Fig 1.
Architecture of the adopted Complete Model of the BG.
FSN, D1 and D2: striatal Fast Spike Neurons, and medium spiny neurons with D1 and D2 dopamine receptors; GPe-TA and GPe-TI: globus pallidus externa type A and type I; STN: subthalamic nucleus; GPi: globus pallidus interna; SNr: substantia nigra pars reticulata; ext: external poissonian input. By convention red/green arrows are inhibitory/excitatory projections. Dashed elements have not been included in our model.
Table 1.
Reference size and neuron model of each population.
Note that sizes have been modulated in a subset of the analysis through the n parameter.
Table 2.
Adopted values of the parameters of each neuronal population.
(*): for the FSN population the units of a is .
Table 3.
Connectivity properties of the adopted model of the BG.
Type I represents inhibitory connections while type E represents excitatory connections.
Fig 2.
D1 and D2 firing rates as a function of dopamine depletion.
Alterations in the mean firing rates of D1 and D2 neurons as a result of the adopted modelization of dopamine depletion for different values of population size n (see Section 1.8).
Fig 3.
Identification of most relevant oscillators and investigation of their spectral properties.
(A) Rationale about the selection of salient nodes in the BG network for a single simulation run. The nodes, taken together, define the STR and the STN loops (in blue and red shadow respectively). (B) STR loop with FSN, GPe-TI and D2 nuclei, connected with feedforward inhibitory projections (in red) and with their natural mode. (C) STN loop with STN and GPe-TI nuclei, connected with excitatory feedforward (in green) and inhibitory feedback projections (in red) and their natural mode.
Fig 4.
Effects of Dopamine Depletion Dd on the two independent oscillators.
(A) Schematic representation of the Simplified Model in the non-interacting case. (B) Mean frequencies of STN (blue) and D2 (red) nuclei as a function of dopamine modulation Dd: note that the two mean frequencies do NOT converge due to the increase of Dd. (C) Unbiased measure of the intensity of β activity as a function of Dd: note that the intensity of the D2 resonance grows for increasing values of Dd. (D-E) Unbiased measure of the intensity of β activity in D2 (D) and STN (E) as a function of Dd and for different sizes n of the populations.
Fig 5.
Evolution of the PSD of the STN and D2 populations for increasing values of the coupling strength ε.
(A) PSD of STN and D2 nuclei related to a low level of coupling (ε ∼ 0.05) showing asynchronous states. (B) PSD of both STN and D2 nuclei in relation with an intermediate level of coupling (ε ∼ 0.45) showing larger peaks increasingly including the intermediate region. (C) PSD of STN and D2 nuclei related to a high level of coupling (ε ∼ 0.85) showing the emergence of a common oscillatory mode.
Fig 6.
Effects of the coupling strength ε on the Simplified Model.
(A) Schematic representation of the Simplified Model: the modulation of the coupling strength between the STR and STN loops is obtained by varying the connection probabilities p(ε, S → T) = εp1,S→T (see Eq (2)) of inter-loops connections. (B) Mean frequencies of STN (blue) and D2 (red) nuclei as function of the coupling strength ε: the two mean frequencies converge due to the increase of the coupling strength between the two oscillators. (C) Unbiased measure of the intensity of β activity as a function of ε: note the remarkable growth of the intensity in the synchronous regime. (D) Unbiased measure of the intensity of the STN β activity as a function of ε for different values of the population size n: the intensity of β activity is preserved only in the synchronous regime. (E) Value of the STN-PSD nuclei computed at the natural frequency of the STR oscillator as a function of the coupling strength. These results are associated with the analogous shown in Fig A in S1 Text.
Fig 7.
Evolution of the PSD of the STN and D2 populations for increasing values of Dopamine Depletion Dd.
PSD of both STN and D2 nuclei related to low (A), intermediate (B) and high (C) levels of dopamine depletion (Dd = 0.9, 0.97 and 1.05 respectively): for low values of Dd the system is characterized by the only STN-loop resonance; the increase of Dd leads to higher degrees of interaction and to the emergence of a unique resonance at an intermediate frequency.
Fig 8.
Effects of Dopamine Depletion Dd on the Simplified Model (ε = 0.75).
(A) Schematic representation of the Simplified model in the interacting case: the targets of Dopamine modulation are highlighted. (B) Mean frequencies of STN (blue) and D2 (red) nuclei as function of dopamine modulation Dd: the two mean frequencies converge due to the increase of Dd. (C) Unbiased measure of the intensity of β activity as a function of Dd: note the remarkable growth of the intensity in the synchronous regime. (D) Unbiased measure of the intensity of the D2 β activity as a function of Dd for different values of the population size n: the intensity of β activity is preserved only in the synchronous regime. (E) Unbiased measure of the intensity of the D2 β activity as a function of Dd for n = 1 and n = 8 and comparison between the interacting (ε = 0.75, continuous lines) and non-interacting condition (ε = 0.00, dashed lines): the intensity of β activity is preserved if and only if the two oscillators are synchronized. These results are associated with the analogous shown in Fig B in S1 Text.
Fig 9.
Effects of Dopamine Depletion Dd on the Complete Model.
(A) Schematic representation of the Complete Model: the targets of Dopamine modulation are highlighted. (B) Mean frequencies of STN (blue) and D2 (red) nuclei as function of dopamine modulation Dd: the two mean frequencies converge due to the increase of Dd. (C) Unbiased measure of the intensity of β activity as a function of Dd: note the remarkable growth of the intensity in the synchronous regime. (D) Unbiased measure of the intensity of the D2 β activity as a function of Dd for different values of the population size n: the intensity of β activity is preserved only in the synchronous regime. Analogous results about STN β activity are shown in Fig C in S1 Text.
Fig 10.
Bursting dynamics for intermediate values of dopamine (Dd = 0.90) in the case of the Complete Model of the BG.
(A) Periodogram of the STN population activity highlighting the bursting characterization along a period of 20 seconds. (B) Difference between the instantaneous mean frequency of STN and D2 nuclei. (C) Instantaneous values of PSD for the STN nucleus. The dashed lines in the inferior subplots represent the median values of Δf and β STN Mean PSD respectively.
Fig 11.
Effects of activity manipulations on network dynamics.
All manipulations are based on the opto-genetic stimulations discussed in [49]. OFF values are measured in pathologic conditions (Complete Model with Dd = 1.03) while ON values are measured when the opto-genetic perturbations are applied. (A) Simulated effects of motor cortex opto-inhibition on STN discharge rate (left) and intensity of β oscillations (right) (see also Figs 1k-l and 1i-j in [49]). (B) Predictions of the model on the intensity of β activity as a consequence of large variations of the STN discharge rate (see also Figs 2e-f-g and 5i-k in [49]). (C) Consequences of GPe opto-inhibition on GPe-TI and GPe-TA nuclei (first panels on the right) and predictions of the model on the effects of GPe opto-inhibition on STN discharge rate and intensity of β oscillations (right panels) (see also Figs 4k-l and 4i-j in [49]). Shaded areas in the plots reporting β intensity correspond to the values of observed for low Dd in the Complete Model (see Fig C in S1 Text).