Fig 1.
Key brain areas forming the “system” underlying tic production.
Fig 2.
Architecture of the system-level model.
The light gray boxes indicate the four components of the model: the basal ganglia component (BG), the cerebellum component (Cer), the thalamus component (Th) and the primary motor cortex component (M1). Each small dark gray circle within the components represents a leaky integrator unit whose activation potential represents the firing rate of a neural population. The three circles in each box represent three BG channels interacting with three different units of Th and M1. Both Cer and M1 project to the lateral and medial descending systems for motor execution, and vestibular nuclei for balance and eye control. Abbreviations: StrD1: D1 Receptor (D1R)-expressing striatal populations; StrD2: D2 Receptor (D2R)-expressing striatal populations, STN: subthalamic nucleus; GPe: external globus pallidus; GPi: internal globus pallidus; SNr: substantia nigra pars reticulata; MF: mossy fibers; GC: granule cells; GO: Golgi cell; PC: Purkinje cells; DN: dentate nuclei; ThBC: thalamic regions where both basal ganglia and cerebellum project; ThC: thalamic regions where only the cerebellum projects; DA: dopamine efflux regulated by a leaky unit and affecting both StrD1 and StrD2.
Fig 3.
Firing rate within the basal ganglia during tic and intertic time intervals.
Left: data recorded in the monkey. Right: same data recorded in the model. First row: Dorsal putamen activity in the intertic (thin-black line) and tic (thick-red line) intervals. Second row: activity from GPi in the two intervals. Third row: same data for the GPe. The real data were extracted from figure 8 of [49] (reprinted with permission).
Fig 4.
Firing rate in the primary motor cortex and cerebellum during tic and intertic time intervals.
Left: data recorded in the monkey. Right: same data recorded in the model. First row: differential M1 activity between the intertic (thin-black line) and tic (thick-red line) intervals. Second row: same data for CbllCx. The real data were extracted from figure 8 of [49] (reprinted with permission).
Fig 5.
Activity of the model subthalamic nucleus and thalamus in TIC and NO-TIC trials.
Top: Subthalamic nucleus. Bottom: Thalamus.
Fig 6.
Statistical comparison between average value and standard deviation of the peak amplitude of the activity in different areas of the model, involving 40 simulated subjects.
The black-thin line indicates the values computed in no-tic events (NO-TIC); the thick-red line refers to the values computed in the tic events (TIC). Statistically significant differences are indicated with three stars.
Fig 7.
Firing rate in the Dorsal putamen (left) and in the primary motor cortex (right) recorded in the real experiment by [49].
The dashed-red vertical line indicates the time of tic onset. Data adapted from figure 8 of [49] (reproduced with permission).
Fig 8.
Delays between the onset of the average activity in M1 and the onset of the average activities in the other areas of the model in the case of a tic.
The black dots indicate the means whereas the bars indicate the standard deviations. The red dot indicates the reference with respect to which the cross-correlation was computed.
Fig 9.
Effects of the interactions between dopamine bursts and M1 activations on tic/no-tic production.
Each graph represents the firing rate of Dorsal putamen (blue trace) and M1 (red trace) for different combinations of three possible levels of dopamine bursts and M1 activations. The three activations of M1 had a shape as the one shown for the DA-none condition.
Fig 10.
Activity of the three units of primary motor cortex.
Data recorded in the case of (a) tic and (b) no-tic. In the case of a tic, the noise signal conveyed by one channel wins the competition and causes a strong activation of the related cortical unit, whereas all cortical units remain silent in the case of no-tic.
Fig 11.
Number of tics with different levels of dopamine.
The dots indicate the dopamine level averaged over 40 simulated subjects in correspondence to different levels of dopamine, the vertical lines indicate the standard deviation.
Fig 12.
Standard deviation, ranked in decreasing order of magnitude, of some of the model parameters sets found with the genetic algorithm optimisation procedure.
The parameter sets used to compute the standard deviation were those having a data fitting error within the first quartile. Abbreviations of neural areas are summarized in S1 Table as well as in the caption of Fig 2. The other symbols used in the figure are as follows: r: unit resting potential (Eq 3); τ: unit decay coefficient (Eq 1); wpre → post: connection weight connecting a unit of the pre component to a unit of the post component (Eq 3); d: dopamine amplitude coefficient (Eqs 4 and 5);