DiffEqs

Plain Bilayer Membrane

A plain lipid bilayer is approximately an ideal capacitor. The equation for an ideal capacitor is

$C \frac{dV(t)}{dt} = I(t)$

$V(0) = 0$

Here C is a constant (parameter), the capacitance of the membrane, proportional to area.

Next V(t) is the membrane potential. This is the quantity of interest.

Next I(t) is the injected current into the cell.

Finally V(0) is the initial membrane potential of the cell.

Bilayer Membrane with Na/K Pumps

Same, except that the initial condition is different.