TITLE 2D-3D diffusion with absorbing boundary
COMMENT
Author: Elena Saftenku, 2003
ENDCOMMENT
NEURON{
POINT_PROCESS GrC_Glubes23
RANGE glu,rPSD,rabs,nu, gluspill,gludir,alpha,Rmf
RANGE Deff,meandist,Popeak,alpha
RANGE inclugludir,inclugluspill, Podir,Pospill, Podir1,td1,tm1,ts1
}
UNITS{
(molar)=(1/liter)
(mM)=(millimolar)
(um)=(micron)
(nA)=(nanoamp)
}
CONSTANT {
PI=3.1415927
}
PARAMETER { Deff=0.08 (um2/ms): effective diffusion coefficient
nu=0.94(1/um2) : density of release sites
rabs= 4.4 (um) : radius of absorbing boundary
c0cleft = 8.769 (mM): initial [glu] after vesicle release
rPSD=0.11 (um) : radius of postsynaptic density
meandist=0.29 (um) : minimal limit of spillover glutamate integration
alpha=5 :1/extracellular volume fraction
h=0.02(um): cleft width
Rmf=2.9(um): radius of mossy fiber
Popeak=0.662: adjusted peak open probability of AMPA receptors
inclugludir=1 : inclusion of direct component
inclugluspill=1 : inclusion of spillover component
tm1=0 (ms) : 0.09 (ms), shift of experimental mEPSC
td1=0 (ms) : 0.16(ms), shift of experimental direct EPSC
ts1=0 (ms) : 0.16 (ms), shift of experimental spillover EPSC
}
VERBATIM
static int i;
static double l[100000];
extern float bessj1(float);
ENDVERBATIM
ASSIGNED{
Podir
Pospill
Podir1
tx1(ms)
gludir (mM)
gluspill(mM)
vspr
glu (mM)
sum (um)
sum0 (um)
sum02
sum2
sum1(um2)
sum01(um2)
}
INITIAL {
tx1=10000000
glu=0
gludir=0
gluspill=0
}
BREAKPOINT
{
at_time(tx1)
if (t<=tx1){
glu=0
gludir=0
gluspill=0
Podir=0
Pospill=0
Podir1=0
}
if(t>tx1) {
VERBATIM
l[0]=0;
l[1]=2.4048;l[2]=5.5201;l[3]=8.6535;
sum=0; i=1;
do
{if (i>=4) l[i]=PI*(4*i-1)/4;
sum0=sum;
sum =sum+bessj1((l[i]/rabs)*rPSD)/((l[i]/rabs)*bessj1(l[i])*bessj1(l[i]))
* exp((l[i]/rabs)*(l[i]/rabs)*Deff*(tx1-t));
i++; }
while (fabs(sum-sum0)>=0.01);
sum2=0;i=0;
do
{sum02=sum2;
sum2=sum2+(4/((2*i+1)*PI))*sin((2*i+1)*PI*h/(2*(rabs-Rmf)))*
exp(Deff*(2*i+1)*(2*i+1)*PI*PI*(tx1-t)/(4*(rabs-Rmf)*(rabs-Rmf)));
i++;}
while(fabs(sum2-sum02)>=0.001);
ENDVERBATIM
UNITSOFF
gludir = 2*c0cleft*rPSD*sum*sqrt(alpha*sum2)/(rabs*rabs)
if (gludir>c0cleft){gludir=c0cleft}
UNITSON
VERBATIM
sum1=0;i=1;
do
{if (i>=4) l[i]=PI*(4*i-1)/4;
sum01=sum1;
sum1=sum1+(Rmf*bessj1((l[i]/rabs)*Rmf)- meandist
* bessj1((l[i]/rabs)* meandist))/
((l[i]/rabs)*bessj1(l[i])*bessj1(l[i]))*exp((l[i]/rabs)*(l[i]/rabs)*
Deff*(tx1-t));
i++;}
while (fabs(sum1-sum01)>=0.0001);
ENDVERBATIM
UNITSOFF
gluspill= 2*PI*nu*c0cleft*rPSD*rPSD*sum1*sqrt(sum2*alpha)/
(rabs*rabs)
UNITSON
glu= inclugludir*gludir + inclugluspill*gluspill
: Experimental waveforms
Podir=(0.94*exp((tx1-td1-t)/0.37(ms))+0.06*exp((tx1-td1-t)/2.2(ms))
-exp((tx1-td1-t)/0.199(ms)))/0.249*(0.43/0.484)*Popeak : direct EPSC
Pospill=(0.39*exp((tx1-ts1-t)/2.0(ms))+0.61*exp((tx1-ts1-t)/9.1(ms))-
exp((tx1-ts1-t)/0.44(ms)))/0.682*(0.125/0.484)*Popeak: spillover EPSC
Podir1=(0.94*exp((tx1-tm1-t)/0.3(ms))+0.06*exp((tx1-tm1-t)/3.1(ms))
-exp((tx1-tm1-t)/0.12(ms)))/0.35*Popeak: mEPSC
}
}
NET_RECEIVE (weight)
{
tx1=t
}