Attentional inhibitory modulation (AIM) network

The AIM network was implemented using the DynaSim package [81], and its structure is illustrated in Fig 1. For simplification purposes, only one frequency channel and three spatial channels are shown. A “spatial channel” refers to the sub-network of neurons that are responsible for processing inputs from a specific spatial location (blue shading, Fig 1). The number of spatial and frequency channels in the network, and their connectivities, depended on the specific simulation being explored.

Five neural populations were created within the network: excitatory input (IC), excitatory (E), inhibitory (I), output cortical (C), and a second inhibitory (I2) population. IC neurons represent the bottom-up inputs to the network from the subcortical model. I2 neurons represent attentional top-down control. With the exception of the C neurons, a number of neurons were created within each population, corresponding to each of the spatial or frequency channels needed in a simulation. All five neural populations are implemented as leaky integrate-and-fire neurons whose dynamics are defined by The following differential equation [82]:

where V is the membrane potential, i_syn is the synaptic input current, C is membrane capacitance, g_leak is the membrane conductance, and E_leak is the equilibrium potential. The spike-and-reset mechanism employed in our model dictates that if V>V_thresh, then V→V_reset. Here, V_thresh is the action potential threshold and V_reset is the reset voltage. Values for these parameters are listed in Table 1.

The dynamics of the synaptic input current is defined by a double exponential:

where t is time since the previous spike, g_syn is the synaptic conductance, τ_D and τ_R are the decay and rise time constants, respectively, and the difference of exponentials represent the excitatory post-synaptic potential (EPSP) waveform. u(t) is the unit step function to ensure that EPSP is zero before the previous spike has occurred. E_syn is the reversal potential, i_e is the externally applied current, i_app is the externally applied current, and netcon refers to a binary matrix of network connectivities that define the connections between populations of neurons. Each row in the netcon matrix represents a presynaptic neuron, and each column represents a postsynaptic neuron. Binary entries of netcon represents presence of a synaptic connection between neurons. Inhibitory synapses have the following parameters: τ_R = 1ms, τ_D = 10ms, E_syn = −80mv. Excitatory synapses have the following parameters: τ_R = 0.4ms, τ_D = 2ms, E_syn = 0mv. The values for g_syn and i_app are simulation- and connection-dependent, and are listed in Table 2. The network connections are illustrated in Figs ​Figs11 and ​and33.

g_syn have units of μS and i_app have units of nA. Parameters of local convergence g_IE, g_EC σ_IE, and σ_EC are also shown (Fig 3).

The default g_syn were chosen such that if I neurons were off, then the inputs would be relayed and combined at the C neuron with a similar firing rate, and if I neurons were on, then E neurons would be completely silenced.