Susin (2021): Gamma vs Drive

Independent excitatory afferent drive strengthens population bursting in a calibrated conductance-based E/I network.

Abstract

We tested whether increased nonrhythmic afferent excitation recruits collective oscillations in a modified replication of Susin and Destexhe’s (2021) PING network. We searched afferent rates and recurrent weights in a smaller conductance-based LIF network for weak baseline correlations and stimulus-dependent bursting. Increased excitation onto both populations raised mean E firing from 3.53 to 11.51 Hz and strengthened bursting in the selected simulation. This single-seed exploratory search characterizes one selected configuration.

Introduction

In the pyramidal–interneuron gamma (PING) network of Susin and Destexhe (2021), increasing nonrhythmic excitatory Poisson drive onto both populations shifted an asynchronous-irregular-like baseline toward stronger gamma oscillations generated by recurrent E/I interactions.[1]

We attempted a modified replication, retaining the reference synaptic decay times, delays and stimulus timing while searching afferent rates and recurrent weights for weak baseline correlations and stimulus-dependent bursting.

Our 2,000-neuron network is smaller and denser but gives each neuron fewer recurrent inputs. Non-adapting LIF neurons replace AdEx neurons; afferent rates and recurrent excitation are lower; inputs are independent across targets; and a 500 ms hidden baseline precedes the display. These changes limit quantitative alignment in firing rates, burst structure or timing.

Results

Recorded circuit

Figure 2: Recorded circuit replay of the seed-7 simulation, looping over displayed time 0–600 ms after the hidden 500 ms baseline. A: E private and I private show recorded aggregate input counts for 160 E-targeted and 40 I-targeted channels, each representing 400 independent afferents to one neuron. E population and I population show the corresponding neurons’ recorded spikes. Blue denotes E-targeted private input and excitatory neurons; rose denotes I-targeted private input and inhibitory neurons. Both private populations provide excitation. Recurrent connections are sampled from the actual nonzero weights; private connections join each channel to its own target. Pulses travel over the recorded 1.5 ms synaptic delay; highlights persist for 3 ms for visibility. Grey pulses show spike transmission. Larger, brighter pulses emphasise recurrent signalling between E and I; private-input pulses are visually subdued. B: The pistons show recorded population means at the same timestep. gE is recurrent plus private excitatory conductance onto E neurons; gI is inhibitory conductance onto E neurons, both in µS. VE and VI are mean membrane voltages across all E and I neurons, in mV. The conductance pair shares a zero-based scale; the voltage pair shares a −80 to −50 mV scale. C: The full prescribed per-source afferent-rate protocol is shown for E-targeted input (blue solid) and I-targeted input (rose dashed); the coincident traces are not measured neuron firing rates. The grey bar marks the current replay time. Speed changes playback only; 1× plays the 600 ms recording over 25 seconds. Positions and pulse appearance are display choices.

Private drive strengthens bursting

In the selected configuration, a 50% increase in E- and I-targeted afferent rates strengthened population bursting (Fig. 3). Mean E/I firing rates rose from 3.53/3.83 Hz at baseline to 11.51/11.93 Hz during the plateau and were 4.28/4.38 Hz in recovery. Mean E spike-count correlation rose from 0.009 to 0.267.

Excitatory and inhibitory neurons formed aligned bursts during increased drive (Fig. 3B). Their plateau spike-count profiles overlap strongly but vary in amplitude and timing (Fig. 3C–D); narrow burst bands alternate with dispersed spikes.

Four-panel plot showing afferent rates, all E and I spikes over 600 ms, a 250–350 ms raster close-up, and unsmoothed population spike counts in 1 ms bins.

Figure 3: Spike timing in the seed-7 simulation, after the hidden 500 ms baseline. A: coincident E- and I-targeted rates (black solid and red dashed). B: all spikes from 1,600 E neurons (black, lower) and 400 I neurons (red, upper); dotted lines mark the pulse and shading the close-up. C: the 250–350 ms plateau window. D: unsmoothed population-total counts in 1 ms bins over that window; E contains four times as many neurons as I.

Reference PING network

Published PING column from Susin and Destexhe Figure 4, showing panels B and C: external Poisson drive and the spike raster.

Figure 4: Cropped from Figure 4 (left PING column, panels B and C) of Susin and Destexhe (2021).[1] © 2021 Susin and Destexhe; reproduced under CC BY 4.0. B shows external Poisson drive; C shows the spike raster. Original panel labels and colours are retained.

The networks share a drive-dependent response but differ in three respects:

  1. Increased E/I excitation strengthens collective activity in both; ours has sharper burst bands (Fig. 4B–C Fig. 3A–B).

  2. Their raster samples 1,000 E and 1,000 I neurons from 25,000; ours shows all 1,600 E and 400 I neurons.

  3. Both show 600 ms with a 200 ms pulse. Their drive is 2→3→2 Hz during ongoing activity; ours is 0.8→1.2→0.8 Hz after a hidden 500 ms baseline.

