A transformation from latency to ensemble coding in a model of piriform cortex

We present a spiking network model that transforms odor-dependent variable-latency olfactory bulb responses into a cortical ensemble code. In the model, which captures basic circuit properties of piriform cortex, the impact of the earliest-activated bulb inputs on the cortical response is amplified by diffuse recurrent collateral excitation, which then recruits strong feedback inhibition that stabilizes cortical activity and decreases the impact of later-responding glomeruli. Because the sequence of olfactory bulb activity for a particular odor is preserved across concentration, the ensemble of activated cortical neurons is robust to concentration changes. Nevertheless, odor concentration is represented by the latency and synchrony of the ensemble response. Using decoding techniques, we show that the ensemble-based coding scheme that arises in the cortical model supports concentration-invariant odor recognition.


INTRODUCTION 12
The coding schemes used to represent odors in the olfactory bulb and piriform cortex (PCx) are 13 different. In the bulb, odorants sequentially activate distinct subsets of glomeruli causing mitral 14 and tufted cells (MTCs) to begin firing at various odor-and cell-specific latencies following the dal cells receives enough input from short-latency mitral cells to reach threshold and start spiking 127 early in the sniff ( Figure 2B, cell 1). This activity produces a small amount of recurrent excitation 128 that is dispersed across the cortex via the long-range recurrent collateral connections. The resulting 129 recurrent input is not strong enough to drive spiking by itself ( Figure 2B, cell 3), but it can recruit 130 other pyramidal cells that receive moderate but subthreshold bulb input ( Figure 2B, cell 2). Be-131 cause more cells received subthreshold than suprathreshold bulb input, more pyramidal cells are 132 activated by the recurrent input, resulting in even stronger recurrent excitation that, in turn, can 133 Spiking rate for the population of pyramidal cells is shown at the bottom (average of 6 trials). Note that the earliest activated glomeruli initiate a cascade of pyramidal cell spiking that peaks after ~50 ms and is abruptly truncated by synchronous spiking of FBIs. (B) Single-trial voltage traces (black) for 3 pyramidal cells in response to the same odor. Inhalation onset is indicated by the dashed line. The red traces show the bulb input and the green traces the recurrent input received by each cell. Cell 1 receives strong bulb input and spikes soon after odor presentation. Cell 2 receives subthreshold input from the bulb and only spikes after receiving addition recurrent input from other pyramidal cells. Cell 3 receives no early odor-evoked input from the bulb, and its recurrent input is subthreshold, so it does not spike over the time period shown. help activate even more pyramidal cells receiving even less bulb input. The result is an explosive 134 increase in total pyramidal cell activity, and therefore a steady increase in the strength of recurrent 135 excitation. However, recurrent excitation onto feedback inhibitory neurons is stronger than onto 136 other pyramidal cells so that feedback inhibitory neurons are recruited before pyramidal cells that 137 have not received any direct bulb input. Thus, feedback inhibition quickly halts the explosive 138 growth of pyramidal cell firing because pure recurrent input always remains subthreshold for py-139 ramidal cells, thereby maintaining the odor-specificity of the cortical ensemble. 140 141

Specific roles for different circuit elements in shaping cortical responses 142
To reveal the specific roles that different circuit elements play in shaping piriform output we com-143 pared responses in the full circuit with those obtained after removing different circuit elements 144 ( Figure 3). The same odor stimulus was used in all cases, so input from the olfactory bulb is iden-145 tical except for the trial-to-trial stochasticity of mitral cell spiking. We first compared responses in 146 the full circuit ( Figure 3A) with those in a purely feedforward network in which pyramidal cells 147 only receive mitral cell inputs ( Figure 3B). In this highly reduced, feedforward circuit, pyramidal 148 cell spiking activity grows more slowly, without any strong initial transient, and it tracks the num-149 ber of spiking mitral cells. In the absence of either feedforward or feedback inhibition, the cortical 150 response continues to grow over the course of the sniff as more glomeruli are activated ( Figure  151 1A), so that a large fraction of cells respond at some point during the course of the entire sniff. 152

