rsnorman at mediaone.net
Sat Sep 16 10:43:37 EST 2000
The theoretical foundation for the relation between conduction velocity
and axon diameter is well established. In fact, it is so well entrenched
that newer textbooks emphasize more recent and more "exciting"
developments, like the molecular biology of gated ion channels and
synaptic signaling mechanisms.
Basically, in the unmyelinated axon, the conduction velocity is
proportional to what is called the "space constant" which indicates
how far down the axon the local current loops will travel. The details
are given by the "cable equation" or "telegraphists equation" which
is a partial differential equation describing voltage as a function of
distance and time on an electrical cable with longitudinal resistance
and transverse resistance and capacitance. I believe Hodgkin and
Rushton in 1938 first did experimental tests on an unmyelinated
axon to demonstrate that the cable equation did accurately describe
the observed potentials. However, I don't have my good references
at home with me and, as I mentioned, most texts skip over these
details. But any good physiology or neurobiology book will describe
the space constant and how it varies with the square root of diameter.
The velocity of the action potential is a bit more complex. It depends
not only on the space constant but also on the time constant which
indicates how fast the potential will change for a given current.
However, the membrane time constant for an unmyelinated cell is
constant with diameter so, for that kind of axon, the velocity increases
with square root of diameter. Hodgkin and Huxley in 1952 considered
the non-linear time-varying partial differential equation which included
both the cable properties plus their analysis of how membrane
varies with voltage and time. They solved the equation by hand
using only a mechanical adding machine for computation, and found
that their computed action potential propagated down the theoretical
axon at pretty close to the observed velocity for the real squid axon.
Myelin produces many complex effects. It greatly increases axonal
resistance while at the same time reducing membrane capacitance.
But the major effect is that the action potential "saltates" or jumps
from node of Ranvier to node, taking roughly a constant amount of
time to make each jump. So the velocity of propagation is mainly
controlled by the internodal distance and it turns out that this
distance is roughly proportional to diameter. Therefore the velocity
varies with diameter.
Interestingly, the theoretical linear relationship for myelinated cells
and square root relationship for unmyelinated crosses for small
diameters -- at large diameters myelin is much faster but for
very small diameters, unmyelinated is a bit faster. And the smallest
cells (under 1 um) in the vertebrate nervous system are generally
"Bill Browning" <bbrownin at nospambellatlantic.net> wrote in message
news:XAAw5.2143$u6.68481 at typhoon1.ba-dsg.net...
> Well, at least Mother Nature acts like a responsible engineer in
> designing the
> connective tissue sheath around nerves.
> You said, "The conduction velocity in unmyelinated axons is
> proportional to
> the square root of diameter, in myelinated axons it is roughly
> proportional to the diameter itself." Such a relationship just cries for
> interpretation. There must be an explanation.
> Also, how does the myelin sheath produce the effect of increasing
> Bill B.
> Richard Norman <rsnorman at mediaone.net> wrote in message
> news:P_yw5.34639$_e4.1567156 at typhoon.mw.mediaone.net...
> > The diameter and mass of peripheral nerve is small compared with
> > that of the skeletal, muscular, and circulatory apparatus in the
> > appendages. So there would be no evolutionary disadvantage
> > in the way you suggest. Of course there always is an advantage
> > to cutting down on biomass wherever possible -- cells need quite
> > a lot of metabolic maintenance just to keep themselves alive.
> > The myelin sheath around each nerve in one sense enormously
> > increases the diameter over that of the naked axon inside. However,
> > that increase is trivial in comparison to the advantage gained in
> > conduction velocity. And large vertebrates need that extra
> > speed for rapid response and coordination.
> > The conduction velocity in unmyelinated axons is proportional to
> > the square root of diameter, in myelinated axons it is roughly
> > proportional to the diameter itself. A 1 um unmyelinated cell
> > conducts at about 1 m/s, a 1 um myelinated mammalian cell at
> > about 5 m/s (the warmer temperature also contributes). As a
> > result, a 16 um myelinated cell might have a conduction velocity of
> > 80 m/s while a similar size unmyelinated cell would be 20 times
> > slower. So the bulk of myelin actually provides for high conduction
> > velocity with relatively much less cell volume than the unmyelinated
> > case. That, combined with the fact that myelin itself is relatively
> > inert metabolically, gives an enormous advantage to vertebrates.
