Activity patterns in a subthalamopallidal network of the basal ganglia model (Terman et al 2002)

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Accession:182758
"Based on recent experimental data, we have developed a conductance-based computational network model of the subthalamic nucleus and the external segment of the globus pallidus in the indirect pathway of the basal ganglia. Computer simulations and analysis of this model illuminate the roles of the coupling architecture of the network, and associated synaptic conductances, in modulating the activity patterns displayed by this network. Depending on the relationships of these coupling parameters, the network can support three general classes of sustained firing patterns: clustering, propagating waves, and repetitive spiking that may show little regularity or correlation. ...". Terman's XPP code and a partial implementation by Taylor Malone in NEURON and python are included.
Reference:
1 . Terman D, Rubin JE, Yew AC, Wilson CJ (2002) Activity patterns in a model for the subthalamopallidal network of the basal ganglia. J Neurosci 22:2963-76 [PubMed]
Citations  Citation Browser
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Basal ganglia;
Cell Type(s): Subthalamic nucleus principal GABA cell; Globus pallidus principal GABA cell; Subthalamus nucleus projection neuron; Globus pallidus neuron;
Channel(s): I K; I Na,t; I T low threshold; I Calcium; I_AHP;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: XPP; NEURON; Python;
Model Concept(s): Activity Patterns; Spatio-temporal Activity Patterns; Parkinson's;
Implementer(s): Terman, David [terman at math.ohio-state.edu]; Malone, Taylor ;
Search NeuronDB for information about:  Globus pallidus principal GABA cell; Subthalamic nucleus principal GABA cell; I Na,t; I T low threshold; I K; I Calcium; I_AHP;
## Set file for model.ode on Thu May 17 09:27:33 2001
120   Number of equations and auxiliaries
103   Number of parameters
# Numerical stuff
1    nout
40    nullcline mesh
8   Qual RK
1999  total
0.4  DeltaT
0  T0
0  Transient
5000  Bound
1e-12  DtMin
1  DtMax
0.001  Tolerance
0.01  Abs. Tolerance
0  Max Delay
100   Eigenvector iterates
0.001  Eigenvector tolerance
0.001  Newton tolerance
0  Poincare plane
1e-05  Boundary value tolerance
1e-05  Boundary value epsilon
20   Boundary value iterates
0   Poincare None
1   Poincare variable
1   Poincare sign
0   Stop on Section
0   Delay flag
1998.8  Current time
1998.8  Last Time
1   MyStart
1   INFLAG
# Delays
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
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0.0
