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ca3_single_compartment.cpp
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ca3_single_compartment.cpp
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/* Cell model: CA3 hippocampal neuron
*
* Created by jun xu @ Clancy Lab of Cornell University Medical College on 3/27/05
*
* Geometry: single-compartment model modified on 04/19/07 */
#include <iostream>
#include <cmath>
#include <cstdlib>
#include <cstdio>
#include <iomanip>
#include "nr.h"
using namespace std;
#define nseg 1
/* Creation of Data File */
FILE *out_one;
void data_file ();
int printdata; // printing counter
int printval; // intervals to output results
// define constant parameters
double F = 96520; // Farady constant (coulomb/mol)
double R = 8.3134; // gas constant (J/K.mol)
double PI = 3.14;
double celsius = 30;
double T = celsius+273.14; // absolute temperature (K)
// define membrane properties
double Rm = 60000; //
double cm = 1.0*1.0e-3; //units
double Ra = 200*1.0e-4; //units
double vrest = -65; // (mv)
double vinit = vrest;
double vk = -91;
double vna = 50;
// define initial ionic concentration
double cai_init = 5.0e-5; // (mM)
double cao = 2; // (mM)
// cout<<"ok"<<endl;
/* Voltage */
double v[nseg]; // Membrane voltage
/* Time and spatial Step */
double dt; // Time step
double t; // Time
// define ionic conductances (S/cm^2)
double gna11 = 2.0;
double gcatbar =0.45; //0.45
double gcat31 = 0.45; //0.45
double gcat32 = 0.45; //0.45
double gcat33 = 0.45; //0.45
double gcatbar_C4565 = 1.6*0.45;
double gcanbar = 0.0025;
double gcalbar = 0.0025;
double gkdr =0.08; // 0.08
double gka =0.0001;
double gkm =0.00002;
double gkc =0.00005;
double gkahp =0.0000018; // 0.0000018 testing
double gpas = 1/Rm;
// define ionic concentration & currents
double cai[nseg];
double ina[nseg], ina11[nseg];
double icat[nseg],icat_alpha1G[nseg],icat_alpha1H[nseg],icat_alpha1I[nseg];
double iC4565[nseg];
double ican[nseg],ical[nseg],ica[nseg];
double ikdr[nseg],ika[nseg],ikm[nseg],ikc[nseg],ikahp[nseg],ipas[nseg];
double ion[nseg],current[nseg];
double Ist;
// gating variables
// Na1.1 gates
double Na_MC3[nseg], Na_MC[nseg], Na_MO[nseg], Na_MI[nseg];
double Na_MIs[nseg], Na_MC2[nseg], IC3[nseg], IC2[nseg];
double Na_MIs2[nseg], M_C3[nseg], M_C2[nseg], M_C[nseg], M_O[nseg];
double M_OP[nseg], Na_OP[nseg], Na_O[nseg], OPs[nseg], M_IF[nseg];
double ina11_wt = 0.0;
double ina11_mt = 0.0;
// Ca N and L type channel gates
double mn[nseg],hn[nseg],ml[nseg];
// CaT gates
double nth[nseg],lth[nseg],ntg[nseg],ltg[nseg],nti[nseg],lti[nseg];
// CaT mutant gates
double ntC4565[nseg],ltC4565[nseg];
// K gates
double nkdr[nseg],lkdr[nseg],nka[nseg],lka[nseg],mkm[nseg],okc[nseg],wkahp[nseg];
// gloable variables
int seg; // segment number from 1: number of segments
// geometry parameters
double area[nseg], diam[nseg], dx[nseg], g[nseg];
void WT_SCN1A_function ();
void cat_human_alpha1G();
void cat_human_alpha1H();
