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HH_memdyn.h
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HH_memdyn.h
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void chn_cond(double *fr, double *tau,double V, string ntype){
double alp,beta;
if( ntype=="OLMa" || ntype=="OLMb" ||ntype=="OLMr"){
if(ntype=="OLMa"){
*fr =1/(1+exp(-(V+14)/16.6));
*tau=5;
}
else if(ntype=="OLMb"){
*fr =1/(1+exp((V+71)/7.3));
*tau=1/( 0.000009/exp((V-26.0)/18.5) + 0.014/(0.2+exp(-(V+70)/11.0)) );
}
else if(ntype=="OLMr"){
*fr=1/(1+exp((V+84)/10.2));
*tau=1/( exp(-14.59-0.086*V) + exp(-1.87+0.0701*V) );
}
return ;
}
if(ntype=="Em"){
alp =0.32*(V+54)/(1-exp(-(V+54)/4.));
beta=0.28*(V+27)/(exp((V+27)/5.)-1);
}
else if(ntype=="En"){
alp =0.032*(V+52)/(1-exp(-(V+52)/5.));
beta=0.5*exp(-(V+57)/40.);
}
else if(ntype=="PVm"){
alp =0.1*(V+35)/(1-exp(-(V+35)/10.));
beta=4*exp(-(V+60)/18.);
}
else if(ntype=="PVh"){
alp =0.07*exp(-(V+58)/20.);
beta=1/(exp(-0.1*(V+28))+1);
}
else if(ntype=="PVn"){
alp =0.01*(V+34)/(1-exp(-(V+34)));
beta=0.125*exp(-(V+44)/80.0);
}
else if(ntype=="OLMm"){
alp =-0.1*(V+38)/(exp(-(V+38)/10)-1);
beta=4*exp(-(V+65)/18);
}
else if(ntype=="OLMh"){
alp =0.07*exp(-(V+63)/20);
beta=1/(exp(-0.1*(V+33))+1);
}
else if(ntype=="OLMn"){
alp =0.018*(V-25)/(1-exp(-(V-25)/25.0));
beta=0.0036*(V-35)/(exp((V-35)/12.0)-1);
}
else if(ntype=="EC5p"){
alp =1/(0.15*(1+exp(-(V+38)/6.5)));
beta =exp(-(V+38)/6.5)/(0.15*(1+exp(-(V+38)/6.5)));
}
else if(ntype=="EC5m"){
alp =-0.1*(V+23)/(exp(-0.1*(V+23))-1);
beta=4*exp(-(V+48)/18.);
}
else if(ntype=="EC5h"){
alp =0.07*exp(-(V+37)/20.);
beta=1/(exp(-0.1*(V+7))+1);
}
else if(ntype=="EC5n"){
alp =-0.01*(V+27)/(exp(-0.1*(V+27))-1);
beta=0.125*exp(-(V+37)/80.);
}
else if(ntype=="EC5_caL_q"){
alp =-0.055*(V+27)/(exp(-(V+27)/3.8)-1);
beta=0.94*exp(-(75+V)/17.0);
}
else if(ntype=="EC5_caL_r"){
alp=0.000457*exp(-(V+13)/50.0);
beta=0.0065/(exp(-(V+15)/28)+1);
}
else if(ntype=="EC5_pyr_m"){ // Middleton,PNAS,2008
alp =-0.32*(V+54)/(exp(-0.25*(V+54))-1);
beta= 0.28*(V+27)/(exp(0.2*(V+27)) -1);
}
else if(ntype=="EC5_pyr_n"){ // Middleton,PNAS,2008
alp =-0.032*(V+52)/(exp(-0.2*(V+52))-1);
beta= 0.5*exp(-0.025*(V+57));
}
else if(ntype=="EC5_pyr_h"){ // Middleton,PNAS,2008
alp =0.128*exp(-1*(V+50)/18.0);
beta=4.0/(exp(-0.2*(V+27))+1);
}
else if(ntype=="EC5_pyr_ahp"){ // Middleton,PNAS,2008
alp =1/(exp(-0.1*(V+41))+1);
beta=500.0/(3.3*exp(0.05*(V+41))+exp(-0.05*(V+41))); //check point original value (400 [ms]), 400->600 2017.6.30 update)
}
(*fr)=alp/(alp+beta);
(*tau)=1/(alp+beta);
if(ntype=="EC5_pyr_ahp"){
(*fr)=alp;
(*tau)=beta;
}
if(ntype=="PVh" || ntype=="PVn") *tau=*tau*0.2;
return;
}
void difffunc_EC3_E(double x[], double dx[], STR_PARA *paras){ // Rotstein,et al., 2006, JCN
//x[0]: membrane potential,x[1]: channel function n, x[2]: h, x[3]: m,x[4]: p x[4]:p, x[5]: rf, x[6]: rs
static double gNa=52.0,gK=11.0,gL=0.5,gp=0.5,gh=1.5;
static double VNa=55.0,VK=-90.0,VL=-65.0,Vh=-20;
// static double C=1.0; C is unity here, so we neglect this term.
