TITLE accum :Ion accumulation, potassium buffering and diffusion between compartments and to the bath
NEURON {
SUFFIX accum
USEION na READ ina, nao, nai WRITE nai, nao, ina
USEION k READ ik, ko, ki WRITE ki, ko, ik
USEION ca READ ica, cai WRITE cai, cao, ica VALENCE 2
USEION cl READ icl, cli, clo WRITE cli, clo, icl VALENCE -1
RANGE volin, volout, volpyram
RANGE nap, kp, cap, clp
POINTER diamp, inap, ikp, icap, iclp
GLOBAL setnap, setkp, setcap, setclp, TotalBuffer
}
UNITS {
(um3) = (liter/1e15)
(mV) = (millivolt)
(mA) = (milliamp)
FARADAY = 96485.309 (coul/mole)
(molar) = (1/liter)
(mM) = (millimolar)
PI = (pi) (1)
R = (k-mole) (joule/degC)
}
PARAMETER {
Difna = 0.1 (um2/ms)
Difk = 1.96 (um2/ms)
Difca = 0.6 (um2/ms)
Difcl = 2.03 (um2/ms)
k1buf = 0.0008 (/ms)
TotalBuffer = 500 (mM)
x0 = 15 (mM)
nab = 140 (mM)
kb = 3.5 (mM)
clb = 135 (mM)
s = 2e4
setvolin=1
setvolout=1
setvolpyram=1
setnap
setkp
setcap
setclp
}
ASSIGNED {
ina (mA/cm2)
ik (mA/cm2)
ica (mA/cm2)
icl (mA/cm2)
inap (mA/cm2)
ikp (mA/cm2)
icap (mA/cm2)
iclp (mA/cm2)
diam (um)
diamp (um)
naflux[3]
kflux[3]
caflux[3]
clflux[3]
dif[3]
nai ki cai cli :Concentrations in interneuron
nao ko cao clo :Concentrations in extracellular space
nap kp cap clp :Concentrations in pyramidal neuron
volin :Interneuron volume
volout :Extracellular volume
volpyram :Pyramidal neuron volume
Kd (/mM)
B0 (mM)
}
STATE { na[3] k[3] ca[3] cl[3] (mM) <1e-4> kbuf Buffer KBuffer (mM) vol[3] }
BREAKPOINT {
SOLVE state METHOD sparse
}
INITIAL {
na[0]=nai
na[1]=nao
na[2]=setnap
k[0]=ki
k[1]=ko
k[2]=setkp
ca[0]=cai
ca[1]=cao
ca[2]=setcap
cl[0]=cli
cl[1]=clo
cl[2]=setclp
:Potassium buffer
Kd = k2buf(k[1])/k1buf
kbuf = 0
B0 = TotalBuffer/(1+Kd*k[1])
Buffer = B0
KBuffer = TotalBuffer - B0
vol[0]=setvolin
vol[1]=setvolout
vol[2]=setvolpyram
volin=vol[0]
volout=vol[1]
volpyram=vol[2]
nap=na[2]
kp=k[2]
cap=ca[2]
clp=cl[2]
}
KINETIC state {
COMPARTMENT i, vol[i]*diam*diam*PI/4 { na k ca cl }
LONGITUDINAL_DIFFUSION i, Difna*diam*diam*PI*vol[i]/4 { na }
LONGITUDINAL_DIFFUSION i, Difk*diam*diam*PI*vol[i]/4 { k }
LONGITUDINAL_DIFFUSION i, Difca*diam*diam*PI*vol[i]/4 { ca }
LONGITUDINAL_DIFFUSION i, Difcl*diam*diam*PI*vol[i]/4 { cl }
:INTRACELLULAR INTERNEURON
naflux[0] = -(ina*diam)*PI*(1e4)/FARADAY
kflux[0] = -(ik*diam)*PI*(1e4)/FARADAY
caflux[0] = -(ica*diam)*PI*(1e4)/(FARADAY*2)
clflux[0] = -(icl*diam)*PI*(1e4)/(FARADAY*-1)
:COMMON EXTRACELLULAR SPACE
naflux[1] = (ina*diam+inap*diamp)*PI*(1e4)/FARADAY
kflux[1] = (ik*diam+ikp*diamp)*PI*(1e4)/FARADAY
caflux[1] = (ica*diam+icap*diamp)*PI*(1e4)/(FARADAY*2)
clflux[1] = (icl*diam+iclp*diamp)*PI*(1e4)/(FARADAY*-1)
:INTRACELLULAR PYRAMIDAL
naflux[2] = -(inap*diamp)*PI*(1e4)/FARADAY
kflux[2] = -(ikp*diamp)*PI*(1e4)/FARADAY
caflux[2] = -(icap*diamp)*PI*(1e4)/(FARADAY*2)
clflux[2] = -(iclp*diamp)*PI*(1e4)/(FARADAY*-1)
:RADIAL DIFFUSION (TO THE BATH)
dif[1] = (Difna*geom(diam)*(nab-na[1])/s)*(setvolout*diam*diam*PI/4)
dif[2] = (Difk*geom(diam)*(kb-k[1]-kbuf)/s)*(setvolout*diam*diam*PI/4)
dif[3] = (Difcl*geom(diam)*(clb-cl[1])/s)*(setvolout*diam*diam*PI/4)
~ na[0] << (naflux[0])
~ k[0] << (kflux[0])
~ ca[0] << (caflux[0])
~ cl[0] << (clflux[0])
~ na[1] << (naflux[1]+dif[1])
~ k[1] << (kflux[1]+dif[2])
~ kbuf << (-k2buf(k[1]+kbuf)*(k[1]+kbuf)*Buffer+k1buf*KBuffer)
~ Buffer << (-k2buf(k[1]+kbuf)*(k[1]+kbuf)*Buffer+k1buf*KBuffer)
~ KBuffer << (k2buf(k[1]+kbuf)*(k[1]+kbuf)*Buffer-k1buf*KBuffer)
~ ca[1] << (caflux[1])
~ cl[1] << (clflux[1]+dif[3])
~ na[2] << (naflux[2])
~ k[2] << (kflux[2])
~ ca[2] << (caflux[2])
~ cl[2] << (clflux[2])
volin=vol[0]
volout=vol[1]
volpyram=vol[2]
nai=na[0] nao=na[1] nap=na[2]
ki=k[0] ko=k[1]+kbuf kp=k[2]
cai=ca[0] cao=ca[1] cap=ca[2]
cli=cl[0] clo=cl[1] clp=cl[2]
}
FUNCTION k2buf(x(mM)) {
TABLE FROM -150 TO 150 WITH 200
k2buf = k1buf/(1+exp((x-x0)/(-1.09)))
}
FUNCTION dr(x(um)) {
TABLE FROM 0 TO 15 WITH 10
dr = x*(sqrt(setvolout+1)-1)/2
}
FUNCTION geom(x(um)) {
TABLE FROM 0 TO 15 WITH 10
geom = PI*(x+2*dr(x))/(dr(x/2)*setvolout*x*x*PI/4)
}
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