Corticothalamic Projections Control Synchronization in Locally Coupled Bistable Thalamic Oscillators

Thalamic circuits are able to generate state-dependent oscillations of different frequencies and degrees of synchronization. However, little is known about how synchronous oscillations, such as spindle oscillations in the thalamus, are organized in the intact brain. Experimental findings suggest that the simultaneous occurrence of spindle oscillations over widespread territories of the thalamus is due to the corticothalamic projections, as the synchrony is lost in the decorticated thalamus. In this Letter we study the influence of corticothalamic projections on the synchrony in a thalamic network, and uncover the underlying control mechanism, leading to a control method which is applicable for several types of oscillations in the central nervous system.

Figure 1

Depending on $\alpha$, the system possesses either one stable fixed point or it shows bistability with a stable fixed point and a stable limit cycle. Left: $U(r,t,\phi )$ for different values of $\alpha$. Right: Bifurcation diagram of (2) with $\alpha (t)$ considered as a bifurcation parameter. Solid lines indicate a stable fixed point, open circles an unstable limit cycle and filled circles a stable limit cycle.

Figure 2

Left: The potential $U_1$ with no coupling and $u=0.15$ and for the case that neuron 2 is in the excited state and $u_{1/2}$ are both 0.15 for a coupling strength of $ϵ=0.23$. See (4) and Fig. 1. Right: Variations of $|r_1-r_2|$ (red) and $|u_1-u_2|$ (green/light gray) as a function of $\epsilon$. As the interwell jumps synchronize at $\epsilon \simeq 0.23$, the variations of $|r_1-r_2|$ and $|u_1-u_2|$ rapidly decrease at this point.

Figure 3

(a) and (c) $r_1$ (red), $r_2$ (green/light gray) and $F(t)$. (a) For a coupling strength of $\epsilon =0.12$ the interwell jumps occur asynchronously. (b) Variations of $|r_1-r_2|$ as a function of $\epsilon$, both oscillators were modulated by $F(t)$. As the interwell jumps synchronize at $\epsilon \simeq 0.14$, the variations of $|r_1-r_2|$ rapidly decrease. For the parameters chosen here, both control signal and internal coupling are needed. (c) For $\epsilon =0.15$ the interwell jumps occur synchronously, triggered by $F(t)$.

Figure 4

Depending on $ϵ$ the network shows either asynchronous ($ϵ<0.029$) or synchronous oscillations ($ϵ>0.057$). Between these two states traveling waves occur.

Figure 5

Correlation of meanfield network activity $V=\frac{1}{2500}\sum _i^{50}\sum _j^{50}{r}_{ij}$ with driving input signal depending on the driving parameter $\kappa$ for $ϵ=1/30$. (a) and (b) Numerical simulation of the network driven by the same EEG spindle sleep data as measured in the experiment [10]. For $\kappa =0.0$ correlations vanish. (a) shows that the internal coupling is needed for proper synchronization as without it the meanfield only shows little variations, the reason for this effect is the same as described above for the two neuron network. (c) and (d) The corresponding experimentally obtained correlations between spindle rms which corresponds to the $r_{ij}$ scaled by a factor of 30 and EEG activity.