Membrane capacitance · Lobeworks/17

Membrane capacitance is the ability of a cell's membrane to hold electric charge on its two faces, as a capacitor does, and it sets how much charge a neuron must move, and how long it takes, to change its voltage.

Membrane capacitance. Membrane capacitance is the ability of a cell's membrane to hold electric charge on its two faces, as a capacitor does, and it sets how much charge a neuron must move, and how long it takes, to change its voltage. The membrane is a lipid bilayer a few nanometres thick, an insulator between two salty, conducting solutions: the cytoplasm inside and the extracellular fluid outside.

That geometry is a capacitor in the textbook sense (capacitance): two conductors separated by a thin insulator. Its value is about 1 microfarad per square centimetre of membrane, large for its size because the gap is so thin. To change the voltage across it, ions must first pile up on one face and leave the other, so part of every current that reaches a patch of membrane is spent charging it before any of it can travel further along the cell. With the leak through the ion channels acting as a resistance, the product of the two gives the membrane's time constant, typically some milliseconds, the delay with which a neuron's voltage follows its inputs.

It is the reason an axon loses signal along its length. Current flowing down the inside of an axon leaks out in two ways: through open channels, and into charging each stretch of membrane it passes. Both drain the current before it reaches the next stretch.

Myelin is the engineering answer. Wrapping the axon in many layers of glial membrane thickens the insulator, which lowers the capacitance and raises the resistance of the wall, so the current reaches the next node of Ranvier almost intact (saltatory conduction).

It is also what extracellular electrodes and the EEG see first: the capacitive currents of many synchronised membranes, not the ions crossing any single channel.

A neuron is a leaky capacitor.

Every signal has to charge the membrane before it can move on, which is why thin bare axons are slow and why the nervous system wraps its fast ones in insulation.

Questions: Why does a signal fade along a bare axon, and what does myelin change? The current of a spike flows along the inside of the axon, carried by ions in the cytoplasm, and the membrane around it drains that current in two ways: some leaks out through open ion channels, and some is spent charging each stretch of membrane it passes, because the membrane is a capacitor that must be charged before its voltage can change. Over a bare stretch the current shrinks with distance, so the spike has to be regenerated at every point by its own sodium channels, which is slow. Myelin wraps the outside of the axon in many layers of glial membrane: the thicker insulation lowers the capacitance and the leak, the current reaches the next gap, the node of Ranvier, almost intact, and the spike is regenerated only there.