double minf,ninf,hinf,pinf,rfinf,rsinf;
double tm,tn,th,tp,trf,trs;
double tmpI =paras->I;
chn_cond(&ninf,&tn,x[0],"EC5n");
chn_cond(&hinf,&th,x[0],"EC5h");
chn_cond(&minf,&tm,x[0],"EC5m");
chn_cond(&pinf,&tp,x[0],"EC5p");
rfinf=1/(1+exp((x[0]+79.2)/9.78));
trf =0.51/(exp((x[0]-1.7)*0.1) + exp(-(x[0]+340)/52.0)) + 1;
rsinf=1/pow((1+exp((x[0]+2.83)/15.9)),58);
trs =5.6/(exp((x[0]-1.7)/14) + exp(-(x[0]+260)/43.0)) + 1;
dx[0] =gNa*x[3]*x[3]*x[3]*x[2]*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])+gp*x[4]*(VNa-x[0])+gh*(0.65*x[5]+0.35*x[6])*(Vh-x[0])+gL*(VL-x[0])+tmpI;
dx[1]=(ninf-x[1])/tn;
dx[2]=(hinf-x[2])/th;
dx[3]=(minf-x[3])/tm;
dx[4]=(pinf-x[4])/tp;
dx[5]=(rfinf-x[5])/trf;
dx[6]=(rsinf-x[6])/trs;
return;
}
// this is an identical function
void difffunc_EC2_stell(double x[], double dx[], STR_PARA *paras){ // Rotstein,et al., 2006, JCN
//x[0]: membrane potential,x[1]: channel function n, x[2]: h, x[3]: m,x[4]: p x[4]:p, x[5]: rf, x[6]: rs
static double gNa=52.0,gK=11.0,gL=0.5,gp=0.5,gh=0.4;
static double VNa=55.0,VK=-90.0,VL=-65.0,Vh=-20;
// static double C=1.0; C is unity here, so we neglect this term.
double minf,ninf,hinf,pinf,rfinf,rsinf;
double tm,tn,th,tp,trf,trs;
double tmpI =paras->I;
chn_cond(&ninf,&tn,x[0],"EC5n");
chn_cond(&hinf,&th,x[0],"EC5h");
chn_cond(&minf,&tm,x[0],"EC5m");
chn_cond(&pinf,&tp,x[0],"EC5p");
rfinf=1/(1+exp((x[0]+79.2)/9.78));
trf =0.51/(exp((x[0]-1.7)*0.1) + exp(-(x[0]+340)/52.0)) + 1;
rsinf=1/pow((1+exp((x[0]+2.83)/15.9)),58);
trs =5.6/(exp((x[0]-1.7)/14) + exp(-(x[0]+260)/43.0)) + 1;
dx[0] =gNa*x[3]*x[3]*x[3]*x[2]*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])+gp*x[4]*(VNa-x[0])+gh*(0.65*x[5]+0.35*x[6])*(Vh-x[0])+gL*(VL-x[0])+tmpI;
dx[1]=(ninf-x[1])/tn;
dx[2]=(hinf-x[2])/th;
dx[3]=(minf-x[3])/tm;
dx[4]=(pinf-x[4])/tp;
dx[5]=(rfinf-x[5])/trf;
dx[6]=(rsinf-x[6])/trs;
return;
}
void difffunc_EC3_E_pyr(double x[], double dx[], STR_PARA *paras){ // Rotstein,et al., 2006, JCN, Saravanan, 2015,Hipp, Middleton, 2008,PNAS
//x[0]: membrane potential,x[1]: channel function n, x[2]: h, x[3]: m,x[4]:ahp
static double gNa=100.0,gK=80.0,gL=0.5,gAHP=0.3; //check point in old version, gh=0.25 (2017.6.30 update) check point gahp=0.6 -> 0.6
static double VNa=50.0,VK=-90.0,VL=-65.0,VAHP=-100; //check
// static double C=1.0 [uF/cm^2], thus, inverse of system time scale is mS/uF = 1/ms
double minf,ninf,hinf,ahpinf,rfinf,rsinf;
double tm,tn,th,tahp,trf,trs;
double tmpI =paras->I;
double tmpgCAN =paras->gCAN;
chn_cond(&ninf,&tn,x[0],"EC5_pyr_n");
chn_cond(&hinf,&th,x[0],"EC5_pyr_h");
chn_cond(&minf,&tm,x[0],"EC5_pyr_m");
chn_cond(&ahpinf,&tahp,x[0],"EC5_pyr_ahp");
rfinf=1/(1+exp((x[0]+79.2)/9.78));
trf =0.51/(exp((x[0]-1.7)*0.1) + exp(-(x[0]+340)/52.0)) + 1;
rsinf=1/pow((1+exp((x[0]+2.83)/15.9)),58);
trs =5.6/(exp((x[0]-1.7)/14) + exp(-(x[0]+260)/43.0)) + 1;
dx[0] =gNa*x[3]*x[3]*x[3]*x[2]*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])+gAHP*x[4]*(VAHP-x[0])+gL*(VL-x[0])+tmpI;
dx[1]=(ninf-x[1])/tn;
dx[2]=(hinf-x[2])/th;
dx[3]=(minf-x[3])/tm;
dx[4]=(ahpinf-x[4])/tahp;
dx[5]=(rfinf-x[5])/trf;
dx[6]=(rsinf-x[6])/trs;
return;
}
#if VER_PROG != 9
void difffunc_EC5_E_CAN(double x[], double dx[], STR_PARA *paras){ // Rotstein,et al., 2006, JCN (we modified sttelate cells in EC2 with decreasing AHP current (see Heys's review in 2012 ), Saravanan, 2015,Hipp
//x[0]: membrane potential,x[1]: channel function n, x[2]: h, x[3]: m,x[4]: p x[4]:p, x[5]: rf, x[6]: rs
static double gNa=52.0,gK=11.0,gL=0.5,gp=0.5,gh=1.0; // original in *6.cpp.bak: gh=1.5 check point 4/7
static double VNa=55.0,VK=-90.0,VL=-65.0,Vh=-20,VCAN=-20;
// static double C=1.0; C is unity here, so we neglect this term.
