Figure 1.
Weak light stimulation of pyramidal cells reduces gamma power.
A. Raw trace of the LFP measured in the CA3 stratum radiatum of a hippocampal slice. Background drive given by 400 nM kainic acid induced gamma oscillations (peak frequency Hz. A 100 ms, weak (1–3
) pulse of blue light, indicated in blue, reduced the amplitude of the ongoing oscillations. B. Population data from 94 trials, 8 slices plotting energy in the gamma band (25–50 Hz) as a function of time. The average energy during the stimulation period was
of the pre-stimulation baseline. The dashed lines indicate one estimated standard deviation.
Figure 2.
Effect of varying parameters on the delay between the arrival of an excitatory synaptic input pulse to an I-cell and the resulting spike of the I-cell.
A: Increase in
resulting from a reduction in drive density to the I-cell from
to
. The dashed vertical line indicates the pulse strength
below which the pulse fails to elicit a spike when external drive density to the I-cell is
. B: Increase
in
resulting from reducing pulse strength by 30%, from
to
. The external drive to the I-cell is fixed at zero in panel B. The dashed vertical line indicates the value of
below which the pulse of strength
fails to elicit a spike.
Figure 3.
Spike rastergrams illustrating breakdown of strong PING rhythm as E-to-I-synapses are weakened.
Blue dots indicate spike times of I-cells (cells 1–20), and red dots indicate spike times of E-cells (cells 21–100). From left to right: mean excitatory conductance density per I-cell (panels A, D, G), 0.08 (B, E, H), and 0.04 (C, F, I, and J)
. The network in panels A, B, and C is homogeneous. In panels D through F, the E-to-I-connection is sparse and random (50% connectivity). In panels G through I, the I-to-E- and I-to-I-connections are sparse and random as well (50% connectivity), and so are external drives: 15% heterogeneity in drives to E-cells, and drives to I-cells vary between
and
. (See paragraph surrounding Eq. S8 in Text S1 for the precise meaning of “15% heterogeneity”.) The parameters in panel J are those of panel I, but mean external drive density to the I-cells is raised from 0 to 0.4
, and there are no I-to-I-synapses.
Figure 4.
Quantitative measure of gamma rhythmicity.
The measure (see Eq. S10 in Text S1) is plotted as a function of mean excitatory conductance density per I-cell,
, with all other parameters as in Fig. 3, bottom row of panels.
Figure 5.
Time between arrival of inhibition and next spike of an E-cell, as a function of time
between previous spike and arrival time of inhibition.
The external drive density to the E-cell is
, and the inhibitory conductance density
is (A) 0.24, (B) 0.12, (C) 0.06, and (D) 0
.
Figure 6.
In a homogeneous network, the strong PING rhythm becomes less and less rapidly attracting as I-to-E-synapses are weakened.
As before, blue dots indicate spike times of I-cells (cells 1–20), and red dots spike times of E-cells (cells 21–100). From top to bottom: , 0.05, 0.02
.
Figure 7.
A simulation similar to that in Fig. 6, but with heterogeneity in drive to the E-cells, and with sparse, random E-to-I-synapses.
The heterogeneity in drive to the E-cells is 10% (see paragraph surrounding Eq. S8 in Text S1). E-to-I-connections are removed with 50% probability, and those that are not removed are doubled in strength to preserve (see Text S1, Section B). Top to bottom:
, 0.05, 0.02
. The rhythm in the I-cells seen in panel C is based entirely on the interaction of the I-cells, i.e., it is an ING rhythm [11]; see Text S1, Section F.
Figure 8.
Ten-fold strengthening the I-to-E-synapses does not erase the effects of heterogeneity on E-cell synchronization.
A: Close-up of Panel A of Fig. 7. B: Close-up of a simulation with raised from 0.2 to 2.0
, all other parameters as in Panel A of Fig. 7.
Figure 9.
Loss of energy in the gamma range, as I-to-E-synapses are weakened, is gradual, not sudden.
Measure of gamma rhythmicity, (see Eq. S11 in Text S1), as a function of
, the mean inhibitory conductance density per E-cell, with all other parameters as in the bottom panel of Fig. 7.
Figure 10.
Breakdown of gamma rhythm, as inhibition is weakened, in a simplified model network.
External drive to the E-cells is heterogeneous. Inhibition is strongest in panel A and weakest in panel C. The network is smaller than in earlier network simulations (20 E-cells and one I-cell), and the E-cells are put in order of linearly increasing external drive. The spike times of the I-cell are indicated by the blue dashed vertical lines. For complete details, see Text S1, Section B.
Figure 11.
Same as Fig. 5, plotting instead of
.
Figure 12.
Same as Fig. 11, plotting the graphs for a range of values of external drives.
The drive to the E-cells varies between 1.4 and 1.8. The bold horizontal red lines in panels A and B indicate the duration of the E-cell spike volley. In panel C, the inhibition is so weak that a rhythm in which each E-cell participates exactly once per cycle no longer exists. Panel D shows the limiting case of no inhibition.
Figure 13.
Breakdown of strong PING as the number of E-cells receiving strong, time-independent drive is reduced.
Neurons 1–80 are I-cells, and neurons 81–400 E-cells. All E-cells receive stochastic drive. In addition, E-cells receive strong tonic drive, with
(A),
(B),
(C), and
(D). Rhythmicity is largely abolished when
(panel C), but weak PING emerges when
(panel D). In Fig. 13C, the rhythm returns when the strength of the E-to-I-synapses is tripled (panel E).
Figure 14.
E-cells (red) and I-cells (blue) placed at random in the unit disk.
E-cells in the center disk (yellow) of radius are given additional drive.
Figure 15.
Breakdown of gamma rhythms as the radius of the driven patch of E-cells is reduced.
(A),
(B),
(C), and
(D). The length scale
characterizing the decay of connection probability with spatial distance (see Text S1, Section, Eq. S12) equals 0.25 here. (Distance is non-dimensionalized.)
Figure 16.
As Fig. 15, with numbers of E- and I-cells doubled, and strengths of individual synapses halved.
The breakdown of the rhythm occurs near the same value of .
Figure 17.
Synchrony measure as a function of radius
of driven patch of E-cells in Figs. 15 and 16.
See Text S1, Section B for definition of .
Figure 18.
Breakdown of gamma rhythms as the synapses become too local.
(panel A), and
(panel B), where
denotes the length constant characterizing the decay of the connection probability with distance (see Text S1, Eq. S12). In panel (C),
as well, but the synaptic strengths have been tripled, and the rhythm is restored.