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First set of review questions for the second hour examAs for the previous exam, questions marked with a * are more difficult, and not many will be asked.Questions marked with ** are even more difficult, and will not be asked on the exam. But please think about them. 1) If you suspect that a newly-discovered embryonic structure is mechanically equivalent to a water balloon, what are some experiments that you could do to test (prove or disprove) your hypothesis? 2) Draw a graph of the relative amounts of curvature along any arbitrarily-drawn curve. (If I draw a curve on the exam, you need to be able to sketch a graph of the relative amounts of curvature at all the different parts of this curved line.) For example, consider the traditional heart shape, used on playing cards. 3) The reverse problem to this: If I draw a graph of amounts of curvature along a line, you should be able to sketch the line, based on knowing how much curvature it has at different points. 4) What two lines have constant amounts of curvature at all points? Sketch both. 5) What three dimensional curve has constant curvature in one direction and zero curvature in the direction perpendicular to the direction in which curvature is constant?(Hint: cylinders) Are there any structures in the body that actually have this combination of surface curvatures? (ducts, blood vessels, the notochord, hair) 6) What geometric property is defined as being the rate of change of angular direction per unit distance along the surface of an object? (curvature)
7) Is it possible for a surface to have positive curvature in one direction and negative curvature in directions perpendicular to those in which curvature is positive? 8) Sketch a gastrulating sea urchin embryo and sketch graphs of the relative amounts of curvature at different areas of its surface. Are there any saddle points? 9) Sketch a cleaving cell, and next to it sketch a pair of graphs of relative amounts of curvatures in perpendicular directions at different parts of the surface of this cleaving cell. Are there any saddle points? Please mark locations of saddle points. 10) Using pairs of double-ended arrows (like those on this diagram of cylinder, sphere, saddle and hen egg), map the distribution of curvatures at different parts of the surface of the brain and spinal cord of an early embryo. (Why is average curvature less in the brain than in the spinal cord?) 11) In order for a flexible, stretched sheet to have equal pressure on both sides, it either has to be saddle-shaped or it has to be what shape? __flat_____ 12) Curvature times __tension______ ? equals change in pressure? 13) On all parts of any curved surface, the direction of maximum curvature has what geometric relation to the direction of minimum curvature? (They are perpendicular to each other) 14) One divided by radius of curvature equals what? (curvature) 15) What are at least two examples of scalar variables? (chemical concentration, osmotic pressure, temperature) 16) What are at least three examples of second order tensor variables? ( Curvature, tension = stress, strain, permeability)
17) What is one example of a fourth order tensor variable?
18) What is Hooke's law? Is it a law of nature? Or is it a simplifying assumption that is often true for small amounts of stress? 19) Visualize a blood vessel that branches into two, with tension in the right branch (for some reason) being twice as strong as tension in the left branch: then sketch the angles between these three blood vessels. 20) Picture a situation in which an artery is supplying blood to two organs. Visualize this artery branching a short distance before reaching the two organs. If equal volumes of blood are being supplied to both organs, then what is the optimal angle of branching? What is the organ on the right needs to receive twice the volume of blood per minute as the organ on the right, how will this affect the optimum angle at which the arteries should branch? Explain your reasoning.
21) Suggest some alternate hypotheses about the mechanisms that control branching of arteries and veins. 22) What is the effect of reduced tension on the geometric arrangements and shapes of developing anatomical structures? Their shapes and positions become less regular. *23) Suggest some possible explanations for this phenomenon? 24) Please list examples of embryonic processes that are mechanically analogous to the inflation of a water balloon? (Expansion of the brain, eye, inner ear, blastocyst)
25) Before gastrulation begins, a teleost embryo has what combination of symmetry? 26) During gastrulation, what symmetries do vertebrate embryos develop? Or break?
27) The curvature of a line is described as the rate of change of what? per distance along what?