0.0
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0.0
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0.0
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0.0
0.0
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0.0
0.0
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0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
# Bndry conds
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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# Old ICs
-59.62828421888404  V1
-61.0485669306943  V2
-59.9232859246653  V3
-58.70506521874258  V4
-59.81316532105502  V5
-60.41737514151719  V6
-60.57000688576042  V7
-60.77581472006873  V8
-59.72163362685856  V9
-59.20177081754847  V10
0.5063486245631907  H1
0.2933274739456392  H2
0.4828268896903307  H3
0.5957938758715363  H4
0.4801708406464686  H5
0.397555659151211  H6
0.3761635970127477  H7
0.3316364917935809  H8
0.4881964058107033  H9
0.5373898124788108  H10
0.0301468039831072  N1
0.04412485475791555  N2
0.02936940165051648  N3
0.03307223867110721  N4
0.02961425249063069  N5
0.02990618866753074  N6
0.03096707115136645  N7
0.03603641291454053  N8
0.02983123244237023  N9
0.03137696787429014  N10
0.0295473069771012  R1
0.07318677802595788  R2
0.03401991571903244  R3
0.01899268957583912  R4
0.0322092810112401  R5
0.04490215539151968  R6
0.0496024428039565  R7
0.05982606979469521  R8
0.03078507359379932  R9
0.02403333448524015  R10
0.2994323366425385  CA1
0.4076730264403847  CA2
0.3271760563827424  CA3
0.2456039126383157  CA4
0.3090126869287847  CA5
0.3533066857313201  CA6
0.3668697913124569  CA7
0.3777575381495549  CA8
0.3008309498107221  CA9
0.2631312497961643  CA10
0.008821617722180833  S1
0.007400276913597601  S2
0.00850582621763913  S3
0.009886276645187469  S4
0.00862235586166425  S5
0.008001611992658621  S6
0.007851916739337694  S7
0.007654426383227644  S8
0.008720434017133022  S9
0.009298664650592724  S10
-67.82599080345415  VG1
-67.93189025010138  VG2
-67.71998331113508  VG3
-67.642675227932  VG4
-67.84176237771105  VG5
-68.20005240297162  VG6
-68.25008741948682  VG7
-67.96902996444675  VG8
-67.94128590225782  VG9
-67.90220199361714  VG10
0.2185706578168535  NG1
0.2172726252685865  NG2
0.2198825985895934  NG3
0.2208386365344371  NG4
0.218376554433867  NG5
0.2139920161919114  NG6
0.2133851309251945  NG7
0.2168122919020363  NG8
0.2171513971203313  NG9
0.2176303246979667  NG10
0.6941693982604106  HG1
0.6960525186649159  HG2
0.6922676967009093  HG3
0.6908829096175084  HG4
0.694450894176868  HG5
0.7008187424839692  HG6
0.701701517982433  HG7
0.6967207207137638  HG8
0.6962284698338927  HG9
