Effect of AL Synaptic Plasticity on Network Responses
Recordings from the locust AL during presentations of novel odors demonstrated two important features used to constrain the model. First, the LFP oscillates very little, if at all, during the first one or two trials with a new odor; rather, 20 Hz oscillations appear gradually over the first several trials. Second, the average number of spikes produced by PNs is greatly decreased during repetitive stimulation with the same odor; the slow patterning that is typical of PN responses is not always evident during the first trials (Stopfer and Laurent, 1999
). Where might this plasticity reside? PN oscillatory coherence can be abolished by the application of picrotoxin to the AL (MacLeod and Laurent, 1996
); this suggests that the strength of fast GABAergic synapses of LNs onto PNs might be low during the first few trials with a novel odor and gradually increase during subsequent presentations of the same odor. Application of picrotoxin, however, does not alter the average number of PN spikes (MacLeod et al., 1998
; MacLeod and Laurent, 1996
). Consistent with this, our previous modeling studies found that blocking fast GABAA
-mediated inhibition in the AL model resulted in a loss of synchrony but did not change the average PN firing rate; in fact, the slow temporal structure of PN firing remained intact (Bazhenov et al., 2001a
). This suggests that both fast-type receptors and slow inhibitory receptors controlling the slow temporal structure and rate of PN output might be modulated during repeated odor encounters.
To test these hypotheses, we prepared three versions of a realistic computational model of the AL (see ): one with fixed synaptic weights, one in which only fast GABAA receptors could facilitate, and one in which both fast and slow inhibitory receptors could facilitate (see Experimental Procedures). In facilitating models, the initial strengths of the inhibitory receptors were set to be too weak to maintain synchronous PN oscilla- tions. shows the average network response (LFP) and membrane potentials for one PN and one LN from the network during the first five trials with an odor stimulus. The model with fixed, strong synapses re- sponded with relatively consistent patterns in all five trials (). The model with initially weak, facilitating fast GABAA receptors () displayed strong onset responses followed by reduced network activity, caused by the increasing activation of slow inhibitory receptors. Although oscillatory synchrony increased, as observed in vivo, the average number of PN spikes changed very little (less than 30%) during subsequent trials with the same odor, inconsistent with experimental results. These results are quantified in (left).
The Network Model Included 90 PNs and 30 LNs
Evolution of the AL Responses over Repeated Stimulus Presentations
Oscillatory Response Increased While Firing Rate Decreased during Repetitive Stimulus Presentations
illustrates the results obtained when both fast and slow inhibition could facilitate. This network started with intense PN responses only partially reduced by initially weak slow inhibition. PN firing rates were high during the first few trials and decreased over subsequent trials, a result of the facilitation of slow inhibition (see , left). shows experimental results from locust illustrating both the increase in oscillatory power and the decrease in spike count over the first few trials. Thus, our model suggests that facilitation of both fast and slow inhibitions during repetitive trials is needed to account for our experimental results.
Modulations of the Synaptic Structure by Odor Stimulation
In the model with facilitating fast and slow inhibition, as in the locust, the power of AL 25–30 Hz oscillations greatly increased during the first few presentations of a stimulus (). Spectral analysis of the LFP produced by the model (, right) showed that 25–30 Hz oscillatory power increased most noticeably within the first three trials. The number of stimulus-induced PN spikes also changed most noticeably during these first three trials (, left). The number of trials required to attain an oscillatory response depended on the rate of facilitation. shows the distribution of synaptic weights for fast and slow LN-PN synapses over the model network for each trial. Most of the changes occurred during the first two to three trials, and the synaptic weight distribution became approximately stationary after seven to eight trials. This figure also shows that only about 40% of the inhibitory synapses in the network became facilitated during stimulation: these were the synapses activated by the stimulus; those not activated remained weak. Similar changes occurred for inhibitory synapses between LNs (data not shown).
