BG network performance was assessed by verifying the attenuation of the signal. We used EI, described by Rubin and Terman (2004), to measure the normality of thalamic throughput. The dieaway of the signal was measured by the number of peaks of TH discharge over a period of time. It has been clarified that the denaturation of dopaminergic neurons in the substantia nigra and the decrease in striatal dopamine levels were the initiation events that induced Parkinson's disease. The reduction of dopamine caused its regulation about basal ganglia to be uncoordinated, resulting in the electrical signal delivered to the effector, this referred to TH, was lost or incomplete. In this paper, the peak type was divided into three kinds: lost peak, incomplete peak, normal peak. We took the rest state as a lost peak; 10–90% of the maximum peak as an incomplete peak; 90–100% of the maximum peak as a normal peak. EI was identified as the number of incomplete peak divided by the number of normal peak. For each state tested, the duration of the simulation was 16 s.

Here, in addition to MSN is a multi-compartment model, all others neurons are single-compartment conductance-based models applied in previous theoretical analysis of the network model.

AMPA, NMDA, and GABA currents were modeled using a modified two-state synapse which based on the Exp2Syn synapse in NEURON, These currents obeyed the following equation:

Where τ_on is the rise time and τ_off is the decay time of the synapse, Decay and rise time constants for NMDA and AMPA channels were taken from the published reports (Gotz et al., 1997), and GABA time constants were taken from neocortical pyramidal cell data (Galarreta and Hestrin, 1997). E_syn is the reversal potential, ḡ_syn is the maximal synaptic conductance. NMDA and AMPA reversal potentials were set to accepted values of 0mV (Moghaddam, 2003), whereas reversal potentials for GABA was set to −80 mV to match published reports (Tepper et al., 2004). The specific parameters value are described in Table 3 in Supplementary Material. The synaptic current from α to β neuron therefore was calculated using:

Here, g_{α → β} is the synaptic connection weight. The specific parameters are described Table 4 in Supplementary Material.

The position of the dendritic spines loss we chose was random. In order to eliminate the effect of the position, we need to discuss the influence of the position where the dendrites were removed on the discharge of the MSN cell body. The model showed that the discharge activity of the cell body remained essentially unchanged under the same stimulus, whether the distal dendrites or the proximal dendrites (closer to the soma) were removed (Figures 3A,B). In addition, as the number of degraded dendrites increased, the mean firing frequency (MFR) of MSN increased significantly (Figures 3C,E,F), as well as the number of peaks in each burst (Figure 3D).

Recordings in monkeys treated with 1-methyl-4-phenyl-1,2,3,6-18 tetrahydropyridine (MPTP), similar to the emergence of Parkinson's disease, indicated that the frequency of spontaneous discharges increased in the striatum neurons (Bamford et al., 2004). Our model shown that the loss of spines increased the MSN firing rate increases (Figure 3C). Therefore, compared to normal conditions, the model of MSN showed a higher spontaneous firing rate in the PD state. In addition, published experimental results have demonstrated that the firing rate increased in the GPi, decreased in the GPe after administration of MPTP (Boraud et al., 1998; Wichmann and Soares, 2006). Similarly, the firing rate of D2 in PD state was higher than in the normal state(Pang et al., 2001; Mallet et al., 2006). In the network model constructed in this paper, the changes in mean firing frequency of these neurons were consistent with the previous experimental results (Figure 4A).

Experimental studies have revealed that GPi, the output nuclei of the basal ganglia, became exceptionally active in PD state (Filion and Tremblay, 1991), resulting in increasing the level of inhibition onto the thalamus. In our model, when the dopamine depletion did not exceed 22%, the mean firing frequency of TH was maintained at a normal level. However, when the amount of dopamine decreased by more than 22%, the mean firing frequency of TH was significantly reduced (Figure 5A). In addition, the discharge pattern of TH has also changed, which exhibited an irregular discharge compared to the previous bursting-like firing patterns (Figure 5B).

In the normal state, the MSN's topology was complete in striatum, the loss of spines would change the mean firing rate of TH. TH reached the normal level in both positions: one was the original state, which was very obvious, the other was the dendritic spine loss in the range 50~60% (Figure 6A). However, for the dendritic trees degradation, the situation tended to become more complex. One of the important reasons might be that the dendritic trees degradation not only caused the spines located on the corresponding dendrites to be lost, resulting in a change in the receiving signal of the striatum. At the same time, the degradation of the dendrites itself also caused an increase in the discharge of in the medium spine neurons, and the greater the dendritic degradation, the greater mean firing rate of the cell (Figure 3C). At the beginning, with the dendrites degradation, the discharge of TH increased, the mean firing rate of TH reached the maximum when the dendrites degraded about 15–28%, subsequently fluctuated downward trend (Figure 6A). During this period, the firing rate of TH could return to normal at some points, such as 31.25% (Figure 6B) or 45%.