0.6955334306358607  HG10
0.2573659658746555  RG1
0.267633438957204  RG2
0.2467211480536698  RG3
0.2393102961633564  RG4
0.25894821881624  RG5
0.29699756425809  RG6
0.3026979450078091  RG7
0.2718222561955378  RG8
0.2692289296543874  RG9
0.265227594196562  RG10
0.009931221391373412  CAG1
0.01105798337560691  CAG2
0.008618198042586294  CAG3
0.007842254082952149  CAG4
0.01009947181199855  CAG5
0.01439779182000786  CAG6
0.01499734401485086  CAG7
0.01153249037272892  CAG8
0.01131645351818554  CAG9
0.01090747666531076  CAG10
5.005384170945523e-06  SG1
4.742408605511108e-06  SG2
5.285062432830586e-06  SG3
5.496855711727898e-06  SG4
4.965314879070837e-06  SG5
4.134036862962592e-06  SG6
4.035693901984886e-06  SG7
4.652783831094474e-06  SG8
4.718489668449042e-06  SG9
4.813260429223516e-06  SG10
# Ending  ICs
-59.57916405433269  V1
-59.32084399762631  V2
-59.15543713125109  V3
-58.69698303986357  V4
-59.9971684612461  V5
-59.67635184530259  V6
-58.7288281491014  V7
-59.8600739939977  V8
-59.66954715854156  V9
-58.93085441090744  V10
0.459276804100721  H1
0.5239177265928148  H2
0.5411940123261303  H3
0.5915775908879864  H4
0.4386686262060252  H5
0.4898865176575397  H6
0.5943888417428496  H7
0.4372005328199611  H8
0.4949485566620549  H9
0.5558068787463094  H10
0.03079938891295496  N1
0.03098859890825655  N2
0.03153229066036133  N3
0.03313126382081862  N4
0.02982252058208219  N5
0.03005278823126852  N6
0.0329876359643384  N7
0.03030758180810951  N8
0.02998452523226201  N9
0.03234682187942989  N10
0.02964000072038302  R1
0.0253923832830916  R2
0.02352139773776181  R3
0.02032668142727715  R4
0.03614208533769497  R5
0.03032716545717655  R6
0.02056603300831896  R7
0.03410317644901437  R8
0.03006029289624212  R9
0.02130888979763192  R10
0.2616013638856305  CA1
0.2695142934529187  CA2
0.2600823732235614  CA3
0.2417666910578375  CA4
0.3108228833832617  CA5
0.2957396252844021  CA6
0.2473611460047318  CA7
0.2887235412626885  CA8
0.2980877757721034  CA9
0.2427888052840327  CA10
0.008875191662178619  S1
0.00916298894884803  S2
0.009352002803110574  S3
0.009896124901955773  S4
0.008428442346197962  S5
0.008769372124419654  S6
0.009857376591649324  S7
0.008572451382170148  S8
0.008776758396063336  S9
0.009614741056619277  S10
-68.02274515218379  VG1
-68.09962348449929  VG2
-67.80494865493337  VG3
-67.92141882449256  VG4
-67.94568917897634  VG5
-67.8201247157854  VG6
-67.59449886858869  VG7
-67.98660964933171  VG8
-67.74605990791041  VG9
-67.85592126037155  VG10
0.2161521551110782  NG1
0.2152119876770614  NG2
0.2188290459900804  NG3
0.2173922836007159  NG4
0.2170980050541124  NG5
0.2186431848455794  NG6