void cat_human_alpha1I();
void C4565();
void can();
void cal();
void kdr();
void ka();
void km();
void kc();
void kahp_new();
void pas();
void ca_dyn();
void geo();
void cable();
int main()
{
/* Opening of Datafiles */
out_one = fopen("out_one", "w");
printdata = 50;
printval = 10;
t = 0.0;
double tstop = 200;
dt = 0.01;
for(int i = 0; i<= nseg-1; i++)
{
v[i] = vrest;
cai[i] = cai_init;
}
// define neuron geometry: CA3 neuron
geo();
/* Beginning of Time Loop */
for ( t = 0.0; t <= tstop; t+=dt)
{
if(t>=2 && t <= 7)
{
Ist = -0.2*100/(PI*diam[0]*dx[0]); //(mA/cm^2)
// Ist = 0.0; // testing
}
else
Ist = 0.0;
// calculate ionic currents
for(seg = 0; seg <= nseg-1; seg++)
{
WT_SCN1A_function ();
cat_human_alpha1G();
cat_human_alpha1H();
cat_human_alpha1I();
C4565();
cal();
can();
kdr();
ka();
km();
kc();
kahp_new();
pas();
ca_dyn();
// debugging
/* cout << "segment ###################################### " << seg << endl;
cout << " The time is at ------------------------------ "<< t << endl;
cout << v[seg] << endl;
cout << ina[seg]<<endl;
cout << icat[seg]<<endl;
cout << ican[seg]<<endl;
cout << ical[seg]<<endl;
cout << ikdr[seg]<<endl;
cout << ika[seg]<<endl;
cout << ikm[seg]<<endl;
cout << ikc[seg]<<endl;
cout << ikahp[seg]<<endl;
cout << ipas[seg]<<endl;
cout << ica_pump[seg]<<endl;
cout << cai[seg]<< endl;
*/
}
cable();
// output results to a file at certain intervals
if(printdata >= printval)
{data_file();
printdata = 0;}
printdata = printdata+1;
cout << "t, v[0] = " << t << " " << v[0] <<endl;
}
// indicate the end of the calculation: beeping
cout << "\a\a";
return (1);
}
// [Ca2+] dynamics using a simplified form
void ca_dyn()
{
cai[0] = cai[0] +0.1*dt*(-0.15*ica[0]+(-cai[0])/5);
}
void data_file()
{
fprintf(out_one,"%.3f\t%g\t%g\t%g\t%g\t%g\t%g\t%g\t%g\t%g\n", t, v[0],ina11[0],icat[0], ican[0], ical[0],icat_alpha1G[0],icat_alpha1H[0],icat_alpha1I[0],cai[0]);
}
// CA3 hippocampal neuron geometry (single-compartment model)
void geo()
{
// define dimension
double r3 = 15, L3 = 25.5; //soma
// define segment length, diameter, area assumng dx = 1, and resistances
diam[0] = 2*r3;
dx[0] = L3/1;
area[0] = PI*diam[0];
// define resistances
g[0] = 4*Ra*dx[0]/(PI*diam[0]*diam[0]);
}
//solve cable equation
void cable()
{
icat[0] = icat_alpha1G[0]+icat_alpha1H[0]+icat_alpha1I[0];
ica[0] = icat[0] + ican[0] + ical[0];
ion[0] = ina11[0]+icat[0]+ican[0]+ical[0]+ikdr[0]+ika[0]+ikm[0]+ikc[0]+ikahp[0]+ipas[0];
current[0] = ion[0];
// inject stimulation current at soma
current[0] = ion[0]+Ist; //(mA/cm^2)
v[0] = v[0]-dt*current[0]/cm;
}
//**************************************************************************************
// FUNCTION TO COMPUTE SCN1A NA CURRENT--Markov Model By Colleen Clancy @ Cornell U
//**************************************************************************************
void WT_SCN1A_function ()
{
// Ena=(r*T/F)*log(Naout/Nain);
double a11, a12, a13, b11, b12, b13, a2, a3, a4, b4, b1, b2, b3, a5, b5, mu1, mu2, aa2, bb2, bb3, aa3;