28) Surface curvatures of what two shapes are the same in all directions? 29) The surface curvature of a cylinder is zero in one pair of directions and some non-zero constant in the directions perpendicular to that.
**30) The stiffness of materials (Young's Modulus) is the ratio of stress (forces of resistance) per amount of strain (% change in dimensions). That makes stiffness a fourth order symmetrical tensor (because its the ratio of one second order tensor to another second order tensor.) *31) The Young-Laplace Equation P = T (1/R1 + 1/R2):
Isn't true for balloons? Isn't true for cells or embryos? Is true only for situations in which tension doesn't vary with either direction or location? Is a law of nature? Is a useful approximation? Can be very inaccurate and misleading? Should be replaced by P = T1/R1 + T2/R2? Should be replaced by P = T1*C1 + T2*C2?
**32) When is 1/(Radius of curvature) = Curvature?
33) In addition to reflection symmetry, what other kinds of symmetry are there? 34) What are at least three examples of each of these kinds of symmetry, two biological examples and one example of a man-made structure?
35) How did Weyl define symmetry? Something has symmetry, if there is something you can do to it (reflect it, rotate it, move it, magnify it) and...
36) A spiral snail shell has a combination of dilation (=magnification) symmetry plus what other symmetry? 37) An adult starfish has five planes of reflection symmetry? 38) A pluteus larva has two planes of reflection symmetry? 39) A sea urchin blastula has an infinite number of planes of reflection symmetry?
40) Which is more difficult to accomplish?
To make something become less symmetrical? To make something become less symmetrical, but not random? (this one) 41) Turing's mechanism is able to change displacement symmetry in what way? 42) Therefore, Turing's mechanism is a way to break displacement symmetry?
43) Does Turing's mechanism increase or decrease displacement symmetry? 44) Therefore, Turing invented a contradiction = counter-example of Curie's Principle? Yes. *45) What changes in dilation and displacement symmetry occur during the formation of Liesegang rings?
46) When a donkey decides which of two equally distant piles of straw to eat first, it is breaking what symmetry?
47) When the higher-pressure chamber of the heart develops on the left side, what symmetry is that breaking?
48) Kartagener's Syndrome is a genetic inability to break what symmetry?
49) Is that a confirmation or a contradiction of Curie's Principle? *50) Imagine that the differences between the left and right side of some kind of organism's body were somehow controlled by the stereo-asymmetry (stereoisomerism) of amino acids. Then would it be possible for a mutation to produce situs inversus? 51) What conclusion can we draw from the observation that almost half of people with Kartagener's Syndrome do NOT have situs inversus? 52) Flagellar basal bodies (axonemes) have nine fold rotational symmetry, but have no planes of reflection symmetry. What is the relation between this lack of reflection symmetry and the preceding four questions? *53) What (abnormal and also normal) planes of reflection symmetry are possessed by the bodies of conjoined twins?
*54) Suggest reasons, in terms of embryological mechanisms, why conjoined twins are always (usually?) mirror images of each other? Think about whether embryological control mechanisms would interact, including either chemical gradients or mechanical forces, and what would be the effects of interactions between them. *55) When human identical twins develop by forming two primitive streaks in the same inner cell mass, then one of these twins will (Usually? Always?) have situs inversus viscerum (aorta on the right side of the heart, etc & everything a mirror image shape and position). Suggest why. 56) Turing's "Reaction Diffusion" mechanism (or "system") is a way to reduce/increase the d----------t symmetry of a spatial pattern?
