Role of inhibitory feedback for information processing in thalamocortical circuits

The information transfer in the thalamus is blocked dynamically during sleep, in conjunction with the occurrence of spindle waves. In order to describe the dynamic mechanisms which control the sensory transfer of information, it is necessary to have a qualitative model for the response properties of thalamic neurons. As the theoretical understanding of the mechanism remains incomplete, we analyze two modeling approaches for a recent experiment by Le Masson et al. [Nature (London) 417, 854 (2002)] on the thalamocortical loop. We use a conductance based model in order to motivate an extension of the Hindmarsh-Rose model, which mimics experimental observations of Le Masson et al. Typically, thalamic neurons posses two different firing modes, depending on their membrane potential. At depolarized potentials, the cells fire in a single spike mode and relay synaptic inputs in a one-to-one manner to the cortex. If the cell gets hyperpolarized, $T$-type calcium currents generate burst-mode firing which leads to a decrease in the spike transfer. In thalamocortical circuits, the cell membrane gets hyperpolarized by recurrent inhibitory feedback loops. In the case of reciprocally coupled excitatory and inhibitory neurons, inhibitory feedback leads to metastable self-sustained oscillations, which mask the incoming input, and thereby reduce the information transfer significantly.

Figure 1

Structure of synaptic connections in a pair of reciprocally coupled RE-TC cells.

Figure 2

(Color online) (a) Spontaneous spindle activity in the computational thalamic circuit. The TC cell receives artificial synaptic retinal bombardment, modeled by a Poisson-distributed spike train. The RE-TC oscillator shows spindle activity. (b) Detail of (a). (c) Total synaptic current injected into the biological TC cell and simultaneous voltage of the TC and RE cell. Bottom: The hyperpolarization of the TC cell activates the $I_T$ current, what initiates a post-inhibitory rebound burst (see also Fig. 5). Calibration bars: $10\mathrm{s}$, $20\mathrm{mV}$ (a); $1\mathrm{s}$, $20\mathrm{mV}$ (b); $10\mathrm{ms}$, $6\mathrm{nA}$, $20\mathrm{mV}$, $1\mathrm{nA}$ (c).

Figure 3

(Color online) Percentage of output spikes triggered by an input spike $\left(T_{SN}\right)$ (solid) and transfer efficiency $T_{TE}$ (dashed) for different values of the inhibitory feedback. Both indices show no significant change when the inhibitory feedback is varied within the stability borders.

Figure 4

Averaged contribution $\left(T_{CI}\right)$ (a) and correlation $\left(T_{CC}\right)$ (b) indices versus synaptic strength.

Figure 5

Schematic diagram illustrating the generation mechanism of spindle oscillations. We distinguish two cycles: First, the spindle cycle is responsible for the spiking; the system runs several time through it before the waxing and waning cycle is activated, leading to bursts of oscillations. The slowly decaying current $I_h$ leads to the long silent epochs during which spike transfer is blocked. Altogether, the interplay of the currents $I_T$ and $I_h$ plays an important role for the genesis of spindle oscillations. (See also Figs. 2, 3.)

Figure 6

Maximum and or minimum bifurcation diagram of $v$ in the fast subsystem (4) as a function of $z$. Heavy lines indicate stable fixed points (limit cycles) and thin lines indicate unstable fixed points (limit cycles). (See Appendix .)

Figure 7

(Color online) $v\left(t\right)$ (black) and $z\left(t\right)$ (red, upper curve) with $I=1.0$. When $z\left(t\right)$ is periodic, $v\left(t\right)$ oscillates with the same period; thus the slow variable $z\left(t\right)$ slaves $v\left(t\right)$.

Figure 8

(Color online) $v\left(t\right)$, $z\left(t\right)$, and $I\left(t\right)$. The system shows a post-inhibitory rebound burst after a hyperpolarizing step of $I\left(t\right)=-0.5$ and a duration of $70\mathrm{ms}$.

Figure 9

(Color online) Right: Reciprocally coupled RE and TC cell. Left: If the excitor cell gets activated by an external pulse, it excites the inhibitor cell, which leads to an inhibitory current. This current hyperpolarizes the excitor cell and evokes a rebound burst in it, and the mechanism repeats, which leads to self-sustained oscillations.

Figure 10

(Color online) Reciprocally coupled inhibitor and excitor; without the $h$ current, the oscillation does not terminate.

Figure 11

(Color online) Top: Time course of the gating variables $S_2$ (red, upper curve) and $F_2$ (green, lower curve) during a spindle cycle. Bottom: The membrane potential $V_{Tc}$ of the biophysical model.

Figure 12

(Color online) Top: Time course of $h$ during a spindle cycle. Bottom: The membrane potential $v_{Tc}$ of the extended Hindmarsh-Rose model.

Figure 13

(Color online) Spontaneous spindle activity in our computational model (the numerical values of the voltages are scaled by a factor of 30 to match with the biophysical values). Similar rescalings have been also necessary in the underlying Hindmarsh-Rose model (see, e.g. [22]). (a) The computational circuit: A TC cell (excitor) modeled by the extended Hindmarsh-Rose model is reciprocally coupled to a model RE cell (inhibitor) represented by the original Hindmarsh-Rose model. The TC cell receives artificial synaptic retinal bombardment modeled by a Poisson distributed spike train. Like in the experiment the system shows spindle activity. (b) Detail of (a). (c) Like in Fig. 8.

Figure 14

(Color online) Percentage of output spikes triggered by an input spike. An increase of the strength of the inhibitory coupling $g_{GABA}$ comes along with a significant decrease in the reliability of the information transfer. As in the experiment of Ref. 2 and in the biophysical model, the transfer efficiency does not vary significantly.

Figure 15

Bifurcation diagram of (24) with $h_{TC}$ treated as a slowly varying parameter; solid lines indicate stable fixed points, dashed lines unstable fixed points, filled circles stable limit cycles, open circles unstable limit cycles. For extreme values of $h$, the system is monostable, i.e., either a stable fixed point or a stable limit cycle coexist.