0.2214384064195788  NG7
0.2165955660567451  NG8
0.2195588649318608  NG9
0.2181993187413597  NG10
0.697679289906415  HG1
0.6990451704949732  HG2
0.6937947287574034  HG3
0.6958788594263219  HG4
0.6963059676069604  HG5
0.6940642258528641  HG6
0.6900146069344422  HG7
0.6970353793980896  HG8
0.6927368092818508  HG9
0.694707958939624  HG10
0.277832986085601  RG1
0.2861114964628164  RG2
0.2552931037755137  RG3
0.2672870574417694  RG4
0.2696924011339038  RG5
0.2567640876869912  RG6
0.2346764643675696  RG7
0.2739519683210631  RG8
0.2493324569918534  RG9
0.2605051279989134  RG10
0.01232557320013942  CAG1
0.01329837600091031  CAG2
0.009736485226497569  CAG3
0.01120826803046665  CAG4
0.01133684499142997  CAG5
0.009854500091955844  CAG6
0.007261217799082016  CAG7
0.01185075458176713  CAG8
0.008962128589565438  CAG9
0.01038230074346499  CAG10
4.525579594462597e-06  SG1
4.350690343990838e-06  SG2
5.059017241706827e-06  SG3
4.765432495794544e-06  SG4
4.708271299392121e-06  SG5
5.0204989055464e-06  SG6
5.634296219273492e-06  SG7
4.610377062914126e-06  SG8
5.214630193897208e-06  SG9
4.928325425249593e-06  SG10
# Parameters
-60  vl
55  vna
-80  vk
30  thetam
15  sm
2.25  gl
37.5  gna
45  gk
1  tn
0.05  th
9  gahp
0.5  gca
140  vca
15  k1
5e-05  eps
22.5  kca
39  thetas
8  ss
1  xp
0  i
-39  thetah
3.1  sh
-32  thetan
-8  sn
1  taun0
100  taun1
80  thn
26  sigman
1  tauh0
500  tauh1
57  thh
3  sigmah
0.75  phi
-63  thetat
-7.8  kt
0.5  gt
0.5  phir
-67  thetar
2  kr
7.1  taur0
17.5  taur1
-68  thr
2.2  sigmar
0.01  eps1
-60  root1
-40  root2
-10  root3
-35  root4
0.6  add
10000  scale
1  gd
5  alpha
1  beta
-30  ab
2.5  gGtoS
-100  vsyn
0.25  rth
-0.07000000000000001  rsig
120  gnag
30  gkg
30  gahpg
0.5  gtg
0.15  gcag
0.1  glg
55  vnag
-80  vkg
120  vcag
-55  vlg
-57  thetasg
2  ksg
-35  thetas1g
2  ks1g
-70  thetarg
-2  krg
30  taurg
-37  thetamg
10  sigmamg
-50  thetang
14  sigmang
0.05  taun0g
0.27  taun1g
-40  thng
-12  sng
-58  thetahg
-12  sigmahg
0.05  tauh0g
0.27  tauh1g
-40  thhg
-12  shg
30  k1g
20  kcag
0.0001  epsg
1  phig
0.05  deltang
0.05  deltahg
-1.2  iapp
0  gGtoG
-100  vsyngg
0.016  gStoG
0  vsyng
2  alphag
0.08  betag
-20  abg
# Graphics
0.7071097251469876  rm
-0.4999999999826661  rm
0.4999958366025518  rm
0.7071038372138506  rm
0.5000041633974482  rm
-0.4999999999826661  rm
0  rm
0.7071038372138506  rm
0.7071097251469876  rm
0    
6    
2    
1    
0    
0    
5    
2    
1    
0    
0    
5    
2    
1    
0    
0    
5    
2    
1    
0    
0    
5    
2    
1    
0    
0    
5    
2    
1    
0    
0    
5    
2    
1    
0    
0    
5    
2    
1    
0    
0    
