Synaptic Plasticity in the Mushroom Body
In insects, projection neurons (PNs) of the antennal lobe (AL) are the only source of olfactory information to the mushroom body (MB). We focused on the effects of plasticity at the synapses connecting PNs to Kenyon cells (KCs) in the MB calyx (). Each synapse was characterized by a nonnegative peak conductance g, and synaptic plasticity was realized as a change in g by the amount Δg, proportional to three independent factors:
Synaptic plasticity and coincidence detection in the model Kenyon cell.
- Lr±: the learning rule factor
- Ci: linear function of instantaneous synaptic conductance
- Fp: binary function of pairing frequency
Learning rules based on spike rate- or spike timing-dependent induction of synaptic plasticity are central in influential models of cortical learning and neural development 
. We investigated the contributions of rate- and timing-based mechanisms in the MB with a series of computational experiments. Specifically, we compared spike-timing dependent plasticity (STDP; ) with a form of plasticity that depends on the rate, but not precise timing, of pre- and postsynaptic firing (). By analogy with STDP 
, we termed this spike-rate dependent plasticity (SRDP).
In most of our computational experiments, we compared the effects of SRDP and STDP at the PNs-to-KCs synapses (). For each experiment, the population response in KCs was quantified before (“naive” case; e.g., ) and after training (e.g., after STDP: ) over repeated presentations of blocks of olfactory stimuli (see Materials and Methods
Our simulations were based on small populations of conductance-based KCs receiving input from 100 PNs (i.e., ~12.5% of total locust PN population). Each model KC received monosynaptic input from 10 PNs 
. To reduce the likelihood of facilitating sparseness by independent connectivity, pairs of KCs shared 50% of their input afferents 
; an extra overlap that did not otherwise affect the results. Following an approach that we previously applied in 
the PN activity of the model (; see Materials and Methods
) included dynamic ensembles of synchronized neurons replicating the behavior of PNs recorded in vivo
as well as of PNs in a complete AL model 
Synaptic Plasticity Enhances Sparseness and Selectivity of Olfactory Representations in KCs
Before olfactory experience, stimulus-evoked response patterns in the MB were dense, with olfactory representations characterized by the participation of a large fraction of the available KCs (often >25%; , left column). Most neurons fired less than one spike per trial (see spike raster in ); thus, reliability was low. Population responses were unselective and largely overlapping across different odors (, left column). Both learning mechanisms made KCs population responses sparser (, middle and right column), such that in most cases only one KC became specifically responsive to a given odor. After olfactory experience with SRDP or STDP over 3 blocks of presentations (150 trials in all), on average, only a few KCs developed sensitivity to a given odor leading to a sparse representation for that odor. This was mainly a result of the odor specific decrease in synaptic weights from AL to MB during learning with repeated odor trials. After learning, only few cells received a combination of the PN inputs that was sufficient to trigger a postsynaptic spike.
Synaptic plasticity favors sparse representations in the MB.
Odor induced sparse responses in KCs usually involved a single spike (e.g., , and middle and right column). Even though all the odors were generated by the same stochastic process, there were a few exceptions: for odors 3 and 8 no KC became specific. Population sparseness was increased in odor 7, without reaching single cell specificity. The lack of specific response in these simulations likely arose because only a small fraction of all PN combinations had real KC targets in our model. Similarly, a single experiment in vivo
sampling only a fraction of the total KC population may reveal no responses to a given odor 
. Overall, odor representations were significantly sparser after synaptic tuning through SRDP (p
<0.0002, paired t
-test on sparseness measures, see Materials and Methods
; ) and STDP (p
<0.0003) compared to the naive case. In general, both SRDP and STDP mechanisms were able to tune the synapses between PNs and KCs such that KC responses to different odors were specific, sparse and reliable across trials.