double err1, err2, err3,err4, err5, err6, err7, err8, err9, err10, err11, err12, err13, err14;
double y1, z1, x1, x2, y2, z2, e1, e2, q1, q2, w1, w2, d1, d2, c1, c2, f1, j2, f2, tap1, tap2, jj1, u2, u1, p1, p2, t1, zz1, zz2;
double dny, dnz, dne1, dne, dne2, dny1, dnz1, dnx, dnx1, dnq1, dnq,dnw, dnw1, dnd,
dnd1, dnc, dnc1, dnu, dnu1, dnp, dnp1, dntap, dntap1, dnf1, dnj1, dnf, dnj, dnzz, dnzz1;
double qt = pow(2.0,(celsius-23.0)/10);
int i4;
//Nain=10.0;
//Naout= 140.0;
//double ina;
int which_channels = 1;
if (which_channels ==1) // WT rates
{
a11= qt*2.802/(0.21*exp(-v[seg]/17.0)+0.23*exp(-v[seg]/150));
a12= qt*2.802/(0.23*exp(-v[seg]/15.0)+0.25*exp(-v[seg]/150));
a13= qt*2.802/(0.25*exp(-v[seg]/12.0)+0.27*exp(-v[seg]/150));
b11= qt*0.4*exp(-v[seg]/20.3);
b12= qt*0.4*exp(-(v[seg]-5)/20.3);
b13= qt*0.4*exp(-(v[seg]-10)/20.3)/4.5;
a3= qt*(3.7933e-7*exp(-v[seg]/7.6))*3;
b3= qt*(0.0084+.00002*v[seg]);
a2= qt*((9.178*exp(v[seg]/29.68))/4.5);
b2= ((a13*a2*a3)/(b13*b3));
a4= (a2/100)*1.5;
b4 = a3/5;
a5= (a2/95000)*80.0;
b5 = (a3/30)/10.0;
mu1= 0.0;
mu2= 0.0;
if (t<dt)
{
ina11[seg] = 0.0;
//initialize the Na+ current
//@-65
Na_MC3[seg]=0.438311;
Na_MO[seg]=2.1544e-6;
Na_MI[seg]=0.000187751;
Na_MIs[seg]=0.000501213;
Na_MC2[seg]=0.0125341;
IC3[seg]=0.527911;
IC2[seg]=0.0150964;
Na_MIs2[seg]=0.00529984;
M_C3[seg]=0;
M_C2[seg]=0;
M_C[seg]=0;
M_O[seg]=0;
M_IF[seg]=0;
Na_MC[seg]= 1-(Na_MO[seg]+Na_MI[seg]+Na_MC2[seg]+Na_MC3[seg]+M_C3[seg]+Na_MIs[seg]
+M_C2[seg]+M_C[seg]+M_O[seg]+IC3[seg]+IC2[seg]+Na_MIs2[seg]);
Na_MC[seg] = 0.000155888;
}
}
else if (which_channels ==2) // RH rates
{
a11= 2.802/(0.21*exp(-v[seg]/17.0)+0.23*exp(-v[seg]/150));
a12= 2.802/(0.23*exp(-v[seg]/15.0)+0.25*exp(-v[seg]/150));
a13= 2.802/(0.25*exp(-v[seg]/12.0)+0.27*exp(-v[seg]/150));
b11= 0.4*exp(-v[seg]/20.3);
b12= 0.4*exp(-(v[seg]-5)/20.3);
b13= 0.4*exp(-(v[seg]-10)/20.3)/4.5;
a3= (3.7933e-7*exp(-v[seg]/7.6))*3;
b3= (0.0084+.00002*v[seg]);
a2= ((9.178*exp(v[seg]/29.68))/4.5);
b2= ((a13*a2*a3)/(b13*b3));
a4= (a2/100)*1.5;
b4 = a3/5;
a5= (a2/95000)*80.0;
b5 = (a3/30)/10.0;
// flicker inactivation rates
aa2= ((9.178*exp(v[seg]/29.68))/4.5);
bb3= (0.0084+.00002*v[seg]);
aa3= (3.7933e-7*exp(-v[seg]/7.7))*83;
bb2= ((a13*aa2*aa3)/(b13*bb3));
mu1= 2e-5;
mu2= 2e-4;
if (t<dt)
{
ina11[seg] = 0.0; //initialize the Na+ current
//@ -65mv
Na_MC3[seg]=0.419443;
Na_MO[seg]=2.06164e-6;
Na_MI[seg]=0.000179635;
Na_MIs[seg]=0.00050059;
Na_MC2[seg]=0.0119946;
IC3[seg]=0.505087;
IC2[seg]=0.0144437;
Na_MIs2[seg]=0.00509992;
M_C3[seg]=0.0418866;
M_C2[seg]=0.00119781;
M_C[seg]=1.4897e-5;
M_O[seg]=2.05662e-7;
M_IF[seg]=7.12628e-7;
Na_MC[seg]= 1-(Na_MO[seg]+Na_MI[seg]+Na_MC2[seg]+Na_MC3[seg]+M_C3[seg]
+Na_MIs[seg]+M_C2[seg]+M_C[seg]+M_O[seg]+IC3[seg]+IC2[seg]+Na_MIs2[seg]+M_IF[seg]);
}
}
/* if (t>=60000.0-dt&&Get_steady_state==1)
{
cout<<"Na_MC3="<<Na_MC3<<";"<<endl;
cout<<"Na_MO="<<Na_MO<<";"<<endl;
cout<<"Na_MI="<<Na_MI<<";"<<endl;
cout<<"Na_MIs="<<Na_MIs<<";"<<endl;
