I'm always interested in analogies & thought experiments. One of them last year was to consider the following:
What would a brain cell (neuron) look like on a vastly expanded scale, where the body of the cell (cross-sectionally) would occupy an area about the size of a small urban residential lot (let's say about 10 x 40 metres, or 35 x 120 feet)?
Interestingly, it took a fair bit of effort to get an accurate picture of this (and even now, I'm sure I could get into a lot more detail). Advanced textbooks of neuroscience may be good at describing a lot of fine details, but they tend not to give the reader a good visual picture of what the brain -- or a neuron -- in action -- really looks like. In order to do this research, it involved digging at length into the neuroscience literature (full references are available to the interested reader).
Here are some of my findings:
A typical neuron cell body is about 20 microns in diameter (about 1/50 of a millimeter). If the cell body were made into a giant which occupied a whole city residential lot, we would be scaling upward by a factor of about 1.85 million.
At this scale, a single atom would be about 0.2 mm wide (well within visual resolution). At this scale, your head would be about 340 km in diameter. This is about the size of a U.S. state such as Ohio, Pennsylvania, or Louisiana; or almost as large as the Canadian provinces of New Brunswick and Nova Scotia combined.
Dendrites are arm-like extensions of a neuron's cell body. Dendrites can be up to 600 microns long, and on our scaled-up neuron, this makes the longest dendrites about 1 km long. Each neuron can have about 20 dendrites. Each dendrite in our model would be about 5 meters wide. In our model, dendrites are similar to the width of streets or alleys coming away from the yard (remember this is really in 3 dimensions), and each street or alley would extend to some outer reach of your local neighbourhood. Inside each dendrite are many mitochondria (the "power plants" of the cell), each of which about 4 x 1 meters in size (each about the size of a hippo).
There are fibers holding the whole cell together (and serving other functions), called neurofilaments and microtubules. They are typically about 10 mm in diameter in our model (like a medium-sized rope), and are spaced about 100 mm apart (so the inside of a neuron could get quite tangled up were it not for the fact that these "ropes" guide everything along smoothly, acting as miniature pulleys and motors).
A synapse is an area where two neurons communicate chemically. There are thousands of synapses on each neuron. In our model, each synapse area would be about 1 meter wide. The distance across the synapse (between neurons) in our model is about 180 mm (6 inches). Nerve cells release vesicles into the synapse containing neurotransmitters such as serotonin and norepinephrine. In our model each vesicle would be about the size of a small grapefruit. Each time the neuron is fully activated, about 300 of these grapefruit-sized vesicles would be released. Smaller activations of the neuron would cause only 5-10 vesicles to be released. After release, the vesicles are "recycled" within about a minute.
If there is a drug such as an antidepressant affecting the neuron, its size on our model would be something like a grain of sand. Concentrations of antidepressants in the brain are something like 1 in 6 million. This corresponds to one, or just a few, molecules of antidepressant -- each one the size of a 1 mm grain of sand -- in every cubic foot in our model. This shows us visually that just a tiny amount of something in the brain can have a powerful effect.
In the actual brain, neurons are "packed" with a density of about 100 000 per cubic millimeter. In our model this corresponds to neurons packed roughly equivalent to how the city lots are "packed" in a residential neighbourhood (but in 3 dimensions).
The brain's surface area, scaled up for our model, would occupy an area about the size of Washington state, or of southern British Columbia, all of which occupied by "houses" or "yards" corresponding to individual neurons (but in the real brain, there are 3 dimensions, of course). The "houses" would be locally connected through dendritic connections in areas corresponding to residential "neighbourhoods". And there would be many axonal connections linking these neighbourhoods to the far reaches of the brain's territory.
The total population of neurons in the brain is about 100 billion, which is 15 times the population of humans on the earth.