XPP model
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# Traveling waves equations for model CA1 pyramidal cell apical dendrite # For simulation in XPPAUT (Bard Ermentrout) # Download: http://www.pitt.edu/~phase/ # Get the book too: Ermentrout B. Simulating, analyzing, and animating dynamical systems: SIAM, 2002. # Corey Acker # Boston University # July 16, 2004 # Membrane equations from Migliore et al. (1999) J Comput Neurosci 7: 5-15 # Model parameters, including shooting parameter K param Cm=2.0,Ra=150 param VNa=55.0,VK=-90,VL=-65 param GNa=32,GKDR=10,GL=0.2,b=0.5 param d_tau=0.1 param d_inf=0.1 param GKA=48 param diam=1.8 param Iapp=0.925 param K=4 # bad initial guess # param K=5.010975 # actual value to be found by shooting method # Wave Speed aux c = sqrt((K*diam*10)/(4*Ra*Cm)) # Initial conditions init V=-68.1,Vdot=0,m=0.016,h=0.99,i=0.95,nKDR=0.0002,n=0.0005,l=0.8 # Dynamic equations V'=Vdot Vdot'=K*(Vdot+(fion(V)-Iapp)/Cm) m'=1/taum(V)*(minf(V)-m) h'=1/tauh(V)*(hinf(V)-h) i'=1/taui(V)*(iinf(V)-i) nKDR'=1/taunKDR(V)*(nKDRinf(V)-nKDR) n'=1/taun(V)*(ninf(V)-n) l'=1/taul(V)*(linf(V)-l) # All other equations fion(V)=INa(V)+IKDR(V)+IKA(V)+IL(V) INa(V)=GNa*m^3*h*i*(V-VNa) IKDR(V)=GKDR*nKDR*(V-VK) IKA(V)=GKA*n*l*(V-VK) IL(V)=GL*(V-VL) # Rate equations # Sodium activation, m minf(V)=alm(V)/(alm(V)+bem(V)) taum1(V)=0.5/(alm(V)+bem(V)) taum(V)=if(taum1(V)<0.02)then(0.02)else(taum1(V)) alm(V)=0.4*(V+30)/(1-exp(-(V+30)/7.2)) bem(V)=0.124*(V+30)/(exp((V+30)/7.2)-1) # Sodium inactivation, h hinf(V)=1/(1+exp((V+50)/4)) tauh1(V)=0.5/(alh(V)+beh(V)) tauh(V)=if(tauh1(V)<0.5)then(0.5)else(tauh1(V)) alh(V)=0.03*(V+45)/(1-exp(-(V+45)/1.5)) beh(V)=0.01*(V+45)/(exp((V+45)/1.5)-1) # Slow Inactivation of INa, i iinf(V)=(1+b*exp((V+58)/2))/(1+exp((V+58)/2)) taui1(V)=3e4*bei(V)/(1+ali(V)) taui(V)=if(taui1(V)<10)then(10)else(taui1(V)) ali(V)=exp(0.45*(V+60)) bei(V)=exp(0.09*(V+60)) # Activation of IKDR nKDRinf(V)=1/(1+alnKDR(V)) taunKDR1(V)=50*benKDR(V)/(1+alnKDR(V)) taunKDR(V)=if(taunKDR1(V)<2)then(2)else(taunKDR1(V)) alnKDR(V)=exp(-0.11*(V-13)) benKDR(V)=exp(-0.08*(V-13)) # Equations for proximal version of IA activation ninfprox(V)=1/(1+alnprox(V)) taunprox1(V)=4*benprox(V)/(1+alnprox(V)) taunprox(V)=if(taunprox1(V)<0.1)then(0.1)else(taunprox1(V)) alnprox(V)=exp(-0.038*(1.5+1/(1+exp(V+40)/5))*(V-11)) benprox(V)=exp(-0.038*(0.825+1/(1+exp(V+40)/5))*(V-11)) # Equations for distal version of IA activation ninfdist(V)=1/(1+alndist(V)) taundist1(V)=2*bendist(V)/(1+alndist(V)) taundist(V)=if(taundist1(V)<0.1)then(0.1)else(taundist1(V)) alndist(V)=exp(-0.038*(1.8+1/(1+exp(V+40)/5))*(V+1)) bendist(V)=exp(-0.038*(0.7+1/(1+exp(V+40)/5))*(V+1)) # Weighted averaging of IA equations taun(V)=d_tau*taunprox(V)+(1-d_tau)*taundist(V) ninf(V)=d_inf*ninfprox(V)+(1-d_inf)*ninfdist(V) # IA inactivation, l linf(V)=1/(1+all(V)) taul1(V)=0.26*(V+50) taul(V)=if(taul1(V)<2)then(2)else(taul1(V)) all(V)=exp(0.11*(V+56)) # Setup XPP's numerics, and plotting @ xp=V,yp=vdot,xlo=-90,xhi=30,ylo=-1000,yhi=300 @ dt=0.01,total=20 @ method=cvode,tol=1e-6,atoler=1e-5,bounds=1e4 @ jac_eps=1e-5,newt_tol=1e-5,newt_iter=10000 done
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Copyright © 2017 Matthias Koenig
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Model :
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type | FunctionDefinitions [45] | name | math | sbo | cvterm |
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FunctionDefinition | max
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minimum | |||
FunctionDefinition | min
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maximum | |||
FunctionDefinition | heav
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heavyside | |||
FunctionDefinition | mod
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modulo | |||
FunctionDefinition | fion
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FunctionDefinition | ina
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FunctionDefinition | ikdr
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FunctionDefinition | ika
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FunctionDefinition | il
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FunctionDefinition | minf
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FunctionDefinition | taum1
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FunctionDefinition | taum
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FunctionDefinition | alm
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FunctionDefinition | bem
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FunctionDefinition | hinf
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FunctionDefinition | tauh1
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FunctionDefinition | tauh
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FunctionDefinition | alh
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FunctionDefinition | beh
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FunctionDefinition | iinf
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FunctionDefinition | taui1
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FunctionDefinition | taui
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FunctionDefinition | ali
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FunctionDefinition | bei
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FunctionDefinition | nkdrinf
