Figure 3. Paradoxical effects in the two-population model.

(A) The network. (B–C) Responses of PCs and PV neurons normalized to baseline vs. the laser intensity, ${\Gamma }_{opto}$ , for different values of the recurrent excitation, j_EE . (B) $j_{EE}=J_{EE}/\sqrt{K}$ , the network exhibits the paradoxical effect. (C) j_EE = 0, the population activity of PV neurons is almost insensitive to small laser intensities. Red: PCs. Blue: PV neurons. Thick lines: population averaged responses. Thin lines: responses of 10 neurons randomly chosen in each population. Firing rates were estimated over 100s. Parameters: N_E = 57600, N₁ = 19200, K = 500 N₁  = 19200. Other parameters as in Tables 1–2. Baseline firing rates are: $r_E=5.7Hz$ , $r_I=11.7Hz$ (B) and $r_E=1.5Hz$ , $r_I=5.7Hz$ (C). At the minimum of $r_I$ in (B), $r_E=0.06Hz$ .

Figure 3—figure supplement 1. Current, $I_{opto}$ , v.s. laser intensity, ${\Gamma }_{opto}$ .

Parameters are ${\displaystyle I_0=8nA}$ , ${\displaystyle {\mathrm{\Gamma }}_0=0.5mW.m{m}^{-2}}$ .

Figure 3—figure supplement 2. Effects of $K$ on the responses of a two-population network to photoactivation of the inhibitory population.

(A) J_EE  = 22 μA.ms.cm^-2, the inhibitory population activity always recovers when the PCs are silenced. (B) J_EE  = 0, as K increases, the response of the inhibitory population becomes more and more insensitive to the perturbation. Cross: K = 50; triangles: K = 100; circles: K = 500. Dashed line: $\to \infty$ . Color code and parameters as in Figure 3. Baseline firing rates: A. K = 50: r_E  = 10.8H_z, r_I  = 16.8 H_z; K = 100: rE = 8.8 H_z, r_I  = 14.7 H_z; K = 500: r_E  = 5.7 H_z, r_I  = 11.7 H_z; $K=\infty$ : r_E  = 3.9 H_z, r_I  = 8.5 H_z. B. K = 500: r_E  = 1.9 H_z, r_I  = 3.6 H_z; K = 100: r_E  = 2 H_z, r_I  = 4.8 H_z; K = 500: r_E  = 1.5 H_z, r_I  = 5.7 H_z; $K=\infty$ : r_E  = 1.4 H_z, r_I  = 9.1 H_z.

Figure 3—figure supplement 3. Two-population model.

The response of the PC and PV populations upon stimulation of the latter are proportional only if parameters are fine-tuned. (A) ${\stackrel{-}{\chi }}_I/{\stackrel{-}{\chi }}_E$ where ${\overline{\chi }}_{\alpha }=\left(r_{\alpha }^{\text{light on}}/r_{\alpha }-1\right)/{\Gamma }_{opto}$ estimated for ${\Gamma }_{opto}=0.5mW.m{m}^{-2}$ . The ratio is close to one only if $J_{EE}\approx J_{EI}{J}_{IE}/J_{II}\text{=}30\mu A.ms.c{m}^{-2}$ . (B) Red star indicates the approximate center of the region with proportionality of the responses together with reasonable activities. Parameters as in Figure 3. K = 500.