double minf,ninf,hinf,pinf,rfinf,rsinf;
double tm,tn,th,tp,trf,trs;
double tmpI =paras->I;
double tmpgCAN =paras->gCAN;
double tmpgate_CAN=paras->gate_CAN;
chn_cond(&ninf,&tn,x[0],"EC5n");
chn_cond(&hinf,&th,x[0],"EC5h");
chn_cond(&minf,&tm,x[0],"EC5m");
chn_cond(&pinf,&tp,x[0],"EC5p");
rfinf=1/(1+exp((x[0]+79.2)/9.78));
trf =0.51/(exp((x[0]-1.7)*0.1) + exp(-(x[0]+340)/52.0)) + 1;
rsinf=1/pow((1+exp((x[0]+2.83)/15.9)),58);
trs =5.6/(exp((x[0]-1.7)/14) + exp(-(x[0]+260)/43.0)) + 1;
dx[0] =gNa*x[3]*x[3]*x[3]*x[2]*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])+gp*x[4]*(VNa-x[0])+gh*(0.65*x[5]+0.35*x[6])*(Vh-x[0])+gL*(VL-x[0])+tmpI
+tmpgCAN*tmpgate_CAN*(VCAN-x[0]);
dx[1]=(ninf-x[1])/tn;
dx[2]=(hinf-x[2])/th;
dx[3]=(minf-x[3])/tm;
dx[4]=(pinf-x[4])/tp;
dx[5]=(rfinf-x[5])/trf;
dx[6]=(rsinf-x[6])/trs;
return;
}
void difffunc_EC5_E_pyr_CAN(double x[], double dx[], STR_PARA *paras){ // the neuron model is based on pyramidal cell in EC2 (E cell in Middleton, 2008,PNAS) + modution on Ca dynamics. (See also Fransen 2006 and 2002. the former paper builds a model of EC5 neuron which is based on EC2 neuron (Fransen 2002).
//x[0]: membrane potential,x[1]: channel function n, x[2]: h, x[3]: m,x[4]:ahp, x[5]: rf, x[6]: rs
static double gNa=100.0,gK=80.0,gL=0.5,gAHP=0.2,gh=0.0; // (modification on 6/19, gahp:0.4->0.2,gh:0.25) check point 0.1->0.2
static double VNa=50.0,VK=-100.0,VL=-65.0,VAHP=-100,Vh=-20,VCAN=-20;
// static double C=1.0; C is unity here, so we neglect this term.
double minf,ninf,hinf,ahpinf,rfinf,rsinf;
double tm,tn,th,tahp,trf,trs;
double tmpI =paras->I;
double tmpgCAN =paras->gCAN;
double tmpgate_CAN=paras->gate_CAN;
chn_cond(&ninf,&tn,x[0],"EC5_pyr_n");
chn_cond(&hinf,&th,x[0],"EC5_pyr_h");
chn_cond(&minf,&tm,x[0],"EC5_pyr_m");
chn_cond(&ahpinf,&tahp,x[0],"EC5_pyr_ahp");
rfinf=1/(1+exp((x[0]+79.2)/9.78));
trf =0.51/(exp((x[0]-1.7)*0.1) + exp(-(x[0]+340)/52.0)) + 1;
rsinf=1/pow((1+exp((x[0]+2.83)/15.9)),58);
trs =5.6/(exp((x[0]-1.7)/14) + exp(-(x[0]+260)/43.0)) + 1;
dx[0] =gNa*x[3]*x[3]*x[3]*x[2]*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])+gAHP*x[4]*(VAHP-x[0])+gh*(0.65*x[5]+0.35*x[6])*(Vh-x[0])+gL*(VL-x[0])+tmpI
+tmpgCAN*tmpgate_CAN*(VCAN-x[0]);
dx[1]=(ninf-x[1])/tn;
dx[2]=(hinf-x[2])/th;
dx[3]=(minf-x[3])/tm;
dx[4]=(ahpinf-x[4])/tahp;
dx[5]=(rfinf-x[5])/trf;
dx[6]=(rsinf-x[6])/trs;
return;
}
#endif
// last update 2017.6.28
void difffunc_EC5_E_pyr_Ca_dyn(double x[], double dx[], STR_PARA *paras){ // the neuron model is based on pyramidal cell in EC2 (E cell in Middleton, 2008,PNAS) + Ca dynamics (Saravanan,2015). (See also Fransen 2006 and 2002. the former paper builds a model of EC5 neuron which is based on EC2 neuron (Fransen 2002).
