The intrinsic parameters of the AdEx model populations.

Square brackets indicate the lower and upper bound of the uniform prior distribution. If a cell contains a single number, that parameter is held constant. ΔT, slope factor; τw, adaptation time constant; a, subthreshold adaptation; b, spike-triggered adaptation; Vr, spike triggered reset voltage; C, capacitance; gL, leak conductance; EL, resting membrane potential; VT, spike threshold. Note that VT determines the point of exponential rise but is not the hard threshold for triggering the spike reset. A spike is triggered when the voltage is larger than 0 mV, see Equation 3.1; n, number of neurons in the population.

The parameters of the Tsodyks-Markram synaptic connections.

ASE, maximum synaptic conductance; τin, time constant of synaptic decay; τrec, synaptic resource recovery time constant; USE, fraction of synaptic resources activated; τfacil, decay of facilitation time constant; p pairwise connection probability in %. NIN GJ NIN, is a gap junction connection, modeled as a fixed conductance between connected NINs.

The quantified outcomes of the simulator.

ISI, interspike interval; CV, coefficient of variation. We implemented the model with Brian2 (Stimberg et al., 2019). All simulations ran for 1 s with a temporal resolution of 0.1 ms.

Sequential NPE finds distributions of parameters that produce different levels of excitability.

A) An illustration of the spiking neuronal network simulator. See methods Section 2.1 for details. B) Simulator outcome from 1122586 simulations. Simulations with zero PC spikes or undefined CV are not shown. The parameters were drawn from the prior distribution (see Table 1 & Table 2). The cross shows the two target outcomes the NPE was conditioned on. C) Shows the result of simulating the MAP parameters from p(θ |xBaseline) and p(θ |xHyperexcitable). The top shows the voltage trace of a single PC, and the bottom shows spike raster plots for 50 of 500 PCs. D) Outcomes from simulating 1000 parameter sets that were drawn from each of the two distributions. The black x marks the value that was targeted with NPE. See Table 3. In the baseline condition, the targeted outcome is well within support of the outcome distribution for all parameters. In the hyperexcitable condition, gamma and fast power targets are not within the interquartile range.

Various parameter pairs can compensate each other to maintain baseline excitability.

200000 samples were drawn from the baseline posterior estimator and pairwise Spearman correlations were calculated for each of the 496 unique pairwise comparisons. A) shows 2D histograms of the 19 pairs with correlation coefficients larger >0.1 or <−0.1. The maximum pixel values read from top left to bottom right are: 813, 588,525,1718,411,863, 3328, 2923, 704, 757, 673, 2371, 327, 294, 3337, 278, 262, 301 and 291. The minimum pixel value is always 0, except for the second to last pair ( vs where the minimum is 3. B) Shows the correlation coefficient of all parameter pairs as a diverging heatmap. The marginal correlation coefficients for the pairs shown in A from top left to bottom right, are: −0.31, −0.21, −0.13, 0.15, 0.13, −0.32, 0.19, −0.25, −0.13, −0.14, 0.54, 0.14, −0.22, −0.12, −0.94, −0.19, −0.16, 0.11, −0.32. C) Shows the correlation coefficients of samples drawn for each parameter pair while conditioning all other parameters on the map estimate. Correlation coefficients for the order in A from top left to bottom right, are: −0.43, 0.06, −0.41, 0.49, −0.01, −0.59, 0.42, 0.35, −0.47, −0.39, 0.59, 0.54, −0.47, −0.35, −0.49, −0.45, −0.47, −0.23, −0.51.

Specific pathophysiological conditions have distinct compensatory parameters that maintain baseline outcomes.

We compared samples from the baseline posterior estimator conditioned on normal and pathophysiological parameter values. To compare distributions, we calculated the Kolmogorov-Smirnov (KS) test statistic. A), B) and C) show the five parameters with the largest test statistic in each condition. A) compares 55 AIns and 54 NINs in each subpopulation (Normal, Equation 7.1) to 15 neurons in each population (IN Loss, Equation 7.2). B) compares PC − PCp of 0.15% (Normal, Equation 8.1) to 3% (Sprouting, Equation 8.2). C) compares (Normal, Equation 9.1), with (Depolarized, Equation 9.2). D) KS test statistic for all parameters and conditions. KS test results for all parameters and conditions are in Table Supp 3.1. E) & F) show the absolute correlation coefficients from Figure 2. IN loss is the average absolute correlation of NINn and AINn with the other parameters. Sprouting is the absolute correlation of PC → PCp with the other parameters. Intrinsic is the average absolute correlation of and with the other parameters.

Specific pathophysiological conditions have distinct compensatory parameters that can change the network from hyperexcitable to baseline.

We compared samples from the baseline posterior estimator to those from the hyperexcitable posterior estimator conditioned on pathophysiological parameter values. To compare distributions, we calculated the Kolmogorov-Smirnov (KS) test statistic. A), B) and C) show the five parameters with the largest test statistic. Each compares baseline and the hyperexcitable estimator for a specific pathophysiological condition. In A) the condition is that the IN numbers are set to 15. In B) the condition is that PC → PCp is set to 3%. In C) the condition is that ) shows the KS test statistic calculated between the baseline and hyperexcitable posterior for each pathophysiological condition. KS test results for all parameters and conditions are in Table Supp 4.1.

The pathophysiological condition changes the effect of parameters on simulated outcomes.

The hyperexcitable posterior estimator was sampled with additional pathophysiological conditions. Then, each parameter was varied to cover 50 points in the parameters prior range and the parameters were simulated. Each of the 50 points on the x-axis contains 100 samples and the error bars show the 95% confidence interval. The asterisks indicate where the p-value of the interaction between parameter and condition is . Figure Supp 5.1 shows the effect of more parameters and Table Supp 5.1 contains the p-values of the interactions.