5    
2    
1    
0    
0    
5    
2    
1    
0    
-1000   
1000   
0    
0   3DFlag
1   Timeflag
0   Colorflag
0   Type
1  color scale
0   minscale
1998.800048828125   xmax
0   xmin
44.52481460571289   ymax
-85.00526428222656   ymin
12   zmax
-12   zmin
999.4000244140625   
0.001000600335772745   
-20.24022483825684   
0.0154404291047353   
0   
0.08333333333333333   
45   Theta
45   Phi
0    xshft
0    yshft
0    zshft
0   xlo
-85.00526428222656   ylo
0   
-80   
1998.800048828125   xhi
44.52481460571289   yhi
1000   
20   
# Transpose variables etc
V1
2   n columns
1   n rows
1   row skip
1   col skip
1   row 0
# Coupling stuff for H funs
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
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0
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0
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0
0
0
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0
0
0
0
0
0
0
0
0
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0
0
0
0
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0
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0
0
0
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0
0
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0
0
0
0
0
0
0
0
0
0
# Array plot stuff

1   NCols
0   Row 1
50   NRows
8   RowSkip
0  Zmin
1  Zmax
# Torus information 
0    Torus flag 1=ON
6.283185307179586  Torus period
# Range information
vl
-1   eq-range stab col
0   shoot flag 1=on
10   eq-range steps
0  eq_range low
1  eq_range high
V1
V1
20   Range steps
0   Cycle color 1=on
1   Reset data 1=on
1   Use old I.C.s 1=yes
0  Par1 low
0  Par2 low
1  Par1 high
1  Par2 high
vl
0   BVP side
0   color cycle flag 1=on
10   BVP range steps
0  BVP range low
1  BVP range high
RHS etc ...
dV1/dT=-(IL(V1)+INA(V1,H1)+IK(V1,N1)+IAHP(V1,CA1)+ICA(V1)+IT(V1,R1))-ISYN1
dV2/dT=-(IL(V2)+INA(V2,H2)+IK(V2,N2)+IAHP(V2,CA2)+ICA(V2)+IT(V2,R2))-ISYN2
dV3/dT=-(IL(V3)+INA(V3,H3)+IK(V3,N3)+IAHP(V3,CA3)+ICA(V3)+IT(V3,R3))-ISYN3
dV4/dT=-(IL(V4)+INA(V4,H4)+IK(V4,N4)+IAHP(V4,CA4)+ICA(V4)+IT(V4,R4))-ISYN4
dV5/dT=-(IL(V5)+INA(V5,H5)+IK(V5,N5)+IAHP(V5,CA5)+ICA(V5)+IT(V5,R5))-ISYN5
dV6/dT=-(IL(V6)+INA(V6,H6)+IK(V6,N6)+IAHP(V6,CA6)+ICA(V6)+IT(V6,R6))-ISYN6
dV7/dT=-(IL(V7)+INA(V7,H7)+IK(V7,N7)+IAHP(V7,CA7)+ICA(V7)+IT(V7,R7))-ISYN7
dV8/dT=-(IL(V8)+INA(V8,H8)+IK(V8,N8)+IAHP(V8,CA8)+ICA(V8)+IT(V8,R8))-ISYN8
dV9/dT=-(IL(V9)+INA(V9,H9)+IK(V9,N9)+IAHP(V9,CA9)+ICA(V9)+IT(V9,R9))-ISYN9
dV10/dT=-(IL(V10)+INA(V10,H10)+IK(V10,N10)+IAHP(V10,CA10)+ICA(V10)+IT(V10,R10))-ISYN10
dH1/dT=PHI*(HINF(V1)-H1)/TAUH(V1)
dH2/dT=PHI*(HINF(V2)-H2)/TAUH(V2)