cout<<"Na_MC2="<<Na_MC2<<";"<<endl;
cout<<"IC3="<<IC3<<";"<<endl;
cout<<"IC2="<<IC2<<";"<<endl;
cout<<"Na_MIs2="<<Na_MIs2<<";"<<endl;
cout<<"M_C3="<<M_C3<<";"<<endl;
cout<<"M_C2="<<M_C2<<";"<<endl;
cout<<"M_C="<<M_C<<";"<<endl;
cout<<"M_O="<<M_O<<";"<<endl;
cout<<"M_IF="<<M_IF<<";"<<endl;
exit (0);
}
*/
if (t>=dt)
{
y1=Na_MO[seg]; z1=Na_MI[seg]; x1= Na_MC2[seg]; q1= Na_MC3[seg]; w1= Na_MIs[seg];
d1= M_C3[seg]; c1= M_C2[seg]; u1= M_C[seg]; p1= M_O[seg]; tap1= Na_MC[seg];
jj1= IC3[seg]; f1= IC2[seg]; e1 = Na_MIs2[seg]; zz1= M_IF[seg];
//UPPER STATES
Na_MC[seg]= 1-(Na_MO[seg]+Na_MI[seg]+Na_MC2[seg]+Na_MC3[seg]+M_C3[seg]
+Na_MIs[seg]+M_C2[seg]+M_C[seg]+M_O[seg]+IC3[seg]+IC2[seg]+Na_MIs2[seg]+M_IF[seg]);
dny=((Na_MC[seg]*a13+Na_MI[seg]*b2+M_O[seg]*mu2)- (Na_MO[seg]*(b13+a2+mu1)))*dt;
dnz=((IC2[seg]*a12+Na_MO[seg]*a2+Na_MC[seg]*b3+Na_MIs[seg]*b4)- (Na_MI[seg]*(b2+a3+a4+b12)))*dt;
dnx= ((IC2[seg]*a3+Na_MC[seg]*b12+Na_MC3[seg]*a11+M_C2[seg]*mu2)-(Na_MC2[seg]*(a12+b11+mu1+b3)))*dt;
dnq= (IC3[seg]*a3+Na_MC2[seg]*b11+M_C3[seg]*mu2-(Na_MC3[seg]*(a11+mu1+b3)))*dt;
dnw= ((Na_MI[seg]*a4+Na_MIs2[seg]*b5)-Na_MIs[seg]*(b4+a5))*dt;
// dntap= (Na_MC2[seg]*a12+Na_MO[seg]*b13+M_C[seg]*mu2+Na_MI[seg]*a3-(Na_MC[seg]*(a13+b12+mu1+b3)))*dt;
dnj= ((Na_MC3[seg]*b3+IC2[seg]*b11)-IC3[seg]*(a11+a3))*dt;
dnf= ((Na_MC2[seg]*b3+IC3[seg]*a11+Na_MI[seg]*b12)-IC2[seg]*(a12+b11+a3))*dt;
dne= (Na_MIs[seg]*a5-Na_MIs2[seg]*b5)*dt;
//LOWER STATES
dnd= (Na_MC3[seg]*mu1+M_C2[seg]*b11-(M_C3[seg]*(a11+mu2)))*dt;
dnc= (Na_MC2[seg]*mu1+M_C3[seg]*a11+M_C[seg]*b12-(M_C2[seg]*(a12+mu2+b11)))*dt;
dnu= (Na_MC[seg]*mu1+M_C2[seg]*a12+M_O[seg]*b13+M_IF[seg]*aa3-(M_C[seg]*(a13+mu2+b12+bb3)))*dt;
dnp= ((M_C[seg]*a13+Na_MO[seg]*mu1+M_IF[seg]*bb2)-(M_O[seg]*(b13+mu2+aa2)))*dt;
dnzz= ((M_O[seg]*aa2+M_C[seg]*bb3)- (M_IF[seg]*(bb2+aa3)))*dt;
// cout<<dny+dnz+dnx+dnq+dnw+dntap+dnj+dnf+dnd+dnc+dnu+dnp+dne+dnzz<<endl; //Use this as a test that derivatives sum to zero
y2=Na_MO[seg]+dny;
z2=Na_MI[seg]+dnz;
x2= Na_MC2[seg]+dnx;
q2= Na_MC3[seg]+dnq;
w2= Na_MIs[seg]+dnw;
// tap2 = Na_MC[seg]+dntap;
j2= IC3[seg]+dnj;
f2= IC2[seg]+dnf;
e2 = Na_MIs2[seg]+dne;
d2= M_C3[seg]+dnd;
c2= M_C2[seg]+dnc;
u2= M_C[seg]+dnu;
p2= M_O[seg]+dnp;
zz2= M_IF[seg]+dnzz;
// Na_MC[seg]= 1-(y2+z2+x2+q2+w2+d2+c2+u2+p2);
err1= y2-y1; err2= z2-z1; err3=x2-x1; err10= 0.0;
err4= q2-q1; err5= w2-w1; err6=d2-d1; err11= j2-jj1;
err7= c2-c1; err8= u2-u1; err9= p2-p1; err12= f2- f1;
err13= e2-e1; err14= zz2-zz1;
dny1= dny;
dnz1=dnz;
dnx1= dnx; //UPPER STATES
dnq1= dnq;
dnw1=dnw;
// dntap1=dntap;
dnj1= dnj;
dnf1= dnf;
dne1= dne;
dnd1= dnd;
dnc1= dnc; //LOWER STATES
dnu1= dnu;
dnp1= dnp;
dnzz1= dnzz;
i4=0;
//cout << "testing is ok" << endl;
while (((err1>1e-5)||(err1<-1e-5)||(err2>1e-5)||(err2<-1e-5)||(err3>1e-5)
||(err3<-1e-5)||(err4>1e-5)||(err4<-1e-5)||(err5>1e-5)||(err5<-1e-5)||
(err6>1e-5)||(err6<-1e-5)||(err7>1e-5)||(err7<-1e-5)||(err8>1e-5)||
(err8<-1e-5)||(err9>1e-5)||(err9<-1e-5)||(err10>1e-5)||(err10<-1e-5)||
