Turning the PING Loop On

Abstract

We compared untrained excitatory–inhibitory circuits with reciprocal feedback disabled or enabled, using one seed and a matched Poisson-drive sweep. In the separate illustrative trials, loop-off E firing was 23.86 Hz at 5 Hz input, versus 8.43 Hz at 45 Hz input with feedback. The matched-drive sweep showed suppression under reciprocal coupling. These observations establish this circuit’s operating behaviour, but do not isolate a causal contribution of gamma timing.

Results

Architecture, spectra and rates

Reciprocal coupling produced recurring E/I volleys and suppressed E firing across the matched-drive sweep. The illustrative raster trials used different drive rates, so their rates alone do not isolate the effect of the loop.

COBA excitatory-neuron dynamics

The selected loop-off E neuron received input excitation and leak without inhibitory feedback. Its voltage and reconstructed currents illustrate a single active neuron rather than a population-average response.

ABC

PING excitatory–inhibitory dynamics

These cellular traces illustrate reciprocal E→I→E feedback (Fig. 3A–F); they do not measure population-wide phase locking or spikes per cycle.

ABCDEF

Methods

We compared untrained loop-off and loop-on networks using the following simulation and measurement procedure.

Compute

1. Construct the two loop conditions. Both networks contained 1024 excitatory (E) and 256 inhibitory (I) neurons. One 1024-channel input layer and the same realized weights were reused across raster trials and the drive sweep within each loop condition. An input layer drove E neurons through feedforward weights; reciprocal E→I and I→E weights formed the PING loop, without E→E or I→I recurrence. Loop coupling was 0 or 1.5; the I→E parent mean was 2 times E→I, and both parent standard deviations were 10% of their means. Input parent weights had mean 1.5 and standard deviation 0.3; lower-clamped Gaussian draws were normalised by fan-in, with 95% initially zero and survivors rescaled.

2. Generate the drive and simulate. Uniform Poisson input drove every channel at the condition’s rate, with seed 42 for input and network initialization. Membranes began at -65 mV and conductances at 0 µS. Exponential-Euler membrane integration used 0.1 ms steps; AMPA and GABA decay constants were 2 and 6 ms, with E/I refractory periods 1.2/0.6 ms.

   Full trial recordings included spikes, voltages and conductances.

Analyse

3. Measure the drive response. Both loop conditions used 1 trial at each of 2, 5, 10, 20, 40, 70, 100 Hz through 1024 input channels for 400 ms, without a discarded transient. Mean per-neuron firing rate was $r_P = n_{\mathrm{spike},P} / (N_P T_{\mathrm{present}}),$ where $P$ identifies E or I, $n_{\mathrm{spike},P}$ is the population’s total spike count, $N_P$ its neuron count, $T_{\mathrm{present}}$ the full presentation duration in seconds and $r_P$ the rate in hertz. No averaging across independent seeds was performed.

4. Estimate the population spectrum. The mean E spike trace was demeaned and passed to Welch’s density estimator with one full-trial window.1 This is a single-window estimate, not an average over independent segments. The largest peak between 5 and 150 Hz was refined by three-bin parabolic interpolation, clamped to half a bin; it was reported only when I spikes were present. This reporting rule is not a test of significant rhythmicity.

Present

5. Reconstruct signed currents. Each displayed neuron was the first neuron attaining the highest total spike count in its population during that raster trial. A silent E population used neuron zero; a silent I population had no selected-neuron panels. Raster trials used 1024 input channels at 5 Hz for COBA and 45 Hz for PING. These trials used the same network setup as the matched-drive sweep; only input rate differed.

   For the selected neurons, recorded conductances and voltages gave $I_X^{\mathrm{in}} = -g_X (V_m - E_X),$ where $X$ identifies excitation, inhibition or leak; $g_X$ is conductance in µS, $V_m$ membrane voltage and $E_X$ reversal potential in mV, and $I_X^{\mathrm{in}}$ inward current in nA. Reversals were 0, -80 and -65 mV, respectively; positive current is depolarising. The sign lives in the driving force, never in the conductance.