Computational model
The simulated networks were adapted from previous works of our group [
18,
29‐
32], for which we refer for more details. Briefly, the simulated networks consisted of
N = 5000 leaky integrate and fire neurons [
33]: 80% excitatory neurons (
NE = 4000) with AMPA-like synapses, and 20% inhibitory neurons (
NI = 1000) with GABA-like synapses [
34]. The network is sparse and random, the connection probability between any directed pair of cells being 0.2 [
35,
36]. The membrane potential
Vk of each neuron k evolves according to [
37]:
$${\tau}_m\frac{d{V}^k(t)}{dt}=-{V}^k(t)+{V}_{leak}+\frac{I_{tot}^k(t)}{g_{leak}}$$
where
τm is the membrane time constant (20 ms for excitatory and 10 ms for inhibitory neurons),
gleak is the leak membrane conductance (25 nS for excitatory and 20 nS for inhibitory neurons),
Vleak = − 70
mV, and
\({I}_{tot}^k(t)\) is the total synaptic input current. The latter was given by the sum of all the synaptic inputs entering the k-th neuron:
$${I}_{tot}^k(t)=\sum_{j\in AMPA}{C}_{jk}{I}_{AMPA}^k(t)+\sum_{j\in GABA}{C}_{jk}{I}_{GABA}^k(t)+{I}_{thal\_S}^k(t)+{I}_{thal\_ NB}^k(t)+{I}_{cort\ noise}^k(t)$$
Where Cjk ≠ 0 if neuron j projects to neuron k, and \({I}_{AMPA}^k(t)\), \({I}_{GABA}^k(t)\), \({I}_{thal}^k(t)\) and \({I}_{cort\ noise}^k(t)\) the different synaptic inputs entering the k-th neuron from recurrent excitatory, inhibitory, and thalamocortical synapses respectively.
The synaptic inputs currents were modeled as:
$${I}_{syn}^k(t)={g}_{syn}{s}_{syn}(t)\left({V}^k(t)-{V}_{syn}\right)$$
where
Vsyn are the synaptic reversal potential (
VGABA = − 80
mV and
VAMPA = 0
mV) and
gsyn are the synaptic conductances [
38‐
41]. The conductances were set as follows (for the simulated WT mice):
\({g}_{GABA^{inh}}^{WT}=2.70\ nS\) and
\({g}_{GABA^{exc}}^{WT}=2.01\ nS\) for GABA-ergic inputs I
GABA to inhibitory and excitatory neurons respectively;
\({g}_{AMPA^{inh}}^{WT}=0.233\ nS\) and
\({g}_{AMPA^{exc}}^{WT}=0.178\ nS\) for recurrent AMPA-mediated inputs I
AMPA to inhibitory and excitatory neurons respectively;
\({g}_{thal\_S\_{AMPA}^{inh}}^{WT}=0.317\ nS\) and
\({g}_{thal\_S\_{AMPA}^{exc}}^{WT}=0.234\ nS\) for sustained thalamocortical AMPA-mediated inputs I
thal_S to inhibitory and excitatory neurons respectively;
\({g}_{thal\_ NB\_{AMPA}^{inh}}^{WT}=0.317\ nS\) and
\({g}_{thal\_ NB\_{AMPA}^{exc}}^{WT}=0.234\ nS\) for narrow band thalamocortical AMPA-mediated inputs I
thal_NB to inhibitory and excitatory neurons respectively;
\({g}_{noise\_{AMPA}^{inh}}^{WT}=0.317\ nS\) and
\({g}_{noise\_{AMPA}^{exc}}^{WT}=0.234\ nS\) for cortical noise AMPA-mediated inputs I
cort_noise to inhibitory and excitatory neurons respectively.
We summarized the FHM1 synaptic alteration observed experimentally [
15,
16] into three factors: increase of (i) intra-cortical (IC) and (ii) thalamocortical (TC) AMPA-mediated synapses; (iii) the thalamocortical synaptic increase is higher in inhibitory rather than excitatory neurons (in the main text this phenomenon was called thalamocortical synaptic asymmetry, TCA). We implemented such alterations in our computational model by increasing the aforementioned conductance levels of those synapses involved in the FHM1 cellular alteration. Specifically:
(i) IC increase was simulated by:
$${g}_{AMPA^{inh}}^{FHM1}={g}_{AMPA^{inh}}^{WT}\left(1+\frac{C{C}_{incr}\%}{100}\right)\ \mathrm{and}\ {g}_{AMPA^{exc}}^{WT}={g}_{AMPA^{exc}}^{FHM1}\left(1+\frac{C{C}_{incr}\%}{100}\right)\frac{}{}$$
(ii and iii) TC increase and TCA were simulated by:
\(\alpha =1+\frac{TCA\%}{100}\); \({g}_{thal\_S\_{AMPA}^{inh}}^{FHM1}=\left(1+\alpha \frac{2\frac{T{C}_{incr}\%}{100}}{1+\alpha}\right){g}_{thal\_S\_{AMPA}^{inh}}^{WT}\) and \({g}_{thal\_S\_{AMPA}^{exc}}^{FHM1}=\left(1+\frac{2\frac{T{C}_{incr}\%}{100}}{1+\alpha}\right){g}_{thal\_S\_{AMPA}^{exc}}^{WT}\). CCincr % , TCincr % and TCA% are the factors, expressed as percentage, representing the corresponding FHM1 cellular alterations.
