A strategy for mapping biophysical to abstract neuronal network models applied to primary visual cortex
Fig 10
The diagram of the steady-state solutions of the canonical firing-rate ring model G on the plane of its parameters J0 and J1 (adapted from [2]).
Amplitude instability corresponds to the state where the activity in the ring increases without any possibility to regulate it. Homogeneous phase (“feedforward” hypothesis) corresponds to a state of weak interactions. The activity in the ring follows directly from the thalamic input, apart from a threshold non-linearity. Marginal phase (“recurrent” hypothesis) corresponds to a state where only a tuned activity profile is stable, partially but not completely determined by the input shape and dynamics. This state occurs for sufficiently strong recurrent tuned inputs (J1) and, to a lesser extent, with sufficiently strong inhibition (J0). The small square marks the parameters found by the mapping expressions for model G (I0 = −26.5, I1 = 44, J0 = −0.52, J1 = 2.8). The small circle in the homogeneous state corresponds to a variation of model G where the value of was derived from the adaptive HH excitatory cell model (I0 = −3.55, I1 = 7.4, J0 = −0.063, J1 = 0.46).