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FunctionDefinition | taunkdr1
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FunctionDefinition | taunkdr
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FunctionDefinition | alnkdr
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FunctionDefinition | benkdr
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FunctionDefinition | ninfprox
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FunctionDefinition | taunprox1
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FunctionDefinition | taunprox
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FunctionDefinition | alnprox
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FunctionDefinition | benprox
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FunctionDefinition | ninfdist
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FunctionDefinition | taundist1
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FunctionDefinition | taundist
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FunctionDefinition | alndist
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FunctionDefinition | bendist
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FunctionDefinition | taun
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FunctionDefinition | ninf
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FunctionDefinition | linf
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FunctionDefinition | taul1
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FunctionDefinition | taul
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FunctionDefinition | all
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type | Parameters [25] | name | constant | value | unit | derived unit | sbo | cvterm |
---|---|---|---|---|---|---|---|---|
Parameter | cm
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cm = 2.0 | F | 2.0 | None | |||
Parameter | ra
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ra = 150 | F | 150.0 | None | |||
Parameter | vna
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vna = 55.0 | F | 55.0 | None | |||
Parameter | vk
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vk = -90 | F | -90.0 | None | |||
Parameter | vl
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vl = -65 | F | -65.0 | None | |||
Parameter | gna
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gna = 32 | F | 32.0 | None | |||
Parameter | gkdr
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gkdr = 10 | F | 10.0 | None | |||
Parameter | gl
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gl = 0.2 | F | 0.2 | None | |||
Parameter | b
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b = 0.5 | F | 0.5 | None | |||
Parameter | d_tau
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d_tau = 0.1 | F | 0.1 | None | |||
Parameter | d_inf
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d_inf = 0.1 | F | 0.1 | None | |||
Parameter | gka
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gka = 48 | F | 48.0 | None | |||
Parameter | diam
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diam = 1.8 | F | 1.8 | None | |||
Parameter | iapp
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iapp = 0.925 | F | 0.925 | None | |||
Parameter | k
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k | F | 0.0 | None | |||
Parameter | v
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v = -68.1 | F | -68.1 | None | |||
Parameter | vdot
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vdot = 0 | F | 0.0 | None | |||
Parameter | m
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m = 0.016 | F | 0.016 | None | |||
Parameter | h
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h = 0.99 | F | 0.99 | None | |||
Parameter | i
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i = 0.95 | F | 0.95 | None | |||
Parameter | nkdr
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nkdr = 0.0002 | F | 0.0002 | None | |||
Parameter | n
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n = 0.0005 | F | 0.0005 | None | |||
Parameter | l
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l = 0.8 | F | 0.8 | None | |||
Parameter | c
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F | 0.0 | dimensionless | None | |||
Parameter | t
|
model time | F | 0.0 | dimensionless | None |
type | InitialAssignments [1] | name | assignment | derived units | sbo | cvterm | |
---|---|---|---|---|---|---|---|
InitialAssignment | k | = | None |
type | Rules [10] | assignment | name | derived units | sbo | cvterm | |
---|---|---|---|---|---|---|---|
Rule | d v/dt
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= | None | ||||
Rule | d vdot/dt
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= | None | ||||
Rule | d m/dt
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= | None | ||||
Rule | d h/dt
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= | None | ||||
Rule | d i/dt
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= | None | ||||
Rule | d nkdr/dt
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= | None | ||||
Rule | d n/dt
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= | None | ||||
Rule | d l/dt
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= | None | ||||
Rule | c
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= | None | ||||
Rule | t
|
= | None |