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We next examined networks without feedforward or feedback inhibition, or without recurrent ex-154 citation and excitatory input to feedback interneurons. Eliminating only feedforward inhibition 155 increases the amplitude of the peak pyramidal response by about 50%, although the general shape 156 of the population response is largely unchanged ( Figure 3C,E) and the fraction of cells activated 157 over the entire sniff only increases modestly (from 13% to 16%). When we selectively eliminated 158 feedback inhibition, odor induces unchecked runaway recurrent excitation, and all the cells end up 159  Figure 2A. (B) Network activity when pyramidal cells get excitatory input from mitral cells but without FFI, recurrent excitation or FBI. Pyramidal cell spiking tracks mitral cell input. Population rate for the full network is shown in grey for comparison. (C) Network activity after eliminating excitatory input to FFIs. Note that sustained FBI spiking increases without FFI, resulting in roughly constant levels of sustained spiking in pyramidal cells. (D) Network activity with no recurrent excitation onto either other pyramidal cells or FBIs. The transient activity peak seen in A-D is absent, and sustained activity is slightly higher. (E) Population rate plots for 3 different odors with the full network (black trace), no FFI (red trace) or no recurrent excitation/FBI (green trace). Insets expand the period around inhalation. Note the population spiking is higher and peaks slightly earlier without FFI, and that responses are slow without recurrent excitation. All population spike rate plots are averaged over 6 trials. The previous analysis showed that population spiking peaks early when recurrent excitation is 170 present (Figures 3A,C) but ramps up more slowly when it is eliminated ( Figures 3B,D), indicating 171 a key role for intracortical circuitry in amplifying the initial response. We examined this directly 172 by comparing population spiking to the sequential activation of individual glomeruli ( Figure 4A). 173 In the full network, population spiking peaks 34 ± 8.3 ms after inhalation onset (mean ± st. dev. 174 for 6 odors with ensemble averages of 6 trials per odor, at the reference concentration; Figure  175 4B,C). At this time, only 15 ± 1.4 glomeruli have been activated out of the 95 ± 6.0 glomeruli that 176 will eventually be activated across the full sniff. In other words, at its peak, PCx activity is driven 177 by the earliest ~15% of activated glomeruli. Mean responses peak slightly earlier when feedfor-178 ward inhibition is eliminated (28 ± 4.5 ms; Figure 4B), but the peak activity is still driven by a 179 similar number of glomeruli (12 ± 0.80 glomeruli; Figure 4C); on individual trials, the peak re-180 sponse is larger without feedforward inhibition ( Figure 3C,D), but this difference is not captured in the average responses). In contrast, population spiking peaks much later without recurrent exci-182 tation (139 ± 29 ms) at a time when most of the responsive glomeruli have been activated (66 ± 183 0.44; Figure 4C). Recurrent excitation therefore plays an important role in shaping the dynamics 184  5C) and total population spiking ( Figure 5D). However, this increase is fairly uniform across con-235 centrations and removing feedforward inhibition does not substantially change the gain of the re-236 sponse (i.e. how rapidly these responses vary with input strength; Figure 5C&D), indicating that 237 the effect of feedforward inhibition is largely subtractive. In contrast, eliminating recurrent exci-238 tation and feedback inhibition destroys concentration invariance by dramatically increasing re-239 sponse gain, indicating that they implement divisive normalization (Carandini and Heeger 2012). 240 Interestingly, cortical output is decreased at low odor concentrations when recurrent excitatory and 241 feedback inhibition are removed, indicating that recurrent collateral excitation amplifies cortical 242 output in response to weak input ( Figure 5C&D). 243 244