// CAN channel is based on Destexhe 1994
// Ca dynamics is based on Destexhe 1994 and Saravanan 2015
//x[0]: membrane potential,x[1]: channel function n, x[2]: h, x[3]: m,x[4]:ahp, x[5]: rf, x[6]: rs, x[7]:qca, x[8]:rca, x[9]:Ca concentration, x[10]:m_can
static double gNa=100.0,gK=80.0,gL=0.5,gAHP=0.1,gh=0.0,gCaL=0.01; // [mS/cm^2] (modification on 6/19, gahp:0.4->0.2,gh:0.25)
static double VNa=50.0,VK=-100.0,VL=-65.0,VAHP=-100,VCAN=-20,VCaL=120; //[mV]
static double I2C=0.51819378374737; //-k/Fd current of Ca to concentration
static double Cainf=0.24; //[uM]
// static double C=1.0; C is unity here, so we neglect this term.
double minf,ninf,hinf,ahpinf,rfinf,rsinf,alpha_qca,beta_qca,alpha_rca,beta_rca,mcaninf;
double tm,tn,th,tahp,trf,trs,t2Ca,tmcan;
double tmpI =paras->I;
double tmpgCAN =paras->gCAN;
double ICaL=0.0;
chn_cond(&ninf,&tn,x[0],"EC5_pyr_n");
chn_cond(&hinf,&th,x[0],"EC5_pyr_h");
chn_cond(&minf,&tm,x[0],"EC5_pyr_m");
chn_cond(&ahpinf,&tahp,x[0],"EC5_pyr_ahp");
rfinf=1/(1+exp((x[0]+79.2)/9.78));
trf =0.51/(exp((x[0]-1.7)*0.1) + exp(-(x[0]+340)/52.0)) + 1;
rsinf=1/pow((1+exp((x[0]+2.83)/15.9)),58);
trs =5.6/(exp((x[0]-1.7)/14) + exp(-(x[0]+260)/43.0)) + 1;
alpha_qca=0.055*(-27-x[0])/(exp((-27-x[0])/3.8)-1);
beta_qca =0.94*exp(-(75+x[0])/17.0);
alpha_rca=0.000457*exp(-(x[0]+13)/50.0);
beta_rca =0.0065/(exp(-(x[0]+15)/28.0)+1);
t2Ca = 250.0; // [ms]
mcaninf=20.0*x[9]*x[9]/(20.0*x[9]*x[9]+6); //chenge the inflection point (2000 (0.02[ms-1]*10^6) -> 100) check point 1 8->6
tmcan =1.0/(20.0*x[9]*x[9]*0.002+0.003); // change from original values 0.002 -> 0.004
ICaL=gCaL*x[7]*x[7]*x[8]*(VCaL-x[0]);
dx[0] =gNa*x[3]*x[3]*x[3]*x[2]*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])+gAHP*x[4]*(VAHP-x[0])+gL*(VL-x[0])+tmpI
+ICaL+tmpgCAN*x[10]*x[10]*(VCAN-x[0]);
dx[1]=(ninf-x[1])/tn;
dx[2]=(hinf-x[2])/th;
dx[3]=(minf-x[3])/tm;
dx[4]=(ahpinf-x[4])/tahp;
dx[5]=(rfinf-x[5])/trf;
dx[6]=(rsinf-x[6])/trs;
dx[7]=alpha_qca*(1-x[7])-beta_qca*x[7];
dx[8]=alpha_rca*(1-x[8])-beta_rca*x[8];
dx[9]=I2C*ICaL+(Cainf-x[9])/t2Ca;
dx[10]=(mcaninf-x[10])/tmcan;
return;
}
void difffunc_EC5_E_pyr_Fransen(double x[], double dx[], STR_PARA *paras){
// the neuron model is based on pyramidal cell in EC2 (Fransen 2006)
// original unit system: [s], [S/m^2], [F/m^2],[V] -> [ms],[mS/cm^2],[uF/cm^2],[mV]
//x[0]: membrane potential,x[1]: channel function n, x[2]: h, x[3]: m,x[4]:ahp, x[5]: s for CaL
//x[6]: x for M , x[7]: m for Na p, x[8]: h for Na p, x[9]: a for K A, x[10]:b for K A
//x[11]: concentration of Ca
//x[12]: c for CAN
//x[13]: c for KC
static double gNa=100.0,gK=80.0,gL=0.5,gAHP=0.05,gKC=196,gM=3.5,gCaL=0.15,gNap=0.2,gKA=0.5; // [mS/cm^2]
// original values of conductances [S/m^2] for capacitance C=0.01 [F/m^2] (unit time=[s]), here mS/cm^2, uF/cm^2, thus we just multiply 0.1 to values of conductance and set capacitance 1 (unit time=[ms]).
