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  • Bi-lateral symmetry vs. asymmetry ...more

    Here is a continuation of our discussion.

    Krystyna Gielo-Perczak, Co-moderator Biomch-L
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    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
    perspective.

    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
    other.
    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
    mathematicians.

    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):
    327-346.

    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:
    95-103.

    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.

    Regards,
    Jon Dingwell
    ----------------------------------------------------------------------------

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