).(B) -Confusion matrices generated by classifiers trained and tested on two halves of the full dataset used in Ai.

Figure 4
Figure4GLM models capture single cell ac7vity (A) -SchemaAc outlining the three steps in our GLM.First, the sAmulus is represented by an N-dimensional (in this schemaAc 5) representaAon which is condensed into a 1-dimensional value (a weighted sum of the 5 components).Second, this value is passed through a non-linearity, in this case an exponenAal funcAon.Third, the output of the exponenAal is used as an esAmate mean of a Poisson processes.(Bi) -An example cell response to all sAmuli (black) with a model firng using only 5 sAmuli bins (green), the same as shown in the schemaAc in A. ii -The same cell as in i, with black) and model fits generated when using a 9 parameter model (yellow), the first 5 of which are simply the sAmulus pa^ern as shown in A and Fig 1B, and an addiAonal 4 bins represenAng rising edges at 20, 40, 60, and 80 ms delay latencies.(C) -Average (black) and model responses (yellow) of three example cells to all sAmuli pa^erns.(D) -The correlaAon coefficient for each cell between two halves of the true cellular response (black) and between a model fit response and an unseen true tesAng response (yellow).(E) -The confusion matrix generated when the fit firing rates generated by the 9-parameter model shown in C is used to generate modelled firing rates for all cells.The fit firing rates shown in C are passed into a Poisson process to generate modelled responses to repeat presentaAons.The modelled responses are passed to classifiers, as in Fig 2 and 3.The unique pa^ern of misclassificaAon is produced here, and is highly correlated with the pa^ern observed in Fig 3Ai.(F) -The correlaAon coefficients between confusion matrices.The True column shows the correlaAon coefficient between the three matrices shown in Fig 3A (square: O2-O3, triangle: O1-O3, circle: O1-O2).All other columns show correlaAons of modelled response matrices (Fig 4E) with these three true matrices for the indicated odour.Different linear filters are used for these different models (Supp Fig 4.1).The idenAty column shows the correlaAon of each true matrix with an idenAty matrix.

Figure 5 Figure 6
Figure 5 Low dimensional representa7ons of GLM weights (A) -The variance explained by each PC for each odour.(B) -The change in the relaAve fit error for all cells with increasing number of PCs the GLM weighAng is projected into.Each grey line represents the change for a single cell (black line: average change).A sharp cutoff is notable aMer 2 PCs.(Ci) -PC1 with weighAngs split into odour presence bins (index 1-5) and into edge bins (index 6-9).The PCs from each odour are coloured as in A. ii -Same as i, but for PC2.(D) -The projecAon of all cell-odour weighAngs into the top 2 PCs.(E) -A separaAon of the first two PC spaces, as shown in D, using K-means clustering of predicted responses generated by sampling areas in the PC space.5 clusters were found using this method.The average response from each region is plo^ed above the associated region of the PC space.

