Why am I so enthusiastic about symmetry?Because symmetry provides a "new" (new to most embryologists) unifying perspective for understanding how anatomical shapes are self-caused - by properties of their component cells and molecules.
For example, I had not thought of Turing's Reaction-Diffusion systems as a way of reducing ("breaking") displacement symmetry. If anything, I assumed such systems were creating symmetry, not reducing it in a controlled way. Actually, Turing's original paper stresses reduction of symmetry by deliberate instability; but somehow that wasn't the message biologists carried away from Turing's reasoning. Instead, they focused on mathematical equations.
Regarding the phenomena of sperm entry locations determining the plane of right-left reflection symmetry, I had thought of this as a creation of a new plane of symmetry (instead of destruction of all other planes of symmetry). And I had thought of gravity as a fundamentally different way of creating symmetry. For me, there were three revelations:
First, that symmetry is being reduced, not increased;
Second, that the key phenomenon is that amphibian oocytes "deliberately" destabilize forces in their cytoplasm, so that even very small disturbances become able to initiate major rearrangements of their cytoplasm;
Third, that deliberate destabilization of pre-existing symmetries is always the best way to think about axis formation, including in kelp eggs, and many other shape-generating phenomena.
Curie's Principle (Effects have the same, or more, symmetries as the sum of their causes) gives us a systematic way to search for embryological mechanisms. Kartagener's syndrome led scientists to the (surprising for everyone) causal connection between flagellar axonemes and the creation of right-left asymmetry. Without that mutation, would anybody even have suspected any such mode of causation? On the other hand, if developmental biologists had been aware of Curie's Principle, they would have realized that aortas can't consistently develop on the left without something playing the role of the "Right Hand Rule" in the Physics of electromagnetism. From that perspective, embryologists would have been searching for cellular structures that strongly depart from reflection symmetry. Flagellar axonemes should have become prime suspects from the first time anybody noticed either that flagella bending lack reflection symmetry or that axonemes have rotational but not reflection symmetry. In the future, anyone trying to explain any reduction of symmetry ought to start by seeking combinations of instabilities and triggers.
It was also a revelation to me that dilation symmetry provides a more systematic way of thinking about Driesch's classic discovery (that miniature larvae develop from separated cells of early starfish). We can ask what other phenomena also have dilation symmetry (or, as physicists say, which phenomena "scale"). Such phenomena include river meanders, streams of water breaking into drops, mushroom-shaped clouds, Dictyostelium slugs, stalks and spore masses; and I hope that fish scales also "scale"). The point is not to ask what particular forces cause scaling, or to visualize echinoderm cells as having evolved anthropomorphic abilities to compensate for being split in two, four etc.
Instead, we should note take note of which properties remain the same despite imposed changes in size. In the cases of river meanders and water droplets (and I suspect also for Dictyostelium) the key reason for dilation symmetry is that perpendicular dimensions automatically adjust so as to keep the same ratios to each other. Shortening a slug stimulates it to get narrower and to elongate, until the length to width ratio returns to what it had been. This, in turn, is an example of my favorite concept, "shape homeostasis".
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