Modelling conductances with H&H model for ionic currents

[erhervert]

Hi there,

Well, first of all I'd like to say that this is my first approach to NMODL and I'm currently in the learning process...

Now, the issue is that I'm trying to insert some conductances in a model but most of the available examples on the internet are wrote in terms of the alpha and beta functions. My problem is that the conductances I'm trying to insert are expressed in terms of the Hudgkin & Huxley model for ionic currents, according to Belluzzi et al., 1991:

Ina=Ina'[1-exp(-t/taum)]^3[exp(-t/tauh)]

My doubt is about how my code file should be structured in order to work properly? Specifically, if in this case I should include an INITIAL and DERIVATIVE blocks or go directly to the PROCEDURE block?

Basically, I'm wondering how my code file should look like and what to include if I'm working with this kind data.

At this point this is what I have, but before I move on I'd like to ask for your expertise advice.

Code: Select all

TITLE Sodium conductance for sympathetic neuron
 
UNITS {
    (ms) = (millisecond)
    (mV) = (millivolt)
    (mA) = (milliamp)
    (mS) = (millisiemen)
}

NEURON {
    SUFFIX Ina
    USEION na READ Ina2 tm th WRITE Ina
}

PARAMETER { 
    Vh = -34.45 (mV)
    k = 6.99 (mV)
    gna = 0.00928 (mS)
}

ASSIGNED {
    tm (ms)
    th (ms)
    m (mV)
    Ina2 (mA)
    Ina (mA)
}

STATE {
    Ina2 tm th
}

BREAKPOINT {
    SOLVE states METHOD cnexp
    Ina = Ina2*((1-exp(-t/tm))*(1-exp(-t/tm))*(1-exp(-t/tm)))*(exp(-t/th))
}

: I don't know where to put this

    tm = 0.06+(1/((42.98*exp(0.08915*V))+(0.9230*exp(-0.03351*V)))
    th = ((-0.0046*V+0.26)+50.85)/((1+exp((-59.46-V)/7.91))+(1+exp((V+40.94)/1.556)))
    m = (1/(1+exp((Vh-V)/k)))

:

I'll appreciate any kind of help and/or suggestions, and example would help me a lot too.

Thanks guys.

[ted]

First step is to throw away your code and start with a clear conceptual model of the mechanism you're trying to implement, expressed in mathematical form. Without that, the game is over before it starts. What are the equations that describe:
--the current, as a product of conductance density, open channel fraction, and electrochemical driving force
--the open channel fraction, preferably expressed as a product of one or more state variables that may be raised to a power other than 1
--the dynamics of the state variables, expressed either in terms of one or more ordinary differential equations or state transitions
--the voltage dependence of the rate constants that govern the state variables or their transitions (analogous to the "alpha" and "beta" of the original Hodgin & Huxley model,
OR
the voltage dependence of the time constants and steady state values of the state variables

If you are unsure about any of these, please provide a complete citation of the paper that describes the mechanism you are trying to reproduce.

[erhervert]

Hi Ted,

Well, thanks for reply. The complete citation of the model that I'm trying to reproduce is the next:

Belluzzi O., Sacchi O. (1991) A five-conductance model of the action potential in the rat sympathetic neurone. Prog Biophys Mol Biol. 1991;55(1):1-30. Review.

I checked the paper again looking for the equations that you asked me but I realise that the only thing they provide is the voltage dependence of the time constants and the steady-state activation and inactivation values.

The paper says textually:

The current records were fitted using the general equation:

I(t,V)=g_max(V-Ei)[a∞-(a∞-a0)exp(-t/tau_a)]^n[h∞-(h∞-h0)exp(-t/tau_h)]

Where:

g_max: maximum conductance
Ei: reversal potential of the ion considered
a0, h0:initial values of a and h during the voltage step
a∞, h∞:final values of a and h during the voltage step
tau_a, tau_h: time constants of the activation and inactivation, respectively.

...

The steady-state activation curves were described by equations having the general form:

a∞= 1/{1+exp[(Va-V)/Ka)]}

Where:

Va: the potential of half activation
Ka: the slope parameter

...

Steady-state inactivation values

h∞= 1/{1+exp[(V-Vh)/Kh)]}

Vh: the potential at which h∞=0.5
Kh: the slope parameter

...

The activation and inactivation time constants were calculated from the fit of the first equation.

Besides that and some numerical values that's all the information they provide and there is not any information relative to the unitary behaviour of the channels like the dynamics, channel densities or open channel fractions in the paper.

Do you think that is possible to reproduce this model with NEURON? or maybe I need to look for a more complete and detailed description?

[ted]

Do you think that is possible to reproduce this model with NEURON?

The question is whether the article contains enough information to reproduce the model. The paper is 20 years old, and written in a narrative style with equations and paramters scattered all over the place. It is very easy to make mistakes when writing such a manuscript, and very easy for additional errors to be introduced by the typesetters (who, in most biological journals, are often not accustomed to dealing with a lot of mathematical formulas)--and very difficult to detect such errors by proofreading.

For each of the five voltage-gated currents you will need a separate NMODL source code file, and each such file should be tested to verify that it reproduces the corresponding voltage clamp data and voltage dependence of the gating variables' time constants and steady state values. You'll also need an NMODL file to specify potassium accumulation.

Assuming that all of this goes well, the real test will be to determine whether the model reproduces any of the simulation results published in the paper. It might, and it might not, depending on whether the paper contains the exact parameters that were used to generate each figure.

So if the authors and the publisher were very very careful, and you are very very lucky, you will be able to reproduce their model. If this is very very important to you, then try it. It'll be a lot of work, but you'll also learn a lot. Or maybe you can find a more recently published paper whose authors can provide working source code. Is there anything similar in ModelDB or in the BioModels database?

[erhervert]

I think you are right Ted. In fact, what I'm trying to do is to reproduce the action potential of a sympathetic neuron and I was thinking in use that paper as a basis but I'm not constricted to it. Now, I'm considering to look for more recent papers with more detailed descriptions or source code for each of the five conductances and try to write separate NMODL source code files as you recommend. Honestly I have not looked yet if there is something in the databases that maybe I could use for my model but probably it would be a good place to start with my search. I will re-formulate my conceptual model using other models from the databases as examples and then try to write some code to see what happens. However, may I ask for your help again if I need it?

[ted]

That's one of the purposes of the NEURON Forum.