Sharper bursts may reflect our non-adapting LIF neurons, altered thresholds and refractory periods, fewer recurrent inputs, recalibrated weights or lower background drive (Table A1); sampling also affects raster density. Controlled comparisons are needed.

Methods

  1. Construct the modified replication. We replaced the adapting AdEx neurons in the PING network of Susin and Destexhe (2021)[1] with 1,600 excitatory and 400 inhibitory conductance-based LIF neurons. Recurrent connections, including possible self-connections, were sampled independently with 10% probability. Table A1 lists the available recorded settings. We used a 0.1 ms timestep.

  2. Apply the input protocol. Each neuron received 400 equivalent independent excitatory Poisson afferents, each adding 4 nS of AMPA conductance. We initialized voltages at −65 mV, simulated a 500 ms hidden baseline, then preserved state through the 600 ms display. From displayed time 200 ms, both populations received a 50% rate increase with a 50 ms rise, 100 ms plateau and 50 ms fall (Fig. 2C).

  3. Measure population activity. We measured per-neuron firing rates during baseline (0–200 ms), plateau (250–350 ms) and recovery (400–600 ms). Synchrony was the mean pairwise Pearson correlation of 10 ms spike counts among up to 100 evenly sampled neurons per population with nonzero count variance. We calculated median interspike-interval coefficient of variation (CV) among neurons producing at least five spikes, retaining the eligible-neuron count.

The retained pipeline reproduces the selected configuration. The earlier exploratory calibration search is not retained as an identified input to this report and is not independently reproducible from this pin. Its selection limits the scope of the displayed result.

Network diagrams

The circuit contains 1,600 excitatory and 400 inhibitory neurons with recurrent AMPA and GABA synapses (Fig. A1). Each neuron receives independent excitatory Poisson input; recurrent I neurons provide inhibition.

Structural diagram of 1,600 excitatory and 400 inhibitory neurons with independent private excitatory afferents and recurrent AMPA and GABA projections.

Figure A1: Structural view of the compiled network, showing the E and I populations, recurrent AMPA and GABA projections, and private excitatory inputs. Input dimensions describe aggregate channels, one per target neuron; both private inputs provide excitation. XEX_E and XIX_I denote private excitatory input banks targeting E and I. Every projection is labelled WXYW_{XY}, with target XX first and source YY second. Arrowheads show excitation; bars show inhibition. Recording aliases and score reductions are omitted.

Parameters

ParameterRecorded value
Network
Native parameter snapshotUnavailable
Input channelsUnavailable
PopulationsUnavailable
Membrane modelUnavailable
Neurons
Membrane capacitanceUnavailable
Leak conductanceUnavailable
Resting potentialUnavailable
Reset potentialUnavailable
ThresholdUnavailable
Refractory periodUnavailable
Membrane time constantUnavailable
Synapses and weights
Native synapse and weight parametersUnavailable
Input and simulation
External afferents per neuron400
Baseline E source rate0.8 Hz
Baseline I source rate0.8 Hz
Stimulus E source rate1.2000000000000002 Hz
Stimulus I source rate1.2000000000000002 Hz
Seed7
Timestep0.1 ms
Duration1100 ms
Hidden baseline500 ms
Pulse onset700 ms
Pulse peak750 ms
Plateau end850 ms
Pulse offset900 ms
Analysis
isi cvmedian across neurons with at least five spikes in epoch
pair correlationmean Pearson correlation of 10 ms counts across at most 100 evenly sampled neurons with nonzero variance
population rate alignmentcausal trailing
population rate window ms20
rhythmicitySNNSIM rhythmicity_metrics contrast, 1 ms bins, maximum lag 100 ms
spectrumWelch population counts, 1 ms bins, 500 ms segments, default Hann window and 50 percent overlap; peak 20-100 Hz and band fraction relative to 1-200 Hz; not a PING classifier
Table A1. Model parameters follow the selected presentation to its original compute's native snapshot; input and protocol settings come from that compute's recorded configuration. Paired neuron values follow E / I order. Missing snapshots or fields are unavailable. Historical figures retain their original evidence; current recipe defaults are never substituted.

Dataset

Upstream: —

Downstream: —

Current runset

RunDateDurationSizeEvidenceStorageRan onVerification
exp099-r010-present1s4.1 MBCurrentR2LocalLocal: absent; R2: catalog-verified
exp099-r002-analyse1s196.9 KBCurrentR2LocalLocal: absent; R2: catalog-verified
exp099-r001-compute6s1.9 MBCurrentR2LocalLocal: absent; R2: catalog-verified

References

  1. E. Susin and A. Destexhe. “Integration, coincidence detection and resonance in networks of spiking neurons expressing Gamma oscillations and asynchronous states.” PLOS Computational Biology 17(9), e1009416 (2021). doi:10.1371/journal.pcbi.1009416