57) What symmetries, or combinations of symmetries, do each of the letters of the alphabet and keyboard symbols possess (approximately)? ABCDEFGHIJKLMNOPQRSTUVWXYZ ! # $ % ^ * <> + = ~.1, 3,8, 0
*58) Sessile and slow moving animals often have several planes of refection symmetry (which most biologists naively call "radial symmetry"). Suggest why? 59) What swimming animals have radial symmetry? And suggest why? 60) Most fish and walking animals have bilateral symmetry; in what sense is this the symmetry of their environment (if we include forward movement as part of their environment)? 61) If a swimming or walking animal spent about as much of its time walking forward as backwards, then what additional symmetry might appear in its anatomy? 62) Burrowing animals (worms and even snakes) tend to evolve back toward "radial symmetry" (= an infinite number of planes of reflection symmetry): is this because they are moving slower? Because they are reversing direction more often? Or because their surroundings consist of front, sideways and rear, with all "sidewayses" being equivalent? 63) For a fish or a walking animal, the directions are up, down, rearward, forward and sideways (how many "sidewayses" do they have, not counting flounders?
64) When a jelly-fish swims by pulsation, its directions are forward, rearward, and sideways (how many "sidewayses"?). How is this related to the symmetry of the anatomy of a jelly-fish? 65) When a force, or balance of forces have spherical symmetry, then what shape will they tend to remold a cell into?
66) If a gene could make an internal force less symmetrical, then could that cause cells and tissues to change from one symmetry to another? *67) What the symmetries are approximated by the path of a meandering river? (Take a look on Google Earth, or the next time you fly somewhere.) 71) Is Turing's theoretical mechanism based on positive feed-back or negative feed-back? Both; but explain
72) Are your finger-prints on the equivalent fingers of your right hand approximate (but not exact) mirror images of your finger-prints of the fingers of your left hand.
73) Physical tension in a thin sheet of material has what combination of symmetries? What combination of symmetries exists at every point within a concrete wall? 74) During the process of mitotic cell division, what symmetries exist in the cell cortex? 75) What about symmetries in a mitotic spindle? *76) Polar body formation differs from ordinary mitosis in what difference in symmetry? 77) When an animal develops regularly spaced stripes, in what way has the symmetry of its skin changed? 78) Suppose an animal develops regularly spaced spots: does it then have more, or less, symmetry than a striped animal? (increased or decreased?) What symmetries did it have before the stripes formed? 79) When a force, or balance of forces have spherical symmetry, then what shape will they tend to remold a cell into? What if they have two planes of reflection symmetry; then what shape will they create? 80) If you see a mass of cells changing from another shape into a sphere, then what do you tentatively conclude about the forces responsible? 81) If a gene could make an internal force less symmetrical, then could that cause cells and tissues to change from one symmetry to another?
**82) If somebody tries to apply the concept of minimization of free energy to explain a shape or shape change, what are they assuming (whether they known it or not!) about the physical forces that are responsible?
*83) Does Turing's (and other "Reaction-Diffusion" systems) only work for scalar variables, or can tensor variables be used also or instead? 84) If you can take a wall-paper pattern and either move it 2 inches to the right, or to the left, or move it 4, 6, 8 etc. inches to either the right or left, and it would look the same, then what kind of symmetry does it have? (Let's assume it looks different if you move it one inch, or 3.5 inches, or any distance but multiples of 2 inches). displacement 85) If this pattern also looks the same after being rotated 60 degrees, 120 degrees, or 180 degrees, then what additional kind of symmetry does the pattern have? reflection 86) If the pattern is all one color, and looks unchanged when moved an inch, or 1/2 inch, or any small distance, and is also apparently unchanged when rotated by any number of degrees, then does it have more or less symmetry than the patterns mentioned above? more 87) When the anterior-posterior axis of an amphibian oocyte is caused to form by the location where the sperm enters, then what change in symmetry has been caused?
*88) If you fertilize an amphibian oocyte exactly at the animal pole, and nevertheless it develops a normal anterior-posterior axis (with only one plane of reflection symmetry), then what does this suggest about the underlying mechanism by which a single anterior-posterior axis is chosen from the infinity axes of reflection symmetry that had existed until then?