dH3/dT=PHI*(HINF(V3)-H3)/TAUH(V3)
dH4/dT=PHI*(HINF(V4)-H4)/TAUH(V4)
dH5/dT=PHI*(HINF(V5)-H5)/TAUH(V5)
dH6/dT=PHI*(HINF(V6)-H6)/TAUH(V6)
dH7/dT=PHI*(HINF(V7)-H7)/TAUH(V7)
dH8/dT=PHI*(HINF(V8)-H8)/TAUH(V8)
dH9/dT=PHI*(HINF(V9)-H9)/TAUH(V9)
dH10/dT=PHI*(HINF(V10)-H10)/TAUH(V10)
dN1/dT=PHI*(NINF(V1)-N1)/TAUN(V1)
dN2/dT=PHI*(NINF(V2)-N2)/TAUN(V2)
dN3/dT=PHI*(NINF(V3)-N3)/TAUN(V3)
dN4/dT=PHI*(NINF(V4)-N4)/TAUN(V4)
dN5/dT=PHI*(NINF(V5)-N5)/TAUN(V5)
dN6/dT=PHI*(NINF(V6)-N6)/TAUN(V6)
dN7/dT=PHI*(NINF(V7)-N7)/TAUN(V7)
dN8/dT=PHI*(NINF(V8)-N8)/TAUN(V8)
dN9/dT=PHI*(NINF(V9)-N9)/TAUN(V9)
dN10/dT=PHI*(NINF(V10)-N10)/TAUN(V10)
dR1/dT=PHIR*(RINF(V1)-R1)/TAUR(V1)
dR2/dT=PHIR*(RINF(V2)-R2)/TAUR(V2)
dR3/dT=PHIR*(RINF(V3)-R3)/TAUR(V3)
dR4/dT=PHIR*(RINF(V4)-R4)/TAUR(V4)
dR5/dT=PHIR*(RINF(V5)-R5)/TAUR(V5)
dR6/dT=PHIR*(RINF(V6)-R6)/TAUR(V6)
dR7/dT=PHIR*(RINF(V7)-R7)/TAUR(V7)
dR8/dT=PHIR*(RINF(V8)-R8)/TAUR(V8)
dR9/dT=PHIR*(RINF(V9)-R9)/TAUR(V9)
dR10/dT=PHIR*(RINF(V10)-R10)/TAUR(V10)
dCA1/dT=PHI*EPS*(-ICA(V1)-IT(V1,R1)-KCA*CA1)
dCA2/dT=PHI*EPS*(-ICA(V2)-IT(V2,R2)-KCA*CA2)
dCA3/dT=PHI*EPS*(-ICA(V3)-IT(V3,R3)-KCA*CA3)
dCA4/dT=PHI*EPS*(-ICA(V4)-IT(V4,R4)-KCA*CA4)
dCA5/dT=PHI*EPS*(-ICA(V5)-IT(V5,R5)-KCA*CA5)
dCA6/dT=PHI*EPS*(-ICA(V6)-IT(V6,R6)-KCA*CA6)
dCA7/dT=PHI*EPS*(-ICA(V7)-IT(V7,R7)-KCA*CA7)
dCA8/dT=PHI*EPS*(-ICA(V8)-IT(V8,R8)-KCA*CA8)
dCA9/dT=PHI*EPS*(-ICA(V9)-IT(V9,R9)-KCA*CA9)
dCA10/dT=PHI*EPS*(-ICA(V10)-IT(V10,R10)-KCA*CA10)
dS1/dT=ALPHA*(1-S1)*SINF(V1+AB)-BETA*S1
dS2/dT=ALPHA*(1-S2)*SINF(V2+AB)-BETA*S2
dS3/dT=ALPHA*(1-S3)*SINF(V3+AB)-BETA*S3
dS4/dT=ALPHA*(1-S4)*SINF(V4+AB)-BETA*S4
dS5/dT=ALPHA*(1-S5)*SINF(V5+AB)-BETA*S5
dS6/dT=ALPHA*(1-S6)*SINF(V6+AB)-BETA*S6
dS7/dT=ALPHA*(1-S7)*SINF(V7+AB)-BETA*S7
dS8/dT=ALPHA*(1-S8)*SINF(V8+AB)-BETA*S8
dS9/dT=ALPHA*(1-S9)*SINF(V9+AB)-BETA*S9
dS10/dT=ALPHA*(1-S10)*SINF(V10+AB)-BETA*S10
dVG1/dT=-(ITG(VG1,RG1)+INAG(VG1,HG1)+IKG(VG1,NG1)+IAHPG(VG1,CAG1)+ICAG(VG1)+ILG(VG1))+IAPP-ISYNGG(VG1,STOT)-ISYNG1
dVG2/dT=-(ITG(VG2,RG2)+INAG(VG2,HG2)+IKG(VG2,NG2)+IAHPG(VG2,CAG2)+ICAG(VG2)+ILG(VG2))+IAPP-ISYNGG(VG2,STOT)-ISYNG2
dVG3/dT=-(ITG(VG3,RG3)+INAG(VG3,HG3)+IKG(VG3,NG3)+IAHPG(VG3,CAG3)+ICAG(VG3)+ILG(VG3))+IAPP-ISYNGG(VG3,STOT)-ISYNG3
dVG4/dT=-(ITG(VG4,RG4)+INAG(VG4,HG4)+IKG(VG4,NG4)+IAHPG(VG4,CAG4)+ICAG(VG4)+ILG(VG4))+IAPP-ISYNGG(VG4,STOT)-ISYNG4
dVG5/dT=-(ITG(VG5,RG5)+INAG(VG5,HG5)+IKG(VG5,NG5)+IAHPG(VG5,CAG5)+ICAG(VG5)+ILG(VG5))+IAPP-ISYNGG(VG5,STOT)-ISYNG5
dVG6/dT=-(ITG(VG6,RG6)+INAG(VG6,HG6)+IKG(VG6,NG6)+IAHPG(VG6,CAG6)+ICAG(VG6)+ILG(VG6))+IAPP-ISYNGG(VG6,STOT)-ISYNG6
dVG7/dT=-(ITG(VG7,RG7)+INAG(VG7,HG7)+IKG(VG7,NG7)+IAHPG(VG7,CAG7)+ICAG(VG7)+ILG(VG7))+IAPP-ISYNGG(VG7,STOT)-ISYNG7