1 2
Olfactometer flow and odour comparisons (Ai) -The average total airflow presented during all trial pa^erns (average of 4 repeAAons).(ii) -Same as i but for the total odour presented during each pa^ern (average of 4 repeAAons).(Bi) -The separability of all 32 pa^erns presented in this study by a linear RandomForest classifier trained on the total flow of each trial.(ii) -Same as i but for classifiers trained on the integral of total odour over each trial.(C) -Flow (blue) and odour (orange) traces for four example sAmuli pa^erns (Iblank-odour-blank-odour-blank; (ii) -odour-blank-odour-blank-blank; (iii) -blank-odourodour-odour-odour; (iv) -blank-blank-blank-blank-blank) Spikesor7ng informa7on (Ai) -An example unit wavefrom.Channels are aranged by their posiAon in space as shown along the x and y axis.The scale bar in the bo^om leM displays 100 uV along y and 1ms along the x axis.(ii) -Same as i but for a different example unit from a recording using an alternaAve silicon probe, hence the difference in channel posiAons.(Bi) -The autocorrelogram for the units shown in Ai. (ii) -Same as i but for the unit in Aii.(Ci) -The average firing rate of each unit shown in Ai and Bi.(ii) -Same as i but for the unit in Aii and Bii.(D) -The average firing rate of all units isolated and used in this study.(E) -The maximum average spike amplitude for all units isolated and used in this study.Supp Fig1.3 Simplis7c clustering of cell responses.Hierarchical clustering of average scaled responses of all units.Units were scaled such that their maximum average firing rate in response to any sAmulus pa^ern was 1. Supp Fig3.1 Discriminability of neural responses over 7me.Classifiers trained on neural responses (as in Fig3) but over different Ame windows.Classifiers were trained on summed spike counts over 500 ms windows, but with varying window onsets.The window end in seconds for each classifier input is displayed along the y-axis of each row (row1 -0.07; row2 -0.09; row3 -0.11; row4 -0.13; row5 -0.15; row6 -0.17; row7 -0.5).The iniAal window -A 1 dimensional representaAon of the neural responses to all 32 pa^erns (presented with O1) at each moment in Ame.Responses were reduced only within each Ame step and had no informaAon on previous or future neural acAvity.The reduced responses to each pa^ern are coloured following the accompanying colour bar.(Bi) -Same as A but over a shorter Ame window.(ii) -Same as I but for responses to O2. (iii) -Same as I and ii but for responses to O3. (Ci) -The Euclidean distances between responses to all pa^erns when presented with O1. (ii) -Same as I but for responses to the pa^erns when presented with O2. (iii) -Same as i, ii but when presented with O3. (Di) -The esAmated distances between responses constructed enArely on the total odour presented in each trial.(ii) -The esAmated distances between responses constructed enArely on the inAal odour latency.(iii) -The esAmated distance between responses constructed from a linear combinaAon of the total odour and the iniAal odour latency.
Preswhich was be^er captured by the latency filter.(D) -Same as A and B but for an example cell which is captured be^er by a combinaAon of both the total odour and the latency of each trial.(Ei) -Confusion matrices, as in Fig4E, generated by training classifiers on the modelled firing rate of cells fit using the total odour filter.(ii) -Same as i but for classifiers trained on the modelled firing rates of cells fit using the latency filter.(iii) -Same as i and ii but for classifiers trained on the combinaAon total odour and latency filter fit models.None of the three confusion matrices seen here were found to generate a similar pa^ern to those seen true firing rate confusion matrices (Fig3A).(F) -RepresentaAon of the DifferenAal filter which consists of five 'presence' bins, where each bin represents one of the five 20 ms odour/blank air pulses (green), and the rising edges present in the sAmulus (yellow).Supp Fig5.3 Addi7onal archetypes (A)-Example cell from region 1. i -The cell weighAng, which indicates that this cell was tuned towards odours and rising edges arriving earlier in the respiraAon cycle.ii -The cell's average response to all sAmuli pa^erns.iii -The instantaneous firing rate of the cell over a 500 ms window post odour onset for all pa^erns presented.The dashed black line indicates odour offset.

1
Addi7onal example cell responses to two odours.(A, B, C, D) -Example cellresponses to O1 and O2, aligned so as to maximise the correlaAon between the average response across each odour.

SuppFig6. 2
Correla7on between responses to O1 and O3 (A, B) -Example cells with high correlaAon between their responses to pa^erns when presented with O1 or O3.(C) -The correlaAon coefficient between the response curves of all cells to O1 and their response to O3.

3
Correla7on between responses to O2 and O3 (A, B) -Example cells with high correlaAon between their responses to pa^erns when presented with O2 or O3.(C) -The correlaAon coefficient between the response curves of all cells to O2 and their response to O3.

4
Model accuracy predic7ng responses to an unseen odour (A)-A schemaAc outlining the comparison technique employed.In short, the responses of cells to one odour are iniAally used to fit a series of GLMs (as in Fig4).The model weights are then used to predict from the training odour population (O2) Fit a model using the weights from the training odour model onto the target unit response Measure the fit error between the select target odour true response and the training odour prediction Target odour fit well by same unit training data Target odour fit poorly by same unit training data Compare the fit of the same unit's training odour prediction with all other units training odour prediction