static double VNa=50.0,VK=-100.0,VL=-65.0,VCAN=-20,VCa=140; //[mV]
static double I2C=0.51819378374737; //-k/Fd current of Ca to concentration
double tmpI =paras->I;
double tmpgCAN =paras->gCAN;
double ICaL=0.0;
double t2Ca=250;
double s_inf, tau_s;
double alpha_s, beta_s;
double tmp_s;
double dtmp;
dx[0] =gNa*x[3]*x[3]*x[3]*x[2]*(VNa-x[0]); // Na channel
dx[0]+=gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0]); // delayed K channel
dx[0]+=gAHP*x[4]*x[4]*(VK-x[0]); // K ahp channel
ICaL=gCaL*x[5]*x[5]*(VCa-x[0]); // CaL channel
dx[0]+=ICaL;
dx[0]+=gM*x[6]*(VK-x[0]); // K M channel
dx[0]+=gNap*x[7]*x[8]*(VNa-x[0]); // Na persistent channel
dx[0]+=gKA*x[9]*x[10]*(VK-x[0]); // K A channel
dx[0]+=tmpgCAN*x[12]*x[12]*(VCAN-x[0]); // CAN channel
dx[0]+=gKC*x[13]*(VK-x[0]); // K C channel
dx[0]+=tmpI;
chn_cond(&s_inf,&tau_s,x[0],"EC5_pyr_n");
dx[1]=(s_inf-x[1])/tau_s;
chn_cond(&s_inf,&tau_s,x[0],"EC5_pyr_h");
dx[2]=(s_inf-x[2])/tau_s;
chn_cond(&s_inf,&tau_s,x[0],"EC5_pyr_m");
dx[3]=(s_inf-x[3])/tau_s;
// ahp
if(x[11]*1000>15){
dtmp=(3.0+0.8*(1000*x[11]-15.0));
alpha_s= dtmp>15.0 ? 15.0 : dtmp; //check point x[11] -> x[11]*30
}
else alpha_s= 1000*x[11]*0.2;
beta_s=1.0;
tmp_s=x[4];
dx[4]=0.001*(alpha_s*(1-tmp_s)-beta_s*tmp_s);
// CaL
alpha_s=1.6/(1+exp(-0.072*(x[0]-65.0)));
beta_s =0.02*(x[0]-51.1)/(exp((x[0]-51.1)*0.2)-1.0);
tmp_s=x[5];
dx[5]=alpha_s*(1-tmp_s)-beta_s*tmp_s;
//KC
if(x[0]<50.0){
alpha_s=exp(0.053782*x[0]-0.66835)/18.975;
beta_s =2.0*exp((6.5-x[0])/27.0)-alpha_s;
}
else{
alpha_s =2*exp((6.5-x[0])/27.0);
beta_s =0.0;
}
tmp_s=x[13];
dx[13]=alpha_s*(1-tmp_s)-beta_s*tmp_s;
//KM
s_inf=1/(1+exp(-(x[0]+35.0)/5.0));
tau_s=1000.0/(3.3*exp((x[0]+35)/40.0)+exp(-(x[0]+35)/20.0));
tmp_s=x[6];
dx[6]=(s_inf-tmp_s)/tau_s;
//Nap
s_inf=1/(1+exp(-(x[0]+48.7)/4.4));
dtmp=x[0]+38.0;
tau_s=1/( (0.091*dtmp/(1-exp(-dtmp/5.0))) + (-0.062*dtmp/(1-exp(dtmp/5.0))) );
tmp_s=x[7];
dx[7]=(s_inf-tmp_s)/tau_s;
s_inf=1/(1+exp(-(x[0]+48.8)/9.98));
tau_s=1/( (-0.00000288*(x[0]-49.1)/(1-exp(-(x[0]-49.1)/4.63))) + (0.00000694*(x[0]+44.7)/(1-exp((x[0]+44.7)/2.63))) );
tmp_s=x[8];
dx[8]=(s_inf-tmp_s)/tau_s;
//KA from Traub 1991
alpha_s=0.02*(x[0]-13.1)/(1-exp((13.1-x[0])/10.0));
beta_s =0.175*(x[0]-40.1)/(exp((x[0]-40.1)/10.0)-1);
tmp_s=x[9];
dx[9]=alpha_s*(1-tmp_s)-beta_s*tmp_s;
alpha_s=0.0016*exp(-(x[0]+13)/18.0);
beta_s =0.05/(1+exp(10.1-x[0])/5.0);
tmp_s=x[10];
dx[10]=alpha_s*(1-tmp_s)-beta_s*tmp_s;
// Ca dyn
dx[11]=I2C*ICaL-x[11]/t2Ca;
// CAN check point
s_inf=48.0*100*x[11]*x[11]/(48.0*100*x[11]*x[11]+0.03);
tau_s=1.0/(48.0*100*x[11]*x[11]+0.03);
tmp_s=x[12];
dx[12]=(s_inf-tmp_s)/tau_s;
}
// last update 2017.7.25
void difffunc_EC5_E_pyr_Ca_dyn_M(double x[], double dx[], STR_PARA *paras){ // the neuron model is based on pyramidal cell in EC2 (E cell in Middleton, 2008,PNAS) + Ca dynamics (Saravanan,2015). (See also Fransen 2006 and 2002. the former paper builds a model of EC5 neuron which is based on EC2 neuron (Fransen 2002).
// Ca-dependent K (AHP) is introduced based on Destexhe 1994
// CAN channel is based on Destexhe 1994
// Ca dynamics is based on Destexhe 1994 and Saravanan 2015
// M current is based on Saravanan, 2015 (this is model for CA1, but ECV model in Fransen 2006 used CA3 model in Traub 1992.)
//x[0]: membrane potential,x[1]: channel function n, x[2]: h, x[3]: m,x[4]:ahp, x[5]: rf, x[6]: rs, x[7]:qca, x[8]:rca, x[9]:Ca concentration, x[10]:m_can
static double gNa=100.0,gK=80.0,gL=0.5,gAHP=0.4,gM=0.004,gCaL=0.01; // [mS/cm^2] (modification on 6/19, gahp:0.4->0.2)
static double VNa=50.0,VK=-100.0,VL=-65.0,VAHP=-100,VCAN=-20,VCaL=120; //[mV]
static double I2C=0.51819378374737; //-k/Fd current of Ca to concentration
static double Cainf=0.24; //[uM]
// static double C=1.0; C is unity here, so we neglect this term.
