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 on material that hasn't been covered yet, and will not be asked on the exam. 1) If you suspect that a newlydiscovered 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 arbitrarilydrawn 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: 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? Are there any structures in the body that actually have this combination of surface curvatures? 6) What geometric property is defined as being the rate of change of angular direction per unit distance along the surface of an object?
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. 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. 10) Using pairs of doubleended 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 saddleshaped or it has to be _______. What shape? 12) Curvature times ________? 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? (What is the one exception to this rule?) 14) One divided by radius of curvature equals what? 15) What are at least two examples of scalar variables? 16) What are at least three examples of second order tensor variables? 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) What is the difference between stress and strain? Or are these two words for the same thing? 20) 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. 21) 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.
22) Suggest some alternate hypotheses about the mechanisms that control branching of arteries and veins. 23) What is the effect of reduced tension on the geometric arrangements and shapes of developing anatomical structures? Would you expect this phenomenon to apply to arteries, tendons, muscles, feathers? What are some possible explanations for this phenomenon?
24) Please list at least five examples of embryonic processes that are mechanically analogous to the inflation of a water balloon? 25) Before gastrulation begins, a teleost embryo has what combination of symmetry? During gastrulation, what symmetries do vertebrate embryos develop? Or break? 26) The curvature of a line is described as the rate of change of what? per distance along what?
27) A surface curvatures of what two shapes are the same in all directions? 28) The surface curvature of a cylinder is zero in one pair of directions and some nonzero constant in the directions perpendicular to that. 29) The mathematical field called differential geometry defines shapes in terms of what properties? NOT distances along x, y and z coordinates.
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 YoungLaplace Equation P = T (1/R1 + 1/R2):
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 manmade 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) Therefore, some kind of symmetry breaking must occur around the time of _________. 41) Does such an event create more symmetry?
42) Which is more difficult to accomplish? 43) Turing's mechanism is able to change symmetry in what way? 44) Therefore, Turing's mechanism is a way to break? or to increase? displacement symmetry?
45) Does Turing's mechanism increase or decrease displacement symmetry? 46) Therefore, Turing invented a contradiction = counterexample of Curie's Principle? 47) What changes in dilation and displacement symmetry occur during the formation of Liesegang rings? 48) When a donkey decides which of two equally distant piles of straw to eat first, it is breaking what symmetry? 49) When the higherpressure chamber of the heart develops on the left side, what symmetry is that breaking? 50) Kartagener's Syndrome is a genetic inability to break what symmetry? 51) Is that a confirmation or a contradiction of Curie's Principle? Explain? *52) Imagine that the differences between the left and right side of some kind of organism's body were somehow controlled by the stereoasymmetry (stereoisomerism) of amino acids. Then would it be possible for a mutation to produce situs inversus? 53) What conclusion can we draw from the observation that half of people with Kartagener's Syndrome do NOT situs inversus? 54) 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? 55) What (abnormal and also normal) planes of reflection symmetry are possessed by the bodies of conjoined twins?
*56) 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. *57) 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. 58) Turing's "Reaction Diffusion" mechanism (or "system") is a way to reduce/increase the dt symmetry of a spatial pattern?
59) What symmetries, or combinations of symmetries, do each of the letters of the alphabet and keyboard symbols possess (approximately)? ABCDEFGHIJKLMNOPQRSTUVWXYZ ! # $ % ^ * <> + = ~.
*60) Sessile and slow moving animals often have several planes of refection symmetry (which most biologists naively call "radial symmetry"). Suggest why? 61) What swimming animals have radial symmetry? And suggest why? 62) 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)? 63) 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? 64) 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? 65) 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? 66) When a jellyfish 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 jellyfish? Hint: except for the space shuttle, what symmetry to most space rockets have? Is there a reason for this? And if the space shuttle used a parachute to land, would it be an exception to the rule about radial (really "axial") symmetry. 67) What is the relation between the lack of reflection symmetry in the body and the lack of reflection symmetry in flagella? 68) When a force, or balance of forces have spherical symmetry, then what shape will they tend to remold a cell into? [A stray question has been edited out here]
69) If a gene could make an internal force less symmetrical, then could that cause cells and tissues to change from one symmetry to another? 70) 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) Are reactiondiffusion mechanisms, that Turing invented, special kinds of homeostatic mechanisms? (That stabilize geometric arrangements in addition to quantitative amounts.) 72) Is Turing's theoretical mechanism based on positive feedback or negative feedback? Both; but explain
73) Are your fingerprints on the equivalent fingers of your right hand approximate (but not exact) mirror images of your fingerprints of the fingers of your left hand.
74) 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? 75) During the process of mitotic cell division, what symmetries exist in the cell cortex? 76) What about symmetries in a mitotic spindle? 77) Polar body formation differs from ordinary mitosis in what difference in symmetry? (In addition to some important genetic differences.) 78) When an animal develops regularly spaced stripes, in what way has the symmetry of its skin changed? 79) 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? 80) 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? 81) If you see a mass of cells changing from another shape into a sphere, then what do you tentatively conclude about the forces responsible? 82) If a gene could make an internal force less symmetrical, then could that cause cells and tissues to change from one symmetry to another?
83) 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? .
84) Does Turing's (and other "ReactionDiffusion" systems) only work for scalar variables, or can tensor variables be used also or instead?
85) If you can take a wallpaper 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). 86) 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? 87) 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? 88) When the anteriorposterior axis of an amphibian oocyte is caused to form by the location where the sperm enters, then what change in symmetry has been caused?