Changes in the Synaptic Strength of the Inhibitory Synapses during Repetitive Stimulus Presentations
In vivo experiments in locusts showed that a novel odorant does not elicit an oscillatory response even when it follows a coherence-inducing series of presentations of a different odor. If the two odors are chemically similar, however, some carryover will occur (Stopfer and Laurent, 1999
). To examine this phenomenon with our model, we used two sets of inputs. “Chemically similar” inputs were simulated by activating significantly overlapping (~50%) sets of PNs and LNs from the network; “chemically distinct” stimuli were simulated by activating nonoverlapping subsets of neurons. shows examples of three different odors where odors A
were distinct, and odors B
were similar. After the first few trials with odor A
, the network response became oscillatory (), the number of PN spikes decreased by more than 50% (, left), and the integrated power of LFP oscillations (20–30 Hz) increased significantly (, right). After nine trials with odor A
, the stimulus was changed to odor B
. Because this input was different from A
, it activated a different subset of inhibitory synapses between LNs and PNs. These synapses were un- trained by odor A
, therefore the network displayed naive responses to the first few trials with B
. PN spike count and integrated LFP power also changed (). Finally, C
was introduced after nine trials with B
. Because C
is similar to B
, changes were less dramatic, and trial 1 displayed very strong oscillations immediately (); PN spike count and integrated LFP power changed little between the last trial with B
and the first trial with C
. These results are in a good agreement with experimental data from locust (). In this example, A
(pentanol) and B
(hexanol) are related, while C
(geraniol) is distinct from both A
. Note the carryover from A
and the naive LFP in trial 1 with C
Effect of Stimulus Change on the Network Response
When a number of different stimuli were presented in sequence to the model network, coherence of the resulting responses depended on the history of stimulation. Depending upon the recovery time to naive synaptic weights, a series of sufficiently different stimuli could saturate the network, such that eventually, any new input immediately produced an oscillatory response (data not shown). This saturation diminished when the interval between stimulus sets increased, so that synaptic weights could decay to initial values between stimuli. In vivo, the half-time for recovery from fast learning plasticity is about 4–6 min (Stopfer and Laurent, 1999
Role for AL Plasticity in Improving Reliability of PN Responses
The processing of olfactory stimuli includes two opposing goals: one is to accurately distinguish different but related odors; the other is to correctly classify noisy instances of the same stimulus. Spatiotemporal representation may increase the sensitivity and capacity of the AL, but they might decrease reliability when faced with noise (e.g., variations of the intensity of activation, identities of activated PNs, or transient or unreliable “background” stimuli). Could fast learning in the AL serve to enhance the reliability of odor identification? During repeated odor presentations, the effects of noise would be minimized, since its contribution would be different on each trial, mainly affecting untrained, weak synapses. Thus, fast learning might enable repetitive presentations of a stimulus in a noisy environment to create a pattern of activity similar to that evoked by repetitive presentations of a noise-free stimulus.
We used the AL model with intact synaptic plasticity to test this idea. To a set of neurons representing a “pure” and consistent stimulus (33% of the population; see ), for each trial, we added a small, variable subset (up to 5% of the total population, 3% in most simulations) of LNs, or of LNs and PNs, as “noise.” These additional neurons were selected randomly every 50 ms. Since we were using a version of the model in which only inhibitory synapses undergo facilitation, we predicted that “noise reduction” should work better when only the LN input contains noise. We start with this unrealistic but simple case, because it allows us to better explore the proposed hypotheses. We will then consider the more realistic case of noisy activity in both LNs and PNs.
