Core conductor model
- Look at impact of topology on electrical properties
- Vm(z,t): different potentials along the cell
- Break into lumps/nodes
- Treat as internal resistors, outer resistors, and unknown boxes connecting inside/outside (membrane potential)
- Inner conductor: resistance Ri = ridz. Ri is in ohms and ri is in ohms/m.
- Outer conductor: resistance Ro = rodz (similar to inner conductor)
- Current through membrane: Im = kmdz Im is in amps and km is in A/m.
- Assume topology, Ohm's law, but nothing about the membrane
- Core conductor equations:
- Ke is externally applied current
- The first 2 equations are continuity of current, the second two are Ohm's law
- Combining equations, we get THE core conductor equation:
- We still have assumed nothing about the membrane
- Suppose no external current. (otherwise charge would build up)
- If we know Vm for all space and time:
- For action potential traveling at constant speed ν
- (wave equation)
- From this model alone, we find that the current at the peak of the action potential is predicted to be inwards!
- For all standard electrical elements (resistor, capacitor, inductor), we would predict outward current
- This model makes no assumption about the membrane, only that Ohm's law holds