I meant 2 HH nodes at the beginning and the end and lots of internodes in the middle

Is that

N-I-N-I-I-I-...-I-N-I-N (i.e. 4 nodes and a bunch of internodes?

or

N-I-N-I-N-I-...-N-I-N (i.e. NNODES nodes and NNODES-1 internodes)

"The slovenliness of our language allows us to think foolish thoughts." from Orwell's "Politics and the English Language" (1946).

Not just in politics, George.

WRT parameters and units--

NEURON needs the cytoplasmic resistivity Ra, which is in units of ohm-cm. This is the resistance between the opposite faces of a 1 cm cube of cytoplasm. The "true" value is very hard to determine experimentally; for squid axon it's 35.4 ohm cm, but for neurons from vertebrates people generally use something between 80 and 200 ohm cm. That aside, what you have is not the value of cytoplasmic resistivity, but something called "longitudinal resistance" which is in units of megohms/mm. Presumbably "longitudinal resistance" is the resistance between the two ends of a 1 mm long cylinder of cytoplasm. But you need the diameter of the cylinder to determine the corresponding value of Ra. Given a cylinder of cytoplasm with resistivity Ra ohm cm, the diameter and length of which are diam and L in um, the resistance between the two ends of the cylinder is (Ra * L * 4 / (PI * diam^2)) ohm * cm * um / um^2

which equals

1e4 Ra * L * 4 / (PI * diam^2) ohms = 0.01 Ra * L * 4 / (PI * diam^2) megohms. For convenience let's call "longitudinal resistance" RL. Then

RL = 0.01 Ra * L * 4 / (PI * diam^2)

and

Ra in ohm cm = RL * 25 * PI * diam^2 / L where diam and L are both in microns. You know that L is 1 mm = 1e3 um, so

Ra in ohm cm = RL * 0.025 * PI * diam^2

So if you knew the numerical value of RL, and the value of diam in um, you could calculate Ra. But you don't know diam.

What about membrane capacitance? NEURON needs specific membrane capacitance in uf/cm2. You can assume that nodal membrane's specific membrane capacitance is 1uf/cm2 ("true" value of specific membrane capacitance is hard to measure experimentally; it's probably somewhere between 0.7 and 2 uf/cm2, and most modelers just assume 1 uf/cm2). But you don't have a handle on the effective internodal specific membrane capacitance (I call this "effective specific membrane capacitance" because it's the equivalent capacitance of the axolemmal specific capacitance in series with the much smaller specific capacitance of the myelin sheath). Instead you have something called "myelin capacitance" which is in pf/mm. Presumably this is the net membrane capacitance of a 1 mm length of internode. The total surface area of a cylinder with length 1 mm and diameter diam um is

PI * diam * 1e3

in units of um^2, which is equvalent to

PI * diam * 1e-5

in units of cm^2 (because 1e4 um = 1 cm).

Using CM to signify internodal specific membrane capacitance in uf/cm2, a 1 mm long internode has a total capacitance of CM * PI * diam * 1e-5 uf, which is equivalent to 10 CM * PI * diam pf. In other words,

10 CM * PI * diam = "myelin capacitance"

so

CM = "myelin capacitance" / (10 * PI * diam).

So if you knew the numerical value of "myelin capacitance" and the value of diam in um, you could calculate Ra. But you don't know diam.

Finally we get to the resistor in that equivalent circuit of internodal membrane, which you're calling "myelin resistance" or "R_m", and which has units of megohms/mm. First, the units make no sense at all. In the case of "myelin capacitance," units of capacitance/length make sense because the longer a cylinder is, the more surface area it has and the larger its total capacitance becomes. Given a cylinder with a particular length, calculate the product of length and capacitance/length and you get . . . capacitance. But in the case of membrane resistance, the more surface area you have, the lower the total resistance should be. After all, the area is all in parallel, right? Take two cylinders of a given length, attach one to the other, and now you have twice as much surface area, so total membrane resistance should be half as much, not twice as much.

OK, let's get past that by assuming that whoever wrote MOhms/mm really meant MOhms mm, so that the numerical value of "myelin resistance" is the net resistance of the membrane of an axon that is 1 mm long. But NEURON expects specific membrane conductance gm, which is in units of Siemens/cm2. The total surface area of the internode is

PI * diam * 1e3

in units of um^2, which is equvalent to

PI * diam * 1e-5

in units of cm^2 (because 1e4 um = 1 cm).

so the net conductance of the internodal membrane in Siemens is

gm * PI * diam * 1e-5

and its net resistance is

1e5 / (gm * PI * diam)

in ohms, or

0.1 / (gm * PI * diam)

in megohms. And once again you're stuck, because

gm = 0.1 / (PI * diam * R_m)

but you need to know diam in order to calculate gm.

And you don't know diam.

Two possible outs:

1. If you can discover somewhere the numerical value (and units) of effective specific membrane conductance of myelinated internode, that could be used to calculate diam.

2. You could just arbitrarily assume a particular value of diam. 10 um is a reasonable internal diameter for a myelinated axon in peripheral nerve. A quick literature search on PubMed should probably turn up some freely available references about diameter ranges.