(err11>1e-5)||(err11<-1e-5)||(err12>1e-5)||(err12<-1e-5)||(err13>1e-5)||(err13<-1e-5)||(err14>1e-5)||(err14<-1e-5))
&&(i4<40))
{
y1=y2; z1=z2; x1=x2; q1=q2; w1= w2;
d1= d2; c1= c2; u1= u2; p1= p2; // tap1= tap2;
jj1= j2; f1= f2; e1= e2; zz1= zz2;
tap1 = 1-y1-z1-x1-q1-w1-d1-c1-u1-p1-jj1-f1-e1-zz1;
dny=((tap1*a13+z1*b2+p1*mu2)- (y1*(b13+a2+mu1)))*dt;
dnz=((f1*a12+y1*a2+tap1*b3+w1*b4)- (z1*(b2+a3+a4+b12)))*dt;
dnx= (((f1*a3+tap1*b12+q1*a11+c1*mu2)-(x1*(a12+b11+mu1+b3)))*dt);
dnq= ((jj1*a3+x1*b11+d1*mu2-q1*(a11+mu1+b3))*dt);
dnw= ((z1*a4+e1*b5)-w1*(b4+a5))*dt;
// dntap= (x1*a12+y1*b13+u1*mu2+z1*a3-(tap1*(a13+b12+mu1+b3)))*dt;
dnj= ((q1*b3+f1*b11)-jj1*(a11+a3))*dt;
dnf= ((x1*b3+jj1*a11+z1*b12)-f1*(a12+b11+a3))*dt;
dne= (w1*a5- e1*b5)*dt;
// cout<<dntap<<setw(15)<<t<<endl;
dnd= (q1*mu1+c1*b11-(d1*(a11+mu2)))*dt;
dnc= (x1*mu1+d1*a11+u1*b12-(c1*(a12+mu2+b11)))*dt;
dnu= (tap1*mu1+c1*a12+p1*b13+zz1*aa3-(u1*(a13+mu2+b12+bb3)))*dt;
dnp= (u1*a13+y1*mu1+zz1*bb2-(p1*(mu2+b13+aa2)))*dt;
dnzz= (p1*aa2+u1*bb3-(zz1*(aa3+bb2)))*dt;
dny= (dny+dny1)/2;
dnz= (dnz+dnz1)/2;
dnx= (dnx+dnx1)/2;
dnq= (dnq+dnq1)/2;
dnw= (dnw+dnw1)/2;
// dntap= (dntap+dntap1)/2;
dnj= (dnj+dnj1)/2;
dnf= (dnf+dnf1)/2;
dne= (dne+dne1)/2;
dnd= (dnd+dnd1)/2;
dnc= (dnc+dnc1)/2;
dnu= (dnu+dnu1)/2;
dnp= (dnp+dnp1)/2;
dnzz= (dnzz+dnzz1)/2;
y2= Na_MO[seg]+dny;
z2= Na_MI[seg]+dnz;
x2= Na_MC2[seg]+dnx;
q2= Na_MC3[seg]+dnq;
w2= Na_MIs[seg]+dnw;
// tap2= Na_MC[seg]+dntap;
j2= IC3[seg]+dnj;
f2= IC2[seg]+dnf;
e2= Na_MIs2[seg]+dne;
d2= M_C3[seg]+dnd;
c2= M_C2[seg]+dnc;
u2= M_C[seg]+dnu;
p2= M_O[seg]+dnp;
zz2= M_IF[seg]+dnzz;
dny1=dny;
dnz1=dnz;
dnx1= dnx;
dnq1=dnq;
dnw1= dnw;
// dntap1= dntap;
dnf1= dnf;
dnj1= dnj;
dne1= dne;
dnd1= dnd;
dnc1= dnc;
dnu1= dnu;
dnp1= dnp;
dnzz1= dnzz;
// Na_MC[seg]= 1-(y2+z2+x2+q2+w2+d2+c2+u2+p2);
err1=y2-y1;
err2= z2-z1;
err3= x2-x1;
err4= q2-q1;
err5= w2-w1;
err6= d2-d1;
err7= c2-c1;
err8= u2-u1;
err9= p2-p1;
err10= 0.0;
err11= j2-jj1;
err12= f2-f1;
err13= e2-e1;
err14= zz2-zz1;
i4++;
}
if (i4<40)
{
Na_MO[seg]=y2; Na_MI[seg]=z2; Na_MC2[seg]= x2; Na_MC3[seg]= q2; Na_MIs[seg]=w2;
M_C3[seg]= d2; M_C2[seg]= c2; M_C[seg]= u2; M_O[seg]= p2; // Na_MC[seg]=tap2;
IC3[seg]= j2; IC2[seg]=f2; Na_MIs2[seg]= e2; M_IF[seg]= zz2;
Na_MC[seg]= 1-(Na_MO[seg]+Na_MI[seg]+Na_MC2[seg]+Na_MC3[seg]+M_C3[seg]
+Na_MIs[seg]+M_C2[seg]+M_C[seg]+M_O[seg]+IC3[seg]+IC2[seg]+Na_MIs2[seg]+M_IF[seg]);
// cout << "Na_Mc" << Na_MC[seg] << endl;
// Na_MC[seg]=1-(Na_MO[seg]+Na_MI[seg]+ Na_MC2[seg]+Na_MIs[seg]+Na_MC3[seg]+M_C3[seg]+M_C2[seg]+M_C[seg]+M_O[seg]);
}
else
{
// cout<<"error_ina"<<setw(15)<<i4<<setw(15)<<t<<endl;
exit(0);
}
}
M_OP[seg]= Na_MO[seg]+M_O[seg];
M_OP[seg]= (M_OP[seg]*1.0);
Na_OP[seg]= Na_O[seg]*0;
OPs[seg]= M_OP[seg]+Na_OP[seg];
ina11[seg]= gna11*0.035*OPs[seg]*(v[seg]-50);
if(which_channels == 1)
ina11_wt = ina11[seg];
else if (which_channels == 2)
ina11_mt = ina11[seg];
}
// Human T-type calcium channels based on Chemin et al., J Physiol., 2002, 540, 3-14.