Early-activated PCx cells support concentration-invariant odor recognition 245
Because the sequence of glomerular activation latencies is preserved across concentrations, odor 246 representations defined largely by the earliest activated glomeruli could support concentration-247 invariant odor recognition. We therefore asked whether the cortical odor representation in our 248 model was well-suited to this purpose. Specifically, we next asked if a downstream observer could 249 reliably identify an odor using population spiking, and whether the odor can be recognized when 250 presented at different concentrations. To do this we trained a perceptron to identify a specific odor 251 at one concentration (10% active glomeruli) and then asked how well it could identify that odor 252 presented at different concentrations. We used spike counts over either the full 200 ms inhalation 253 or the first 50 ms as input. Perceptron performance was excellent when trained and tested at a 254 single concentration, indicating that despite considerable trial-to-trial variability, responses to dif-255 ferent odors can be distinguished reliably ( Figure 5E). We then examined classifier performance 256 when tested on different concentrations without retraining. Performance using the full 200 ms re-257 sponse was generally excellent but fell off at both the lowest and highest concentrations. However, 258 classification using only the early transient response as input was essentially perfect across all 259 tested concentrations. This decoding analysis supports the idea that the earliest cortical response 260 provides an especially good substrate for concentration-invariant odor identification. to be used to represent intensity. We therefore examined the dynamics of population spiking in 266 response to odors at different concentrations ( Figure 6A). As with the mitral cell activity, cortical 267 response latencies decrease at higher concentrations by a factor of about 2 over a 10-fold increase 268 in input from bulb ( Figure 6B), suggesting that a latency code could be used. We also found that 269 the peak of the population response increases by more than a factor of 5 over this range of odor 270 concentration ( Figure 6C). Given that total spike output is largely constant, this result indicates 271 that the synchrony of the population piriform response is particularly concentration-dependent. 272 Furthermore, unlike latency, synchrony thus provides an representation of odor intensity that does 273 not require an external reference. The increase in synchrony occurs primarily because activation 274 latencies of the earliest responding glomeruli, which cannot be activated before inhalation onset, 275 compress as odor concentrations increase. causing responses to become more coincident. Thus, 276 the early peak in the PCx response can be used to rapidly decode both odor identity and concentra-277 tion. 278 earliest responsive glomeruli and discounts the impact of glomeruli that respond later. Why would 348 a sensory system discard so much information about the stimulus? To represent a large extent of 349 potential odorant space, the olfactory system employs a huge number of distinct odorant receptors 350 that are each highly selective for a small fraction of potential odorants. Thus, any given odorant 351 will strongly activate only a few, optimally-tuned receptors, while many other receptors will be 352 moderately or weakly activated if they receive input from sensory neurons expressing receptors 353 with lower affinity for the odor, especially at high concentrations. However, the few odorant re-354 ceptors with the highest affinities to a given odorant will always be more strongly activated, and 355 therefore their associated glomeruli and MTCs will be activated earlier than those receiving input 356 from lower affinity receptors, regardless of odorant concentration. By defining odors according to 357 the earliest responding glomeruli, the olfactory system retains the specificity of the odor represen-358 tation and discards spurious information provided by non-specific receptor activations. 359

Model olfactory bulb 362
The model bulb includes 900 glomeruli with 25 model mitral cells assigned to each glumerulus. 363 It is useful to describe the strengths of the different synapses we have discussed in terms of unitary 423 PSP sizes rather than using the parameters given above. Using the constants we have given and 424 the synaptic and membrane dynamics, we calculated peak EPSPs and IPSPs. All inhibitory inputs 425 create IPSPs at the postsynaptic cell with a peak deflection of . EPSPs from mitral cell produce . 426 The EPSP for input from pyramidal to pyramidal or to FBI cell has or respectively. from trials using other odors. If such a perceptron weight vector exists, we know that pyramidal 457 cell activity in response to a specific odor are inherently distinguishable from activity for other 458 odors. Furthermore, because the activity vectors we use do not contain temporal information, we 459 know that the discrimination relies solely on the identity of the active pyramidal cells, these are 460 the pyramidal cell ensembles, and their firing rates. 461 462 During training, 100 odors were presented at a specific concentration (10% activated glomeruli) 463 over a total of 600 trials. Odor 1 was chosen as the target, and the trials alternated between this 464 target odor and all odors. Thus, odor 1 was presented 303 times and every other odor 3 time. On 465 training procedure was repeated twice, once with activity vectors that included spikes counts 470 around the peak of the piriform activity (the first 50 of inhale) and once using spikes counts 471 from the entire inhalation. 472

473
To test the perceptron, each odor was presented at many concentrations (even though training was 474 done only for a single fixed concentration). For the target odor 100 trials were tested at each 475 concentration (30 different concentrations ranging between 3% activated glomeruli and 30% acti-476 vated glomeruli). Each trial that gave • > 0 was considered a correct classification. For each 477 concentration, the percentage of trials that were correctly classified was calculated. Trials with 478 non-target odors were tested as well, one trial for each odor at each concentration. All the non-479 target odors were correctly classified as not target ( • < 0) across all concentrations. The testing 480 procedure was done using both the peak and full activity vectors, with the corresponding percep-481 tron weight vectors.   Figure 2A.