A model for recurrent spreading depolarizations (Conte et al. 2017)

 Download zip file 
Help downloading and running models
Accession:235377
A detailed biophysical model for a neuron/astrocyte network is developed in order to explore mechanisms responsible for cortical spreading depolarizations. This includes a model for the Na+-glutamate transporter, which allows for a detailed description of reverse glutamate uptake. In particular, we consider the specific roles of elevated extracellular glutamate and K+ in the initiation, propagation and recurrence of spreading depolarizations.
Reference:
1 . Conte C, Lee R, Sarkar M, Terman D (2018) A mathematical model of recurrent spreading depolarizations. J Comput Neurosci 44:203-217 [PubMed]
Citations  Citation Browser
Model Information (Click on a link to find other models with that property)
Model Type: Extracellular; Glia; Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Astrocyte;
Channel(s): I K; I Na,p; I Cl, leak; Na/K pump; Na+-glutamate transporter;
Gap Junctions:
Receptor(s): Glutamate;
Gene(s):
Transmitter(s): Glutamate;
Simulation Environment: XPP;
Model Concept(s): Detailed Neuronal Models; Potassium buffering; Spreading depression; Spreading depolarization;
Implementer(s): Terman, David [terman at math.ohio-state.edu];
Search NeuronDB for information about:  Glutamate; I Na,p; I K; Na/K pump; I Cl, leak; Na+-glutamate transporter; Glutamate;
## Set file for single_cells.ode on Wed Dec 13 10:25:52 2017
19   Number of equations and auxiliaries
72   Number of parameters
# Numerical stuff
1    nout
40    nullcline mesh
8   Qual RK
4000000  total
0.5  DeltaT
0  T0
0  Transient
500000  Bound
1e-12  DtMin
1  DtMax
1e-07  Tolerance
0.001  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
4000000  Current time
4000000  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
# Bndry conds
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
# Old ICs
-58.81137764996264  V
0.432356959113168  N
0.8538036058454112  HP
0.002082416993486555  SG
0.08000000000046259  IMAXA
-39.02998140466573  VA
149.1319593988436  KI
16.41369332787475  KE
1.285281166395606  NAI
116.0901080839575  NAE
71.95968297063686  KIA
66.24314341750998  NAIA
12.52512787448607  CLI
111.3857579081404  CLE
0.004525191854168424  GLUT
0.0009387716976116532  CAI
0.05904737645069838  CAER
2.801142735550066  CAE
0.9981259767393746  HER
# Ending  ICs
-62.52638004813665  V
0.3687463987794178  N
0.9166237311852015  HP
0.3333333333333334  SG
0.08000000000046259  IMAXA
-26.3566736314976  VA
138.9603521990604  KI
10.84005294617766  KE
7.222072086379609  NAI
129.0789158035363  NAE
29.67248554159209  KIA
108.5285057274632  NAIA
11.03269938780366  CLI
112.0102445460947  CLE
0.05796814244940238  GLUT
0.00176875116910499  CAI
0.1920086511206416  CAER
0.1877525063186725  CAE
0.9964749701503084  HER
# Parameters
8310  R
310  Temp
96485  F
1e-05  pna
2e-09  pnal
-34  thm
5  sigm
3e-08  pnap
10000  taubar
-40  thmp
6  sigmp