// CaT--alpha 1G CaV3.1
void cat_human_alpha1G() {
double n_inf,l_inf,tau_n,tau_l,vv;
double gbar = 0.008; // s/cm2
double vhalfn = -49.3; //mv
double vhalfl = -74.2;
double kn = 4.6;
double kl = -5.5;
double q10 = 2.3;
double qt = pow(q10,(celsius-28)/10);
double pcabar = 0.0001; // cm/s
double z= 2;
if(t<dt) {
vv = -65;
n_inf = 1/(1+exp(-(vv-vhalfn)/kn));
l_inf = 1/(1+exp(-(vv-vhalfl)/kl));
if(vv > -56)
tau_n = (0.8+0.025*exp(-vv/14.5))/qt;
else
tau_n = (1.71*exp((vv+120)/38))/qt;
tau_l = (12.3+0.12*exp(-vv/10.8))/qt;
ntg[seg] = n_inf;
ltg[seg] = l_inf;
}
n_inf = 1/(1+exp(-(v[seg]-vhalfn)/kn));
l_inf = 1/(1+exp(-(v[seg]-vhalfl)/kl));
if(v[seg]>-56)
tau_n = (0.8+0.025*exp(-v[seg]/14.5))/qt;
else
tau_n = (1.71*exp((v[seg]+120)/38))/qt;
if(v[seg]>-60)
tau_l = (12.3+0.12*exp(-v[seg]/10.8))/qt;
else
tau_l = 137/qt;
ntg[seg] = (ntg[seg] + dt*n_inf/tau_n)/(1+dt/tau_n);
ltg[seg] = (ltg[seg] + dt*l_inf/tau_l)/(1+dt/tau_l);
double w = v[seg]*0.001*z*F/(R*(celsius+273.16));
double ghk = -0.001*z*F*(cao-cai[seg]*exp(w))*w/(exp(w)-1);
icat_alpha1G[seg] = gcat31*pcabar*ntg[seg]*ntg[seg]*ltg[seg]*ghk;
}
// CaT--alpha 1H CaV3.2
// based on Vitko et al., 2005, J Neurosci, 25, 4844-4855
// provided by Dr Edward Perez-Reyes on 6/30/05
void cat_human_alpha1H() {
double n_inf,l_inf,tau_n,tau_l,vv;
double gbar = 0.008; // s/cm2
double vhalfn = -48.4; //mv
double vhalfl = -75.6;
double kn = 5.2;
double kl = -6.2;
double q10 = 2.3;
double qt = pow(q10,(celsius-28)/10);
double pcabar = 0.0001; // cm/s
double z= 2;
if(t<dt) {
vv = -65;
n_inf = 1/(1+exp(-(vv-vhalfn)/kn));
l_inf = 1/(1+exp(-(vv-vhalfl)/kl));
if(vv > -56)
tau_n = (1.34+0.035*exp(-vv/11.8))/qt;
else
tau_n = (2.44*exp((vv+120)/40))/qt;
tau_l = (18.3+0.005*exp(-vv/6.2))/qt;
// tau_n = (1.9+1.0/(exp((vv+21.0)/11.9)+exp(-(vv+115)/21)))/qt;
// tau_l = (18.3+(1942+exp((vv+164)/9.2))/(1+exp((vv+89.3)/3.7)))/qt;
nth[seg] = n_inf;
lth[seg] = l_inf;
}
n_inf = 1/(1+exp(-(v[seg]-vhalfn)/kn));
l_inf = 1/(1+exp(-(v[seg]-vhalfl)/kl));
if(v[seg] > -56)
tau_n = (1.34+0.035*exp(-v[seg]/11.8))/qt;
else
tau_n = (2.44*exp((v[seg]+120)/40))/qt;
if(v[seg]>-60)
tau_l = (18.3+0.005*exp(-v[seg]/6.2))/qt;
else
tau_l = 500/qt;
// tau_n = (1.9+1.0/(exp((v+21.0)/11.9)+exp(-(v+115)/21)))/qt;
// tau_l = (18.3+(1942+exp((v+164)/9.2))/(1+exp((v+89.3)/3.7)))/qt;
nth[seg] = (nth[seg] + dt*n_inf/tau_n)/(1+dt/tau_n);
lth[seg] = (lth[seg] + dt*l_inf/tau_l)/(1+dt/tau_l);
double w = v[seg]*0.001*z*F/(R*(celsius+273.16));
double ghk = -0.001*z*F*(cao-cai[seg]*exp(w))*w/(exp(w)-1);
icat_alpha1H[seg] = gcat32*pcabar*nth[seg]*nth[seg]*lth[seg]*ghk;
}
// Ca3.2 mutant channel
void C4565() {
double nC4565_inf,lC4565_inf,tauC4565_n,tauC4565_l, carev;
double vhalfnC4565 = -59.36; //mv
double vhalflC4565 = -85.5;
