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Supplementary Information for “Break-up and Recovery
of Harmony between Direct and Indirect Pathways in The
Basal Ganglia; Huntington’s Disease and Treatment”
Sang-Yoon Kim ·Woochang Lim
Abstract This is the Supplementary Information (SI) for “Break-up and Recovery
of Harmony between Direct and Indirect Pathways in The Basal Ganglia; Hunt-
ington’s Disease and Treatment.” In this SI, we briefly describe a spiking neural
network of the basal ganglia, considered in our recent work (Kim and Lim, 2023).
1 Spiking Neural Network for The Basal Ganglia
Recently, based on the spiking neural networks for the basal ganglia (BG) devel-
oped in previous works (Humphries et al., 2009; Tomkins et al., 2014; Fountas
and Shanahan, 2017), we made refinements on the BG spiking neural network to
become satisfactory for our study to quantify harmony between direct and indirect
pathways for the healthy and Parkinsonian states (Kim and Lim, 2023). Details
on the BG spiking neural network are given in Sec. 2 and Appendices in (Kim and
Lim, 2023). Here, we make brief description on the BG spiking neural network;
for more details, refer to Sec. 2 and Appendices in (Kim and Lim, 2023).
Figure 1 shows a box diagram of major neurons and synaptic connections in
the BG spiking neural network. Based on the anatomical property of the BG
(Oorschot, 1996; Bar-Gad et al., 2003; Mailly et al., 2003; Sadek et al., 2007), we
consider the BG spiking neural network, composed of D1/D2 spine projection neu-
rons (SPNs), subthalamic nucleus (STN) neurons, globus pallidus (GP) neurons,
and substantia nigra pars reticulata (SNr) neurons. For more details on the num-
bers of the BG cells and their synaptic connection probabilities, refer to Sec. IIA
and Tables I and II in (Kim and Lim, 2023).
S.-Y. Kim
Institute for Computational Neuroscience and Department of Science Education, Daegu Na-
tional University of Education, Daegu 42411, Korea
E-mail: sykim@icn.re.kr
W. Lim (corresponding author)
Institute for Computational Neuroscience and Department of Science Education, Daegu Na-
tional University of Education, Daegu 42411, Korea
Tel.: +82-53-620-1348
Fax: +82-53-620-1525
E-mail: wclim@icn.re.kr

2 Sang-Yoon Kim, Woochang Lim
D
2
SPN
Basal Ganglia
SNr
D
1
SPN
GP
Thalamus/
Brainstem
DA Modulated; Excitatory; Inhibitory
Striatum
STN
Cerebral
Cortex
Fig. 1 Box diagram of our spiking neural network for the basal ganglia (BG). Excitatory
and inhibitory connections are denoted by lines with triangles and circles, respectively, and
dopamine-modulated cells and connections are represented in blue color. Striatum and STN
(subthalamic nucleus), receiving the excitatory cortical input, are two input nuclei to the BG.
In the striatum, there are two kinds of inhibitory spine projection neurons (SPNs); SPNs
with the D1 receptors (D1 SPNs) and SPNs with D2 receptors (D2 SPNs). The D1 SPNs
make direct inhibitory projection to the output nuclei SNr (substantia nigra pars reticulata)
through the direct pathway (DP; green color). In contrast, the D2 SPNs are connected to the
SNr through the indirect pathway (IP; red color) crossing the GP (globus pallidus) and the
STN. The inhibitory output from the SNr to the thalamus/brainstem is controlled through
competition between the DP and IP.
Next, we make brief descriptions on the single neuron models and the dopamine
(DA) effects in the BG spiking neural network; for details refer to Sec. IIB and
Appendix A in (Kim and Lim, 2023). As the single neuron model, we use the
Izhikevich spiking neuron model (which is not only biologically plausible, but
also computationally efficient) as the elements of the BG spiking neural network
(Izhikevich, 2003, 2004, 2007a,b). The BG spiking neural network consists of 5
populations of D1/D2 SPNs, the STN, the GP, and the SNr; for parameter val-
ues of each BG cells, refer to Table III in (Kim and Lim, 2023). The modulation
effect of dopamine (DA) on the D1/D2 SPNs are also considered (Humphries et
al., 2009; Tomkins et al., 2014; Fountas and Shanahan, 2017). For details, refer to
Sec. IIB, Appendix A, and Table IV in (Kim and Lim, 2023).
The state of a neuron in each population is characterized by its membrane
potential and slow recovery variable. Time-evolution of the membrane potential
and the slow recovery variable is governed by 3 kinds of currents into the neuron
such as the external current from the external background region, the synaptic
current, and the injected stimulation current. Here, we consider the case of no
injected stimulation current. The external current is modeled in terms of sponta-
neous (in-vivo) current (to get the spontaneous in-vivo firing rate) and random
background input; for more details, refer to Sec. IIB, Appendix A, and Table V in
(Kim and Lim, 2023).

Supplementary Information 3
Finally, we consider the synaptic currents and the DA effects; detailed expla-
nations are given in Sec. IIB and Appendix B in (Kim and Lim, 2023). There are 3
kinds of synaptic currents from a presynaptic source population to a postsynaptic
neuron in the target population; 2 kinds of excitatory AMPA and NMDA receptor-
mediated synaptic currents and one type of inhibitory GABA receptor-mediated
synaptic current. For each R(AMPA, NMDA, and GABA) receptor-mediated
synaptic current, the synaptic conductance is given by a product of the maximum
synaptic conductance, the average number of afferent synapses, and the fraction of
open postsynaptic ion channels. The time course of fraction of open ion channels is
provided by a sum of exponential functions over presynaptic spikes. The synaptic
parameters are given in Table VI in (Kim and Lim, 2023). These synaptic param-
eter values are based on physiological property (Park et al., 1982; Nakanishi et
al., 1990; Fujimoto and Kita, 1993; G´ongora-Alfaro et al., 1997; G¨otz et al., 1997;
Richards et al., 1997; Bevan and Wilson, 1999; Bevan et al., 2000; Dayan and Ab-
bott, 2001; Bevan et al., 2002; Liu et al., 2022; Hallworth et al., 2003; Baufreton et
al., 2005; Wolf et al., 2005; Shen and Johnson, 2006; Moyer et al., 2007; Gertler et
al., 2008; Bugaysen et al., 2010; Connelly et al., 2010; Ammari et al., 2011). The
modulation effect of DA on afferent synapses into the D1/D2 SPNs, the STN, and
the GP is also taken into consideration (Humphries et al., 2009; Tomkins et al.,
2014; Fountas and Shanahan, 2017); for details, refer to Table VII in (Kim and
Lim, 2023).
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