Units - Again!

Many modelers define the conductances, etc in absolute terms, such as a capacitance of, say, 0.29 nF. Most of the time, I will define my units in terms of ``size per unit area,'' but some of the models I describe (in particular, the big cortical mix and match model) will be in absolute numbers. A modeler who does that is making an implicit assumption about the size of the cell. For example, in the above capacitance example, if I assume a capacitance value of $1 \mu F/cm^2$then 0.29 nF corresponds to a cell with a total membrane area of 29000 $\mu m^2.$ Given that typical conductances are in units of mS/cm² then typical absolute conductances would be of the order of microsiemens, currents are in nanoamps, capacitance in nanofarads. In McCormick's and Huguenard's model (J. Neurophys 68:1373, 1384) sodium has a conductance of 12 $\mu S$ for the 29000 $\mu^2$ cell which translates into 41 mS/cm². (Make sure you can do this calculation - keep in mind that $1\mu^2 = 1\times 10^{-8}cm^2.$

Since currents are in nanofarads, let's see what the conversion factors are for the influx of calcium. Recall that a farad is a coulomb per second. The Faraday constant, F has units of coulombs per mole. Concetration is moles per liter, so that we need to know the volume in which the calcium is relevant. Volume is area times depth, so if we take a depth of 100 nM under our spherical cell, we can figure out the volume. Thus, with a linear uptake in cacium, the calcium concentration is satisfies:

$$\frac{d[Ca_i]}{dt} = -k I_{Ca} /(d\cdot A) - \beta [Ca_i]$$

where $k=5.18 \times 10^{-3}$ to convert current (nanoamperes), time (milliseconds) and volume (cubic microns) to concentration in moles/liter. (To see this, note

Thus

$$\frac{ 1 \times 10^{-12} \hbox{ Coulombs/msec}}{2\times 9648... ... liters}/\mu^3} = 5.18\times 10^{-3} \hbox{ moles/liter/msec}$$

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