dVG8/dT=-(ITG(VG8,RG8)+INAG(VG8,HG8)+IKG(VG8,NG8)+IAHPG(VG8,CAG8)+ICAG(VG8)+ILG(VG8))+IAPP-ISYNGG(VG8,STOT)-ISYNG8
dVG9/dT=-(ITG(VG9,RG9)+INAG(VG9,HG9)+IKG(VG9,NG9)+IAHPG(VG9,CAG9)+ICAG(VG9)+ILG(VG9))+IAPP-ISYNGG(VG9,STOT)-ISYNG9
dVG10/dT=-(ITG(VG10,RG10)+INAG(VG10,HG10)+IKG(VG10,NG10)+IAHPG(VG10,CAG10)+ICAG(VG10)+ILG(VG10))+IAPP-ISYNGG(VG10,STOT)-ISYNG10
dNG1/dT=DELTANG*(NINFG(VG1)-NG1)/TAUNG(VG1)
dNG2/dT=DELTANG*(NINFG(VG2)-NG2)/TAUNG(VG2)
dNG3/dT=DELTANG*(NINFG(VG3)-NG3)/TAUNG(VG3)
dNG4/dT=DELTANG*(NINFG(VG4)-NG4)/TAUNG(VG4)
dNG5/dT=DELTANG*(NINFG(VG5)-NG5)/TAUNG(VG5)
dNG6/dT=DELTANG*(NINFG(VG6)-NG6)/TAUNG(VG6)
dNG7/dT=DELTANG*(NINFG(VG7)-NG7)/TAUNG(VG7)
dNG8/dT=DELTANG*(NINFG(VG8)-NG8)/TAUNG(VG8)
dNG9/dT=DELTANG*(NINFG(VG9)-NG9)/TAUNG(VG9)
dNG10/dT=DELTANG*(NINFG(VG10)-NG10)/TAUNG(VG10)
dHG1/dT=DELTAHG*(HINFG(VG1)-HG1)/TAUHG(VG1)
dHG2/dT=DELTAHG*(HINFG(VG2)-HG2)/TAUHG(VG2)
dHG3/dT=DELTAHG*(HINFG(VG3)-HG3)/TAUHG(VG3)
dHG4/dT=DELTAHG*(HINFG(VG4)-HG4)/TAUHG(VG4)
dHG5/dT=DELTAHG*(HINFG(VG5)-HG5)/TAUHG(VG5)
dHG6/dT=DELTAHG*(HINFG(VG6)-HG6)/TAUHG(VG6)
dHG7/dT=DELTAHG*(HINFG(VG7)-HG7)/TAUHG(VG7)
dHG8/dT=DELTAHG*(HINFG(VG8)-HG8)/TAUHG(VG8)
dHG9/dT=DELTAHG*(HINFG(VG9)-HG9)/TAUHG(VG9)
dHG10/dT=DELTAHG*(HINFG(VG10)-HG10)/TAUHG(VG10)
dRG1/dT=PHIG*(RINFG(VG1)-RG1)/TAURG
dRG2/dT=PHIG*(RINFG(VG2)-RG2)/TAURG
dRG3/dT=PHIG*(RINFG(VG3)-RG3)/TAURG
dRG4/dT=PHIG*(RINFG(VG4)-RG4)/TAURG
dRG5/dT=PHIG*(RINFG(VG5)-RG5)/TAURG
dRG6/dT=PHIG*(RINFG(VG6)-RG6)/TAURG
dRG7/dT=PHIG*(RINFG(VG7)-RG7)/TAURG
dRG8/dT=PHIG*(RINFG(VG8)-RG8)/TAURG
dRG9/dT=PHIG*(RINFG(VG9)-RG9)/TAURG
dRG10/dT=PHIG*(RINFG(VG10)-RG10)/TAURG
dCAG1/dT=EPSG*(-ICAG(VG1)-ITG(VG1,RG1)-KCAG*CAG1)
dCAG2/dT=EPSG*(-ICAG(VG2)-ITG(VG2,RG2)-KCAG*CAG2)
dCAG3/dT=EPSG*(-ICAG(VG3)-ITG(VG3,RG3)-KCAG*CAG3)
dCAG4/dT=EPSG*(-ICAG(VG4)-ITG(VG4,RG4)-KCAG*CAG4)
dCAG5/dT=EPSG*(-ICAG(VG5)-ITG(VG5,RG5)-KCAG*CAG5)
dCAG6/dT=EPSG*(-ICAG(VG6)-ITG(VG6,RG6)-KCAG*CAG6)
dCAG7/dT=EPSG*(-ICAG(VG7)-ITG(VG7,RG7)-KCAG*CAG7)
dCAG8/dT=EPSG*(-ICAG(VG8)-ITG(VG8,RG8)-KCAG*CAG8)
dCAG9/dT=EPSG*(-ICAG(VG9)-ITG(VG9,RG9)-KCAG*CAG9)
dCAG10/dT=EPSG*(-ICAG(VG10)-ITG(VG10,RG10)-KCAG*CAG10)
dSG1/dT=ALPHAG*(1-SG1)*SINFG(VG1+ABG)-BETAG*SG1
dSG2/dT=ALPHAG*(1-SG2)*SINFG(VG2+ABG)-BETAG*SG2
dSG3/dT=ALPHAG*(1-SG3)*SINFG(VG3+ABG)-BETAG*SG3
dSG4/dT=ALPHAG*(1-SG4)*SINFG(VG4+ABG)-BETAG*SG4
dSG5/dT=ALPHAG*(1-SG5)*SINFG(VG5+ABG)-BETAG*SG5
dSG6/dT=ALPHAG*(1-SG6)*SINFG(VG6+ABG)-BETAG*SG6
dSG7/dT=ALPHAG*(1-SG7)*SINFG(VG7+ABG)-BETAG*SG7
dSG8/dT=ALPHAG*(1-SG8)*SINFG(VG8+ABG)-BETAG*SG8
dSG9/dT=ALPHAG*(1-SG9)*SINFG(VG9+ABG)-BETAG*SG9
dSG10/dT=ALPHAG*(1-SG10)*SINFG(VG10+ABG)-BETAG*SG10

where ...
