Figures and data in Compensation of hyperexcitability with simulation-based inference

Figures
Tables
Additional files

7 figures, 4 tables and 2 additional files

Figures

Figure 1 with 1 supplement

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

(A) An illustration of the spiking neuronal network simulator. See ‘Key resources table’ for details. (B) Simulator outcome from 1,122,586 simulations. Simulations with zero PC spikes or undefined CV are not shown. The parameters were drawn from the prior distribution (see Tables 1 and 2). The cross shows the two target outcomes the NPE was conditioned on. (C) shows the result of simulating the MAP parameters from $p (θ | x_{B L})$ and $p (θ | x_{H E})$ . Top: voltage trace of a single PC. Bottom: spike raster plots for 50 of 500 PCs. (D) Outcomes from simulating 1000 parameter sets drawn from each of the two distributions. The black cross marks the value targeted by the NPE. See Table 3. In the baseline condition, the targeted outcome was well within support of the outcome distribution for all parameters. In the hyperexcitable condition, gamma and fast power targets were not within the interquartile range.

Figure 1—figure supplement 1

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Simulation-based calibration results of an amortized posterior estimator.

The red bars indicate the ranks distribution of ranks. Each histogram is for a specific parameter. If the posterior estimates were well calibrated, the rank distributions would be uniformly distributed. The gray background indicates the 99% confidence interval of a uniform distribution given the number of samples. The p-values of the null-hypothesis that the ranks are drawn from a uniform distribution were as follows: 0.6784; 0.1548; 0.0008; 0.0245; 0.0000; 0.0000; 0.0001; 0.0000; 0.0000; 0.0801; 0.0000; 0.0023; 0.0001; 0.0000; 0.0296; 0.2425; 0.0000; 0.0034; 0.0010; 0.0000; 0.0000; 0.0004; 0.0003; 0.0007; 0.0015; 0.0001; 0.0000; 0.0008; 0.0000; 0.0000; 0.0000; 0.0000. Since several of the p-values were well below 0.001, we concluded the amortized estimate was miscalibrated.

Figure 2 with 1 supplement

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

(A) shows seven representative 2D histograms of pairs with marginal correlation coefficients larger >0.1 or <−0.1. The maximum pixel values in order are 813, 588, 525, 1718, 411, 863, 3328. All minimum values are zero. (B) MAP conditional sample histograms for the same parameters as in (A). The maximum pixel values in order are: 626, 606, 517, 627, 277, 519, 738. (C) 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. (D) 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.

Figure 2—figure supplement 1

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Marginal versus MAP conditioned correlation coefficient.

Only $P C_{C}$ vs $P C_{E_{L}}$ was not meaningfully correlated with marginal sampling but became non-meaningfully correlated with conditioned sampling. Interestingly $P C_{g_{L}}$ vs $P C \to P C_{A_{S E}}$ switched from negative correlation with marginal sampling to positive correlation with conditional sampling. The $N I N \to P C_{A_{S E}}$ vs $A I N \to P C_{A_{S E}}$ switched from positive in the marginal to negative in the conditional.

Figure 3

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Putative compensatory parameters of specific pathophysiological conditions.

(A) A schematic illustration of the three conditions. IN loss compares 55 AINs and 54 NINs in each subpopulation (Normal, Equation 7a) to 15 neurons in each population (IN Loss, Equation 7b). Sprouting compares $P C \to P C_{p}$ of 0.15% (Normal, Equation 8a) to 3% (Sprouting, Equation 8b). Depolarized compares $P C_{g_{L}} = 3.0 n S, P C_{E_{L}} = - 68 m V$ (Normal, Equation 9a), with $P C_{g_{L}} = 2.5 n S, P C_{E_{L}} = - 66 m V$ (Depolarized, Equation 9b). (B) shows the five parameters with the largest difference in each condition. KS test statistic for all parameters and conditions. (C) shows the KS statistics for all parameters and all conditions. KS test results for all parameters and conditions are in Supplementary file 1A.

Figure 4

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Reproducibility of the posterior estimator with different training data.

The dot and the x are results from separately trained estimators. (A) Original KS statistics versus those from two separately trained replicates. See Figure 3D for original data. (B) Original conditional correlation coefficients versus those from the two replicates. See Figure 3E for original data. (C) Same as (B) but with marginal correlations. See Figure 3F for original data. Correlation coefficients of (A), (B), and (C) are 0.87, 0.84, and 0.89, respectively.

Figure 5

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Putative compensatory parameters that can restore baseline activity given hyperexcitability.

(A) Schematic illustration of the three pathophysiological conditions and the comparison of baseline versus hyperexcitable network output. (B) shows the five parameters with the largest test statistic. Each compares baseline and the hyperexcitable estimator for a specific pathophysiological condition. (C) 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 Supplementary file 1B.

Figure 6 with 1 supplement

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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 $p < \frac{0.0001}{\sqrt{56}}$ . Figure 6—figure supplement 1 shows the effect of more parameters and Supplementary file 1C contains the p-values of the interactions.

Figure 6—figure supplement 1

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An extended version of Figure 6 showing the effect of more parameters.

Figure 7

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Representative illustrations of the AdEx neuron model (A) and the Tsodyks–Markram synapses (B) properties of the microcircuit simulator.

In this example, parameters were fixed to the MAP of the baseline condition.

Tables

Table 1

The intrinsic parameters of the AdEx model populations.

Square brackets indicate the lower and upper bounds of the uniform prior distribution. If a cell contains a single number, that parameter is held constant. $Δ T$ , slope factor; $τ_{w}$ , adaptation time constant; a, subthreshold adaptation; b, spike-triggered adaptation; $V_{r}$ , spike-triggered reset voltage; $C$ , capacitance; $g_{L}$ , leak conductance; $E_{L}$ , resting membrane potential; $V_{T}$ , spike threshold. Note that $V_{T}$ 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 3a; n, number of neurons in the population.

