# 6.021/Notes/2006-10-20

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## Core conductor model

• Look at impact of topology on electrical properties
• : 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 . is in ohms and is in ohms/m.
• Outer conductor: resistance (similar to inner conductor)
• Current through membrane: is in amps and is in A/m.
• Assume topology, Ohm's law, but nothing about the membrane
• Core conductor equations:
• 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 for all space and time:
• For action potential traveling at constant speed
• (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