We next asked whether plasticity could tune synaptic strengths for a wide range of initial conductance values at KC synapses. Training experiments were performed over 4 blocks of stimuli, starting from different values of initial conductance that were derived from the 100% reference value used for all other experiments (see Materials and Methods
). When initial conductance was increased, naive responses became denser: more and more KCs were recruited in the stimulus-induced population firing, and most KCs started to fire repeatedly during a single odor trial (, left column). Training with either SRDP or STDP made the population response much sparser (, mid and right column). Even for initial conductances in the 130–140% range, almost all neurons involved in the response fired a single spike after olfactory experience, whereas more than half of the KC population remained silent for all odors. For example, across all odor samples, the sparseness measure at 130% was significantly different from the naive case for both SRDP (p
<0.0001; paired t
-test) and STDP (p
<0.0001; , bottom row). In general, population sparseness across all odors decreased linearly with increasing initial conductance in the naive case (). Yet both rate- and timing-dependent plasticity mechanisms produced the same near maximal sparseness, with somewhat lower sparseness when initial conductances exceeded 120%. Thus, activity-dependent synaptic tuning is able to normalize postsynaptic neuronal responses over a wide range of initial conditions, and can do so without a global scaling signal 
. Additionally, this finding strongly mitigates the choice of initial synaptic strengths for computational models incorporating synaptic mechanisms with forms of plasticity analogous to SRDP or STDP: such models require less fine-tuning to work well. Finally, these forms of synaptic plasticity appear to favor a sparser code within a neuron population of fixed size, thereby increasing the global storage capacity of the system 
. We therefore asked whether the system is able to respond precisely and sparsely to additional odors after being trained by one odor.
Synaptic tuning over a wide range of initial conductance values.
The Persistence of Olfactory Representations
Once generated, an olfactory representation should not only be reliable whenever activated by the same odor (), but should also be reproducible after training with other odors. When plasticity is active, representations risk corruption by exposure to new odors and by ongoing activity. We compared the ability of SRDP and STDP to tune synaptic strengths such that multiple odor representations could coexist in a stable manner within a fixed pool of KCs. In doing so, we did not assume that odor memories are stored exclusively at the AL-MB synapses, nor did we aim to fully characterize the degree to which representations are protected against degradation. Rather, we tested whether an activity dependent tuning mechanism is compatible with multiple coexisting representations. Other mechanisms not further explored here may collectively support long-term memory retention 
We trained simulated olfactory circuits on four different odor blocks (odors 1, 2, 3, 4) delivered in various sequences (). Each sequence consisted of 200 1-s trials in total, each odor block contributing the same 50 trials to every sequence. The sequences were labeled 1234, 2143, 3412 and 4321, indicating the order in which each odor block was presented. In an additional sequence, the 200 1-s trials were randomly permuted. After the training period, each model circuit was tested as usual on a single odor block, without modifying synaptic strengths.
The persistence of olfactory representations.
To quantify the extent to which a given odor representation (e.g., odor 2) acquired during training from a sequence (e.g., 1234) deviated on average from the representation obtained without presentation of other odorants, we computed its Euclidean distance (in KC odor space, see Materials and Methods
) from the average response after training with the test odor alone (e.g. 2222). A null distance indicated perfect response matching. For reference, the average pairwise distance between representations obtained after training with a single odor (, 8 odor-specific responses) was 1.3±0.9 for SRDP and 2.7±1.7 for STDP.
After SRDP- or STDP–based training with the multiple odor sequences, the observed KC population responses to single odors were significantly more sparse than in the naive case, and comparable across different sequences (SRDP: F
<0.0015; STDP: F
<0.0001; 1-way analyses of variance).
Olfactory representations for single odors acquired during training with STDP on multiple sequences had firing patterns that were very similar to those observed after learning each odor alone (). The random sequence was less effective at producing reliable odor representation, indicating that repeated consecutive presentations of 1-s trials from the same odor are needed to form a more stable representation. Exposure to odors not included in the training sequences (e.g. odors 5, 6, 7, 8, in ) in one case reproduced the expected pattern with remarkable similarity (odor 6, ). For the other odors, the responses after olfactory experience remained similar to their respective naive case (not shown). These results suggest that training by a set of odors presented even in random sequences could tune the system and lead to high KCs specificity for each of them. What is important is an extensive “coverage” of the odor space by the set of odors used for training. Thus, training by a set of similar odors can leave some of AL to MB afferents unchanged, so the following presentation of another “different” odor may lead to a non-sparse response. In contrast, a set of more distinct odors would tune the whole system for all possible inputs including those not used for training. This “tuning” with even an impoverished set of odorants could occur at early stages of development. This result suggests some behavioral consequences, e.g., animals growing in a very stable and poor odor environment should show poor performance in discriminating among similar odors if these odors belong to a novel (for that animal) chemical group.
