How flexible is NEURON ?

[Mahozi]

Hi,

I have been trying to build new channels for an STG model, with functions that obey this equation :

I = g m^p h^q (v-e)

The activation and inactivation variables (m, h) are described by these equations :

mtau(v) m' = minf(v) - m
htau(v) h' = hinf(v) - h'

Now the voltage dependencies for m and h are given , i.e xtau and xinf,
however the alpha and beta values are not given, they're incorporated in the xtau and xinf. I'm asking this because in every example for constructing new channels in the book values are used for alpha and beta for the function block to slove derivative states.
My question is this: Can NEURON "figure out" the alpha and beta values? If, for example, I used this solution for the Na channel :

I = g m^3 h (v-e)

m = minf(v) - mtau(v) m'
h = hinf(v) - htau(v) h'

minf(v) = malpha(v)/(malpha(v)+mbeta(v))
mtau(v) = 1/(malpha(v)+mbeta(v))
hinf(v) = halpha(v)/(halpha(v)+hbeta(v))
htau(v) = 1/(halpha(v)+hbeta(v))

m' = malpha(v) (1-m) - mbeta(v) m
h' = halpha(v) (1-h) - hbeta(v)h

where
minf = 1/(1+exp(-(v+24.7)/5.29))
mtau = 1.32-(1.26/(1+exp(-(v+120)/25)))
hinf = 1/(1+exp((v+48.9)/5.18))
htau = 0.67/(1+exp(-(v+62.9)/10))

I know this looks messy, I'm a beginner and I couldn't find a solution for this.
My question again, can NEURON derive the values of alpha and beta through these relations, to solve the derivative state, in order to solve the breakpoint equation?
If yes, how can I achieve that in the NMODL language?

(note : i'm using data from this paper
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1941697/
)

Thanks,

Ahmad.

[ted]

Soto-Treviño et al. (2005) is an interesting paper. Unfortunately it's not in ModelDB yet.

How flexible is NEURON? Let me count the ways . . .
* two interpreted programming languages (hoc and Python) that can be used individually and in combination (Python calling hoc or hoc calling Python or both) for constructing model cells and networks
* one compiled programming language (NMODL) for adding new equations and mechanisms specified by algebraic equations, linear and nonlinear ordinary differential equations, kinetic schemes, and state machines, and can also be used to add arbitrary C code
* a graphical user interface that includes tools for adding new voltage- and ligand-gated channels and constructing models of cells and networks
* tools for importing detailed morphometric reconstructions of cells, analyzing models and displaying their properties in a browsable outline, importing and exporting NeuroML

Yep, pretty flexible.

in every example for constructing new channels in the book values are used for alpha and beta for the function block to slove derivative states.

Did you see Example 9.5: A calcium-activated, voltage-gated current? You might also look at C:\nrn*\src\nrnoc\hh.mod (if you're using Linux or OS X, download and expand nrn*tar.gz, then check out nrn/src/nrnoc/hh.mod). And there are hundreds or thousands of examples in ModelDB.

So the good news is you don't have to convert the inf-tau form of the HH equations to the alpha-beta form. More good news is that the paper you cite uses mV and ms in the formulas that govern the gating variables. Hopefully their Tables 1 and 2 don't contain any typographical errors.

The not so good news, if you try to reproduce their complete model, is that they use absolute units, rather than density units, for membrane conductance and capacitance. But there are ways to deal with this.

My question is this: Can NEURON "figure out" the alpha and beta values?

About as much as C, Matlab, or Python can. Those are pretty flexible, but they don't do algebraic manipulations for you. You have to do that yourself. The alpha-beta form of the Hodgkin-Huxley style ODEs is mathematically equivalent to the inf-tau form, and a little algebra converts one to the other (see ** below).

But this is now a moot point because you can just go ahead and use the inf-tau form of the ODEs.


** Equivalence of the alpha-beta and inf-tau forms of the HH style ordinary differential equations:

y' = -a*y + (1-y)*b
= b - (a + b)*y
Let ytau = 1/a+b and yinf = b/a+b, and you get (after intermediate steps which are "left to the reader")
y' = (yinf - y)/ytau
From inspection
b = yinf/ytau
a + b = 1/ytau
and from that it is easy to get a.

[Mahozi]

Thanks Ted, that was really helpful.

Could you elaborate on this point?

The not so good news, if you try to reproduce their complete model, is that they use absolute units, rather than density units, for membrane conductance and capacitance. But there are ways to deal with this.

I understand the issue, but I'd like to learn how to deal with it.


Many thanks,

Ahmad.

[ted]

The problem usually arises in the contex of single compartment model cells. When it does, it's easy to solve. Assume specific membrane capacitance of 1 uf/cm2, and calculate how much surface area would be needed to produce the total membrane capacitance used by a model cell. Given that surface area, and the peak conductance for each of the distributed ion channel mechanisms (e.g. sodium, potassium, leak)) you can then calculate each channel's conductance density in S/cm2.

Multicompartment model cells specified in terms of net (total) membrane conductance and capacitance are a pain in the neck to recast in terms of connected sections because section diameters and lengths and cytoplasmic resistivity must be adjusted so that the resistance between segment centers match the resistances between compartments. It is much better to start from the original cell geometry and assumed biophysical properties of cytoplasm and membrane.