Model of transient oscillatory synchronization in the locust antennal lobe

Abstract

Transient pairwise synchronization of locust antennal lobe (AL) projection neurons (PNs) occurs during odor responses. In a Hodgkin-Huxley-type model of the AL, interactions between excitatory PNs and inhibitory local neurons (LNs) created coherent network oscillations during odor stimulation. GABAergic interconnections between LNs led to competition among them such that different groups of LNs oscillated with periodic Ca(2+) spikes during different 50-250 ms temporal epochs, similar to those recorded in vivo. During these epochs, LN-evoked IPSPs caused phase-locked, population oscillations in sets of postsynaptic PNs. The model shows how alternations of the inhibitory drive can temporally encode sensory information in networks of neurons without precisely tuned intrinsic oscillatory properties.

Figure 1. Network Geometries

(A) Two reciprocally connected neurons. (B) A simple network model of 6 PNs and 2 LNs. Four neurons were stimulated by current pulses to simulate the effect of odor presentation. (C) A network model of 90 PNs and 30 LNs. All interconnections were random with probability 0.5. Thirty-three percent of the total population was stimulated by time-modulated current pulses. Dashed lines illustrate connections to the rest of the network.

Figure 2. Stimulus-Evoked Oscillations in PN and LN Models

(A) Responses of isolated PN and LN to current pulses of different amplitude. (B) A reciprocally connected LN-PN pair oscillated out-of-phase at about 15 Hz. (C) Frequency of oscillations in reciprocal LN-PN pair versus decay time constant of inhibitory synapse (_{gLN → PN} = 0.8 μS) and versus maximal conductance of inhibitory synapse (τ = ms). (D) Oscillations in a network of 6 PNs and 2 LNs. (D1) Lateral inhibition between LNs led to alternations in the temporal patterns of LN oscillation. Variations in LN-evoked fast IPSPs changed the temporal patterns of PN activity. (D2) Blocking LN-LN reciprocal connections made these cells oscillate regularly thus decreasing the complexity of PN responses.

Figure 3. The Response Properties of a Network of 90 PNs and 30 LNs

(A) Averaged PN activity (field potential) showed periodic oscillations at about 20 Hz during stimulation. (B) Network response, spikes indicated with dots. Firing rates of PNs and LNs increased during stimulation. During 1 s intervals between stimulus presentations, the PNs displayed spontaneous activity leading to occasional Na⁺ spikes. (C) To simulate odor presentations, two 500 ms time-modulated current pulses with added Gaussian noise were introduced to 33% of the PNs and LNs. (D) Different PNs and LNs participated in the coherent network oscillations during different portions of the stimulus presentation. (E) Power spectrum of averaged PN activity had a sharp peak near 20Hz. (F) Typical odor responses recorded in vivo. Odor stimulation evoked oscillations in the local field potential (upper trace, recorded in the mushroom bodies), and action potentials in a PN (lower trace).

Figure 4. PN Responses for Different Stimuli and Role of the Strength of LN Inhibition

Four cells (rows) are shown. The response of each cell has been divided into 11 epochs of about 50 ms, each corresponding to oscillatory cycles of activity. In each epoch, the positions (phases) of the action potentials relative to the maximum of the corresponding field potential were calculated and plotted (rows labeled PN1, PN2, etc.). This operation was repeated 20 times for each odor (rasters within each epoch). The number of Ca²⁺ spikes in all presynaptic LNs, averaged over 20 trials, is shown for each cycle (rows labeled N_LN). (A and B) During stimulation of similar sets of neurons, almost identical subsets of PNs responded, but with different temporal patterns. (C) A different subset of PNs was stimulated during these trials, and different PNs responded.

Figure 5. Standard Deviation of PN Spike Phases Measured over Repeated Stimulus Presentations

(A) Standard deviation (20 trials) is shown as a function of oscillatory cycle number for 90 PNs. Zero deviation (black) corresponded to precise phase-locking of PN spikes with field oscillations. Maximal deviation (white) corresponded to complete desynchronization of PN spikes with field oscillations. White also indicates silent PNs. (B) Standard deviation of PN spike phases (shown in Figures 4A and 4B) plotted against the total number of LN spikes in all presynaptic LNs. The data for four PNs and two stimuli are plotted with different symbols. Straight line is linear regression.

Figure 6. Effect of Fast Inhibition and LN Spike Adaptation for PN Responses

(A) Blocking LN-LN GABA_A inhibition. (A1) Average PN activity (field potential). (A2) PN responses for the two different stimuli presented in Figures 4A and 4B. Most of the PNs were now phase-locked with the field potential during the whole trial, reducing the discriminability of PN responses for similar stimuli. (B) Blocking Ca²⁺-dependent K⁺ current in LNs. (B1) Average PN activity shows oscillations at higher frequency (about 30 Hz). (B2) PN responses for the two different stimuli presented in Figures 4A and 4B. Now PN synchronization (or its absence) usually endured throughout the whole stimulus duration.

Figure 7. Effect of LN-LN Inhibition and LN Spike Adaptation on Spike Time Variability and Stimulus Discrimination

(A) Average (over cycles 3–7) distance between two different responses (see Experimental Procedures) versus the percentage of overlap of activated sets of neurons. (B) A clustering algorithm (τ = 100 ms) was applied to spike trains in 3 PNs to illustrate discrimination between two stimuli presented in Figures 4A and 4B. Each trial was characterized by the distances to the centers of two clusters corresponding to stimuli 1 and 2 (see Experimental Procedures); these distances are plotted on axes x and y. (B1) Intact network. (B2) Fast LN-LN inhibitory synapses blocked. (C) Misclassification rate calculated for all PNs for intact and disinhibited networks and for the network where Ca²⁺-dependent K⁺ channels in all LNs were blocked.