We found that the rate-based learning rule was less successful in storing multiple odors. Exposure to a single odor after olfactory experience with multiple odor sequences with SRDP induced firing patterns with mixed degrees of similarity to those expected and observed after training with a single odor (Figure S1
). The expected pattern was reproduced only in 44% of the tested samples. The remaining combinations either yielded “wrong” patterns (13%) or did not elicit any reliable response. In some cases, odor sequence training induced a KC to become specific to an odor to which it was not responding when trained on the same odor alone (e.g., sequence 1234 tested with odor 2; Figure S1
). Interestingly, the best reproductions of the expected, single odor-trained olfactory representation were observed when presenting the first odor of each training sequence, e.g. odor 1 for 1234, odor 2 for 2143, etc., indicating that under SRDP the first odor in the sequence had a major effect on the synaptic strengths of KCs. Also in the SRDP case, the random sequence did not induce any significant persistent odor representation.
Finally, exposure under SRDP to odors not included in the training sequences did not reproduce the original patterns, and responses were often characterized by widespread silence. Thus, although the two learning rules performed similarly in the previous experiments, the results with odor sequences indicate that synaptic changes induced by STDP are more specific and less disruptive than SRDP, allowing persistent coexistence of multiple olfactory representations. This result can be explained in part by the more significant alternations of synaptic weights observed with SRDP model (see below). Note that the performance difference between the two plasticity models cannot be equalized by modifying the model parameters to reduce synaptic changes associated with SRDP. Such a change would actually decrease the SRDP model performance in experiments with single odor presentations.
It is important to emphasize a difference between olfactory stimuli and other modes of sensory input, e.g., visual. In our model, each odor stimulus could be considered a sequence of independent pulses or bins, each bin corresponding to one cycle of LFP oscillations. Each cycle consisted of a unique combination of active PNs that were synchronized to each other, and all together provided an input that may be sufficient to induce spiking in a postsynaptic KC. Only small subset of all possible 10 cell combinations of PNs had a “real” target (one of 19 KCs) in our model. Each KC produced typically zero or one spike during the whole 1 sec odor stimulus, responding to a unique combination of synchronized PNs found at one of many LFP cycles. Coincidence detection properties of the KCs in our model prevented integration across many cycles making each cycle essentially independent. In other words, each unique pattern of PN activity at each LFP cycle during 1 sec odor presentation could be treated as a separate stimulus – brief odor pulses. Therefore, one possible interpretation of the above experiments on representation persistence is that a set of 20 different stimuli presented as a sequence (first 1 sec odor) was used to train a model circuit, followed by application of 3x20 (2d, 3d and 4th odors) independent stimuli. Finally, the representation persistence was tested using the original set of 20 stimuli. Results of simulations support a coexistence of multiple odor representations; the sparseness of KC responses guaranteed little interaction between different odor representations.
Synaptic Strength Dynamics
To better understand the mechanisms underlying the formation of the response patterns to multiple odor sequences, we analyzed the evolution of the synaptic strengths under each learning mechanism. While training with odor sequences, changes under SRDP affected most KCs, and most synapses at each KC (, upper row). The proportion of synapses undergoing strong changes was larger than for STDP, as shown by the wider and higher kurtotic distributions of synaptic efficacies for increasing number of training trials and learned odors (, upper rows). In contrast, synaptic changes under the STDP rule were subtler, and restricted to fewer KCs and fewer synapses (). As expected from the specified dependence on instantaneous conductance (), both rules generated unimodal distributions of synaptic efficacies, for both single odor and odor sequence olfactory experiences (). The average evolution of synaptic strength shows that SRDP had a stronger impact on KC synapses (). After SRDP learning of the first odor in a sequence (or 50 single odor learning trials), the average change was comparable to the value reached with STDP after exposure to the full 4-odor sequence (200 trials, ). Thus, under these conditions, STDP is more selective than SRDP. This selectivity should allow for a larger number of odors to be learned and represented with a fixed number of synapses.
