// Rubinstein model of Ranvier Node's action potentials as in
// Rubinstein JT (1995) Biophys J 68: 779-785.
// Mino H, Rubinstein JT, White JA (2002) Ann Biomed Eng 30: 578-587.
// Bruce IC (2007) Ann Biomed Eng 35: 315-318;
// Voltage is shifted so that resting voltage = 0 mV (the reversal of the leak)
// This script simulates 1000 sweeps and calculates
// firing efficiency, mean firing time and firing time variance
// 100 (nsim) simultaneous sweeps, 10 times
// Lines 49, 62, 63, 86 and 87 are intended to make a voltage trace
// It is advisable to reduce nsim before uncommenting them
//
// UNcoupled (two-state) activation particles, 3 m and 1 h particle per Na channel
// Difussion Approximation algorithm (F algorithm) with mean values of the variables in the random terms
nsim=100;
gNa=0.02569; //mS/cm2
ENa=144; //mV
Cm=0.0000714; Rm=1953.49;
NNa=1000;
Tstop=1; dt=0.0001; //ms
points = round(Tstop/dt)
Idel=0; Idur=0.1; //ms, ms
threshold=80;
rand('normal');
Eff=[];
meanFT=[];
varFT=[];
tic()
currents=[5:0.1:6.5];
NNa3=3*NNa;
Eff=[];
meanFT=[];
varFT=[];
NaNs=[];
tic()
for curr=1:size(currents,'*')
Iamp=ones(1,nsim)*currents(curr)/265;
firetimes=[];
NNaNs=0;
for nn=1:10
p=1;
//If you want to uncomment the following reduce nsim
//vrec = zeros(points,nsim);
v = 0*ones(1,nsim);
alpha_m=1.872*(v-25.41)./(1-exp((25.41-v)/6.06));
beta_m=3.973*(21-v)./(1-exp((v-21)/9.41));
alpha_h=-0.549*(27.74+v)./(1-exp((v+27.74)/9.06));
beta_h=(22.57)./(1+exp((56-v)/12.5));
m=ones(1,nsim)./(1+beta_m./alpha_m);
h=ones(1,nsim)./(1+beta_h./alpha_h);
firetime=zeros(1,nsim);
firing=zeros(1,nsim);
for t = dt:dt:Tstop
//vrec(p,:) = v; //uncomment with a reduced nsim
//p=p+1;
if or(~firing&v>=threshold) then
ind=find(v>=threshold&~firing);
firetime(ind)=t;
firing(ind)=1;
end
alpha_m=1.872*(v-25.41)./(1-exp((25.41-v)/6.06));
beta_m=3.973*(21-v)./(1-exp((v-21)/9.41));
alpha_h=-0.549*(27.74+v)./(1-exp((v+27.74)/9.06));
beta_h=(22.57)./(1+exp((56-v)/12.5));
SDm = sqrt(2*alpha_m.*beta_m./(alpha_m+beta_m));
SDh = sqrt(2*alpha_h.*beta_h./(alpha_h+beta_h));
Iapp=Iamp*(t>Idel&t<(Idel+Idur));
Imemb=-Iapp+gNa*m^(3).*h.*(v-ENa)+v./Rm;
m=m+dt*(alpha_m.*(1-m)-beta_m.*m+rand(1,nsim).*SDm/sqrt(3*NNa*dt));
h=h+dt*(alpha_h.*(1-h)-beta_h.*h+rand(1,nsim).*SDh/sqrt(NNa*dt));
v=v-dt*Imemb/Cm;
end
printf("round %d Iamp %g\n",nn,currents(curr))
//clf //uncomment with a reduced nsim
//plot(dt:dt:Tstop,vrec)
firetimes=[firetimes firetime];
NNaNs=NNaNs + sum(1*(isinf(v)|isnan(v)));
end
Eff=[Eff;size(find(firetimes<>0),'*')];
meanFT=[meanFT;mean(firetimes(find(firetimes<>0)))];
if size(find(firetimes<>0),'*')>1 then
varFT=[varFT;variance(firetimes(find(firetimes<>0)))];
else
varFT=[varFT;0];
end
NaNs=[NaNs;NNaNs];
end
realt=toc();
printf("time = %g",realt)
fprintfMat('EffN-Rb2 Fss-N'+string(NNa)+'-dt'+string(dt)+'-'+string(realt)+'s.txt',[currents' Eff meanFT varFT NaNs],'%g\t')
scf(0);
clf
subplot(3,1,1)
plot(currents,Eff)
subplot(3,1,2)
plot(currents,meanFT)
subplot(3,1,3)
plot(currents,varFT)