S1 File - Bursting Reverberation as a Multiscale Neuronal Network Process Driven by Synaptic Depression-Facilitation

The Supporting Information contains:

Table A: Burst durations in island cultures and acute slices.

Table B: Comparison of burst durations for different extracellular calcium concentrations

A derivation section for formula [5]: Analytical estimation of the reverberation time TR

5 figures described below:

Figures in the Supporting Information file

Figure A. Reverberation bursting ratio when the interval between pulses varies. Using the parameters for culture (see table A in S1 File, the ratio converges to one after ten seconds.

Figure B. Effect of noise on the reverberation burst.(A) Burst duration after the first and the second pulse as a function of the noise amplitude σ, for each value of the noise amplitude σ (500 runs). (B) Numerical simulations of the evoked bursts, generated at 5 and 35 seconds intervals with a source noise, extracted from the experimental data (σ = 2 Hz). Spontaneous activity is not enough to generate a response comparable to the evoked one.

Figure C. Blocking astroglial metabolism does not affect the bursting reverberation.(A) Evoked burst triggered by a single synaptic stimulation with a 5 s interval in the presence of fluoroacetate (FAC, 5 mM). (B) Simultaneous depolarization of astrocyte during the bursting pulse. (C) Bursting duration at 0 and 5 s before and after FAC application. (**P < 0.01, compared with 0 s, Student’s paired t-test). (D) Ratio of bursting duration at 5 s before and after FAC application (P > 0.05, compared with control, Student’s paired t-test, n = 4).

Figure D. Comparison of system of Eq 1 (continuous line) and the approximated system 2 (dashed line). We use three different values of the connectivity parameter J. The firing rate h, the facilitation x and the depression y variables are plotted as functions of time. For a low enough connectivity parameter J, the firing rate is well approximated.

Figure E. Comparison between the depression variable y estimated by equation 8 (blue) and the exact one obtained by numerical simulation of system 2 (black).

Figure F. Comparison between numerical simulations and estimates of the reverberation time TR. The reverberation time is plotted as a function of J for the exact model (solid line), the approximated model (dash black line), and the estimates given by equations 37 (dash red line) and 39 (blue dash line).

Table A: Burst durations in island cultures and acute slices.
Table B: Comparison of burst durations for different extracellular calcium concentrations
A derivation section for formula [5]: Analytical estimation of the reverberation time TR
5 figures described below:
Figure A. Reverberation bursting ratio when the interval between pulses varies. Using the parameters for culture (see table A in S1 File, the ratio converges to one after ten seconds.
Figure B. Effect of noise on the reverberation burst.(A) Burst duration after the first and the second pulse as a function of the noise amplitude σ, for each value of the noise amplitude σ (500 runs). (B) Numerical simulations of the evoked bursts, generated at 5 and 35 seconds intervals with a source noise, extracted from the experimental data (σ = 2 Hz). Spontaneous activity is not enough to generate a response comparable to the evoked one.
Figure C. Blocking astroglial metabolism does not affect the bursting reverberation.(A) Evoked burst triggered by a single synaptic stimulation with a 5 s interval in the presence of fluoroacetate (FAC, 5 mM). (B) Simultaneous depolarization of astrocyte during the bursting pulse. (C) Bursting duration at 0 and 5 s before and after FAC application. (**P < 0.01, compared with 0 s, Student’s paired t-test). (D) Ratio of bursting duration at 5 s before and after FAC application (P > 0.05, compared with control, Student’s paired t-test, n = 4).
Figure D. Comparison of system of Eq 1 (continuous line) and the approximated system 2 (dashed line). We use three different values of the connectivity parameter J. The firing rate h, the facilitation x and the depression y variables are plotted as functions of time. For a low enough connectivity parameter J, the firing rate is well approximated.
Figure E. Comparison between the depression variable y estimated by equation 8 (blue) and the exact one obtained by numerical simulation of system 2 (black).
Figure F. Comparison between numerical simulations and estimates of the reverberation time TR. The reverberation time is plotted as a function of J for the exact model (solid line), the approximated model (dash black line), and the estimates given by equations 37 (dash red line) and 39 (blue dash line).
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