ISYN1 = GSYN*(SG10+SG2)*(V1-VSYN)   
ISYN2 = GSYN*(SG7+SG9)*(V2-VSYN)   
ISYN3 = GSYN*(SG4+SG6)*(V3-VSYN)   
ISYN4 = GSYN*(SG5+SG3)*(V4-VSYN)   
ISYN5 = GSYN*(SG1+SG8)*(V5-VSYN)   
ISYN6 = GSYN*(SG2+SG9)*(V6-VSYN)   
ISYN7 = GSYN*(SG5+SG6)*(V7-VSYN)   
ISYN8 = GSYN*(SG1+SG7)*(V8-VSYN)   
ISYN9 = GSYN*(SG4+SG10)*(V9-VSYN)   
ISYN10 = GSYN*(SG3+SG8)*(V10-VSYN)   
ISYNG1 = GSYNG*S1*(VG1-VSYNG)   
ISYNG2 = GSYNG*S2*(VG2-VSYNG)   
ISYNG3 = GSYNG*S3*(VG3-VSYNG)   
ISYNG4 = GSYNG*S4*(VG4-VSYNG)   
ISYNG5 = GSYNG*S5*(VG5-VSYNG)   
ISYNG6 = GSYNG*S6*(VG6-VSYNG)   
ISYNG7 = GSYNG*S7*(VG7-VSYNG)   
ISYNG8 = GSYNG*S8*(VG8-VSYNG)   
ISYNG9 = GSYNG*S9*(VG9-VSYNG)   
ISYNG10 = GSYNG*S10*(VG10-VSYNG)   
STOT = SG1+SG2+SG3+SG4+SG5+SG6+SG7+SG8+SG9+SG10   

User-defined functions:
SINF(V) = 1./(1.+EXP(-(V+THETAS)/SS))  
MINF(V) = 1./(1.+EXP(-(V+THETAM)/SM))  
HINF(V) = 1./(1.+EXP((V-THETAH)/SH))  
NINF(V) = 1./(1.+EXP((V-THETAN)/SN))  
TAUN(V) = TAUN0+TAUN1/(1+EXP((V+THN)/SIGMAN))  
TAUH(V) = TAUH0+TAUH1/(1+EXP((V+THH)/SIGMAH))  
RINF(V) = 1/(1+EXP((V-THETAR)/KR))  
TAUR(V) = TAUR0+TAUR1/(1+EXP((V+THR)/SIGMAR))  
TINF(V) = 1/(1+EXP((V-THETAT)/KT))  
RNEW(R) = 1/(1+EXP((R-RTH)/RSIG))-1/(1+EXP(-RTH/RSIG))  
SINFG(VG) = 1/(1+EXP(-(VG-THETASG)/KSG))  
SINF1G(VG) = 1/(1+EXP(-(VG-THETAS1G)/KS1G))  
RINFG(VG) = 1/(1+EXP(-(VG-THETARG)/KRG))  
MINFG(VG) = 1./(1.+EXP(-(VG-THETAMG)/SIGMAMG))  
NINFG(VG) = 1./(1.+EXP(-(VG-THETANG)/SIGMANG))  
TAUNG(VG) = TAUN0G+TAUN1G/(1+EXP(-(VG-THNG)/SNG))  
HINFG(VG) = 1./(1.+EXP(-(VG-THETAHG)/SIGMAHG))  
TAUHG(VG) = TAUH0G+TAUH1G/(1+EXP(-(VG-THHG)/SHG))  
IL(V) = GL*(V-VL)  
INA(V,H) = GNA*(MINF(V))^3*H*(V-VNA)  
IK(V,N) = GK*N^4*(V-VK)  
IAHP(V,CA) = GAHP*(V-VK)*CA/(CA+K1)  
ICA(V) = GCA*((SINF(V))^2)*(V-VCA)  
IT(V,R) = GT*(TINF(V)**3)*(RNEW(R)^2)*(V-VCA)  
HVASOD(V,D) = GD*(-(V-ROOT1)*(V-ROOT2)*(V-ROOT3)/SCALE+ADD-D)  
ITG(VG,RG) = GTG*(SINFG(VG)^3)*RG*(VG-VCAG)  
INAG(VG,HG) = GNAG*(MINFG(VG)^3)*HG*(VG-VNAG)  
IKG(VG,NG) = GKG*(NG^4)*(VG-VKG)  
IAHPG(VG,CAG) = GAHPG*(VG-VKG)*CAG/(CAG+K1G)  
ICAG(VG) = GCAG*((SINF1G(VG))^2)*(VG-VCAG)  
ILG(VG) = GLG*(VG-VLG)  
ISYNGG(VG,SG) = GSYNGG*STOT*(VG-VSYNGG)