Here is a continuation of our discussion.

Krystyna Gielo-Perczak, Co-moderator Biomch-L
From: "Greiner, Thomas M. Ph.D."

If I may, I think some clarification would be helpful on the meaning of the
word "symmetry" -- at least as it applies to animal body design. I bring
this up only because the word "asymmetry" is a non sequitur in this

There are two basic forms of development -- bilateral and radial
(embryological development is what I mean here, although it may also apply
to phylogenetic development by inference). At the earliest stages of
development, zygote through blastocyst, either term would be descriptively
correct. At the beginning of the gastrulation stage is when the two types of
symmetry begin to take hold. Bilateral symmetry requires that the left and
right halves of the body start out as mirror images of each other -- later
developmental accommodations to body size may result in slight differences
between these two halves, but every unpaired organ in the body (eg, heart,
liver, stomach, etc) starts its development as a midline structure.
Therefore, they are still following perfect bilateral symmetry.

Radially symmetry (more common in plants, but hardly restricted to them)
means that there is a central point, with concentric circles of
differentiation radiating out from that point. Asymmetries that develop in
this plan, are again accommodations to body size or accidents of
environmental interactions.

The concept of developmental (or morphological) constraint is very germane
to the discussion of why one type of symmetry predominates among the animals
(although it is perhaps a little flippant to make that claim without further
study of what we mean by "predominate"). Thus humans develop bilateral
symmetry because mammals do, and mammals have bilateral symmetry because
vertebrates do, and so on and so on. There may ultimately be a good
functional explanation why bilateral symmetry was successful, but I must
remind everyone that this choice (and the developmental constraint that
results from it) occurred when life was limited to microscopic creatures.
So, when I claimed that "dumb luck" was the basis for bilateral symmetry in
most animals I was basically admitting my ignorance of microscopic
functional morphology/ecology.

Thomas M. Greiner, Ph.D.
From: "Jenkyn, Thomas"

Dear list-members,

Continuing with this stimulating discussion of bi-lateral symmetry and
why it is so predominant in large land animals has brought up the point
that a uni-lateral strength (or weakness) would be a evolutionary hinderance

to an animal; making it susceptable to attack from one side more than the
The valid point was raised that humans (and other animals) are side
dominant in writing and tool-using side (85-90% on the right side).
But we are missing an enormous point that should be right in front of
our faces (or ironically, directly behind us).
We are indeed grossly assymetric when it come to perception with one side by
far more alert to danger than the other. Front to back!! I thought this
would have been obvious to us all.

Also, assymetry in alertness does not require that the organism be
evolutionarily hindered by lacking attention is a certain direction. It
doesn't seem to hinder humans (although a little more foresight would not
hurt us as a species: philosophical sidebar). It seems to me, as alert as
star fish are, they are radially symmetry in their attention.

Keep in mind that there are plenty of assymetric and odd-numbered
architecture schemes for locomotion in animals that are perfectly feasible,
but that are not seen in the animal or microbe kingdoms. Their absence from
the fauna of this planet is not evidence of their unfeasibility.

Gotta go, I can hear my boss creeping up behind me....
Tom Jenkyn
From: Jon Dingwell

Dear Biomch-L:

This is an interesting discussion, which I believe may have already been
answered, not by biologists and physiologists, but by physicists and

My freshman Physics teacher always told us that the second most important
two-word phrase in the English language was "by symmetry" (the *MOST*
important, of course, being "check enclosed"). Symmetry is one of the most
powerful concepts in nature and in mathematics, because is greatly
simplifies both physical systems and their mathematical descriptions.

A number of people have worked on the idea that central pattern generators
(CPGs) in the spinal cord can be modeled as sets of coupled nonlinear
oscillators. As it turns out, when CPGs are modeled as *SYMMETRIC* rings
of coupled oscillators, they exhibit all of the gaits (and the appropriate
gait transitions) exhibited by terrestrial animals in nature, regardless of
the number of pairs of legs. It is the symmetry conditions on these rings
of coupled oscillators that produces pairs (even numbers) of legs.

There are a number of published articles on this, which may not be familiar
to many in the biomechanics community, the most prominent of which are (in
my opinion) the following:

Collins, J.J. and Stewart, I.N. (1993). "Coupled Nonlinear Oscillators and
The Symmetries Of Animal Gaits." Journal of Nonlinear Science, 3: 349-392.

Golubitsky, M., et al. (1999). "Symmetry in Locomotor Central Pattern
Generators and Animal Gaits." Nature, 401 (6754; Oct. 14): 693-695.

For those of you who wish to dig around into the details a bit further:

Buono, P.-L. (2001). "Models of Central Pattern Generators for Quadruped
Locomotion I. Secondary Gaits." Journal of Mathematical Biology, 42 (4):

Buono, P.-L. and Golubitsky, M. (2001). "Models of Central Pattern
Generators for Quadruped Locomotion I. Primary Gaits." Journal of
Mathematical Biology, 42 (4): 291-326.

Collins, J.J. and Richmond, S.A. (1994). "Hard-Wired Central Pattern
Generators For Quadrupedal Locomotion." Biological Cybernetics, 71: 375-385.

Collins, J.J. and Stewart, I.N. (1993). "Hexapodal Gaits And Coupled
Nonlinear Oscillator Models." Biological Cybernetics, 68: 287-298.

Collins, J.J. and Stewart, I.N. (1994). "A Group-Theoretic Approach to
Rings of Coupled Biological Oscillators." Biological Cybernetics, 71:

Golubitsky, M., et al. (1998). "A Modular Network for Legged Locomotion."
Physica D, 115: 56-72.

I am forwarding this message also to Pietro-Luciano Buono and Marty
Golubitsky because I think they have done the most recent work on this
topic and because I am not sure if they receive Biomech-L. I would be very
interested to hear their comments on this issue.

Jon Dingwell

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