-48  thhp
-6  sighp
-49  vt
6  sig
0.05  phihp
6.999999999999999e-05  pk
4e-07  pkl
-55  thn
14  sgn
0.05  taun0
0.27  taun1
-40  thnt
-12  sn
0.8  phin
3e-06  pnmda
-10  thetat
2  trise
1  tdecay
0.5  alphag
3  pca
0.01  thg
0.001  sigmag
2e-07  pcl
5  imax
4.8e-06  pka
1.5e-08  pnaa
3e-05  eps
0.08  imin
0.5  hr
3e-05  gnagl
2160  voln
922  s
1600  Sa
2000  vola
0.05  alpha0
1e-05  gnab
2e-05  gkb
6e-06  gclb
140  na0
4  k0
110  cl0
1  glui0
0.001  glut0
60  minute
1000  second
0.3  ip3
0.5  pcytosol
75  dcytosol
0.1  per
1000  der
0.01  fi
3000  vip3
0.01  vleak
0.25  dip3
0.5  dinh
1  dact
4  tau
110  vserca
0.4  kserca
6e-06  gcab
3  cae0
# Graphics
0.7071097251469876  rm
-0.4999999999826661  rm
0.4999958366025516  rm
0.7071038372138505  rm
0.5000041633974482  rm
-0.4999999999826661  rm
0  rm
0.7071038372138505  rm
0.7071097251469876  rm
0    
1    
1    
1    
0    
0    
1    
1    
1    
0    
0    
1    
1    
1    
0    
0    
1    
1    
1    
0    
0    
1    
1    
1    
0    
0    
1    
1    
1    
0    
0    
1    
1    
1    
0    
0    
1    
1    
1    
0    
0    
1    
1    
1    
0    
0    
1    
1    
1    
0    
-1000   
1000   
0    
0   3DFlag
1   Timeflag
0   Colorflag
0   Type
1  color scale
0   minscale
4000000   xmax
0   xmin
0   ymax
-90   ymin
12   zmax
-12   zmin
2000000   
5e-07   
-45   
0.02222222222222222   
0   
0.08333333333333333   
45   Theta
45   Phi
0    xshft
0    yshft
0    zshft
0   xlo
-90   ylo
0   
-80   
4000000   xhi
0   yhi
50000   
0   
# Transpose variables etc
V
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
# 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
R
-1   eq-range stab col
0   shoot flag 1=on
10   eq-range steps
0  eq_range low
1  eq_range high
V
V
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
R
0   BVP side
0   color cycle flag 1=on
10   BVP range steps
0  BVP range low
1  BVP range high
RHS etc ...
dV/dT=-(INA(V,N,NAE,NAI)+INAP(V,HP,NAE,NAI)+IK(V,N,KE,KI)+ICL(V,CLE,CLI)+IPUMP+INMDA)
dN/dT=PHIN*(NINF(V)-N)/TAUN(V)
dHP/dT=PHIHP*(HINFP(V)-HP)/TAUHP(V)
dSG/dT=-SG/TDECAY+ALPHAG*SINFG(GLUT)*(1-SG)
dIMAXA/dT=EPS*(IMIN-IMAXA)
dVA/dT=-(IKA(VA,KE,KIA)+INAA(VA,NAE,NAIA)+IPUMPA(KE,NAIA)+INAGL)
dKI/dT=-CFN*(IK(V,N,KE,KI)+IKPUMP+IKNMDA)
dKE/dT=CFNE*(IK(V,N,KE,KI)+IKPUMP+IKNMDA)+CFAE*(IKA(VA,KE,KIA)-2*IPUMPA(KE,NAIA)-INAGL)+GKB*(K0-KE)
dNAI/dT=-CFN*(INA(V,N,NAE,NAI)+INAP(V,HP,NAE,NAI)+INAPUMP+INANMDA)
dNAE/dT=CFNE*(INA(V,N,NAE,NAI)+INAP(V,HP,NAE,NAI)+INAPUMP+INANMDA)+CFAE*(INAA(VA,NAE,NAIA)+3*IPUMPA(KE,NAIA)+(3)*INAGL)+GNAB*(NA0-NAE)
dKIA/dT=-CFA*(IKA(VA,KE,KIA)-2*IPUMPA(KE,NAIA)-INAGL)
dNAIA/dT=-CFA*(INAA(VA,NAE,NAIA)+3*IPUMPA(KE,NAIA)+(3)*INAGL)
dCLI/dT=CFN*ICL(V,CLE,CLI)
dCLE/dT=-CFNE*ICL(V,CLE,CLI)+GCLB*(CL0-CLE)
dGLUT/dT=CFAE*INAGL
dCAI/dT=-FI*CFN*(ICANMDA)-FI*(PER*DER*(JSERCA-JEROUT))/(PCYTOSOL*MINUTE*SECOND)
dCAER/dT=FI*(PER*DER*(JSERCA-JEROUT))/(PER*MINUTE*SECOND)
dCAE/dT=CFNE*ICANMDA+GCAB*(CAE0-CAE)
dHER/dT=(DINH-(CAI+DINH)*HER)/TAU

where ...