> > The axons are wrapped in a connective tissue sheath for strength
> > and mechanical protection. Bundling the axons into nerves
> > significantly reduces the amount of connective tissue needed to
> > wrap the ensemble, as opposed to wrapping the individual fibers.
> > Having the nerves travel together throughout most of their course
> > might also be important in the way they develop and find their
> > way to the proper destination. This tendency for nerve fibers
> > to collect in ensembles rather than being diffusely scattered in
> > a nerve plexus is generally called "centralization", and is clearly
> > seen in the difference between, say, the CNS of a flatworm and
> > that of annelids, arthropods, or mollusks.
> > "Bill Browning" <bbrownin at nospambellatlantic.net> wrote in message
> > news:jgww5.2070$T6.54682 at typhoon2.ba-dsg.net...
> > > Thanks for your informative response.
> > > Referring to peripheral nerves, I expected that evolutionary
> > selection
> > > would have
> > > bundled the related axons to reduce bulk. Other components of legs
> > arms
> > > are
> > > slimmed down in a way that reduces weight and improves mobility.
> > > separate
> > > myelin sheaths around each axon in the sciatic nerve must increase its
> > > diameter
> > > enormously and reduce the mobility of the hip joint over what it could
> > have
> > > been if
> > > they were bundled. I suppose the evolutionary path had passed the
> > of
> > > no
> > > return before the consequences began to affect survival.
> > > I don't blame you; besides it's too late to change it now.
> > > Bill B.
> > > ---------------------------------------------
> > > Bill B. had asked:
> > > As I understand it, a nerve signal is carried by multiple nerve
> > not
> > > just by a
> > > single axon. Is the myelin sheath around single axons; or is it
> > > groups of fibers
> > > which carry the same signal?
> > > I visualize a nerve structure like a stranded electrical wire
> > an
> > > insulating
> > > jacket.
> > > Bill B.
> > > And the following reply ensued:
> > > From: Richard Norman <rsnorman at mediaone.net>
> > > Subject: Re: Nerves bundled?
> > > Date: Sunday, September 03, 2000 10:43 PM
> > >
> > > This depends to some extent on what you mean by nerve "signal".
> > >
> > > Individual neurons carry information down individual axons, although
> > > the axon can branch in a complex pattern. Axons in the peripheral
> > > system are bundled into nerves, like the multiple wires in a telephone
> > > cable. However, the separate nerve fibers seem to function without
> > > any significant interaction, even if they are quite close together.
> > >
> > > The myelin that wraps single axons of vertebrate axons is more than
> > > an insulator, it dramatically alters the speed of conduction. One
> > > oligodendrocyte in the CNS can wrap an average of some 15 different
> > > axons, while the Schwann cells in the periphery only wrap single
> > > However, I have never seen any suggestion that the group of cells
> > > surrounded by a single oligodendrocyte are functionally related in any
> > > way except to the extent that neighboring cells are likely to have
> > > function. The myelin "interconnection" has no functional
> > >
> > > All the above indicates that the neurons are distinct individuals,
> > > with a different signal. However, in a broader sense, there is
> > > a population of neurons that serves any particular function especially
> > > in the vertebrate animals A group of several to several hundred
> > > or more cells all participate in the same general function and each
> > > carries a slightly different aspect of the information. In that
> > > the nerve signal is really carried by the population of cells. For
> > example
> > > intensity of a signal can be carried by the frequency of firing of an
> > > individual cell or by the total number of cells in the population that
> > > are active. Look up the terms "labeled line" and "across fiber"
> > > in any good neurophysiology text to see more complex examples of
> > > how a population of cells can transmit information.
> > >
> > >
> > >
> > >
> > >
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