How large is the nerve pulse?

Does it matter how large the nerve pulse is? Yes, in fact it matters for the choice of the level of the theoretical description. If the nerve pulse were tiny, it would make sense to employ molecular modeling. If it were large, then one would rather go for macroscopic theories such as thermodynamics or hydrodynamics. Each phenomenon requires a description the works on the the same scale. But what actually is the scale of a nerve pulse, and which approach is the right one? 

When the voltage changes during a nerve pulse are measured with electrodes, one finds that the pulse lasts about one or two milliseconds. This seems like something very small and it influences our conception of how the nerve pulse looks like. We envision it as something of the dimension of the thickness of an axon or a dendrite, or of the size of a synapse. 

Action potential in a single neuron from lobster connectives. From Gonzalez-Perez et al. 2016. Biophys. Chem. 216:51-59. 

Impression of an artist of the action potential in nerves, represented by tiny bright spots on the axons and dendrites. Image from wallpapercave, where you find many similar artistic renderings.

This conception manifests itself in the artistic drawings of neural networks on hundreds of web sites of Neuroscience departments and Science Blogs from all over the world (see the image above). Other examples (found after a very short search on the Web) can be found at the pages of the Boston Children Hospital, Sidney Medical School and the Science Blog Medical News Today. On the basis of this picture it seems natural to assume that the excitation during synaptic transmission is of the dimensions of the synapse itself.

Synaptic transmission as imagined by the  Electric Engineering Department of the University of Michigan.

Synaptic transmission as imagined by the  Electric Engineering Department of the University of Michigan.

Admittedly, all these images are artistic drawings, which are meant to illustrate the situation in the nervous system without scientific rigor. However, judging from the images: How large do many if not most neuroscientists imagine the length of an action potential? Maybe a micrometer, or a few micrometers? Definitely smaller than the cell nucleus and much smaller than the nerve cell. Maybe something comparable to the size of proteins or the distance between them?! This might explain the dominance of molecular explanations in biology.

All of these drawing have one thing in common: They are all wrong. 

This is very easy to see if one calculates the length of a nerve pulse by multiplying the timescale of the nerve pulse ∆t (1-2 milliseconds) with its velocity v (1-100 m/s) using the simple equation 

∆x=v·∆t  ,

where ∆x is the length of the nerve pulse. One finds a range of possible sizes of nerve pulses ranges from 1mm to 20 cm depending on nerve. Nerve pulses are in fact very large - larger than some cells. I have listed below the dimensions of the action potential for various nerves: 

	myelinated	velocity m/s	length cm
motor neuron type Aα	yes	80-100	8-10
peripheral median motor neuron	yes	49-64	4.9-6.4
motor neuron type Aν	yes	4-24	0.4-2.4
sensory fibers type c	no	0.5-2	0.05-0.2
lobster connective	no	6	0.6
squid axon	no	24	2.4

Don’t grill me because of a factor of two in length of the pulse because it depends on how one defines the time scale of the nerve pulse. For the calculation above I made the simplifying assumption that the time scale of the nerve pulse is always ∆t=1 ms. It does not really matter because the point is that nerve pulses are very long. Definitely much, much longer than cell bodies and synapses, and also much longer than the diameter of axons and dendrites - they are also larger than the distance between nodes of Ranvier in myelinated nerves. Therefore, the term saltatory conduction does not make sense.  In fact, nerve pulses are macroscopic and larger than many cells. Motor neurons in mammals can have a length of 1m or longer. This corresponds to the length of about 10 action potentials. Squid axons have a length of a few cm, which corresponds to the length of only a few single action potentials. In contrast, an astrocyte (which is a kind of glia cell) has a diameter of 50-100 µm including its extensions. They are much smaller than any action potential. If they are excited, they must be excited as a whole. It is possible, the one single action potential spans several cells.

Astrocyte, from SynapseWeb

Since it is unavoidable to conclude that nerve pulses are macroscopic, it is very peculiar that the models to explain the nervous impulse are built on the methods of molecular biology, meaning that they explain the nerve pulse bottom up on the basis of single molecules. 

However, in physics it is well known that there exist emerging phenomena on larger scales (for instance waves or phase transitions) that cannot be understood on the scale of a single molecule. Why is this so? The reason is that the typical density or temperature gradients  in a wave on the length scale across a single molecule is often smaller than the thermal motion. This means, that single molecules do not see the waves at all, and something like waves cannot be explained on the level of single molecules. To explain phenomena on larger scales one needs theories that apply to the large scales. These are particularly the laws of analytical mechanics and hydrodynamics, which can not be constructed by adding single molecule features. It would be absolutely unreasonable to assume that phenomena such as waves - phenomena that everybody knows to exist from daily experience - should not exist in biology. 

But strange enough, when it comes to biological systems a complete community has chosen to use a scientific language that excludes well-known physics from the list of possible explanations of biological function. This cannot be correct.

For this reason, we and others have proposed that one needs macroscopic physics to explain phenomena on the scale of a nerve pulse. I will discuss this in more detail in later posts.

Stay tuned.