TTX-R Na+ current effect on cell response (Herzog et al 2001) (MATLAB)

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Accession:120117
"Small dorsal root ganglion (DRG) neurons, which include nociceptors, express multiple voltage-gated sodium currents. In addition to a classical fast inactivating tetrodotoxin-sensitive (TTX-S) sodium current, many of these cells express a TTX-resistant (TTX-R) sodium current that activates near -70 mV and is persistent at negative potentials. To investigate the possible contributions of this TTX-R persistent (TTX-RP) current to neuronal excitability, we carried out computer simulations using the Neuron program with TTX-S and -RP currents, fit by the Hodgkin-Huxley model, that closely matched the currents recorded from small DRG neurons. ..." See paper for more and details.
Reference:
1 . Herzog RI, Cummins TR, Waxman SG (2001) Persistent TTX-resistant Na+ current affects resting potential and response to depolarization in simulated spinal sensory neurons. J Neurophysiol 86:1351-64 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s): I Na,p; I Na,t; I K;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: MATLAB;
Model Concept(s): Ion Channel Kinetics; Nociception;
Implementer(s): Andersson, Thomas [toma at math.su.se];
Search NeuronDB for information about:  I Na,p; I Na,t; I K;
clear
% MAIN SIMULATION MODULE - SUBFUNCTIONS BELOW
Cm=0.81; % Capacitance
Ena=62.94; % Reversal potential Na (mV)
Ek=-92.34; % Reversal potential K (mV)
El=-54.3; % Reversal potential Leak (mV)
gnats=35.135; % Peak Conductance Na TTX-S (mS/cm2)
gnatr=6.9005; % Peak Conductance Na TTX-R (mS/cm2)
gkdr=2.1; % Peak Conductance Potassium (mS/cm2)
gl=0.14; % Peak Conductance Leak (mS/cm2)
dt=.1; % Integration step (ms)
tmax=1000; % Simulation time (ms)
T=1:dt:tmax; % Timeline (ms)
% Memory allocation;
Inats(size(T))=0;
Inatr(size(T))=0;
Ikdr(size(T))=0;
If(size(T))=0;
Il(size(T))=0;
Is(size(T))=0;
ms(size(T))=0;
hs(size(T))=0;
mr(size(T))=0;
hr(size(T))=0;
sr(size(T))=0;
n(size(T))=0;
f(size(T))=0;
% Initial values
Vm(1)=-65;
[tmNats,pmNats,thNats,phNats]=Nats(Vm(1));
ms(1)=pmNats;
hs(1)=phNats;
[tmNatr,pmNatr,thNatr,phNatr,tsNatr,psNatr]=Natr(Vm(1));
mr(1)=pmNatr;
hr(1)=phNatr;
sr(1)=psNatr;
[tnKdr,pnKdr]=Kdr(Vm(1));
n(1)=pnKdr;
for i=1:size(T,2)
    Inats(i)=gnats*(ms(i)^3)*hs(i)*(Vm(i)-Ena);
    Inatr(i)=gnatr*mr(i)*hr(i)*sr(i)*(Vm(i)-Ena);
    Ikdr(i)=gkdr*n(i)*(Vm(i)-Ek);
    Il(i)=gl*(Vm(i)-El);
    Vm(i+1)=Vm(i)-(dt/Cm)*(Inats(i)+Inatr(i)+Ikdr(i)+Il(i));
    [tmNats,pmNats,thNats,phNats]=Nats(Vm(i+1));
    [dpms]=dp(dt,tmNats,pmNats,ms(i));
    ms(i+1)=ms(i)+dpms;
    [dphs]=dp(dt,thNats,phNats,hs(i));
    hs(i+1)=hs(i)+dphs;
    [tmNatr,pmNatr,thNatr,phNatr,tsNatr,psNatr]=Natr(Vm(i+1));
    [dpmr]=dp(dt,tmNatr,pmNatr,mr(i));
    mr(i+1)=mr(i)+dpmr;
    [dphr]=dp(dt,thNatr,phNatr,hr(i));
    hr(i+1)=hr(i)+dphr;
    [dphs]=dp(dt,tsNatr,psNatr,sr(i));
    sr(i+1)=sr(i)+dphs;
    [tnKdr,pnKdr]=Kdr(Vm(i+1));
    [dpkdr]=dp(dt,tnKdr,pnKdr,n(i));
    n(i+1)=n(i)+dpkdr;
end
plot(Vm)

% FUNCTION "NATS" - CALCULATION OF STATIONARY DISTRIBUTION
% AND TIME CONSTANT FOR Na TTX-S

function [tmNats,pmNats,thNats,phNats]=Nats(V);
am=11.49/(1+exp((V+8.58)/-8.47));
bm=11.49/(1+exp((V+67.2)/27.8));
ah=0.0658*exp(-(V+120)/20.33);
bh=3/(1+exp((V-6.8)/-12.998));
tmNats=1/(am+bm);
pmNats=am/(am+bm);
thNats=1/(ah+bh);
phNats=ah/(ah+bh);
return

% FUNCTION "NATR" - CALCULATION OF STATIONARY DISTRIBUTION
% AND TIME CONSTANT FOR Na TTX-R

function [tmNatr,pmNatr,thNatr,phNatr,tsNatr,psNatr]=Natr(V)
am=1.032/(1+exp((V+6.99)/-14.8712));
bm=5.79/(1+exp((V+130.4)/22.9));
ah=0.06435/(1+exp((V+73.26)/3.719));
bh=0.135/(1+exp((V+10.28)/-9.093));
as=0.00000016*exp(-(V)/12);
bs=0.0005/(1+exp(-(V+32)/23));
tmNatr=1/(am+bm);
pmNatr=am/(am+bm);
thNatr=1/(ah+bh);
phNatr=ah/(ah+bh);
tsNatr=1/(as+bs);
psNatr=as/(as+bs);
return

% FUNCTION "KDR" - CALCULATION OF STATIONARY DISTRIBUTION
% AND TIME CONSTANT FOR POTASSIUM

function [tnKdr,pnKdr]=Kdr(V)
a=0.001265*(V+14.273)./(1-exp((V+14.273)/-10));
b=0.125*exp((V+55)/-2.5);
tnKdr=1/(a+b);
pnKdr=(1+exp((V+14.62)/-18.38)).^-1;
return

% FUNCTION "DP" - RUNGE-KUTTA CALCULATION OF DIFFERENTIAL

function [dp]=dp(dt,tau,Inf,p0)
d1=(Inf-p0)/tau;
p1=p0+.5*dt*d1;
d2=(Inf-p1)/tau;
p2=p0+.5*dt*d2;
d3=(Inf-p2)/tau;
p3=p0+dt*d3;
d4=(Inf-p3)/tau;
dp=dt*(d1+2*d2+2*d3+d4)/6;
return

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