Figure 2.
Reduction of Eanion compromises inhibitory control of firing rate. Output firing rate (fout) is plotted against the total rate of EPSPs received from all presynaptic neurons (fexc) for different values of Eanion tested at 5 mV increments from -70 mV (purple) to -45 mV (orange). The fout-fexc curve for no inhibition (α = 0) is shown as a thick black line on each panel. Parts A-C are based on simulations in the basic model. (A) With proportional inhibition, finh = α fexc. Each panel shows results for a different value of α. Divergence of the colored curves increases as α increases. (B) Feedback inhibition was added to proportional inhibition with α = 0.5. Incorporating feedback inhibition had much the same effect as increasing α under conditions with pure proportional inhibition (see part A) except that, with feedback inhibition, the increased divergence of the colored fout-fexc curve was particularly pronounced for Eanion = -50 and -45 mV. This is because those values of Eanion cause paradoxical excitation, meaning feedback inhibition actually becomes feedback excitation (i.e. a positive feedback loop), which makes for an extremely hyperexcitable system. (C) The final two panels show constant inhibition (i.e. finh is independent of fexc). Under these conditions, the fout-fexc curves tend to remain parallel rather than diverge with increasing fexc, but increasing finh nonetheless increases the vertical spacing of those curves. Comparing across parts A-C shows that reduction of Eanion has a similar effect on inhibitory control of firing rate for all three conditions. The fout-fexc curves for Eanion = -50 and -45 mV (yellow and orange) exhibit paradoxical excitation since they lie above the fout-fexc curve for no inhibition (black). The fout-fexc curve for Eanion = -55 mV (light green) exhibits complete disinhibition since it lies very close to the fout-fexc curve for no inhibition. The fout-fexc curves for Eanion = -60 and -65 mV (dark green and blue) exhibit modest disinhibition since they lie below the fout-fexc curve for no inhibition but above the fout-fexc curve for Eanion = -70 mV (purple). Based on proportional inhibition with α = 1, simulations were repeated in the tonic-spiking model (D) and in the single-spiking model (E). Although the fout-fexc curves vary between cell types (compare also with basic model in part A), the more important comparison is between curves for different Eanion within a specific cell type: in the basic and tonic-spiking models, reduction of Eanion to -55 mV causes complete disinhibition, while complete disinhibition in the single-spiking model seems to require a slightly greater reduction, to around -50 mV.