Figure 1.
Abrupt transition from the theta to the hyper-excitable regime in a SI minimal network.
A: Diagram of the minimal SI network. Stellate cells (S) excite each other (AMPA) and receive inhibition (GABAA) from an interneuron (I). The maximal synaptic conductances and
are represented by
and
respectively. B and C: show the transition from the theta to the persistent hyper-excitable regime as the result of a small decrease in inhibition. In the theta regime SCs are synchronized in phase while in the hyper-excitable regime SCs are synchronized slightly out of phase. The right panel in C is a magnification of the left one. The parameters used are
, and
.
Figure 2.
The role of synaptic excitation and inhibition in the abrupt transition from the theta to the hyper-excitable regimes in two recurrently connected SCs.
A–D: Abrupt transition from the theta to the hyper-excitable regime in two recurrently connected SCs as a result of a small increase in the amount of excitation. A: In the absence of recurrent excitation the SCs fire out of phase. B and C: Recurrent excitation synchronizes the SCs in phase but the firing frequency remains almost unchanged in the theta regime. D: A small increase in the maximal synaptic conductance causes the abrupt transition to the hyper-excitable regime. The parameters used are . E and F: A small increase in inhibition to the two recurrently connected SCs reverses the firing frequency from the hyper-excitable to the theta regime. The parameters used are
.
Figure 3.
The abrupt transition from the theta to the hyper-excitable regime is the result of phasic but not tonic excitation.
A: Firing frequency of a single isolated SC as a function of the applied DC current . The transition from low to high frequencies is smooth. B: Firing frequency of a single SC self-excited via an autapse as a funciton of the autapse maximal synaptic conductance
(
). The transition from low to high frequencies is abrupt. C: Effects of persistent sodium and h-currents on hyperexcitability in a self-connected single SC. Top-left panel: A decrease in the h-current maximal conductance
facilitates hyperexcitability for a fixed applied DC current
. Appropriate values of
were chosen in order to obtain close values of the SC's firing frequency for for
(isolated cell). Top-right panel: A decrease in the h-current maximal conductance
facilitates hyperexcitability for a fixed maximal persistent sodium conductance
. Appropriate values of
were chosen in order to obtain close values of the SC's firing frequency for for
(isolated cell). Bottom-left panel: Changes in the h-current maximal conductance
have little effect on hyperexcitability for fixed values of
and
. Bottom-right panel: An increase in the amount of persistent sodium facilitates hyperexcitabilit for fixed values of
and
. In all cases, simulations were performed using the (7D) “full” SC model.
Figure 4.
The NAS-SC model self-connected with an autpase captures the abrupt transition between the theta and hyper-excitable regimes as the result of small changes in the maximal synaptic conductance .
A: Spiking frequency vs. for representative values of
and
. The spiking frequency is measured in number of spikes per second. The transition point corresponds to
. B: Voltage traces for one representative values of
on each side of (and close to) the transition point. The value of the persistent sodium maximal conductance is
. The interspike intervals are
ms (top-left) and
ms (bottom-left). The right panels are magnifications of the left ones.
Figure 5.
Phase-space diagram for the NAS-SC model in the theta regime (slow time scale).
Trajectories begin evolving from reset values (
measured in mV). A: Voltage trace corresponding to the trajectory shown in B and C:. The bottom panel is a magnification of the top one and shows subthreshold oscillations. B: Two-dimensional projection of the phase-space diagram shown in C. The two curves in red are contained in the V-nullsurface. The bottom panel is a magnification of the top one. C: For different views of the
phase-space diagram showing only the V-nullsurface and the trajectory. The values of the parameters are
.
Figure 6.
Voltage traces and two-dimensional phase-space representations for the NAS-SC model for increasing values of .
Each row shows the voltage trace (left) for a particular value of and the corresponding phase space diagram (right). As the value of
gradually increases (top row lowest value of
, bottom row highest value of
, the V-nullsurface gradually moves down causing the firing frequency to increase. As the model is not self-connected in this case, increasing
causes a gradual increase in firing rate proportional to the applied current. Increasing values of
cause a progressive decrease in the influence of the slow manifold on the trajectory and thus no rapid transitions in firing rate are observed.
Figure 7.
Dynamic two-dimensional phase-space representation of one firing phase for the self-connected NAS-SC model in the theta regime.
Parameter values are and
and fixed for all diagrams. The value of
is below the threshold for hyper-excitable firing and thus a theta frequency ISI is observed. Each panel shows the evolution of the phase space for time points through one firing phase. Time increases from A to H. As the trajectory evolves it is captured by the slow-manifold (vicinity of the V-nullsurface) and is forced to move around it on a slow time scale thus causing subthreshold oscillations.
Figure 8.
Dynamic two-dimensional phase-space representation of one firing phase for the self-connected NAS-SC model in the hyper-excitable regime.
Parameter values are as in Figure 7 except that the value of is above the threshold for hyper-excitable firing and thus a very short ISI is observed. Each panel shows the evolution of the phase space for time points through one firing phase. Time increases from A to D. The trajectory evolves along the fast time scale and it manages to escape the subthreshold regime without being captured by the slow manifold (vicinity of the V-nullsurface).
Figure 9.
Sudden transitions from regular spiking to burst firing in EC stellate cells.
A: Instantaneous frequency (the frequency corresponding to a single ISI, see Methods) jumps rapidly in autapse ramp experiments. In this representative example, autapse strength () was ramped up gradually exposing a threshold (dotted vertical line) above which firing frequency jumps to the hyper-excitable, bursting regime. Prior to ramp onset (data not shown) and low levels of autapse strength stellate cells fire at baseline, DC current dependent frequencies. At a critical level of autapse strength (0.8 nS in this example) a small further increase in autapse conductance causes a sudden transition to the high frequency firing regime consistent with our modeling work. B: Instantaneous frequency jumps rapidly with increasing tonic current in autaptically coupled SCs. A control stellate cell (not coupled with an autapse) is given DC current steps increasing in magnitude. Firing rate increases gradually and continuously as a function of input current (right axis). When the same cell is coupled with an autapse of constant strength firing frequency undergoes a rapid transition to the hyper-excitable regime when identical current steps are presented (left axis, note difference in scale). C: Linopirdine increases autapse-induced burst duration. Representative example of an autapse experiment. After a period of baseline firing was observed (first panel), the autpase was turned on inducing hyper-excitable, burst firing (second panel). A magnified view of a single burst is seen in the last panel. D: After 10
M linopirdine was washed on the same experiment was done on the same cell using the same autapse magnitude. Baseline, uncoupled firing remained qualitatively unchanged (first panel). However, once the autapse is turned on and burst firing is induced, significantly more spikes per burst are observed. The second panel shows a single burst magnified in the last panel to show individual spikes. E: M-current blockade with linopirdine significantly increases number of spikes per burst. For all recorded autapse experiments we observed no significant difference between burst ISIs with and without linopirdine application (left bar graph, n = 6). However, burst duration measured as the number of spikes per burst increased significantly (
) with linopirdine application (right bar graph, n = 6). Error bars are SEM. Linopirdine alters the shape of the spike after hyperpolarization on a fast time scale.
Figure 10.
Abrupt transition from the theta to the bursting hyper-excitable regime in a SI minimal network in a stellate cell model including a M-current.
The parameters used are and
.