89) Which symmetries, or combinations of symmetries are possessed by the following? 90) Becoming less symmetrical means losing (?) or gaining (?) elements of symmetry? Either way, what alternative kinds of mechanisms can be used to choose which specific planes or axes, or other symmetry elements, will be gained or lost? (Sperm entry? Gravity? Random fluctuations? Anything else?) What if you just poked it at some time of special sensitivity? 91) If a gene could make an internal force less symmetrical, then could that cause cells and tissues to change from one symmetry to another? *92) Invent a new kind of symmetry, based on distortions in shape produced by curved mirrors. Could some shapes look the same? Or could reflection, plus some other change (like inflation), in combination, leave some shapes looking the same. *93) Try comparing the symmetries of brick locations in brick walls or sidewalks: how many different combination of symmetries can you find? How many different ones are possible, in principle? (it's in the teens, I think; not infinity). *94) To prove the occurrence of an actual Turing mechanism, would you need to isolate and identify the actual chemicals? Or can you invent experimental criteria, such as how the resulting patterns are altered by water currents or by more viscous fluids, or barriers to permeability, or something else. 95) What phenomenon, discovered by Hans Driesch, indicates that developmental mechanisms of echinoderms have dilation symmetry? Does Driesch's entelechy have dilation symmetry!?
*96) Can you invent an alternative set of rules for chemical reactions that would produce alternating peaks of concentrations of two chemicals? It is easier than it might seem. *97) Compare and contrast the geometric pattern of Liesegang Rings with those produced by other reaction diffusion systems.
98) In the photograph of Liesegang rings shown on the course web page, can you figure out why rows of dots form in some places, in contrast to continuous lines formed in other places? How could you test whether your hypothesis is correct? { ** Should Turing, Meinhart and other hypothesizers of reaction-diffusion systems be paying more attention to concentrations of A multiplied by concentrations of B, rather than just their concentrations? Why or why not?} 99) Does action at a distance need to occur by diffusion? What other possibilities can you invent?
100) In the particular version of Turing's mechanism that I asked you to memorize,
?? These chemicals are increased in concentration in proportion to what? ??? These chemicals are destroyed or otherwise decreased in concentration in proportion to what? ???? Which of these chemicals either diffuses faster than the other, or in some other way produces its effects at longer range? 101) Describe the spatial patterns produced by this combination of rules in a one-dimensional graph of the concentrations of the diffusible chemicals.
102) Is Brownian motion sufficient to initiate pattern formation by this set of rules? *103) Is the resulting pattern more irregular when initiated by random variations than when initiated by regularly-spaced stimuli? (Actually, the exact opposite is true; but how can computers be used to answer this question?)
104) What are some embryological phenomena that could possibly be produced by this kind of "reaction-diffusion system", like the ones invented by Alan Turing?
105) Imagine that some cells obey the following sets of rules:
Osmotic pressure stimulates decreased tension, and also stimulates a decrease in pressure. Tension spreads faster than osmotic pressure can diffuse.
106) Imagine cells that obey the following rules:
Cell type B stimulates death of both A and B cells. Cell type B crawls faster than cell type A.
Hint: What if the diffusion rate of substance B increased in proportion to the total size of the space within which the chemical reactions are occurring? What then? *108) Why are computer simulations useful (or necessary?) to answer such questions as whether the patterns generated can be regular, whether their wave-lengths can vary with diffusion rates or sizes of tissues where the reaction is going on? (I realize you probably have not yet experimented with such computer programs, but you have observed them in class and on web sites.)