In the PD state, due to the reduction of dopamine, the regulation of the substantia nigra on the basal ganglia was impaired, the electrical signals transmitted to the effector were lost or incomplete. Therefore, the EI indicator of the PD patients was greater than the normal people (Figure 4B), which might be attributed to a decrease in the number of normal peaks or an increase in the number of incomplete peaks.

As one of the primary information input nuclei to the basal ganglia, the discharge characteristics of the cortical neurons are crucial for BG network. We considered the cortical neuron model with electromagnetic induction, and magnetic flux φ was imposed on the cortical neuron to describe the effect of electromagnetic induction. Moreover, the effects of alternating current electric field induced by magnetic stimulation were also considered to explore the mode transition of electrical activities. The improved neuron model is described by the following dynamical equation:

Where φ, V_e represents the magnetic flux across the membrane and additive induction membrane induced by external magnetic stimulation, respectively. In fact, V_e = A_esin(ωt) is alternating current electric field mentioned above, which can be seen as an additive perturbation to the membrane potential (V_cor) (Yu et al., 2013). This time, we change υ_cor to υ_cor+V_e, and CmdVedt=(Aesin(ωt))′=AeωCmcos(ωt). This is what the right side of the Equation (12) describes. The function ρ(φ) is the memory conductance used to describe the relationship between magnetic field and membrane potential of neuron, which develop from the magnetic flux-controlled memristor (Bao et al., 2010). I_app represents the external forcing current, and here we only consider the direct-current type. k, k₁, k₂ are parameters that describe the interaction between membrane potential and magnetic flux. α and β are two positive constant parameters. Detailed description of these parameters can refer to the literature (Lv et al., 2016), and the other parameters such as ω, A_e, and I_app are differently changes. The membrane capacitance and the gate variable for channels will remain the same.

First, we discussed the modes of electrical activities induced by the alternating current electric field and without external forcing current being considered. We selected k = 0.001, k₁ = 0.1, k₂ = 1, α = 0.4, β = 0.01, and fixed ω = 6.27Hz. Then multiple discharge modes in cortical neuron could be observed through tuning the intensity (A_e) of AC electric field, and the time series of membrane potential with different values of A_e were plotted. In Figure 7, when a small intensity A_e = 0.4 acted on the membrane, the discharge patterns of the cortical neuron are subthreshold membrane potential oscillation (SMPO). As the intensity increased, the SMPO state of the cortical neuron was excited into a single spiking state. Further, when the intensity A_e was increased to 2.0, the spiking state with one spike of the discharge patterns is transited to have more spikes.

Next, we discussed the modes of electrical activities when external forcing current was considered, here I_app = 3.0. Fixing ω = 5.2 Hz, variations in stimulus intensity A_e could also generate multiple fring patterns, the results for neuronal action potentials were shown in Figure 8. With the increase of A_e from 0 to 1.6, the discharge patterns transited from period-1 fring to bursting, then turned into a mixed-mode oscillations. Moreover, Figures 7, 8 illustrated that bursting was more prefer to occur when A_e was large, and a small value of A_e would cause the cortical neurons to become spiking or quiescent or subthreshold membrane potential oscillation.

Then we explored other interesting modes of the discharge patterns. For k = 0.001, k₁ = 0.1, k₂ = 1, α = 0.4, β = 0.01, A_e = 1.2, ω = 6.28, Figure 9 showed that the firing patterns in cortical neuron were much dependent on the external forcing current. As the external forcing current was increased from 0 to 11.0 displayed in Figures 9A–D, we could found that the electrical activities transited from spiking to period-2 bursting, then from chaotic bursting to period-3 bursting. That is to say, the number of spikes in each burst increased with increase of stimulus intensity.

Studies have shown that the clinical symptoms of Parkinson's disease occured when the death of dopaminergic neurons in substantia nigra was more than 50% and the loss of dopamine in the striatum exceeded 80%. In response to the reduction of dopamine, some excitatory input synapses as well as their postsynaptic spines were lost (Stephens et al., 2005). Day et al. also found that selective loss of glutamatergic synapses would appear in MSN when the concentration of dopamine in the striatum was reduced (Day et al., 2006). Therefore, it was a reasonable assumption that dendritic spines were preferred to fall off at the location where the binding site of dopamine receptor had been lost. We divided the dendritic spines from two types: Type-1 indicated that the loss of dendritic spines occured at the site where the dopamine receptor binding site had been lost. Type-2 indicated that the loss of dendritic spines occured at sites where the dopamine receptor binding site has not been lost. According to our assumptions, we could divide the dynamic changes of the BG network into two stages: First, the dendritic spines lost in the type-1 position, and the corresponding glutamatergic synapses were also lost, protecting D2 against too much excitation, reducing the inhibition of indirect pathway on TH. Second, type-2 spines began to fall off, the excitatory input from the cortex to D2 was decreased, while the inhibitory input from dopaminergic neurons was also reduced. The discharge activity of D2 would not always be enhanced or weakened, but in a fluctuating change. Therefore, the process of dendritic spine loss in fact was a complex regulatory process of basal ganglia.