*89) If you fertilize an amphibian or nematode oocyte exactly at the animal pole, and nevertheless it develops a normal anteriorposterior axis (with only one plane of reflection symmetry), then what does this suggest about the underlying mechanism by which a single anteriorposterior axis is chosen from the infinity axes of reflection symmetry that had existed until then? 90) Which symmetries, or combinations of symmetries are possessed by the following? Starfish? Jellyfish? Propellers? Flowers? Daisies, Sunflowers, Orchids, Lilies, Trees? Blastocysts? Gastrulas? Paramecia? Diatoms? Honeycombs? Apples? Bananas? Mitotic spindles? Flagella? Microtubules? Actin fibers? Muscle sarcomeres? Snails? Clams? Limpets? Barnacles? Feathers? Hairs? Claws? Teeth? Lungs? Glands? Lenses of eyes? Vertebrae? Arteries? Muscles and fibers in the walls of arteries? Bamboo? Fern leaves?! * Cauliflower? ** Mulberry leaves! Morulae? Knives? Forks? Spoons? Scissors? {Some of these are rather subtle and difficult; but please give each some thought.} 91) 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? 92) If a gene could make an internal force less symmetrical, then could that cause cells and tissues to change from one symmetry to another? *93) 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.
94) Try comparing the symmetries of brick locations in brick walls or sidewalks: how many different combination of symmetries can you find? *95) 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. 96) What phenomenon, discovered by Hans Driesch, indicates that developmental mechanisms of echinoderms have dilation symmetry? Does Driesch's entelechy have dilation symmetry!?
97) 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. . 98) Compare and contrast the geometric pattern of Liesegang Rings with those produced by other reaction diffusion systems.
99) In the photograph of Liesegang rings shown on the course web page, 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? . [Note: Liesegang rings will be the topic of the labs on February 22/23.] 100) Does action at a distance need to occur by diffusion? What other possibilities can you invent?
101) In the particular version of Turing's mechanism that I asked you to memorize, 102) Describe the spatial patterns produced by this combination of rules in a onedimensional graph of the concentrations of the diffusible chemicals.
103) Is Brownian motion sufficient to initiate pattern formation by this set of rules? 104) Is the resulting pattern more irregular when initiated by random variations than when initiated by regularlyspaced stimuli? (Actually, the exact opposite is true; but how can computers be used to answer this question?)
105) What are some embryological phenomena that could possibly be produced by this kind of "reactiondiffusion system", like the ones invented by Alan Turing?
106) Imagine that some cells obey the following sets of rules:
107) Imagine cells that obey the following rules:
108) Why can't Turing's and other reactiondiffusion systems explain embryonic regulation (what Driesch discovered)? *109) Why are computer simulations useful (or necessary?) to answer such questions as whether the patterns generated can be regular, whether their wavelengths 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?
*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 reactiondiffusion 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 reactiondiffusion 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?
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? (By coincidence, both got interested in occult seances)
**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?
**127) Because ectoderm that normally comes in contact with notochord normally neurulates, but will NOT neurulate if it is dissected away or otherwise prevented from contacting the notochord, do you think that induction would have been recognized as important and given the Nobel prize based on the failure of neural tubes to form in endoderm that had been prevented from touching the notochord?
**128) Grafted 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 (which I guess become chimeric for their notochord): what do you think this means, in terms of mechanisms and similarity of signaling mechanisms in different kinds of animals?
**129) What other experiments do these results suggest to you?
**130) What other major similarity is there between the Hensen's node and the dorsal lip of the blastopore? (hint, the cells of which mesodermal organ are internalized at both these locations. **129) What other experiments do these results suggest to you?
**131) There must have been a gradual evolutionary transition from embryos with blastopores to embryos with primitive streaks. Suggest what changes in the movements of future mesoderm and endoderm cells would have produced this transition. 132) Pairs of somites develop along both sides of what mesodermal organ? Along what ectodermal part? 133) Each somite subdivides into what three parts, one whose cells differentiate as skeletal muscle, another forms skeleton, and the third forms the innerleathery layer of the skin. 134) 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. *135) 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 if cells. *In fact, why use aggregated blocks of cells at all? People hypothesize that wavelike 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) In what sequence do somites become separated from each other? First on one side, then on the other? First near the front, then one pair after another toward the rear? First at the rear and gradually toward the anterior? First in the middle, and then sequentially toward both ends? Or what? 137) Contrast the rearrangements of cells that occur when somites are formed in mammal and bird embryos, as compared with frog embryos, and as compared with embryos of the nonvertebrate chordate Amphioxus.
138) 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.
**139) Describe as many examples as you can in which differentiated cells have crawled from one part of the embryo to another. (for example: the cells that form the dentine of the teeth). 140) 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.) *141) The notochord is a long cylinder with rounded ends. It consists of vacuolefilled cells tightly wrapped by collagen fibers, aligned in spiral directions. Based on this photograph of fluorescent collagen wrapped around an embryonic blood vessel, suggest a possible mechanism for the embryonic shaping of the notochord. Incidentally, the currently accepted theory on this subject is that notochord cells reach out sideways with cytoplasmic protrusions, and then contract these inward. Notochord cells tend to be highly flattened, perpendicular to the long axis of the notochord, so that the cells are shaped and arranged like a stack of coins. How can these shapes be produced by cellular forces? Nobody knows: nobody even knows how to find out; the question is whether you can build hypotheses using available information.
**142) What is the relation between Hensen's node and the notochord? *143) Contrast "growth" and "rearrangement" as ways of producing anatomical structures.
144) What are the four subdivisions that develop from mesoderm? 145) What are the three subdivisions of somites [hint: sclerotome and what else?], and what structures do they form? 146) What does the notochord consist of? Describe its overall structure. 147) How are vertebrae formed from somites? 148) What did Turing mean by "morphogen"? Compare to how Wolpert uses this word. 149) What is meant by "prepattern"? 150) Explain how something that appears to be a gradient can be created without diffusion of any substance.