double minf,ninf,hinf,ahpinf,rfinf,rsinf,alpha_qca,beta_qca,alpha_rca,beta_rca,mcaninf,Minf;
double tm,tn,th,tahp,trf,trs,t2Ca,tmcan,tM;
double tmpI =paras->I;
double tmpgCAN =paras->gCAN;
double ICaL=0.0;
chn_cond(&ninf,&tn,x[0],"EC5_pyr_n");
chn_cond(&hinf,&th,x[0],"EC5_pyr_h");
chn_cond(&minf,&tm,x[0],"EC5_pyr_m");
rfinf=1/(1+exp((x[0]+79.2)/9.78));
trf =0.51/(exp((x[0]-1.7)*0.1) + exp(-(x[0]+340)/52.0)) + 1;
rsinf=1/pow((1+exp((x[0]+2.83)/15.9)),58);
trs =5.6/(exp((x[0]-1.7)/14) + exp(-(x[0]+260)/43.0)) + 1;
alpha_qca=0.055*(-27-x[0])/(exp((-27-x[0])/3.8)-1);
beta_qca =0.94*exp(-(75+x[0])/17.0);
alpha_rca=0.000457*exp(-(x[0]+13)/50.0);
beta_rca =0.0065/(exp(-(x[0]+15)/28.0)+1);
t2Ca = 250.0; // [ms]
mcaninf=20.0*x[9]*x[9]/(20.0*x[9]*x[9]+6); //chenge the inflection point (2000 (0.02[ms-1]*10^6) -> 100) check point 1 8->6
tmcan =1.0/(20.0*x[9]*x[9]*0.002+0.003); // change from original values 0.002 -> 0.004
Minf=1.0/(1.0+exp(-(x[0]+35)/10.0));
tM =1000/(3.3*exp((x[0]+35)/20.0)+exp(-(x[0]+35)/20.0));
ahpinf =48.0*x[9]*x[9]/(48.0*x[9]*x[9]+90);
tahp =1.0/(48.0*x[9]*x[9]*0.002+0.015); // change from original values 0.002 -> 0.004
ICaL=gCaL*x[7]*x[7]*x[8]*(VCaL-x[0]);
dx[0] =gNa*x[3]*x[3]*x[3]*x[2]*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])+gAHP*x[4]*x[4]*(VAHP-x[0])+gL*(VL-x[0])+tmpI
+ICaL+tmpgCAN*x[10]*x[10]*(VCAN-x[0])+gM*x[11]*(VK-x[0]);
dx[1]=(ninf-x[1])/tn;
dx[2]=(hinf-x[2])/th;
dx[3]=(minf-x[3])/tm;
dx[4]=(ahpinf-x[4])/tahp;
dx[5]=(rfinf-x[5])/trf;
dx[6]=(rsinf-x[6])/trs;
dx[7]=alpha_qca*(1-x[7])-beta_qca*x[7];
dx[8]=alpha_rca*(1-x[8])-beta_rca*x[8];
dx[9]=I2C*ICaL+(Cainf-x[9])/t2Ca;
dx[10]=(mcaninf-x[10])/tmcan;
dx[11]=(Minf-x[11])/tM;
return;
}
void difffunc_EC5_E_pyr_Ca_dyn1(double x[], double dx[], STR_PARA *paras){ // the neuron model is based on pyramidal cell in EC2 (E cell in Middleton, 2008,PNAS) + Ca dynamics (Saravanan,2015). (See also Fransen 2006 and 2002. the former paper builds a model of EC5 neuron which is based on EC2 neuron (Fransen 2002).
// Cal-dependent Kahp is introduced instead of normal AHP (Destexhe 1994)
// CAN channel is based on Destexhe 1994
// Ca dynamics is based on Destexhe 1994 and Saravanan 2015
//x[0]: membrane potential,x[1]: channel function n, x[2]: h, x[3]: m,x[4]:ahp, x[5]: rf, x[6]: rs, x[7]:qca, x[8]:rca, x[9]:Ca concentration, x[10]:m_can
static double gNa=100.0,gK=80.0,gL=0.5,gAHP=0.1,gh=0.0,gCaL=0.01; // [mS/cm^2] (modification on 6/19, gahp:0.4->0.2,gh:0.25)
static double VNa=50.0,VK=-100.0,VL=-65.0,VCAN=-20,VCaL=120; //[mV]
static double I2C=0.51819378374737; //-k/Fd current of Ca to concentration
static double Cainf=0.24; //[uM]
// static double C=1.0; C is unity here, so we neglect this term.
