Embryology Biology 441 Spring 2010 Albert Harris
Over-view of Embryo Pattern Causes & Symmetries
"Prepatterns" versus "Positional Information" are 2 major alternative methods for what Slack calls "Regional Specification". (1) Prepatterns are chemical maps of future anatomy,
but can't explain size regulation (Dreisch and all that).
Turing's reaction-diffusion systems are methods to make prepatterns by magnifying random fluctuations.
Scott Gilbert & many others assume "random in: random out": but computer simulations prove regularity.
Advantages of "Positional Information: (a) can explain size regulation (i.e. Driesch and all that)
(b) and is confirmed by Bicoid gene pattern in Drosophila fly development, and Dorsal & some others.
A whole different approach is for mechanical forces within embryos to create anatomy directly.
(as forces create mountains, clouds, storms, bubbles, galaxies etc. except with genes adjusting the mechanical forces so as to create many more different, & more consistent, anatomical patterns.)
What forces?: Adhesions between cells, & between cells and matrix; Water pressure inside neurocoel, blastocoel, eye, blood vessels etc.; Osmotic pressure inside cartilages; Traction exerted by crawling cells;
Strengths and cross-linking between collagen & other fibers, Self-assembly of proteins. (crystallization)
Steinberg's Differential Adhesion Hypothesis ("thermodynamic" theory of cell sorting) claims that
sorting out of dissociated cells (Wilson-Holtfreter-Trinkaus), gastrulation, neurulation, organ formation etc.
are pulled by maximization of cell-cell adhesions )"reversible work of adhesion."
Slack & Gilbert are convinced this theory has now been proved true, by molecular experiments.
I claim they are really measuring strengths of cell contraction, instead of strengths of cell-cell adhesion,
& they misunderstood some key thermodynamics, which doesn't apply when active forces are exerted.
Driving force in Haptotaxis isn't cells being pulled by process of adhesion formation, but by a "tug of war".
D'Arcy Thompson's book "Growth and Form" tried to explain anatomical and cell shapes as direct effects of physical forces, and used analogies to soap bubbles, in which T behaves as if it were a constant scalar.
"Stem cell" methods can never build organs until these kinds of questions are understood.
Some key math known to few biologists: Tensors and Symmetry
Stress (=tension & compression), strain (=distortion) , surface curvature (angular change/distance)
All have an amount in each direction at each point = are symmetric second order tensors
Scalar variables include chemical concentrations, temperature, fluid pressures (zeroeth order tensors)
Notice how prepatterns and positional information use only scalar variables, merely from ignorance!
Some, including me, have tried to develop tensor equivalents of prepatterns, that could regulate! (Driesch)
(Incidentally, vectors are first order tensors, but turn out not to be very important in embryological shape.)
A key equation: Pressure difference across a flexible layer deltaP= C*T + c*t
C, c being curvatures in perpendicular axes, and T and t being tensile stresses in perpendicular axes.
Pressure equal to curvature times tension: for example in blood vessels, the large curvature of capillaries allows them to withstand very high pressures with only small tensions. (Did you ever wonder how?)
Arteries have smaller curvatures, and therefore need high tensions to withstand these same high pressures.
Even a little too much swelling decreases curvature enough that tensions can't withstand pressure,
causing more swelling, therefore even smaller curvature, & so T gets bigger, making C smaller.
This vicious cycle results in aneurisms, burst arteries, many strokes & some heart attacks
Symmetry: How to cause and change ("break") symmetry;
Some methods of breaking symmetry of early embryos (a) point of sperm entry,
(b) Direction of gravity (c) Flagella serving as equivalent of "Right-Hand-Rule (in courses on electromagnetism) (d) Turing's "Reaction Diffusion System, which magnifies random variations to make spatial patterns that can be very regular (contrary to what Scott Gilbert assumes and shows in an illustration)
(e) Someone (you?) needs to discover/invent more methods for magnifying tiny disturbances, to explain how embryos break symmetry. The punching dummy analogy was meant to show that a system can be converted from stable to unstable behavior, by internal changes invisible from the outside, but people would thank the instability is caused by external disturbances (e.g. wind, flies, Brownian motion)
(conclusion: sperm entry, gravity, flagellar asymmetry, etc must be "setting off" internal instabilities that have mechanisms of their own, analogous to Turing's mechanism &/or some positive feedback.
Curie's Law says that results have the symmetry of their causes (sometimes more; never less)
Pressures and tensions that act equally in all directions (=have spherical symmetry) cannot help producing spherical shapes (e.g. most oocytes including humans'). To produce less symmetrical shapes, some force or signal needs to be less symmetrical. Crystals have the same symmetry as the packing of the ions they are made from; X-ray diffraction patterns have the same combinations of displacement, reflection and rotational symmetries as does the packing of the ions they are made from. & there are many examples.
Developing embryos either use less symmetrical forces to make their anatomy less symmetrical,
Or they find ways to break symmetry (and disobey Curie's Law).
Turing's mechanism is a way to break displacement symmetry; so is the Clock & Wave-Front theory.
The Clock & Wave-Front was invented specifically to account for embryonic regulation (Dreisch etc)
Specifically how embryos can always produce the same total numbers of somites, despite having different amounts of paraxial mesoderm to make them from (which some species do, but others don't.
Such regulation (in Driesch's sense) can be regarded as dilation symmetry, between embryos.
Different symmetries defined by any geometric change (reflection, displacement, magnification, distortion?) that leaves the object (embryo, organ) looking the same.
You could invent new symmetries for animal color patterns that repeat with variations.
Conservation of energy, momentum, electrical charge etc. result from symmetries in laws of nature!
(displacement in time, space etc.) Holtfreter might have said "Wow!", except not in contempt.
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