Dopamine depletion leads to pathological synchronization of distinct basal ganglia loops in the beta band

Motor symptoms of Parkinson’s Disease (PD) are associated with dopamine deficits and pathological oscillation of basal ganglia (BG) neurons in the β range ([12-30] Hz). However, how dopamine depletion affects the oscillation dynamics of BG nuclei is still unclear. With a spiking neurons model, we here capture the features of BG nuclei interactions leading to oscillations in dopamine-depleted condition. We highlight that both the loop between subthalamic nucleus (STN) and Globus Pallidus pars externa (GPe) and the loop between striatal fast spiking and medium spiny neurons and GPe display resonances in the β range, and synchronize to a common β frequency through interaction. Crucially, the synchronization depends on dopamine depletion: the two loops are largely independent for high levels of dopamine, but progressively synchronize as dopamine is depleted due to the increased strength of the striatal loop. The model is validated against recent experimental reports on the role of cortical inputs, STN and GPe activity in the generation of β oscillations. Our results highlight the role of the interplay between the GPe-STN and the GPe-striatum loop in generating sustained β oscillations in PD subjects, and explain how this interplay depends on the level of dopamine. This paves the way to the design of therapies specifically addressing the onset of pathological β oscillations.

2 D2 nucleus PSD as function of ε interaction parameter   5 Effects on pathological oscillations of connectivity alterations due to dopamine depletion Throughout this work, the condition of Dopamine Depletion is modeled as the complementary modulation of the mean discharge rate of the D1 and D2 populations in the Striatum (see Figure 2 in the main text). However, several works [57,[74][75][76] showed that dopamine depletion leads also to alterations in Basal Ganglia connectivity. In mice, as a result of dopamine depletion, the number of GPe-STN synapses doubles with no alteration in synapse size and efficacy [74] and FSN cells double their connectivity to D2 MSNs, whereas connections to D1 MSNs remain unchanged [75]. In this section we investigate the effects of a more detailed modelization of dopamine depletion on STR and STN loop, accounting also for these evidences. In addition to the modulation of the external input rate to the striatal populations (see equation 3), dopamine depletion is here modeled by modulating the connection probabilities p FSN→D2 and p GPe-TI→STN (see panel A in Figure D) according to: where p FSN→D2,1 and p GPe-TI→STN,1 are the reference values indicated in Table 3, D * d,min = 0.9 and D * d,min = 1.1.
Taking into account also dopamine depletion effects on connectivity, the intensity of β activity increases in the STR loop (panel B in Figure D), in a very similar way to what observed taking into account only the effects dopmamine depletion effects on D1 and D2 rate (panel C in Figure D). The increase in β activity observed in the STN loop is smaller than what observed in the STR loop (panel D in Figure D), but still different from what is observed when modeling only dopamine depletion effects on rate, in which no modulation was observed (panel E in Figure D). However the intensity of β activity is not robust in the limit of large n. This suggests that the introduction of a more detailed modelization of dopamine depletion, including also the strenghtening of the GPE → STN and FSN→D2 connectivity, is not sufficient to account for the emergence of prominent β activity within the isolated oscillators. As shown by the results in the main text, the key element for the emergence of prominent β activity is not determined by these alterations, but lies in the interplay between the two identified oscillators. For the sake of simplicity in results interpretations, we did not include then dopamine-dependent connectivity alterations in the main text as they would not change the presented results on a qualitative description, but only affect minor details at a quantitative level.

Robustness of pathological oscillations onset to alterations of model parameters
In order to test whether the main result of our work, i.e., the process of synchronization associated with dopamine depletion, critically depends on the choice of the model parameters, we repeated the analysis after small alterations of the model parameters.
We first consider the connectivity properties of the model and slightly alter the value of the parameters regulating the connection probability p i and the synaptic weight w i of each connection i in the model. Particularly, for each connection i, we considered the pair (p i , w i ) and, in order to maintain the mean firing activity of the different nuclei in the realistic range, we jittered these parameters according to: with {x i } i independently extracted for each connection from a gaussian distribution with mean µ = 1 and a standard deviation σ = 0.1. We repeated the extraction of the {x i } i values four times independently and, for each of these extractions we performed the analysis on the intensity of β activity as a function of D d . The results of this study are reported in panels A and B of Figure E, and show that, despite small variations, the process of synchronization and the emergence of prominent β activity is robust to the described alterations.
We now consider the network parameters regulating the neuron model and the size of each population k in our model. Particularly, in order to maintain the mean firing activity of the different nuclei in the realistic range, we jittered the parameters: • N k , τ ex,k , τ in,k , ν ext,k according to: with x extracted from a gaussian distribution with mean µ = 1 and a standard deviation σ = 0.1 • dev ext weight k , V res,k , t ref,k , V peak,k , E L,k , E ex,k , E in,k , I e,k , C m,k , g L,k , and the adaptation parameters a k , b k and τ w,k according to: with {x j,k } j,k and {y j,k } j,k independently extracted for each population k from a gaussian distribution with mean µ = 1 and a standard deviation σ x = 0.1 and σ y = 0.01 respectively.
In this case also, we repeated the extraction of the x, {x j,k } j,k and {y j,k } j,k four times and, for each of these extractions, we performed the analysis on the intensity of β activity as a function of D d . Similarly to the previous case, the results of the study highlight that the process of synchronization and the emergence of prominent β activity is qualitatively robust to the considered alterations (see panels C and D in Figure E).