Biology 441, Spring 2013 Review for Second Hour Exam, part 3


More questions regarding symmetry:

1) 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).

2) 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?

3) 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?

4) When an animal develops regularly spaced stripes, in what way has the symmetry of its skin changed?

5) Suppose an animal develops regularly spaced spots: does it then have more, or less, symmetry than a striped animal? (increased or decreased?) 5.5 What combinations of symmetries do Venetian blinds have?

6) What symmetries, or combinations of symmetries, do each of the letters of the alphabet possess (approximately)? ABCDEFGHIJKLMNOPQRSTUVWXYZ ! # $ % ^ * <> + = ~

Which have rotational symmetry but not reflection symmetry? Which have more than one plane of reflection symmetry? Which comes closest to having "glide-reflection" symmetry?

7) 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? (And likewise for nematode oocytes).

*8) If you fertilize an amphibian or nematode 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? (Hint: maybe it can be initiated either by small stimuli, like sperm entry, or when those are not available then maybe random fluctuations can initiate symmetry breaking, as in Turing's mechanism, or as when a punching dummy has its internal weight raised too high?)

9) Which symmetries, or combinations of symmetries are possessed by the following? Starfish? Jelly-fish? Propellers? Flowers? Daisies, Sun-flowers, Orchids, Lilies, Trees? Blastocysts? Gastrulas? Paramecia? Diatoms? Honeycombs? Apples? Bananas? Mitotic spindles? Flagella? Microtubules? Actin fibers? Muscle sarcomeres? Spirally-cleaving embryos? Radially cleaving embryos? [don't worry about these 2] 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? Other tools? Suggest something else. {Some of these are rather subtle and difficult; but please give each some thought.}

10) What (abnormal and also normal) planes of reflection symmetry are possessed by the bodies of conjoined twins?

*11) 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. (Hint: maybe what first becomes doubled are the elements of these control mechanisms?)

*12) 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.

*13) Sessile and slow moving animals often have several planes of refection symmetry (which most biologists naively call "radial symmetry"). Suggest why? For those who have dived on tropical reefs, consider the symmetries of sea fans, relative to the predominant directions of water flow around them.

14) What swimming animals have radial symmetry? And suggest why?

15) 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)?

16) 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?

17) 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 "sidewases" being equivalent?

18) 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?)

19) 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? 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.

20) Using the cellular automata computer program available on my faculty web site, how would you produce patterns with (a) One plane of reflection symmetry; (b) Two planes, (c) Four planes? (d) Two fold rotational symmetry (without reflection symmetry)? (e) Four-fold rotational symmetry (without reflection symmetry) [Try starting with a blank field and create two filled squares in the upper right corner, and two more filled squares in the lower left corner, with one of each two being above the other.]

This program will be covered in the laboratories on February 27th and 28th, but you can go ahead and explore it before then. See the instructions and background information if you need help getting started.

When tested last year, this program worked on PCs running Internet Explorer (with Java enabled), but unfortunately not on recent Macs with any browser. We're looking for someone with Java programming experience who could modify this so it will run on Macs.

21) What symmetry does the counting of neighbors have? (in this program)

*22) Can you imagine and suggest some other symmetry in the counting? What if the right and left neighbors counted twice as much as the above and below neighboring squares? What if the right hand square counted twice as much as the left hand square? Could these differences affect the symmetries of the patterns? (hint: sure, But can you visualize what forms the alterations would take?)

23) Can you create a sequence of patterns with time displacement symmetry? (That keeps cycling through a repeated series of identical spatial patterns) [For an easy way to do this try the "opposite" buttons]

24) One a pattern has a given symmetry, do later patterns ever lack this symmetry? Do later patterns ever have MORE symmetry? Can you explain why? What did Pierre Curie have to say on the subject?

**25) Invent something analogous to a Turing mechanism (for cellular automata) that can decrease ("break") symmetry in some regular way, not just becoming random.

26) What is the relation between the lack of reflection symmetry in the body and the lack of reflection symmetry in flagella?

27) When a force, or balance of forces have spherical symmetry, then what shape will they tend to remold a cell into?

28) If you see a mass of cells changing from other shape into a sphere, then what do you tentatively conclude about the forces responsible?

