Figure 1

Membrane potential distribution. The analytical results, $P_0(V)$, (full thick lines) are compared with the simulated distributions (dashed lines). Top: relatively short synaptic time constants, ${\tau }_{E(I)}=10\mathrm{m}\mathrm{s}$, in a subthreshold condition with $g_s=30\mathrm{n}\mathrm{S}$, $V_s=-60\mathrm{m}\mathrm{V}$ (giving $V_R=-56.7\mathrm{m}\mathrm{V}$) and ${\sigma }_E=3.95\mathrm{n}\mathrm{S}$, ${\sigma }_I=5.59\mathrm{n}\mathrm{S}$. The contributions from the active (thin line) and the inactive (dotted line) subpopulations are also shown. Middle: as before but in two different conditions: subthreshold with $g_s=25\mathrm{n}\mathrm{S}$, $V_s=-72\mathrm{m}\mathrm{V}$ (left, $V_R=-59.6\mathrm{m}\mathrm{V}$) and suprathreshold with $g_s=37.5\mathrm{n}\mathrm{S}$, $V_s=-48\mathrm{m}\mathrm{V}$ (right, $V_R=-52.8\mathrm{m}\mathrm{V}$). Bottom: same as the middle graphs but for longer synaptic time constants, ${\tau }_{E(I)}=50\mathrm{m}\mathrm{s}$. Besides ${\sigma }_E=1.77\mathrm{n}\mathrm{S}$, ${\sigma }_I=2.5\mathrm{n}\mathrm{S}$. In this case the prediction is much better and the distributions become narrower. The other parameters are: $C_m=0.25\mathrm{n}\mathrm{F}$, $g_L=12.5\mathrm{n}\mathrm{S}$, $g_{E,0}=20\mathrm{n}\mathrm{S}$, $g_{I,0}=40\mathrm{n}\mathrm{S}$, $\Theta =-54\mathrm{m}\mathrm{V}$, $H=-60\mathrm{m}\mathrm{V}$, $V_L=-65\mathrm{m}\mathrm{V}$, $V_E=0\mathrm{m}\mathrm{V}$, and $V_I=-80\mathrm{m}\mathrm{V}$. With these values ${\tau }_m\sim 3\mathrm{m}\mathrm{s}$.Reuse & Permissions

Figure 2

Population firing rate and $CV$ as a function of $g_{\mathrm{t}\mathrm{o}\mathrm{t}}$. Input noises are changed as ${\sigma }_E^2=6.25\times {10}^{-4}{C}_m{g}_{\mathrm{t}\mathrm{o}\mathrm{t}}/{\tau }_E$, ${\sigma }_I^2=125\times {10}^{-4}{C}_m{g}_{\mathrm{t}\mathrm{o}\mathrm{t}}/{\tau }_I$, and $V_R=-55.7\mathrm{m}\mathrm{V}$ remains fixed. Besides ${\tau }_E=3\mathrm{m}\mathrm{s}$, ${\tau }_I=10.5\mathrm{m}\mathrm{s}$, $V_I=-70\mathrm{m}\mathrm{V}$, and the other parameters are as in Fig. 1. Triangles are the results from simulations and full curves the prediction of Eq. (18). Asterisks in the left graph correspond to a population with low conductance (left) and another with high conductance (right) firing with approximately the same rate. Asterisks in the right graph indicate their $CV$’s.Reuse & Permissions

Figure 3

Distribution of firing probability densities across a population of neurons in the HCS. The example shown is in the subthreshold regime. Although most neurons are silent (vertical bar) a small subpopulation fires (smooth curve). The probability of a neuron being in the latter is 0.05. The membrane potentials of an inactive (top inset) and of an active (bottom inset) neuron are plotted for 60 ms (simulations). Parameters are as in the top panel of Fig. 1 except ${\sigma }_E=2.5\mathrm{n}\mathrm{S}$, ${\sigma }_I=3.95\mathrm{n}\mathrm{S}$.Reuse & Permissions