double knC4565 = 7.53;
double klC4565 = -7.18;
double knl = 1.143;
double q10 = 2.3;
double qt = pow(q10,(celsius-25)/10);
double pcabar = 0.0001; // cm/s
double z= 2;
if(t<dt) {
v[seg] = vinit;
nC4565_inf = 1/(1+exp(-(v[seg]-vhalfnC4565)/knC4565));
lC4565_inf = 1/(1+exp(-(v[seg]-vhalflC4565)/klC4565));
tauC4565_n = (1.52+1.0/(exp((v[seg]+40.3)/10.06)+exp(-(v[seg]+144.3)/28.6)))/qt;
tauC4565_l = (13.7+(1943+exp((v[seg]+164)/9.2))/(1+exp((v[seg]+89.3)/3.7)))/qt;
ntC4565[seg] = nC4565_inf;
ltC4565[seg] = lC4565_inf;
}
nC4565_inf = 1/(1+exp(-(v[seg]-vhalfnC4565)/knC4565));
lC4565_inf = 1/(1+exp(-(v[seg]-vhalflC4565)/klC4565));
tauC4565_n = (1.52+1.0/(exp((v[seg]+40.3)/10.06)+exp(-(v[seg]+144.3)/28.6)))/qt;
tauC4565_l = (13.7+(1943+exp((v[seg]+164)/9.2))/(1+exp((v[seg]+89.3)/3.7)))/qt;
ntC4565[seg] = (ntC4565[seg] + dt*nC4565_inf/tauC4565_n)/(1+dt/tauC4565_n);
ltC4565[seg] = (ltC4565[seg] + dt*lC4565_inf/tauC4565_l)/(1+dt/tauC4565_l);
// carev = (1e3)*(R*(celsius+273.15))/(2*F)*log(cao/cai[seg]);
// iC4565[seg] = 0.0001*gcatbar_C4565*ntC4565[seg]*ntC4565[seg]*ltC4565[seg]*(v[seg]-carev);
double w = v[seg]*0.001*z*F/(R*(celsius+273.16));
double ghk = -0.001*z*F*(cao-cai[seg]*exp(w))*w/(exp(w)-1);
iC4565[seg] = gcatbar_C4565*pcabar*ntC4565[seg]*ntC4565[seg]*ltC4565[seg]*ghk;
}
// CaT--alpha 1I CaV3.3
void cat_human_alpha1I() {
double n_inf,l_inf,tau_n,tau_l,vv;
double gbar = 0.008; // s/cm2
double vhalfn = -41.5; //mv
double vhalfl = -69.8;
double kn = 6.2;
double kl = -6.1;
double q10 = 2.3;
double qt = pow(q10,(celsius-28)/10);
double pcabar = 0.0001; // cm/s
double z= 2;
if(t<dt) {
vv = -65;
n_inf = 1/(1+exp(-(vv-vhalfn)/kn));
l_inf = 1/(1+exp(-(vv-vhalfl)/kl));
// tau_n = (9.3+8.0/(exp((vv+30.0)/11.9)+exp(-(vv+120)/21)))/qt;
// tau_l = (13.7+(1942+exp((vv+164)/9.2))/(1+exp((vv+89.3)/3.7)))/qt;
if(vv > -60)
tau_n = (7.2+0.02*exp(-vv/14.7))/qt;
else
tau_n = (0.875*exp((vv+120)/41))/qt;
if(vv>-70)
tau_l = (79.5+2.0*exp(-vv/9.3))/qt;
else
tau_l = 260/qt;
nti[seg] = n_inf;
lti[seg] = l_inf;
}
n_inf = 1/(1+exp(-(v[seg]-vhalfn)/kn));
l_inf = 1/(1+exp(-(v[seg]-vhalfl)/kl));
// tau_n = (9.3+8.0/(exp((v+30.0)/11.9)+exp(-(v+120)/21)))/qt;
// tau_l = (13.7+(1942+exp((v+164)/9.2))/(1+exp((v+89.3)/3.7)))/qt;
if(v[seg] > -60)
tau_n = (7.2+0.02*exp(-v[seg]/14.7))/qt;
else
tau_n = (0.875*exp((v[seg]+120)/41))/qt;
if(v[seg]>-60)
tau_l = (79.5+2.0*exp(-v[seg]/9.3))/qt;
else
tau_l = 260/qt;
nti[seg] = (nti[seg] + dt*n_inf/tau_n)/(1+dt/tau_n);
lti[seg] = (lti[seg] + dt*l_inf/tau_l)/(1+dt/tau_l);
double w = v[seg]*0.001*z*F/(R*(celsius+273.16));
double ghk = -0.001*z*F*(cao-cai[seg]*exp(w))*w/(exp(w)-1);
icat_alpha1I[seg] = gcat33*pcabar*nti[seg]*nti[seg]*lti[seg]*ghk;
}
// N-channel
void can() { //N-channel from Jaffe et al. 1994, J of Neurophisiology
