Each synaptic input was modeled as a time-varying conductance fit to an alpha function: with a time constant 5 ms and an amplitude determined by the excitatory input parameter of the model (ranging from 0.3 to 6 n8).

NMDA channels were added to the model only for S6 Fig (e-f.) The time constants used for the alpha function governing the time varying conductance for the NMDA channel was 63 ms (fast component) and 200 ms (slow component), with a peak amplitude ratio of 0.88:0.12 (fast: slow).

The ratio of the peak amplitude between the AMPA channel ( time constant of 5 ms) and NMDA channel was 1:0.3 (AMPA:NMDA) [29].

The synchronization limit of simulated neurons was also sensitive to this time constant; increasing this time constant (S6 Fig, ad) or adding an additional NMDA-based conductance (S6 Fig (e-f) [29], see Methods) shifted the synchronization limit of simulated neurons to longer IPIs (mean synchronization limit: sync = 15.9 ms, mixed 2 15.3 ms).

We tested our model With acoustic pulse trains spanning the perceptual range of flutter/ fusion perception, with interpulse intervals (IPIs) ranging between 3—75 ms. Each acoustic pulse was modeled as a change in the excitatory and inhibitory conductance, governed by an alpha function with a 5 ms time constant (Fig.

Dependence of synchronization limit on conductance time constant .

Simulated synchronizing neuron With IE delay 2 5 ms, excitatory strength 2 3 n8, I/E ratio = 1.7. a. Raster plot of acoustic pulse train response, 5 ms time constant used for input conductance.

b. Raster plot of acoustic pulse train response, 10 ms time constant used for input conductance.

A stimulation instantaneously activates a fraction Use of synaptic resources r, Which then inactivates With a time constant Time and recovers With a time constant rm In the simulations, at time t = tstl-m, r and e respectively decreases and increases by the value User.

Recovery time constant

Inactivation time constant

Approximation of time constants .

Time constants T of simulated extracellular K+ transients were fitted to curves using a single exponential (e‘i) (Fig.

Time constants T of experimental and simulated astroglial membrane potentials were calculated by computing the rise and decay times between 20% and 80% of the maximal peak amplitude responses (Fig.

In that case, using equation 23, the time constant of Kir4.1 channel-mediated return to equilibrium of astroglial membrane potential TA is defined as

This time constant is consistent with the fitted exponential decay time obtained in our simulations and experiments for a single stimulation where we obtained 1‘ z 0.75.

For current inputs eliciting small changes in voltage (5 mV), the resulting voltage trajectory was fit accurately with an exponential function and used to extract the membrane time constant near -75 mV (12.0 i 0.9 ms, n = 19).

Thus, the voltage trajectories to spike threshold starting either from resting voltages or the trough of the AHP were relatively linear compared to that expected from our measures of the membrane time constant at—75 mV.

For comparison, the exponential approximation using the membrane time constant measures taken at -75 mV is also shown.

We used a presynaptic population consisting of the equal number of excitatory and inhibitory neurons, with log-normal distribution of synaptic amplitudes (same distribution, positive weights for excitatory, negative weights for inhibitory), and PSC kernels consisted of the same difference of two exponentials with time constants of 0.5ms and 5ms.

Thus, the model parameters are N (the number of presynaptic neurons), k and 6 (the shape and scale parameters for the homogeneous Gamma renewal processes), [,4 and o (the shape and log-scale parameters of the log-normal amplitude distribution), and T1 and 72 (the time constants of the artificial PSCs).

R denotes membrane resistance (1 / gL), 1‘ denotes the membrane time constant , DT determines the strength of the exponential nonlinearity near threshold, While a, b, and TW determine the dynamics of the adaptation variable.