The time course of synaptic currents, i.e.,
ssyn(
t), was incremented by an amount described by a delayed difference of exponentials every time a pre-synaptic spike occurred at time
t∗ [
37]:
$$\Delta {s}_{syn}(t)=\frac{\tau_m}{\tau_d-{\tau}_r}\left[\exp \left(-\frac{t-{\tau}_l-{t}^{\ast }}{\tau_d}\right)-\exp \left(-\frac{t-{\tau}_l-{t}^{\ast }}{\tau_r}\right)\right]$$
where the latency
τl represented the axonal delay, and
τr and
τd represented respectively the rise and decay time of the post-synaptic currents. The time constants values were set as follows [
38,
40,
42‐
45]: the latency
τl was set to 1 ms and 2 ms for GABA-ergic and AMPA-like synapses respectively; the rise time
τr was set to 1 ms, 0.2 ms and 0.4 ms for GABA-ergic, AMPA-like on excitatory, and AMPA-like on inhibitory synapses respectively; the decay time
τd was set to 5 ms, 1.25 ms and 2.25 ms for GABA-ergic, AMPA-like on excitatory and AMPA-like on inhibitory synapses respectively.
All neurons received three external (meaning non-recurrent) inputs
\({I}_{thal\_S}^k(t)+{I}_{thal\_ NB}^k(t)+{I}_{cort\ noise}^k(t)\).
\({I}_{thal\_S}^k(t)\) is an excitatory input representing the sustained component of thalamocortical afferents [
18] that increases with visual contrast.
\({I}_{thal\_S}^k(t)\) was implemented as a series of spike times that activated excitatory synapses with the same kinetics as recurrent AMPA synapses, but different strengths (see
gsyn values reported above). These synapses were activated by independent realizations of random Poisson spike trains, with a rate
vext _ thal _ S = [
S(
K)]
+ identical for all neurons.
\({I}_{thal\_ NB}^k(t)\) is another excitatory input that simulated the narrow ɣ band component of thalamocortical afferents [
18,
46] that decreases with visual contrast. The Poisson spike trains that simulate
\({I}_{thal\_ NB}^k(t)\) had a rate
vext _ thal _ NB = [
A(
K,
t)
εγ(
t)]
+.
A(
K,
t) is the amplitude of a ɣ range filtered white constant noise
εγ(
t).
εγ(
t) was obtained by applying a 3rd-order bandpass Butterworth filter of central frequency equal to 57 Hz and bandwidth equal to 10 Hz to white noise [
18].
A(
K) and
S(
K) values were chosen as to maximize the agreement with WT experimental data [
18]. Specifically:
A(
K ≥ 30) = 0
sp. /
s and
S(
K ≤ 30) = 1000
sp. /
s;
A(
K = 0, 6, 8,10,20) = [50,45,40,30,15]
sp. /
s and
S(
K = 30,50,90) = [1000,1040,1080]
sp. /
s;
S(
pre −
visual stim.) = 1000
sp. /
s and
A(
pre −
visual stim.) = 0
sp. /
s.
\({I}_{cort\ noise}^k(t)\) is colored noise mimicking stimulus-unspecific cortical activity. Its spike times were simulated with a Poisson process with rate vcort _ noise = [ϑnn(t)]+. The noise term n(t) is a z-scored colored noise, with the PSD following S(f) = 1/f1.5, and an amplitude factor ϑn = 0.4 sp. /ms. […]+ is a threshold-linear function, [𝑥] + =𝑥 if 𝑥> 0, [𝑥] + =0 otherwise.
The LFPs of the simulated networks were estimated as the sum of the absolute value of the GABA and AMPA currents (both external and recurrent) that enter all excitatory neurons [
47].
Network simulations were performed using a finite difference integration scheme based on the second-order Runge Kutta algorithm [
48,
49] with time step Δ𝑡=0.05 𝑚𝑠. To focus on stationary responses, the first 200 ms of every simulation were discarded. Simulations were set to simulate 5 seconds of neuronal activity. Each network parameter combination was simulated 40 times.
All simulations were conducted with custom-made Python scripts within the Brian 2 simulator environment [
50,
51].
Permutation statistical analysis
We decided to adopt non-parametric permutation statistical analysis throughout the manuscript to avoid, when possible, any apriori assumptions on the data. Furthermore, appropriate corrections for multiple comparisons can easily be incorporated into such analysis [
52].
Throughout the manuscript, we applied two different multiple comparison correction strategies [
28]: (i) pixel-based for two-dimensional data (in our case, time-frequency points of scalogram modulations of Fig.
2A, C); (ii) cluster-based for one-dimensional data (in our case, VEPs of Fig.
1B, temporal average of scalogram modulations of Fig.
2B, D, and power spectral density of pre visual activity of Fig.
3B). In both cases, scalogram modulations were pooled across animals and recordings.
Correcting for multiple comparisons using pixel-based statistics involves creating a null distribution containing the most and least pixel extreme values (i.e., the minimum and maximum value of time-frequency tile of scalogram modulations). The 2.5th and 97.5th percentile of this null distribution were consequently chosen as corrected alpha values of a two-tailed test.
As with pixel-based correction, cluster-based statistics involve generating a null distribution. At each iteration of permutation testing, a threshold is applied to the permuted data at an uncorrected alpha level of 0.05. The maximal length of consecutive significant values for each iteration is then retained and considered as a proxy for the multiple comparison null distribution. Hence, only those clusters of significant values in real data that were larger(lower) than 97.5th (2.5th) percentile of this null distribution.