double am,bm,ah,bh,tau_m,tau_h,m_inf,h_inf;
if(t<dt) {
v[seg] = -65;
am = 0.1967*(-v[seg]+19.88)/(exp((-v[seg]+19.88)/10)-1);
bm = 0.046*exp(-v[seg]/20.73);
ah = 1.6e-4*exp(-v[seg]/48.4);
bh = 1/(exp((-v[seg]+39)/10)+1);
tau_m = 1/(am+bm);
tau_h = 1/(ah+bh);
m_inf = am*tau_m;
h_inf = ah*tau_h;
mn[seg] = m_inf;
hn[seg] = h_inf;
ican[seg] = 0.0;
}
am = 0.1967*(-v[seg]+19.88)/(exp((-v[seg]+19.88)/10)-1);
bm = 0.046*exp(-v[seg]/20.73);
ah = 1.6e-4*exp(-v[seg]/48.4);
bh = 1/(exp((-v[seg]+39)/10)+1);
tau_m = 1/(am+bm);
tau_h = 1/(ah+bh);
m_inf = am*tau_m;
h_inf = ah*tau_h;
mn[seg] = (mn[seg] + dt*m_inf/tau_m)/(1+dt/tau_m);
hn[seg] = (hn[seg] + dt*h_inf/tau_h)/(1+dt/tau_h);
double ki = 0.001;
double KTF = 25/293.15*(celsius+273.15);
double f = KTF/2;
double nu = v[seg]/f;
double efun;
if(fabs(nu)<1e-4)
efun = 1-nu/2;
else
efun = nu/(exp(nu)-1);
double ghk = -f*(1-cai[seg]/cao*exp(nu))*efun;
// double gcanbar = 0.0003;
double gcan = gcanbar*mn[seg]*mn[seg]*hn[seg]*ki/(ki+cai[seg]);
ican[seg] = gcan*ghk;
// return ican;
}
// L-channel
void cal() { //L-channel Jaffe et al. 1994. J Neurophisiology
double am,bm,tau_m,m_inf;
if(t<dt) {
v[seg] = - 65;
am = 15.69*(-v[seg]+81.5)/(exp((-v[seg]+81.5)/10)-1);
bm = 0.29*exp(-v[seg]/10.86);
tau_m = 1/(am+bm);
m_inf = am*tau_m;
ml[seg] = m_inf;
ical[seg] = 0.0;
}
am = 15.69*(-v[seg]+81.5)/(exp((-v[seg]+81.5)/10)-1);
bm = 0.29*exp(-v[seg]/10.86);
tau_m = 1/(am+bm);
m_inf = am*tau_m;
ml[seg]= (ml[seg] + dt*m_inf/tau_m)/(1+dt/tau_m);
double ki = 0.001;
// double gcalbar = 0.003;
double gcal = gcalbar*ml[seg]*ml[seg]*(ki/(ki+cai[seg]));
double KTF = 25/293.15*(celsius+273.15);
double f = KTF/2;
double nu = v[seg]/f;
double efun;
if(fabs(nu) < 1e-4)
efun = 1-nu/2;
else
efun = nu/(exp(nu)-1);
double ghk = -f*(1-cai[seg]/cao*exp(nu))*efun;
ical[seg] = gcal*ghk;
// return ical;
}
// K channels
// Kdr channel (Ca-independent k channel)
void kdr() { // From Migliore et al. 1995. J Neurophysiology
double an,bn,al,bl,tau_n,tau_l,n_inf,l_inf;
if(t<dt) {
v[seg] = -65;
an = 0.03*exp(1.e-3*5*0.4*(v[seg]+32)*F/(R*T));
bn = 0.03*exp(-1.e-3*5*0.6*(v[seg]+32)*F/(R*T));
al = 0.001*exp(-1.e-3*2*(v[seg]+61)*F/(R*T));
bl = 0.001;
tau_n = 1/(an+bn);
tau_l = 1/(al+bl);
n_inf = an*tau_n;
l_inf = al*tau_l;
nkdr[seg] = n_inf;
lkdr[seg] = l_inf;
ikdr[seg] = 0.0;
}
an = 0.03*exp(1.e-3*5*0.4*(v[seg]+32)*F/(R*T));
bn = 0.03*exp(-1.e-3*5*0.6*(v[seg]+32)*F/(R*T));
al = 0.001*exp(-1.e-3*2*(v[seg]+61)*F/(R*T));
bl = 0.001;
tau_n = 1/(an+bn);
tau_l = 1/(al+bl);
n_inf = an*tau_n;
l_inf = al*tau_l;
nkdr[seg] = (nkdr[seg] + dt*n_inf/tau_n)/(1+dt/tau_n);
lkdr[seg] = (lkdr[seg] + dt*l_inf/tau_l)/(1+dt/tau_l);
ikdr[seg] = gkdr*nkdr[seg]*nkdr[seg]*nkdr[seg]*lkdr[seg]*(v[seg]+91);
// return ikdr;
}