The BG network model we constructed showed that the loss of spines could bring the EI index to the normal level under the circumstance of the dopamine concentration decreasing by no more than 60%. The reduction of dopamine was different, the changes of EI index with the dendritic spine loss were also different. Here, the cases could be divided into three types: First, when the amount of dopamine depletion did not exceed 22% (Figure 10B), the EI index of the model did not increase significantly, suggesting that it could not cause disorder about the regulatory functions of basal ganglia. However, a small amount of spines loss made the EI index rise, one of the possible reasons was the reduction of D1 activity with the loss of glutamatergic synaptic contacts, making the function of the direct path transmitting signal weakened. With the dendritic spine further loss (approximately in the range of 47~62%), glutamate excitatory utility and dopamine inhibition achieved a dynamic balance, thus the regulatory function of the basal ganglia temporarily returned to normal. The function of the basal ganglia again disorder when the amount of dendritic spine loss more than 70%. At this time, the connection point of the dopamine receptor was greatly reduced, and its effect was equal to the reduction in dopamine concentration. Second, the EI index of the BG network reached the normal level in two ranges when the concentration of dopamine was decreased by 30~60% (Figure 10C). One place that made the EI reach the normal level was the spines reduced by 9~18%. A reasonable explanation was that the amount of dopamine reductions was relatively higher, the type-1 spines were first lost, and the activity of D2 was reduced because of a reduction about excitatory input to D2, the important regulatory function of the indirect pathway was restored so that cerebral cortical information was regulated by the basal ganglia and communicated correctly to the effector (TH). At this moment, a phenomenon that the lower the degree of dopamine damage, the less spines that need to lose to return to normal EI could also be observed. Another range that made the EI reach the normal level was the spines reduced by 47~62%. At this time, type-1 dendritic spines have been completely lost and type-2 spines began to fall off, thus the proper ratio of excitatory stimulus and inhibitory stimulus was established for optimal basal ganglia regulatory function. Third, the dendritic spines loss have already not been able to make EI reach the normal level when the amount of dopamine decreased up to 70% (Figure 10D).

The effect of dendrites tree degeneration on EI was also significant. In the case where the dopamine reduction was not more than 22%, the EI could be maintained at a normal level or even below the normal level as long as the dendrites trees degradation were no higher than 34% (Figure 11A). With the further degradation of the dendrites, the EI gradually rose, which might drop and approach the normal value at some point in the future. But this was only a case, the overall EI was still showing a rising trend.

When the dopamine concentration decreased by 30~60% (Figure 11B), EI was significantly increased, indicating that the basal ganglia appeared dysfunction and could not effectively transmit the signal. This moment, dendrites trees degradation could protect D2 from too much glutamate excitatory stimulation, reducing the activity of D2, thus restoring the regulation of indirect pathway. Different with dendritic spines loss, the elimination of the glutamatergic synaptic contact also coincided with the shrink of dendritic trees in D2, resulting in D2 activity was also affected by its topological structure. In addition, it could be seen that the lower the dopamine content, the more the amount of dendrites trees degradation required for EI to achieve normal values for the first time. In addition to some points would decline, EI overall showed a fluctuations rise trend in the case where the amount of dendrites trees degradation was over 50%. When dopamine decreased up to 70% (Figure 11C), the dendrites trees degradation could not make the function of the basal ganglia back to normal even if it made EI decrease. The results also showed that dopamine concentration was different, the range of dendrites trees degradation which made the EI reach the normal level was not the same. The lower the dopamine concentration, the shorter the length of interval maintaining EI at customary levels.

Modulation of cortical activity might prevent dopamine depletion-induced dendritic spines loss. Box-plots were obtained from ten trials of 16 s each. The stimulus form that we chose was alternating current electric field, given by the equation: I_stim=Asin(ωt), where A corresponds to stimulation amplitude, ω to stimulation frequency. We attempted to explore the effect of different levels of stimulus frequency, amplitude in the case of dopamine reduction of 50%. Figure 12 showed that in our results, stimulus frequency <30 Hz did not attain improvement in basal ganglia dysfunction evoked by dopamine depletion. Further, stimulation at quite low frequencies (about 0.001~0.9 Hz) actually led to further disorders. As the stimulus frequency increases, approximately 1–30 Hz, the error index remained at the same level as the PD state. Unlike the effects of stimulus frequency with a almost monotonous dependence, the effect of stimulus amplitude on the network was irregular. When the intensity of the stimulus was <0.003 nA, that was very low, EI could restore to the healthy level. Moreover, EI significantly also dropped for the stimulus amplitude between 17 and 30 nA, and saturated at 80 Hz. Stimulus intensity between 0.003 and 17 nA or strong enough (>80 nA) in cortical neuron resulted in little or no improvement of basal ganglia dysfunction.

