## Membrane current scaling

The basics of how to develop, test, and use models.
calu
Posts: 19
Joined: Fri Feb 19, 2016 10:07 am

### Membrane current scaling

Dear all,

Following this table https://www.neuron.yale.edu/neuron/stat ... chart.html
the membrane current density has a unit of mA/cm^2 = E-3 A / E-4 m^2 = E1 A/m^2
the area of a segment has an area of um^2 = E-12 m^2
when I multiply those, I get E1 A/m^2 * E-12 m^2 = E-11 A
so to obtain the current in nA (E-9), I would multiply this with E2, meaning a multiplication by a factor of 100.

In previous code and posts here, I saw a factor of 1/100. This would be obtained, if one took cm^2 as E-2 m^2 and um^2 as E-6 m, ignoring that it's squared?

Thanks!
ted
Posts: 5784
Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
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### Re: Membrane current scaling

If you've lost your chem class notes about unit conversion, maybe the following will help.

1 megabuck is one million dollars.
1 grand = 1e-3 megabucks.
1 buck = 1e-6 megabucks.

So if you had N bucks and wanted to know how many grand that was,
"1 buck is 1e-6 megabucks, and 1 grand is 1e-3 megabucks, so to convert bucks to grand I'd multiply the number of bucks by a factor of 1000."

Try that on your bookie and see what happens.

1 grand / 1e-3 megabucks = 1
1 buck / 1e-6 megabucks = 1
Then realize that
1 grand / 1e-3 megabucks = 1 buck / 1e-6 megabucks
rearrange
1 grand / 1 buck = 1e-3 megabucks / 1e-6 megabucks
eliminate the common unit factor on the right hand side
1 grand / 1 buck = 1e-3 / 1e-6
multiply the right hand side by 1e6/1e6 (i.e. by 1)
1 grand / 1 buck = 1000
and finally divide both sides by 1000 to get the identity
1 grand / 1000 bucks = 1

Suppose Joe says he has 3 grand. How many bucks is that? Multiply by a ratio that equals 1. What ratio is that? 1000 bucks / 1 grand
3 grand * 1000 bucks / 1 grand = 3000 bucks (the grands in the numerator and denominator cancel out, leaving bucks)
And if Louie says he has 25 bucks, how many grand is that?
25 bucks * 1 grand / 1000 bucks = 0.025 grand (the bucks cancel out, and Louie might get canceled out himself if his bookie expected a grand).

Now that your unit conversion skills are on a par with those of a bookie, you're ready to tackle the sterile world of um, cm, nA, mA/cm2 and all that. Be careful, though--it'll take some practice before your unit conversion expertise rises to the level of a narcotraficante.
calu
Posts: 19
Joined: Fri Feb 19, 2016 10:07 am

### Re: Membrane current scaling

Right, I went in the wrong direction in the end. Thanks