Figure 1.
Scheme of the two-neuron model of the sleep-wake cycle [18].
The red arrow from the orexin-producing neuron A (red circle) to the neuron B (blue circle) represents the glutamate projection as well as the orexin projection regulating the homeostatic process. The blue arrow represents the
glutamate projection. The neuron A is also acted upon by a periodic signal representing the effect of the circadian clock.
Table 1.
Parameters of the two-neuron model [18].
Figure 2.
Response of the two-neuron model.
Main variables and inter-spike times (
) versus time for a pulse height
(left) and
(right), see text for details.
Figure 3.
Scheme of the heterogeneous model.
Example of model system with orexin-producing neurons
,
(red spheres) and one neuron B (blue sphere). The neurons A interact with each other through an all-to-all coupling (red lines). Blue and red projections have a meaning similar to those of Fig. 1: the neuron B is coupled to the neurons
through parallel glutamate projections, while each neuron
is coupled to neuron B through a glutamate and an orexin projection. The neurons A are also acted upon by a stimulus representing the effect of the circadian clock (gray arrows).
Figure 4.
(A). Ten periods of the raster plots of neuron B for different intensities of the noise acting on neurons
. Vertical dashed lines mark the beginning of the pulses of the external current
, see text for details. (B). Coefficient
, from Eq. (16), versus current noise intensity
.
Figure 5.
Sample of four periods of some relevant variables and inter-spike times (
) versus time of neuron
and neuron B for an intensity of noise in neurons A
(left) and
(right). Compare Fig. 4 and see text for details.
Figure 6.
(A). Sample of ten periods of the raster plots of neuron B for different values of the intensity of the noise acting on neuron B. Vertical dashed lines mark the beginning of the pulses of the external current
, see text for details. (B). Quality of the sleep-wake cycle from the coefficient
, Eq. (16), versus current noise intensity
.
Figure 7.
Sample of four periods for some relevant variables and inter-spike times (
) versus time for neuron
and neuron B for an intensity of the noise acting on neuron B
(left) and
(right). Compare Fig. 6 and see text for details.
Figure 8.
Effect of diversity in the synapses.
(A). Sample of ten periods of the raster plots of neuron B for different heterogeneity levels in the
glutamate synapse thresholds, see text for details. (B). Quality of the sleep-wake cycle from the coefficient
, Eq. (16), for various threshold diversities
.
Figure 9.
Effect of diversity in the synapses.
Sample of four periods of some relevant variables and inter-spike times (
) versus time for neuron
and neuron B for different levels of the threshold diversity
(left) and
(right). Compare Fig. 8 and see text for details.
Figure 10.
Effect of diversity in the synapses.
Comparison between the responses of the heterogeneous system (left column) and homogeneous system (right column) in the first part of the time period during the action of the
long current pulse starting at
and ending at
. (A) and (B) (top panels). External current pulse. (C) and (D) (central panels). Behavior of some representative glutamate activation variables of the heterogeneous system,
for
(panel (C)), and the (common) time dependence
of the homogeneous system activation variables (panel (D), black continuous curve); in the latter figure also the average value
of the heterogeneous system (dashed grey curve) is shown for comparison. (E) and (F) (bottom panels). Raster plots of all the neurons of the system. See text for further details.
Figure 11.
Effect of diversity in the synapses.
(A). Sample of ten periods of raster plots of neuron B for different heterogeneity levels in the
glutamate synapse thresholds, see text for details. (B). Coefficient
, Eq. (16), for various degrees of diversity
.
Figure 12.
Effect of diversity in the synapses.
Sample of four periods of the time dependence of some relevant system variables and inter-spike times (
) of neuron
and neuron B for a threshold diversity
(left) and
(right). Compare Fig. 11 and see text for details.