We quantified response reliability by comparing the firing phase of PN spikes in consecutive trials. For each cycle i
of the LFP oscillation, the phase of each PN spike, pi
) (where k
is trial number and l
is cell number) was measured relative to the nearest LFP peak (−0.5 < pi
< 0.5; pi
= 0 corresponds to the i
th peak of LFP; pi
= ±0.5 corresponds to the nearest LFP minima). Ten trials with different input noise were simulated, and the difference between phase distributions of each two consecutive trials [Δpi
) = pi
) − pi
)] was calculated. shows the results (first four cycles of LFP oscillations) when only LN input contained noise. Red pixels indicate neurons where spike phase changed greatly between trials (phase shift was more than 10% of the period of LFP oscillations), and light blue pixels indicate the neurons with only small changes in spike phases (phase shift was less than 10% of the period of LFP oscillations). Results show that the network with synaptic plasticity responded with much more consistent spatiotemporal patterns from trial to trial despite random input fluctuations. The network lacking fast learning, however, responded with patterns that changed markedly between trials, reflecting the input variability. This difference between the two models was most prominent during the first 200–250 ms of odor stimulation and became less significant later. After the fourth odor-induced oscillatory cycle, across-trial variability was slightly increased in the model that included plasticity but was reduced in the model lacking plasticity (see ). This change of correlation between response patterns over the odor duration is similar to dynamic odor decorrelation found in the experiments with zebrafish (Friedrich et al., 2004
; Friedrich and Laurent, 2001
Odor Learning and the Reliability of PN Responses
To quantify the effect of plasticity, the difference between PN spike phases at nearby trials with noise [Δpi(k,l) as shown in ] was first averaged across all PNs and across all trial pairs [<Δpi(k,l)>k,l]. This experiment was repeated independently N = 10 times with different noise; the average phase difference [<Δpi(k,l)>k,l,N] was plotted versus cycle number i (, left). During the first three cycles in the network with plasticity, this amount of variability was greatly reduced, to about 30% of that for the AL model with fixed synapses. In both models, average difference started to increase at cycle 4 and was saturated near the end of the trial (cycles 8 to 9). However, when we added noise to the inputs of both PNs and LNs, the result was quite different. Since excitatory synapses were fixed in the model, plasticity could not compensate for the variations of PN activity; each PN activated by random in- put noise could affect activity of all its postsynaptic PNs and LNs, thus changing the network activity (, right).
Effect of Learning on the Precision of PN Spiking
presents another measure of the reliability of PN responses. PN spikes were counted in 10 ms bins. For each bin, the standard deviation of PN spikes across ten trials with noisy stimuli was calculated and then averaged for all PNs in the network (<STD>l). The average STD is plotted versus time (, top left). Again, the network with plasticity produced more reliable responses. We repeated this experiment indepen- dently N = 10 times, each with different noise. Average STD was calculated (<STD>l,N), and the result obtained with plasticity was subtracted from the result obtained without plasticity (<STD>l,NNoPlasticity – <STD>l,NOnlyGABA) (see , bottom left). This analysis indicates consistently higher variability (observed through all cycles) of spike count in the model without plasticity. This was true, however, when noise was provided to the LN input only. The models performed similarly when noise was delivered to both LN and PN inputs (, right).
AL Model with All Synapses Possessing Plasticity
In an effort to bring the results of the model in line with experimental observations, we next examined a network in which all intrinsic synapses, excitatory as well as inhibitory, could undergo plasticity. Afferent synapses delivering odor input to the AL network remained fixed. presents results for an AL model identical to the previous one except that excitatory PN-PN and PN-LN synapses were no longer fixed. Their initial values were set to 33% of the weights of the previous model, and the rate of facilitation was chosen such that they saturated at the same rate as in the previous model, after a few trials. shows details of LFP evolution during first five trials. As in the previous models (), the network responded with almost no oscillations during the first trial but began to display strong oscillatory responses after the first few stimulus presentations. The main difference in LFP spectral content was a reduction in the initial (onset) response in the new model, explained by the initially lower synaptic weights between PNs. The number of stimulus-elicited PN spikes decreased during first few trials in the full plasticity model and for trial 1 was similar to that in the model with GABAA plasticity only (compare and ). However, asymptotic behavior in the model with full plasticity was the same as for the model with GABAA and GABAB plasticity. This suggests that excitatory and slow inhibitory couplings can balance each other with respect to PN spike count during early trials. LFP oscillatory power increased noticeably within the first three trials (see , inset).
Plasticity of Excitatory Synapses and Reliability of PN Responses
The average difference between phases of PN spikes in consecutive trials is shown in (left), and the average STD of PN spikes counted in 10 ms bins for ten trials is presented in (right). presents the same phase analysis as shown in , but with noise included in both PN and LN inputs. It shows that trial-to-trial PN spiking was much more reliable in the full plasticity model compared to the model with inhibitory plasticity only. The responses in these experiments with noise added to the input of both LNs and PNs were at least as reliable as in simulations in which only LN input included noise (compare with , left). All these results indicate strongly enhanced reliability with all synapses undergoing activity-dependent facilitation for stimuli with random noise.