Multiple-time-scale framework for understanding the progression of Parkinson's disease

Parkinson's disease is marked by neurodegenerative processes that affect the pattern of discharge of basal ganglia neurons. The main features observed in the parkinsonian globus pallidus pars interna (GPi), a subdomain of the basal ganglia that is involved in the regulation of voluntary movement, are pathologically increased and synchronized neuronal activity. How these changes affect the implemented neuronal code is not well understood. Our experimental temporal structure-function analysis shows that in parkinsonian animals the rate-coding window of GPi neurons needed for the proper performance of voluntary actions is reduced. The model of the GPi network that we develop and discuss here reveals indeed that the size of the rate-coding window shrinks as the network activity increases and is expanded if the coupling strength among the neurons is increased. This leads to the novel interpretation that the pathological neuronal synchronization in Parkinson's disease in the GPi is the result of a collective attempt to counterbalance the shrinking of the rate-coding window due to increased activity in GPi neurons.

Figure 1

Basal ganglia-thalamocortical circuit scheme before (a) and after (b) the emergence of PD. The variation of the arrow thickness from the left to right panel encodes the quantitative changes observed. Blue, exitatory input; red, inhibititory input.

Figure 2

Model architecture. GPi neurons are arranged in a ring and diffusively coupled to each other ($n=101$, circles). The Str afference to the GPi (inhibitory) is modeled with 101 axons, each of which connected to one GPi neuron with a high synaptic weight ($w_{\text{Str-GPi-I}}=0.9$) and to 9 GPi neurons with a lower weight ($w_{\text{Str-GPi-II}}=0.01$). STN input, excitatory, is represented by 101 axons, each of which produces 10 collaterals to adjacent GPi neurons with the same synaptic weight ($w_{\text{STN-GPi}}=0.1$). Small-range interactions are modeled by diffusive coupling among GPi cells.

Figure 3

Order-1 structure functions of the four modeled groups representing our neuronal classes of behavior. (I, II) Control group, deep anesthesia, and alert condition, respectively; (III, IV) PD, deep anesthesia, and alert condition, respectively. With alertness, for groups I to III, the breakpoint moves to the right and finally disappears in group IV, and a progressive reduction of the zero-slope scale range is observed, indicating a loss of the rate-coding capability for PD neurons. $f$ indicates the average frequency connected with the index interval $\tau$ and $1/f$ the corresponding “typical” time scale (in the model in units of iterations).

Figure 4

Average network activity: Growing external input entrains increased activity (a) healthy conditions [$|A_i/A_e|=0.8$, external input $<5$, typically $\in (1.5,2)$], (b) toward parkinsonian conditions [$|A_i/A_e|=0.9$, external input $\in (25,50)$], (c) healthy conditions [$D=0.01$, typically $D<0.1$, external input $<5$, typically $\in (1.5,2)$], (d) toward parkinsonian conditions [$D=0.3$, typically D $\in (0.3,0.5)$, external input $\in (25,50)$].

Figure 5

White arrows: Suggested development of PD. The parameters (activity, $D$) provide a coherent qualitative description of the situation, although they are not fully independent. (a) ${\tau }_1$ evaluated as a function of the network activity and $D$ (at $|A_i/A_e|=0.95$). Blue (${\tau }_1<100$) and black ($100<{\tau }_1<500$) indicate viable rate-coding windows. Red: Vanishing rate-coding window (${\tau }_1>500$). In the course of PD increased activity, to escape a coding window collapse, $D$ must increase as well. From $|A_i/A_e|=0.90$ to $|A_i/A_e|=0.95$, the red area increases from the dashed boundary to the final one. (b) Network synchronization as a function of the network activity and on $D$ (at $|A_i/A_e|=0.9$). The situation remains essentially unchanged for $|A_i/A_e|$ in (0.8, 0.95). White, unaccessible regime; black, viably unsynchronized ($A_m<1$). Regime I, highly synchronized across all of the interval ($A_m>2$); Regime II, very strong synchronization at $|A_i/A_e|=0.8$, subject to a decrease toward $|A_i/A_e|=0.95$ (from $A_m\approx 4$ to $A_m=1.5$); Regime III, synchronized across the whole interval ($1<A_m<2$). This regime is likely to trigger the typical PD synchronization phenomena.