Parameter	PC	AIN	NIN
$Δ T$	0.8 mV	5.5 mV	3.0 mV
$τ_{w}$	88 ms	1 ms	16 ms
a	0.8 nS	2.0 nS	1.8 nS
b	65 pA	55 pA	61 pA
$V_{r}$	-53 mV	-54 mV	−54 mV
$C$	[10 pF, 100 pF]	[96 pF, 209 pF]	[10 pF, 323 pF]
$g_{L}$	[2.0 nS, 20.0 nS]	[2.0 nS, 6.4 nS]	[3.0 nS, 13.5 nS]
$E_{L}$	[−80 mV, −64 mV]	[−65 mV, −51 mV]	[−70 mV, −58 mV]
$V_{T}$	[−49 mV, −39 mV]	[−63 mV, −44 mV],	[−52 mV, −37 mV]
n	500	[10, 100]	[10, 100]

Table 2

The parameters of the Tsodyks–Markram synaptic connections.

$A_{S E}$ , maximum synaptic conductance; $τ_{i n}$ , time constant of synaptic decay; $τ_{r e c}$ , synaptic resource recovery time constant; $U_{S E}$ , fraction of synaptic resources activated; $τ_{f a c i l}$ , decay of facilitation time constant; $p$ pairwise connection probability. NIN GJ NIN, is a gap junction connection, modeled as a fixed conductance between connected NINs.

Connection	$A_{S E}$	$τ_{i n}$	$τ_{r e c}$	$U_{S E}$	$τ_{f a c i l}$	$p$
Input→ PC	5.5 nS	5.5 ms	800 ms	0.5	0 ms	0.2
Input→ NIN	7.0 nS	6.3 ms	800 ms	0.5	0 ms	0.1
PC→ PC	[0.0 nS, 50.0 nS]	10.0 ms	800 ms	0.5	0 ms	[0.0, 0.3]
PC→ AIN	[0.0 nS, 50.0 nS]	4.0 ms	130 ms	0.03	530 ms	[0.0, 0.3]
PC→ NIN	[0.0 nS, 50.0 nS]	10 ms	800 ms	0.5	0 ms	[0.0, 0.3]
NIN→ PC	[0.0 nS, 50.0 nS]	5.5 ms	800 ms	0.5	0 ms	[0.0, 0.3]
NIN→ NIN	[0.0 nS, 50.0 nS]	2.5 ms	800 ms	0.5	0 ms	[0.0, 0.3]
AIN→ PC	[0.0 nS, 50.0 nS]	6.0 ms	800 ms	0.5	0 ms	[0.0, 0.3]
AIN→ NIN	[0.0 nS, 50.0 nS]	6.0 ms	50 ms	0.03	0 ms	[0.0, 0.3]
AIN→ AIN	[0.0 nS, 50.0 nS]	5.5 ms	130 ms	0.03	530 ms	[0.0, 0.3]
NIN GJ NIN	[0.0 nS, 4.0 nS]	–	–	–	–	[0.0, 0.3]

Key resources table

Reagent type (species) or resource	Designation	Source or reference	Identifiers	Additional information
Software, algorithm	Python	Python	RRID:SCR_008394	3.9.18 or 3.10.14
Software, algorithm	Brian2	Brian2	RRID:SCR_002998	2.5.0.3 or 2.7.1
Software, algorithm	matplotlib	Matplotlib	RRID:SCR_008624	3.9.1
Software, algorithm	seaborn	Seaborn	RRID:SCR_018132	0.13.2
Software, algorithm	pandas	Pandas	RRID:SCR_018214	2.2.3
Software, algorithm	statsmodels	Statsmodels	RRID:SCR_016074	0.14.4
Software, algorithm	scipy	scipy	RRID:SCR_008058	1.13.1

Table 3

The quantified outcomes of the simulator.

ISI, interspike interval; CV, coefficient of variation.

Outcome	Mean rate (Hz)	Mean ISI entropy	Theta power	Gamma power	Fast power	Correlation	ISI CV
Baseline (BL)	18	2.7	1⋅10⁻⁷	1⋅10⁻⁸	1⋅10⁻⁹	0.05	0.45
Hyperexcitable (HE)	75	1.0	9⋅10⁻⁶	7⋅10⁻⁹	6⋅10⁻¹⁰	0.99	4.0

Additional files

Supplementary file 1 Tables containing test statistics for Figures 3, 5, and 6.: https://cdn.elifesciences.org/articles/107045/elife-107045-supp1-v1.xlsx
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MDAR checklist: https://cdn.elifesciences.org/articles/107045/elife-107045-mdarchecklist1-v1.pdf
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Daniel Müller-Komorowska
Tomoki Fukai

(2026)

Compensation of hyperexcitability with simulation-based inference

eLife 14:RP107045.

https://doi.org/10.7554/eLife.107045.4

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

Simulation-based calibration results of an amortized posterior estimator.

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

Marginal versus MAP conditioned correlation coefficient.

Putative compensatory parameters of specific pathophysiological conditions.

Reproducibility of the posterior estimator with different training data.

Putative compensatory parameters that can restore baseline activity given hyperexcitability.

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

An extended version of Figure 6 showing the effect of more parameters.

Representative illustrations of the AdEx neuron model (A) and the Tsodyks–Markram synapses (B) properties of the microcircuit simulator.

The intrinsic parameters of the AdEx model populations.

The parameters of the Tsodyks–Markram synaptic connections.

The quantified outcomes of the simulator.

Supplementary file 1

MDAR checklist

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Open citations (links to open the citations from this article in various online reference manager services)

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)