double minf,ninf,hinf,ahpinf,rfinf,rsinf,alpha_qca,beta_qca,alpha_rca,beta_rca,mcaninf;
double tm,tn,th,tahp,trf,trs,t2Ca,tmcan;
double tmpI =paras->I;
double tmpgCAN =paras->gCAN;
double ICaL=0.0;
chn_cond(&ninf,&tn,x[0],"EC5_pyr_n");
chn_cond(&hinf,&th,x[0],"EC5_pyr_h");
chn_cond(&minf,&tm,x[0],"EC5_pyr_m");
rfinf=1/(1+exp((x[0]+79.2)/9.78));
trf =0.51/(exp((x[0]-1.7)*0.1) + exp(-(x[0]+340)/52.0)) + 1;
rsinf=1/pow((1+exp((x[0]+2.83)/15.9)),58);
trs =5.6/(exp((x[0]-1.7)/14) + exp(-(x[0]+260)/43.0)) + 1;
alpha_qca=0.055*(-27-x[0])/(exp((-27-x[0])/3.8)-1);
beta_qca =0.94*exp(-(75+x[0])/17.0);
alpha_rca=0.000457*exp(-(x[0]+13)/50.0);
beta_rca =0.0065/(exp(-(x[0]+15)/28.0)+1);
t2Ca = 250.0; // [ms]
ahpinf =48.0*x[9]*x[9]/(48.0*x[9]*x[9]+90);
tahp =1.0/(48.0*x[9]*x[9]*0.002+0.015); // change from original values 0.002 -> 0.004
mcaninf=20.0*x[9]*x[9]/(20.0*x[9]*x[9]+6); //chenge the inflection point (2000 (0.02[ms-1]*10^6) -> 100) check point 1 8->6
tmcan =1.0/(20.0*x[9]*x[9]*0.002+0.003); // change from original values 0.002 -> 0.004
ICaL=gCaL*x[7]*x[7]*x[8]*(VCaL-x[0]);
dx[0] =gNa*x[3]*x[3]*x[3]*x[2]*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])+gAHP*x[4]*x[4]*(VK-x[0])+gL*(VL-x[0])+tmpI
+ICaL+tmpgCAN*x[10]*x[10]*(VCAN-x[0]);
dx[1]=(ninf-x[1])/tn;
dx[2]=(hinf-x[2])/th;
dx[3]=(minf-x[3])/tm;
dx[4]=(ahpinf-x[4])/tahp;
dx[5]=(rfinf-x[5])/trf;
dx[6]=(rsinf-x[6])/trs;
dx[7]=alpha_qca*(1-x[7])-beta_qca*x[7];
dx[8]=alpha_rca*(1-x[8])-beta_rca*x[8];
dx[9]=I2C*ICaL+(Cainf-x[9])/t2Ca;
dx[10]=(mcaninf-x[10])/tmcan;
return;
}
void difffunc_CA1_E(double x[], double dx[], STR_PARA *paras){
//x[0]: membrane potential,x[1]: channel function n
static double gNa=100.0,gK=80.0,gL=0.1;
static double VNa=50.0,VK=-100.0,VL=-67.0;
// static double C=1.0; C is unity here, so we neglect this term.
double minf,ninf;
double tn;
double hfrc;
double dummy;
double dtmp;
double tmpI =paras->I;
chn_cond(&minf,&dummy,x[0],"Em");
chn_cond(&ninf,&tn,x[0],"En");
dtmp=(1-1.25*x[1]);
hfrc=( dtmp> 0 ? dtmp : 0);
dx[0]=gNa*minf*minf*minf*hfrc*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])+gL*(VL-x[0])+tmpI;
dx[1]=(ninf-x[1])/tn;
return;
}
void difffunc_CA1_E_Ih(double x[], double dx[], STR_PARA *paras){
//x[0]: membrane potential,x[1]: channel function n, x[2]: ahp, x[3]:fast , x[4]: slow
static double gNa=100.0,gK=80.0,gL=0.1,gAHP=0.2,gh=0.1; //check point gh0.1->0.2->0.1
static double VNa=50.0,VK=-100.0,VL=-67.0,VAHP=-100,Vh=-20;
// static double C=1.0; C is unity here, so we neglect this term.
double minf,ninf,ahpinf,rfinf,rsinf;
double tn,trf,trs,tahp;
double hfrc;
double dummy;
double dtmp;
double tmpI =paras->I;
chn_cond(&minf,&dummy,x[0],"Em");
chn_cond(&ninf,&tn,x[0],"En");
chn_cond(&ahpinf,&tahp,x[0],"EC5_pyr_ahp");
dtmp=(1-1.25*x[1]);
hfrc=( dtmp> 0 ? dtmp : 0);
rfinf=1/(1+exp((x[0]+79.2)/9.78));
trf =0.51/(exp((x[0]-1.7)*0.1) + exp(-(x[0]+340)/52.0)) + 1;
rsinf=1/pow((1+exp((x[0]+2.83)/15.9)),58);
trs =5.6/(exp((x[0]-1.7)/14) + exp(-(x[0]+260)/43.0)) + 1;
dx[0]=gNa*minf*minf*minf*hfrc*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])+gL*(VL-x[0])+gAHP*x[2]*(VAHP-x[0])+gh*(0.65*x[3]+0.35*x[4])*(Vh-x[0])+gL*(VL-x[0])+tmpI;
dx[1]=(ninf-x[1])/tn;
dx[2]=(ahpinf-x[2])/tahp;
dx[3]=(rfinf-x[3])/trf;
dx[4]=(rsinf-x[4])/trs;
return;
}
void difffunc_CA1_E_Ih_Caspk(double x[], double dx[], STR_PARA *paras){ // cal. spike dynamics is in Chua, 2015,front.
//x[0]: membrane potential,x[1]: channel function n, x[2]: ahp, x[3]:fast , x[4]: slow
static double gNa=100.0,gK=80.0,gL=0.1,gAHP=0.2,gh=0.1;
static double VNa=50.0,VK=-100.0,VL=-67.0,VAHP=-100,Vh=-20;
static double gca=1.0,Vca=30.0,tmca=5.0,thca=50.0; // in the paper, gca = 70 nS on a dendritic part. here, we consider point neuron(presumably soma) and set gca=1.
