Synaptic communication

Previous studies highlighted that the coordinated activities in cell cultures are determined by the chemical synapses and not by gap junctions or extracellular substances [56]. Therefore, we modelled the dynamics of excitatory AMPA and NMDA as well as inhibitory GABA chemical synapses. Synaptic transmission was delayed by a fixed time (0.5 ms) to account for synapse activation and a variable delay (maximum 1.5 ms) to account for the propagation of the pre-synaptic spike. Each type of synapse contributed with a current I_syn modelled as follows:

where g_syn is the synaptic conductance and E_rev is its reversal potential. The synaptic conductance has a bi-exponential profile (parameters in S3 Table):

Each time an action potential is delivered to a target neuron (i.e., a time t_sp), the conductance parameters g_syn and g_rise are increased by g¯×y, where g¯ is the maximum value for the synaptic conductance and y is the fraction of the active resources (i.e., released neurotransmitters). The synaptic current exhibits short-term depression modelled under the assumption of finite synaptic resources [57]:

where x, y and z represent the fraction of available, active and recovered resources, respectively. The time constant τ₁ regulates the transition between the available and active state, τ_rec is the recovery time constant and u represents the fraction of available resources transferred to the active ones, when the synapse is activated.

The NMDA current was modelled similarly to the AMPA and GABA currents, with an additional magnesium block mechanism [58]:

where k₀ = 6 mV (steepness of voltage dependence) and v₀ = −40 mV (half-activation potential). The maximum NMDA conductance (g¯NMDA) is written in terms of the AMPA conductance: g¯NMDA=KNMDA⋅g¯AMPA such that in basal/standard conditions K_NMDA = 0.09 (i.e., g¯NMDA = 4.32 nS), and while under APV application, an NMDA antagonist, K_NMDA = 0. All parameter values are reported in S3 Table. To mimic the effects of the NMDA and GABA synaptic blockers (APV and BIC), the conductance of the target receptor was set to zero. Networks with only the AMPA and GABA synapses are called AG-networks in the text, and networks with in addition the NMDA current are called AGN-networks.