01 July 2010

The elephant and the shrew, an axonal story

The world is different for small animals and big animals. J.B.S. Haldane said it best:

To the mouse and any smaller animal (gravity) presents practically no dangers. You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes.

ResearchBlogging.orgWhat does scale mean for neurons? As an animal gets bigger, it’s going to take longer for neural signals to get from one part of the animal to another – all other things being equal. But, typically, not all things are equal. You can speed up how fast a signal travels down the length of a neuron by making that neuron larger. just like water current can flow faster through a bigger pipe, an electrical current can flow faster down a larger axon.

There’s more going on in this paper by More and colleagues (so it’s literally More going on), but that gives you a starting point for the rationale here. If you take the teensiest mammal you can find, and one of the biggest mammals you can find, how different are those axons, and how fast they can send their signals, going to be?

To test this, they did neurophysiology and neuroanatomy on the neurons of a least shrew and an Asian elephant. These two animals are about as different in size as mammals can get. The shrew’s mass measures in milligrams, and the elephant’s measures in megagrams – tonnes!

But because you don’t want to draw a line using only two data points, they also went into the existing literature for mammalian neuroanatomy, and got equivalent measures for about nine other species of mammals.

The axon sizes scaled – bigger animals had bigger axons – but much, much less than the animal’s size. I mentioned mass before, but distance is the more relevant measure, though less impressive. An elephant’s leg is about 100 times longer than a shrew’s, but the elephant’s axons are only about twice as big. That’s about as close to scale-free a relationship in biology as you’re likely to find.

Okay, the neurons may be about the same size, but maybe there’s some other mechanism that might make the actual speed of the signals a better match to the animals’ proportions. Nope. A similar story held when they stimulated the nerves electrically and measuring the delay to the muscle twitch.

All of this means that big animals are going to be slower to detect and react to the world around them. It’s a real cost to being massive, which are no doubt compensated for by other factors. Like being able to sit anywhere you want.

Unfortunately, More and company point out that all this means that dinosaurs and other large creatures probably weren’t as as agile as they are often portrayed.


More, Heather L., Hutchinson, John R., Collins, David F., Weber, Douglas J., Aung, Steven K. H., & Donelan, J. Maxwell (2010). Scaling of sensorimotor control in terrestrial mammals Proceedings of the Royal Society B: Biological Sciences : 10.1098/rspb.2010.0898

Additional: Brian Switek also summarizes this paper here.


AK said...

"Maximum shrew axonal CV was 42 ± 6 m s−1 (mean ± standard deviation) and maximum elephant axonal CV was 70 m s−1".

Now, for any animal with a nerve length less than a meter, the actual time required for the action potential to travel would be 1-2 milliseconds. OTOH the typical delay from one neuron firing to the next is also measured in milliseconds, while calculations that require intervening inhibitory interneurons are probably measured in tens of milliseconds. Even the elephant, with a max 2-3 meters between the reflex center in the spinal cord and the muscles would only experience a 3-4 millisecond delay, compared to tens of milliseconds involved in even the fastest reflexes, and likely even greater times actually available before a reaction is too slow for the size.

When I started out checking refs, I discovered the following (in More et al. which you've reviewed here):

"If all other sources of delay are constant, responsiveness is proportional to axonal conduction velocity (CV), which is in turn directly proportional to axon diameter (Gasser & Grundfest 1939; Hursh 1939; Rushton 1951; Boyd & Kalu 1979; Arbuthnott et al. 1980; Hoffmeister et al. 1991) (figure 1a)"

1. As noted above, the response time of even spinal reflexes are probably at least an order of magnitude greater than the conduction times for the long axons. Therefore responsiveness is NOT proportional to axonal conduction velocity.

2. The refs do NOT in general support the statement made. I'm not going to waste time on a general analysis (and if I did I'd do it in my own blog), but consider from the abstract of Boyd & Kalu 1979 (ref'ed in More et al. quoted above):

(Continued in my next comment.)

AK said...

