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### main differential equation for voltage

Posted: **Tue Oct 13, 2009 5:25 am**

by **reimar**

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?

### Re: main differential equation for voltage

Posted: **Tue Oct 13, 2009 3:58 pm**

by **ted**

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.

### Re: main differential equation for voltage

Posted: **Wed Oct 28, 2009 7:18 am**

by **reimar**

hello ted,

thank you for your quick answer. i have read it some time ago but wanted to get some more information about the spatially discretized cable equation from the neuron book. that´s why i reply so late.

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".

did i overread that?

best regards,

reimar

### Re: main differential equation for voltage

Posted: **Wed Oct 28, 2009 10:42 am**

by **ted**

Chapter 4 does cover many important details, but if you're looking for a "bottom line" statement that NEURON calculates membrane potential by numerical integration of the spatially discretized cable equation, see the second paragraph in **3.3 Cables** (pages 50-51 of The Neuron Book).