State transitions through inhibitory interneurons in a cortical network model
Fig 5
FS interneurons enhance PC gain and promote transition to an ISN regime in a rate model.
A) A rate model was optimised with synaptic weights (W) based on features of the spiking network. During baseline conditions the gain of each population was set to 1.0. B) Under the assumption that synaptic weights remain fixed, changes of PC population gain (BE) in the rate model were required to reproduce firing rates from the spiking network associated with increased FS/NFS rheobase. Increased FS rheobase increased BE such that the effective recurrent excitatory synaptic strength (BE x WEE) exceeded 1.0. C) Two rate models were developed based on changes in PC gain shown in B: one approximating increased NFS rheobase (‘NFS model’) and one FS rheobase (‘FS model’, firing rates during baseline conditions in lower left caption). C) The FS model loses stability via a Hopf bifurcation as BE x WEE exceeds 1.0 (asterix) and exhibits sustained oscillations, whereas a qualitative change in network behaviour does not occur in the NFS model. D) Phase portraits and firing rate trajectories of the NFS and FS models for inputs shown in C under the condition of fixed NFS firing rate. The PC nullcline of the FS model has a rightward inflection, and stimulation of the FS population moves the fixed point to lower PC and FS firing rates, suggestive of an ISN regime. In contrast, stimulation of the FS population in the NFS model increases the steady-state FS firing rate, suggestive of a non-ISN regime. These findings are confirmed by changes of inhibitory current onto the PC population in response to stimulation of the FS and NFS population (S5 Fig).