110*) Consider and compare which is more useful for understanding how genes cause embryos to form spatial patterns:
two) Computer programs that test the effects of any combination of rules that you choose? three) Mathematical equations? **111) How could a computer program be useful for testing whether hypotheses actually predict the phenomena that they were invented to explain. (Don't the inventors of hypotheses know what they predict? Why not just ask the author of a theory?) **112) Did you ever notice that zebra stripes are narrower around the legs, as compared with the broader stripes that encircle the main body like belts? Does this contradict the possibility that these patterns are generated by reaction-diffusion systems? Might the cause help understand what Driesch discovered (when separating embryonic cells)? **113) Notice that animals with spotted color patterns tend to have rings around their tails, instead of spots. Is that a confirmation of reaction diffusion systems; or does it confirm what they predict. How could you use a computer to find out? **114) If developing embryos really do use reaction-diffusion systems (like those invented by Turing) to generate anatomical patterns (like pigmentation patterns), does that mean that they can only have a limited range of geometrically different patterns? In contrast, if development uses Lewis Wolpert's "positional information" type of mechanism would any such limitation be expected? hint: why not? Maybe we have 5 fingers for reasons related to the reason echinoderms have 5 planes of reflection symmetry. Argue pro or con.
115) Did Driesch discover what amounts to dilation symmetry? *116*) If so, do echinoderm embryos have this dilation symmetry? Or is dilation symmetry possessed by the mechanisms that echinoderm embryos use to break reflection and displacement symmetry?
117) Do tensor variables have more or less symmetry than scalar variables? **118) In terms of historical dates, could Curie have met Driesch? What could they have learned from each other? **119) Argue pro or con: Gastrulation in mammals breaks reflection symmetry? Or maybe primitive streak formation? Or formation of Hensen's node? 120) Argue pro or con: Somite formation breaks displacement symmetry? *121) Alternatively, are such embryological processes controlled by mechanisms that break symmetry? Or are the physical processes (the various cell reorientations and rearrangements) themselves what break symmetry?
*122) Argue pro or con (while demonstrating knowledge and creative imagination) 123) Neurulation subdivides what into what three subdivisions? 124) Name these 3 subdivisions; what parts of the body, and what cell types develop from each?
*125) What tissue induces neurulation and the subdivision of the ectoderm?
*126) What sort of abnormality might you expect if a thin sheet of impermeable mica were surgically inserted just below the dorsal ectoderm, between it and the mesoderm? *128) Grafting Hensen's nodes from chick embryos can induce second neural tubes and whole second embryos, not only in early bird embryos, but also in mammal embryos: what do you think this means, in terms of mechanisms and similarity of signaling mechanisms in different kinds of animals? 129) If a sweater looks the same after you turn it inside out, is that another kind of symmetry? 130) Pairs of somites develop along both sides of what mesodermal organ? Along both sides of what major part of the ectoderm? 131) Each somite subdivides into what three parts, one whose cells differentiate as skeletal muscle, another forms skeleton, and the third forms the inner-leathery layer of the skin. 132) Which of these three subdivisions then subdivides into an anterior and a posterior part? Each anterior part then fuses with the posterior part of what, so as to form what anatomical structure. **134) Somite cells all disperse, and later in development you can only see remnants of where they had been: Can you suggest functional or mechanical reasons why the vertebrate body is segmented by transient rather than permanent blocks of cells? **135) In fact, why use aggregated blocks of cells at all? People hypothesize that wave-like gradients of diffusing chemicals are what control where the somites are formed; so why not have those chemical gradients directly determine which cells will differentiate into muscle, bone and dermis. (Why not eliminate the middleman?) 136) If you had a drug or treatment that could cause more somites to form on one side of the body than on the other side, then list all the anatomical abnormalities this would be expected to produce. 137) In embryos of mammals and birds, the diameter of the notochord is much smaller than the diameter of the neural tube; but in embryos of salamanders and frogs, the notochord is almost as big as the neural tube, and sometimes bigger. What sense does this make in relation to the function of the notochord in swimming? (Hint: as compared with its inductive function.)
*138) What is the relation between Hensen's node and the notochord? *139) Contrast "growth" and "rearrangement" as ways of producing anatomical structures.
140) What are the four subdivisions that develop from mesoderm? 141) What are the three subdivisions of somites [hint: sclerotome and what else?], and what structures do they form? 142) Explain how something that appears to be a gradient can be created without diffusion of any substance. More questions will be added.
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