Sparse Representations for Similar Odors
In honeybees, it has been demonstrated that selective disruption of oscillatory synchronization by picrotoxin injections into the AL impaired the discrimination of molecularly similar odors 
. If oscillatory synchronization of neuronal assemblies is essential for fine sensory discrimination, and MB decoding in part depends on the identity of active KCs, then KCs must be able to build distinct sparse representations for similar odors based on differences in stimulus-evoked oscillatory synchronization of the PN neural assemblies. We investigated how STDP in the MB might help to shape distinct sparse representations for odorants with similar encoding in the AL (see Materials and Methods
for a description of similar and different odors).
First, we tested the model's ability to discriminate pairs of very similar odors extracted from a set of 10 odors (PS
≈0, see Materials and Methods
; ). We defined an odor trial as correctly classified if its representation in KC odor space was, with cross-validation, closer to its corresponding average response than to any other average odor response. The classification error was defined as the percentage of wrongly classified trials in a block of 50 trials. Olfactory representations for two similar odors A and B were largely overlapping in naive circuitry (, left), and many responses to odor A were closer to the average response to B. After synaptic tuning, all single-trial responses to odor A were closer to its own corresponding response average (, right), leading to perfect odor classification. This indicates that the strong increase in KC sensitivity to the fine synchrony structure induced by plasticity effectively improves discrimination of similar odors.
Discrimination of similar odors in 19-dimensional KC space.
To track the evolution of this enhancement for different amounts of training, we quantified the portion of wrongly classified trials across all possible odor pairs from the set of 10 very similar odors (). Distinct olfactory representations were already obtained with one training block. With two training blocks (100 trials), odor classification improved further, resulting in only three cases of partial overlap. The average evolution of the classification error rate across all odor pairs suggests that an asymptotically small (~2%) number of classification errors was reached after 100 trials (). We noted that, corresponding to this saturation point, the divergence of average odor responses (cloud centers) in KC odor space also reached an asymptotic value (). After 100 training trials the distance between two cloud centers was always larger than twice the average distance of single responses from their respective centers (cloud radius), explaining the optimal classification results.
To what extent does plasticity-based improvement of KC decoding abilities depend on the difference between PN responses elicited by odors, that is, their mutual distance in PN space? To explore those features over a homogeneous distribution of pairwise distance values, we generated several sets of 10 odorants with increasing degree of dissimilarity between odors within sets (see Materials and Methods
; ). The closest odors were characterized by very similar (identical for PS
0; , upper rows) slow temporal structure but different patterns of PN synchronization (fine structure). For each odor pair in a set, we quantified the distance (or divergence, see Materials and Methods
) in PN space (, bottom panel) and classification error in KC space (as above) between the two representations. Before synaptic tuning with STDP (, upper panel), odor pairs with a high degree of similarity in slow structure gave a wide range of error rates (0–45%), suggesting that the naive circuitry is unable to exploit synchrony information to create distinct representations. The fraction of pairs with poor classification was very high, particularly over the range of PN distances covered by the two sets with very similar odors. For larger PN distances, the error rate was nearly constant and mostly below 5%. Thus the classification rate was influenced by differences already expressed in, and transmitted from the AL. After olfactory experience, the error rate for most odor pairs plummeted to below 5% over the whole PN distance range (, mid panel). This suggests that the strong enhancement of classification ability for similar odors (, insert) was provided by the increased sensitivity to oscillatory synchronization patterns after STDP, as expected 
. Only a small discrete set of odor pairs very close in PN space continued to elicit high rates of classification error. Taken together these results indicate that fine tuning for ensemble selection through a timing-dependent plasticity mechanism in the MB may increase the ability to discriminate between two odorants ( insert).
Discrimination in MB versus intrinsic distance in AL.