"1. Compound action potentials were recorded from certain muscle and cutaneous nerves in normal and chronically de-efferentated hind limbs of cats during stimulation of the appropriate dorsal spinal roots, 2. The peaks for groups I, II and III in the compound action potential were correlated with the corresponding peaks in the fibre-diameter histograms of the same de-efferentated nerve after processing it for light microscopy. 3. The scaling factor (ratio of conduction velocity in m/sec to total diameter in micrometer) was not constant for all sizes of fibre nor did it increase progressively with fibre size. Evidence is presented that a logarithmic relation between conduction velocity and fibre diameter is not appropriate. 4. In muscle nerves the scaling factor for fibres fixed by glutaraldehyde perfusion and embedded in Epon was 5.7 for group I afferent fibres and 4.6 for myelinated fibres in both group II and group III. 5. In cutaneous nerves the scaling factor was 5.6 for large fibres (group I or Abeta) and 4.6 for small fibres (group III or Adelta). 6. The scaling factor for group I fibres is the same as was found previously for alpha-efferent fibres, and that for groups II and III is the same as for gamma-efferent fibres (Boyd & Davey, 1968). 7. The possibility that there is a clear discontinuity in scaling factor between fibres in groups I and alpha, and those in other functional groups, is discussed. 8. It is concluded that there must be some structural feature of alpha and group I fibres which differs from that of smaller myelinated fibres. It is likely that a difference in the relative thickness of the myelin sheath is involved and possibly also in the conductances responsible for generating the action potential. [bolding mine]"

Overall this (More et al.) is a very disappointing paper. I've done an occasional literature search looking for some reliable formulas for predicting axon CV based on axon diameter and myelin thickness, and found nothing suitable. Obviously, neither did More et al. The latest ref for their statement (quoted above) is Hoffmeister et al. 1991 which is titled: " A proposed relationship between circumference and conduction velocity of unmyelinated axons from normal and regenerated cat hindlimb cutaneous nerves. [bolding mine]".


Zen Faulkes said...

Dang, now I have to go back and read the paper again...

Well spotted!

Unknown said...

Great post, thanks for an excellent summary of our research! I especially like the Haldane quote and its graphic reference to the fate of the horse. I do want to clear up a few concerns mentioned in the comments though.

If we assume that the distance from the foot to the spinal cord is 3 cm in the shrew and 3 m in the elephant, the conduction delay from the foot to the spinal cord and back again would be about 1.5 milliseconds in the shrew and 85 milliseconds in the elephant. Since the delay in transmitting the signal from one neuron to the next is on the order of milliseconds, the time required for a spinal reflex to occur in small animals such as the shrew is still on the order of milliseconds whereas that of the elephant is closer to 100 milliseconds – two orders of magnitude larger than that of the shrew, and significantly larger than the transmission delay between axons.

It is generally accepted that conduction velocity and axon diameter are approximately linearly related, and although there is some debate over the exact scaling factor in this relationship most estimates are within a fairly tight range – for example, estimates range from 5 m/s to 7 m/s per micron of diameter in myelinated axons. There is some evidence that the scaling factor is slightly different in different types of fibers, however the range of scaling factors found is still quite small and would make no major impact to our conclusions. Further, since we consider all types of axons (including both myelinated and unmyelinated) when looking at possible delays in sensing and responding to stimuli, we felt it was important to reference evidence supporting linear relationships between conduction velocity and diameter in a variety of axon types.

I hope that helps! Thanks again for the report on our research.

Zen Faulkes said...

Thanks, Heather!

This has got me wondering, though, about how myelin changes the scaling effect. Intuitively, I would think that myelin would flatten the relationship between axon size and conduction velocity.

But because I work mostly with invertebrates, where myelin is less common (though not absent, as some people claim), my intuition may not be at all good. :)

Unknown said...

Interesting point! Rushton (1951) did some really cool theoretical work on myelination and conduction velocity, and related it to experimental results from other studies. It turns out that, theoretically, conduction velocity is directly proportional to axon diameter in myelinated axons and proportional to the square root of axon diameter in unmyelinated axons. These relationships intersect at an axon diameter of about 1 um. Axons less than 1 um in diameter actually conduct impulses faster if they are unmyelinated. But, for axons greater than 1 um in diameter, myelinated axons conduct faster than unmyelinated axons. So for larger axons, whether they are myelinated or unmyelinated can make a huge difference in conduction velocity.

In the same paper, Rushton shows that for an axon to have its maximum conduction velocity the diameters measured inside (internal) and outside (external) the myelin sheath should have a ratio of 0.6 (internal:external diameter). And in fact, most myelinated axons do have this ratio!