The model we constructed showed that the basal ganglia could be restored to normal function in some (more than one) ranges of dendritic spine loss under the same dopamine depletion. When the amount of dopamine decreased in the range of 3~21.9%, there were two ranges of the dendritic spine loss, 0~10% and 50~62%, respectively, making the EI indicator reduce to normal level. However, their impact on the downstream neurons were not the same. The discharge patterns of GPi, D1, D2, TH were observed when the concentration of dopamine was reduced by 12.5% (Figure 10A). It could be seen from the discharge diagram of GPi that the loss of dendritic spines could effectively inhibit GPi activity, thereby reducing its inhibition on TH.

D1 activity was higher in the case of dendritic spines reduced by 30%, compared to reducing by 50%, indicating that the excitability of the direct pathway to thalamus of the former was greater than the latter. At the same time, D2 activity was also higher in the case of dendritic spines reduced by 30%, showing that the inhibition of the indirect pathway to the thalamus of the former was also stronger than the latter. The combined effects of these two factors eventually led to a fact that their effects of basal ganglia on thalamus were almost equivalent, although the principles were distinct. Similarly, when the amount of dopamine decreased by 31.2~59.4%, the loss of dendritic spines could restore the basal ganglia to normal function in two places as well. The principle was similar to the above discussion.

Considering the degradation of dendrites trees (Figure 10A), the EI index was the same in the case of a 19 and 50% degradation when the concentration of dopamine decreased by 12.5%. D1 activity was higher in the case of dendrites degraded by 19%, compared to degrading by 50%. However, the D2 activity of the former was also significantly higher than the latter. The direct pathway of the former had a stronger excitatory effect on thalamus, and the inhibitory effect of the indirect pathway on thalamus was also stronger. Both states could be linked and might well play the decisive role in normal function of the basal ganglia.

We applied the phase diagram to gain insight into the mechanism of signal degradation. Since GPi is the output nucleus of the basal ganglia, the signal from the cortex is transmitted to the thalamus through the integration of the basal ganglia. Therefore, in this analysis, we detected how thalamic cells responded to inhibition of GPi neuron. According to the phase diagram proposed numerical results presented above section by using GPi-thalamic channel. Here, we considered four types of GPi neuron input: these would be known as the normal, PD, 16% of the dendritic spines loss in PD state, and 19% of the dendrites tree degeneration in PD state. The phase diagram provided a very powerful way to understand how the signal was attenuated during transmission. In the PD state, the amplitude range of TH was larger in the case where the amplitude of GPi exceeds −70, compared to the normal state (Figures 13A,B). More specifically, the values that could be obtained were very scattered, and there was no specific regular pattern. That is to say, it could not accurately determine the value of TH, causing TH to fail to respond correctly to the output of GPi. These results indicated that there was a problem with the channel GPi-thalamic of the signal output of the basal ganglia. However, when the dendritic spines lost or the dendrites trees degraded to a certain proportion (Figures 13C,D), the phase diagram was basically similar to the normal. That is, thalamus could correctly respond to the inhibition of GPi, thereby slowing down the functional disorder of the GPi-thalamic channel caused by the denaturation of dopaminergic neurons.

The loss of dendritic spines is to help confront dopamine depletion, but also at a cost. With the dendritic spines loss, the density of spines on which dopamine receptor binding points are normally located decreased. This would render a Parkinson's disease patient less response to L-dopa (Deutch, 2006), are there any other interventions that prevent MSN morphology change? Early reports suggested that prolonged blockade of excitatory transmission in vivo led to an increase in the density of dendritic spines (Rocha and Sur, 1995). Observations made by Neely et al. who found that spine density and the length of stubby spines had a significant increase in decortication cultures (Neely et al., 2007). They also observed that there were no morphology changes of MSN in cultures where the cortex was stripped when the dopamine was depleted. These findings all supported the hypothesis proposed by Deutch et al. that the cortical played an important role in dopamine-depletion induced degeneration in dendritic spines. Our calculation model showed that the appropriate adjustment of the cortical stimulus intensity and stimulus frequency could restore the basal ganglia to normal function. It was thus stated that proper adjustments to cortical activity did stop the changes in dendritic spines induced by dopamine depleted. These results suggested that modifying cortical drived onto MSN could prevent the decreased responsiveness to L-dopa medical treatment induced by the loss of spines in process of PD, thus leading to effective therapeutics for late-stage parkinsonism. Therefore, our study about cortical activity might provide a new idea on novel clinical therapeutic strategies for Parkinson's disease.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.