. 2021 Dec 24;15:757790. doi: 10.3389/fnins.2021.757790

Table 2.

Description of the network model (continuation of Table 1).

Connectivity

• Connection probabilities C_YX from population X to population Y with {X, Y} ∈ {L2/3, L4, L5, L6} × {E, I}. Values are given in (Potjans and Diesmann, 2014, Table 5).
• Self-connections (autapses) are prohibited; multiple connections between neurons (multapses) are allowed.

Fixed total number models

Total number of synapses (Potjans and Diesmann, 2014, Equation 1):

S_{Y X} = \frac{log (1 - C_{Y X})}{log ((N_{Y} N_{X} - 1) / (N_{Y} N_{X}))}

(1)

In- and out-degrees are binomially distributed.

Fixed in-degree models

In-degree:

K_{Y X} = \frac{S_{Y X}}{N_{Y}}

(2)

Neuron and synapse model

Neuron

Leaky integrate-and-fire neuron (LIF)
• Dynamics of membrane potential V_i(t) for neuron i:
• Spike emission at times

t_{s}^{i}

with

V_{i} (t_{s}^{i}) \geq V_{θ}

• Subthreshold dynamics with

τ_{m} = R_{m} C_{m} : τ_{m} {\dot{V}}_{i} = - V_{i} + R_{m} I_{i} (t) if \forall s : t \notin (t_{s}^{i}, t_{s}^{i} + τ_{ref}]

(3)

• Reset + refractoriness:

V_{i} (t) = V_{reset} if \forall s : t \in (t_{s}^{i}, t_{s}^{i} + τ_{ref}]

• Exact integration with temporal resolution h (Rotter and Diesmann, 1999)

Postsynaptic currents

• Instantaneous onset, exponentially decaying postsynaptic currents
• Input current of neuron i from presynaptic neuron j:

I_{i} (t) = \sum_{j} J_{i j} \sum_{s} e^{- (t - t_{s}^{j} - d_{i j}) / τ_{s}} Θ (t - t_{s}^{j} - d_{i j})

(4)

Synaptic weights (reference distribution)

• Normally distributed (clipped to preserve sign):

w_{i j} ~ N {{\bar{w}}_{\infty, Y X}, Δ w_{\infty, Y X}^{2}}, {\bar{w}}_{\infty, Y X} = g_{Y X} \cdot {\bar{w}}_{\infty}

(5)

Spike transmission delays

• Normally distributed (left-clipped at h):

d_{i j} ~ N {{\bar{d}}_{X}, Δ d_{X}^{2}}

(6)

Initial membrane potentials

• Normally distributed:

V_{i j} ~ N {{\bar{V}}_{0, X}, Δ V_{0, X}^{2}}

(7)