## main differential equation for voltage

NMODL and the Channel Builder.
reimar

### main differential equation for voltage

hello!

i have been working with neuron for some time but i can´t find the main differential equation for the ion channel dynamics (eg. for the hodgkin-huxley model)
the hh model consists of 4 differential equations:

m'=(minf-m)/mtau
h'=(hinf-h)/htau
n'=(ninf-n)/ntau
v'=(-ina-ik-il+istim)*1/c

in the hh.mod-file (nrn70\src\nrnoc\hh.mod) there are only the first three differential equations.
can you tell me where the last one is?

best regards,
reimar

ps: the equation for v' doesn´t have to to anything with the statement "SOLVE states METHOD cnexp", does it?
ted
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### Re: main differential equation for voltage

in the hh.mod-file (nrn70\src\nrnoc\hh.mod) there are only the first three differential equations.
can you tell me where the last one is?
Good question. You get the fourth one for free, just by saying
create soma
or whatever the name of the section is, into which you insert the hh mechanism. Actually, you're getting the spatially discretized cable equation, which gives you one membrane potential ODE for every compartment (segment) in your model. And you're getting as many ODEs for m, n, h, and other gating variables, as there are segments into which you have inserted the mechanisms that have these gating variables.
the equation for v' doesn´t have to to anything with the statement "SOLVE states METHOD cnexp", does it?
Yes, it doesn't.
reimar

### Re: main differential equation for voltage

hello ted,

the most informative part was chapter 4, but i could only find some theoretical aspects on that topic. what i didn´t find was the connection between the theory (chapter 4) and neuron, e.g. i was looking for a statement like "neuron computes the voltage via the spatially discretized cable equation".