FRT = R*TEMP/F   
INANMDA = PNMDA*SG*BINF(V)*F*PHI(V)*(NAE*EXP(-PHI(V))-NAI)/(EXP(-PHI(V))-1)   
IKNMDA = PNMDA*SG*BINF(V)*F*PHI(V)*(KE*EXP(-PHI(V))-KI)/(EXP(-PHI(V))-1)   
ICANMDA = PCA*2*PNMDA*SG*BINF(V)*F*PHI(2*V)*(CAE*EXP(-PHI(2*V))-CAI)/(EXP(-PHI(2*V))-1)   
INMDA = INANMDA+IKNMDA+ICANMDA   
IPUMP = IMAX/(((1+2/KE)^2)*(1+7.7/NAI)^3)   
INAPUMP = 3*IPUMP   
IKPUMP = -2*IPUMP   
ENAGL = (FRT/2)*LN(((NAE/NAIA)^3)*(KIA/KE)*(GLUT/GLUI)*HR)   
INAGL = GNAGL*(VA-ENAGL)   
VOLE = ALPHA0*VOLN   
CFN = 10.0*S/(F*VOLN)   
CFNE = 10.0*S/(F*VOLE)   
CFA = 10*SA/(F*VOLA)   
CFAE = 10*SA/(F*VOLE)   
GLTOT = CFAE*GLUI0+CFA*GLUT0   
GLUI = (1/CFAE)*(GLTOT-CFA*GLUT)   
JEROUT = (VIP3*((IP3/(IP3+DIP3))^3)*((CAI/(CAI+DACT))^3)*(HER^3)+VLEAK)*(CAER-CAI)   
JSERCA = VSERCA*CAI^2/(KSERCA^2+CAI^2)   

User-defined functions:
PHI(V) = V/FRT  
MINF(V) = 1./(1.+EXP(-(V-THM)/SIGM))  
INA(V,N,NAE,NAI) = PNA*(MINF(V)^3*(1-N)+PNAL)*F*PHI(V)*(NAE*EXP(-PHI(V))-NAI)/(EXP(-PHI(V))-1)  
MINFP(V) = 1./(1.+EXP(-(V-THMP)/SIGMP))  
HINFP(V) = 1./(1.+EXP(-(V-THHP)/SIGHP))  
TAUHP(V) = TAUBAR/COSH((V-VT)/(2*SIG))  
INAP(V,HP,NAE,NAI) = PNAP*MINFP(V)*HP*F*PHI(V)*(NAE*EXP(-PHI(V))-NAI)/(EXP(-PHI(V))-1)  
NINF(V) = 1./(1.+EXP(-(V-THN)/SGN))  
TAUN(V) = TAUN0+TAUN1/(1+EXP(-(V-THNT)/SN))  
IK(V,N,KE,KI) = PK*(N^4+PKL)*F*PHI(V)*(KE*EXP(-PHI(V))-KI)/(EXP(-PHI(V))-1)  
BINF(V) = 1/(1+EXP(-(V-THETAT)/16.13))  
SINFG(X) = 1./(1.+EXP(-(X-THG)/SIGMAG))  
ICL(V,CLE,CLI) = -PCL*F*PHI(-V)*(CLE*EXP(-PHI(-V))-CLI)/(EXP(-PHI(-V))-1)  
IKA(V,KE,KI) = PKA*F*PHI(V)*(KE*EXP(-PHI(V))-KI)/(EXP(-PHI(V))-1)  
INAA(V,NAE,NAI) = PNAA*F*PHI(V)*(NAE*EXP(-PHI(V))-NAI)/(EXP(-PHI(V))-1)  
IPUMPA(KE,NAI) = IMAXA/(((1+2/KE)^2)*(1+10/NAI)^3)