// static double C=1.0; C is unity here, so we neglect this term.
double minf,ninf,ahpinf,rfinf,rsinf,mcainf,hcainf;
double tn,trf,trs,tahp;
double hfrc;
double dummy;
double dtmp;
double tmpI =paras->I;
chn_cond(&minf,&dummy,x[0],"Em");
chn_cond(&ninf,&tn,x[0],"En");
chn_cond(&ahpinf,&tahp,x[0],"EC5_pyr_ahp");
dtmp=(1-1.25*x[1]);
hfrc=( dtmp> 0 ? dtmp : 0);
rfinf=1/(1+exp((x[0]+79.2)/9.78));
trf =0.51/(exp((x[0]-1.7)*0.1) + exp(-(x[0]+340)/52.0)) + 1;
rsinf=1/pow((1+exp((x[0]+2.83)/15.9)),58);
trs =5.6/(exp((x[0]-1.7)/14) + exp(-(x[0]+260)/43.0)) + 1;
mcainf=1/(1+exp(0.5*(x[0]+18.0))); // original 21
hcainf=1/(1+exp(-0.5*(x[0]+21.0))); // original 24
dx[0]=gNa*minf*minf*minf*hfrc*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])+gL*(VL-x[0])+gAHP*x[2]*(VAHP-x[0])+gh*(0.65*x[3]+0.35*x[4])*(Vh-x[0])+gL*(VL-x[0])+gca*x[5]*x[6]*(Vca-x[0])+tmpI;
dx[1]=(ninf-x[1])/tn;
dx[2]=(ahpinf-x[2])/tahp;
dx[3]=(rfinf-x[3])/trf;
dx[4]=(rsinf-x[4])/trs;
dx[5]=(mcainf-x[5])/tmca;
dx[6]=(hcainf-x[6])/thca;
return;
}
void difffunc_CA1_OLM(double x[], double dx[], STR_PARA *paras){
//x[0]: membrane potential,x[1]: channel function n,x[2]: channel function h, x[3]: channel function m,
//x[4]: channel function a,x[5]: channel function b,x[6]: channel function r,
static double gNa=40.0,gK=23.0,gL=0.05,gA=16.0,gh=6.0; // gNa:30->40
static double VNa=60.0,VK=-100.0,VL=-70.0,VA=-90.0,Vh=-32.0;
static double Cinv=1/1.3;
double minf,ninf,hinf,ainf,binf,rinf;
double tm,tn,th,ta,tb,tr;
double dtmp;
double tmpI =paras->I;
chn_cond(&minf,&tm,x[0],"OLMm");
chn_cond(&ninf,&tn,x[0],"OLMn");
chn_cond(&hinf,&th,x[0],"OLMh");
chn_cond(&ainf,&ta,x[0],"OLMa");
chn_cond(&binf,&tb,x[0],"OLMb");
chn_cond(&rinf,&tr,x[0],"OLMr");
dx[0]=Cinv*(gNa*x[3]*x[3]*x[3]*x[2]*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])
+gA*x[4]*x[5]*(VA-x[0])+gh*x[6]*(Vh-x[0])+gL*(VL-x[0])+tmpI);
dx[1]=(ninf-x[1])/tn;
dx[2]=(hinf-x[2])/th;
dx[3]=(minf-x[3])/tm;
dx[4]=(ainf-x[4])/ta;
dx[5]=(binf-x[5])/tb;
dx[6]=(rinf-x[6])/tr;
return;
}
void difffunc_CA1_PV(double x[], double dx[], STR_PARA *paras){
//x[0]: membrane potential,x[1]: channel function n,x[2]: channel function h
static double gNa=35.0,gK=9.0,gL=0.1;
static double VNa=55.0,VK=-90.0,VL=-65.0;
// static double C=1.0; C is unity here, so we neglect this term.
double minf,ninf,hinf;
double tn,th;
double hfrc;
double dummy;
double dtmp;
double tmpI =paras->I;
chn_cond(&minf,&dummy,x[0],"PVm");
chn_cond(&ninf,&tn,x[0],"PVn");
chn_cond(&hinf,&th,x[0],"PVh");
dx[0]=gNa*minf*minf*minf*x[2]*(VNa-x[0])+gK*x[1]*x[1]*x[1]*x[1]*(VK-x[0])+gL*(VL-x[0])+tmpI;
dx[1]=(ninf-x[1])/tn;
dx[2]=(hinf-x[2])/th;
return;
}
void RG4(double x[],int n_DOF, double *tp, STR_PARA *paras,void (*p_diff_func)(double xtmp[],double dx[],STR_PARA *paras)){
int i0;
double htmp,hh,h6;
double dxm[n_DOF],dxtmp[n_DOF],xtmp[n_DOF],dxdt[n_DOF];
htmp=hstp;
hh=0.5*htmp;
h6=htmp/6.0;
(*p_diff_func)(x,dxdt,paras); // 1st step
for(i0=0;i0<n_DOF;i0++)xtmp[i0]=x[i0]+hh*dxdt[i0];
(*p_diff_func)(xtmp,dxtmp,paras); // 2nd step
for(i0=0;i0<n_DOF;i0++)xtmp[i0]=x[i0]+hh*dxtmp[i0];
(*p_diff_func)(xtmp,dxm,paras); // 3rd step
for(i0=0;i0<n_DOF;i0++){
xtmp[i0]=x[i0]+htmp*dxm[i0];
dxm[i0]+=dxtmp[i0];
}
(*p_diff_func)(xtmp,dxtmp,paras); // 4th step
for(i0=0;i0<n_DOF;i0++) x[i0]+=h6*(dxdt[i0]+2.0*dxm[i0]+dxtmp[i0]);
return;
}