Figure 1.
Schematic wiring diagram of the network model, with connectivity densities and average post-synaptic potential amplitudes as measured in the soma indicated.
Hypercolumns are shown with light grey background, minicolumns with dark grey. The middle hypercolumn shows the mutual inhibition via basket cells between minicolumns in the same hypercolumn. The pyramidal cell to the left in this column shows how pyramidal cells project locally and globally. Percentages are given as the chance of one cell of the pre-population being coupled to one cell of the post-population. Note that global connectivity is exaggerated since the number of hypercolumns is down-scaled. Each cell sees about the same number of active synapses as it would in vivo assuming 1% activity. 1Connectivity of pyramid-RSNP cells given the two minicolumns are in different patterns, otherwise 0%. 2Global connectivity of pyramid-pyramid given the two minicolumns are in the same pattern, otherwise 0%.
Figure 2.
Spike raster showing bistability.
A: A subsample of 5880 pyramidal cells (4 out of 9 hypercolumns) is shown. Each dot represents a spike occurring at a particular time (x-axis) and in a particular cell (y-axis). In the beginning of the simulation the stable, non-specific ground state was active. When a part of a pattern (first minicolumn in 5 out of 9 hypercolumns, see Methods) was stimulated it completed and was then persistently active, even after stimulation terminated. The foreground pattern consisted of the first minicolumn in each hypercolumn, so the activity after stimulation also marks the borders between the hypercolumns. Each of the four highly active and synchronous bands is the collective spike output of 30 pyramidal cells within the first minicolumn. The three bottom hypercolumns in the raster plot received direct stimulation and activated the top hypercolumn. After stimulation, the background pyramidal cells lowered their firing rates. B: Activity histograms of 30 pyramidal cells (top) going from ground state to foreground in the active state, and 30 pyramidal cells (bottom) going from ground state to background. The vertical bar marks 10 s−1 (top) and 1 s−1 (bottom), respectively, measured as the number of spikes divided by time and number of cells. C: Zoom in of the part of the spike raster that is indicated by the dashed vertical lines in A. Only the cells in the foreground population are shown. Active minicolumns are not tightly synchronized in terms of phase. D: Synthetic LFP spectrograms. The network started out in the ground state and entered an active state after 2 seconds due to stimulation. The signal was produced from 30 pyramidal cells entering foreground (left) and background (right) respectively. The average signal from 5 runs is plotted.
Figure 3.
Intracellular potential traces of pyramidal cells and inhibitory interneurons in a simulated hypercolumn.
To the left is a sketch of a hypercolumn, where the red minicolumn is in foreground and the blue is in background state. The voltage traces to the right are taken from the same simulation that yielded the raster plot in Figure 2. They show how the neurons behave as the network switches from ground state to a persistent active state (indicated by horizontal stimulation bar). The two upper voltage plots show basket cells, B1 and B2, adjacent to red and blue minicolumn respectively. Middle voltage traces show RSNP neuron membrane potential. R2 is far away from the active minicolumn and maintains an firing rate (although lower than in the ground state). R1, located in the active minicolumn, will fire at a low rate activated only by the low activity of background pyramidal cells. P1 is a pyramidal cell that ends up in the foreground after stimulation, and P2 becomes part of the background.
Table 1.
Bistable range as a function of number of hypercolumns.
Figure 4.
Upper panel (A–D): Shows average voltage of one minicolumn and the spiking output within (circles) and from other connected (dots) minicolumns. A is taken from the ground state in a one-hypercolumn network, B from the active state in the same network. C from the ground state in a nine- hypercolumn network, D from the active state. Lower panel (E–G): Spike histogram showing spike latency to the nearest membrane potential peak. In the one-hypercolumn case (E) all excitatory input arrives around the peak while in the case with four (F) and especially nine (G) hypercolumns incoming excitation is more distributed in time.
Figure 5.
Balance of currents in a single cell during three different models of activity of the network.
From 0–0.5 s network is in its ground state, from 0.5–1.5 s it is in an active state. Between 0.5–1 s the cell is part of the foreground and between 1–1.5 s it is part of the background. A: Plot of the soma potential. Note that the soma was injected with a negative current (−0.2 nA), so that the cell did not spike while we measured the balance of currents. B: Net, i.e. total excitatory+inhibitory, currents into soma. C: Top line is the excitatory current into soma, and the bottom is the inhibitory current that almost perfectly balances the excitatory one. The middle line is the net synaptic current of panel B, the result of imbalance between excitatory and inhibitory currents. Notice its significantly smaller amplitude. D: Plot of firing frequency as a function of current injected into the soma in three different cells in ground state. The dashed line corresponds to the mean firing rate in the active state in the same network.
Figure 6.
A: <CV2> histograms for the foreground pyramidal cells in the active state for three different networks, displaying weak, strong and non-oscillatory activity. We move between the different networks by manipulating the level of recurrent excitatory conductance. B: Relative recurrent excitatory conductance vs <CV2>, where weak (“W”), strong (“S”) and non-oscillatory (“N”) networks are marked. Recurrent excitatory conductance = 1 is defined as the smallest possible recurrent excitatory conductance for which we had stable memory retrieval. The solid line is for a network with basket to basket cell connections, the dashed line corresponds to the same network, but with no basket to basket cell connections. Note that we here go outside the bistable range (Table 1) for high levels of excitation. C: <CV2> against average firing rate. The solid line represents the network with basket to basket cell connections, the dashed line the one without such connections.
Figure 7.
Spiking activity and soma potentials of pyramidal cells in foreground and background.
A: Pyramidal cell spike output from two minicolumns, one entering the foreground of the active state (bottom), the other entering the background of the active state (top) at t = 0.3 s. B: Mean soma potentials of the same two minicolumns. The mean potential of the foreground cells (dashed) is systematically above the mean potential of the background cells (solid). Firing threshold is marked with solid horizontal line. C: Summed pyramidal cell spike output of one hypercolumn. The number of spikes within the hypercolumn in ground state (0–0.3 s) and active state (0.3–0.6 s) stayed almost constant. Measured over longer intervals the total spike output was slightly lower in active state.