How we change what others think, feel, believe and do
The brain and entire nervous system is driven by electricity.
The membrane potential is a voltage drop found across the outer membrane 'skin' of neurons. The interior of the neuron has a negative potential of about -70 millivolts, representing an excess of negatively charged particles within it.
When undisturbed, this differential is called the resting potential.
How it works
The membrane potential is caused by ions in the intracellular fluid and extracellular fluid. Organic anions, A- (which are negatively charged) exist only inside the cell. Cations K+ are mostly found inside the cell whilst Na+ and Cl- are mostly found outside (think of a 'saline sea').
A- cannot leave the cell. K+ can diffuse out of the cell, though electrostatic pressure tends to press it back in. Na+ and Cl- can diffuse into the cell, though electrostatic pressure tends to push them out. Another force, the sodium-potassium pump, also tends to keep the Na+ cells out.
The sodium-potassium pump works through proteins in the membrane which are fuelled by ATP molecules from mitochondria (these are organ-like parts of the cell). These molecules are called sodium-potassium transporters and push three sodium ions out for every two potassium ions they push in.
The result is a net greater negative charge inside the cell.
When a stimulus is applied in the form of a positive charge inside the neuron, the membrane potential swings positive (in depolarization) to about +30mV, over a period of about one millisecond or so, thus depolarizing the cell. The voltage then swings back past -70mV a little (in hyperpolarization) before settling back to normal.
This 'spike' of potential change is called the action potential and sets off a chain of events which 'fires' the neuron, sending a signal down its axon.
In order to trigger the action potential, the stimulus must be above a threshold of excitation, pushing the potential to around -60mV (ie. adding about +10mv). Voltages below this are called subthreshold.
How it works
Ion channel protein molecules in the membrane can open and close to allow ions to pass or not. When lightly stimulated, sodium channels open, allowing a rush of Na+ sodium ions through to rebalance the charge. In fact an excess may pass through, leading to the positive potential. After about 1ms the sodium channels become refactory, closing up. However potassium channels also open up, allowing K+ ions to leave easily, thus the tide turns and the cell returns to its original charge, whence the sodium-potassium pump takes over again to restore the status quo.
Note that all this action happens near the membrane -- ions do not need to suffuse the whole cell.
Axons conduct charges on an all-or-none law. That is, once triggered, an action potential travels like a rippling wave down the length of the axon without petering out or decreasing in charge. Neuron firing is thus digital: it is a 1 or 0 and nothing in between.
So how do neurons tell muscle to clench gently or strongly? This happens by the rate law, where the frequency of firing determines the intensity of bodily action. And the frequency of firing itself may be determined by the strength of a received stimulus.
Note that in contrast to the uniform progression of the action potential, subthreshold transmission (too weak to cause an action potential) is passive, with the axon acting like a resistive cable (and are thus called cable properties) such that the signal decreases along the length of the axon.
Action potentials do in fact suffer from cable property effects, but the nodes of Ranier (the gaps between myelin sheath segments) act like repeaters, recreating and boosting the signal to keep it strong. This 'hopping' from node to node is called saltatory conduction. This process is both economic and fast, and is key to our quick thinking.
As with electric cables, larger axons also conduct faster. Myelination boosts the speed thus allowing for thinner axons.