. Author manuscript; available in PMC: 2013 May 1.

Published in final edited form as: J Comput Neurosci. 2011 Oct 5;32(3):499–519. doi: 10.1007/s10827-011-0366-4

Table 6.

Differences between original Rubin and Terman Model and modified basal ganglia model

Original Rubin and Terman model
(2004)

Modified BG model

Thalamic model

I_K

E_K = −90

E_K = −75

I_T

τ_{r} (v) = 28 + exp (- \frac{v + 25}{10.5})

τ_{r} (v) = 0.15 [28 + exp (- \frac{v + 25}{10.5})]

STN model

I_T

τ_{r} (v) = 40 + 17.5 / [1 + exp (- \frac{v + 68}{- 2.2})]

τ_{r} (v) = 7.1 + 17.5 / [1 + exp (- \frac{v + 68}{- 2.2})]

I_ca

\begin{matrix} I_{ca} = g_{ca} S_{\infty} {(v)}^{2} (v - E_{ca}) \\ S_{\infty} (v) = 1 / [1 + exp (- \frac{v + 39}{8})] \\ g_{ca} = 0.5 \end{matrix}

\begin{array}{l} I_{ca} = g_{ca} c^{2} (v - E_{ca}) \\ c_{\infty} (v) = 1 / [1 + exp (- \frac{v + 20}{8})] \\ τ_{c} (v) = 1 + 10 / [1 + exp (\frac{v + 80}{26})] \\ g_{ca} = 2 \end{array}

I_ahp

g_ahp = 9

g_ahp = 20

GP model

I_L

E_L = −55

E_L = −65

I_ahp

\begin{array}{l} I_{ahp} = g_{ahp} (v - E_{ahp}) (\frac{CA}{CA + 30}) \\ g_{ahp} = 30 \end{array}

\begin{array}{l} I_{ahp} = g_{ahp} (v - E_{ahp}) (\frac{CA}{CA + 10}) \\ g_{ahp} = 10 \end{array}

Applied constant currents

I_{app_stn} = 25
I_{app_gpe} = 2/2.2 (healthy/PD)
I_{app_gpi} = 5

I_{app_stn} = 33/23 (healthy/PD)
I_{app_gpe} = 21/8 (healthy/PD)
I_{app_gpi} = 22/16 (healthy/PD)

Synaptic currents

I_syn = g_synS(v − E_syn)
For all synaptic connections,

\begin{array}{l} \frac{dS}{dt} = 2 (1 - S) H_{\infty} (v - 20) - 0.04 S \\ H_{\infty} (v) = 1 / [1 + exp (- \frac{V + 57}{2})] \end{array}

I_syn = g_synS(v − E_syn)
For STN→GPe, STN→GPi, GPi→TH (alpha synapse),

\begin{array}{l} \frac{dS}{dt} = z \\ \frac{dz}{dt} = 0.234 u (t) - 0.4 z - 0.04 S \end{array}

u(t)=1 if the presynaptic cell crosses a threshold of −10mV at time t, indicating the presence of an action potential in the presynaptic cell. Otherwise, u(t)=0.

For GPe→STN, GPe→GPi, GPe→GPe,

\begin{array}{l} \frac{dS}{dt} = 2 (1 - S) H_{\infty} (v - 20) - 0.04 S \\ H_{\infty} (v) = 1 / [1 + exp (- \frac{V + 57}{2})] \end{array}

g_STN→GPe = 0.3
g_STN→GPi = 0.3
g_GPe→STN = 0.9
g_GPe→GPe = 1.2/1 (healthy/PD)
g_GPe→GPi = 1
g_GPi→TH = 0.06

g_STN→GPe = 0.15
g_STN→GPi = 0.15
g_GPe→STN = 0.5
g_GPe→GPe = 0.5
g_GPe→GPi = 0.5
g_GPi→TH = 0.17

E_STN→GPe = 0
E_STN→GPi = 0
E_GPe→STN = −100
E_GPe→GPe = −80
E_GPe→GPi = −100
E_GPi→TH = −85

E_STN→GPe = 0
E_STN→GPi = 0
E_GPe→STN = −85
E_GPe→GPe = −85
E_GPe→GPi = −85
E_GPi→TH = −85

Connections

3 STN →1 GPe
1 STN →1 GPi
2 GPe →1 STN
2 GPe →1 GPe
2 GPe →1 GPi
8 GPi →1 TH

2 STN →1 GPe
2 STN →1 GPi
2 GPe →1 STN
2 GPe →1 GPe
2 GPe →1 GPi
1 GPi →1 TH