29) If a gene could make an internal force less symmetrical, then could that cause cells and tissues to change from one symmetry to another?

30) 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 flucuations? Anything else? What if you just poked it at some time of special sensitivity?

*31) 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.p> *32) 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.

*33) 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.) [Hint: glide reflection, plus something else, that involves narrowing widths and shorter wave-lengths.

34) Does Driesch's entelechy have dilation symmetry!? What about dilation symmetry of the mechanisms that shape early echinoderm embryos?

35) 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).

36) When Dictyostelium amoebae aggregate to form a hemisphere, symmetry has increased? In what way? And by what cause?

37) When this sphere distorts itself into a long slug, has symmetry changed? How? Why?

38) When such a slug is cut in pieces, and the fragments become smaller slugs that have the same length to width as the original slug had had, then what sort of symmetry are we going to say this is an example of? * What symmetries in the causal forces are possible explanations?

39) What are at least two different reasons why an aggregation of cells can behave as if it has a contractile surface?

40) Please name, and/or draw some objects that have each of the following combinations of symmetry:

Two planes of reflection symmetry
Four planes of reflection symmetry
Two-fold rotational symmetry, combined with one plane of reflection symmetry
Two-fold rotational symmetry, without any planes of reflection symmetry
Displacement symmetry along one axis. (hint: somites, stripes around a snake, vertebrae.)
A snail shell combines rotational and dilation symmetry: please explain this in terms of Weyl's definition of symmetry.


Imagine that you are one of Driesh's "entelechies" whose job it is to adjust the sizes of the parts of embryos that have been separated into halves, or quarters, or fused into double-sized embryos. Could you accomplish this goal by adjusting the diffusion rates of "morphogen" chemicals? Hint: yes; for example in an embryo cut in two, each of its entelechies could make morphogen "B" diffuse twice as fast as in a normal embryo, so that the normal number of somites (or any periodic structures) would form in half the distance, with each one being half as big as normal, and made of half the amount it tissue.

Continuing this fantasy of being an entelechy, if embryos control organ location by "positional information" (in Wolpert's sense), then how would you need to change the gradients of morphogens in separated embryo halves, or quarters?

If the concentration gradient of a morphogen formed because messenger RNA for the morphogen was concentrated at one end of the embryo, then how could cutting the embryo into two result in formation of two concentration gradients, each twice as steep as normal? Or can it?

Remembering how the mammal body develops from the primitive streak in the inner cell mass, would you expect a morphogen gradient to have its maximum where the primitive node forms? Or would its minimum form there? Hint: in principle, it could work either way.

Armadillo embryos develop as identical quadruplets, by formation of four primitive streaks in the middle of an inner cell mass, with the heads of the four embryos pointing toward the center, and the tails pointing outward in four perpendicular directions. Suggest how this pattern could be produced by chemical diffusion gradients or Wolpert's positional information.

What is the symmetry of an early armadillo embryo, before each of the quadruplets develops its right-left asymmetry? This symmetry is then changed in what way when all four quadruplets develop their right left asymmetry? In other words, tell what symmetry is possessed by the whole set of quadruplets.

True or false: and explain your reasoning: Reaction-diffusion systems (such as were invented by Turing) are a hypothetical method for reducing ("breaking") the displacement symmetry of developing tissues, in the sense that tissues that previously had infinite displacement symmetry (for displacement by any distance) then have displacement symmetry for certain distances. Hint: true; but you should be able to explain.

Remember the "clock and wave-front" theory of somite formation? What symmetry does it break?

Suppose you were to dissect two early chicken embryos out of their eggs, into tissue culture dishes, and lay one embryo right on top of the other: then make a time-lapse video of somite segmentation in both embryos. You might need to focus up and down frequently, so as to see both the upper and the lower embryo. Alternatively some very long working distance microscopy might be possible - or confocal microsopy? The goal is to find out whether the embryos somehow influence each other's times of somite separation. For example, these times might tend to synchronize! Would you interpret synchronization as evidence supporting the clock and wave-front hypothesis? Or would synchronization be evidence in favor of control by a reaction-diffusion system? Or would synchronization be predicted by both those theories?

Would it matter whether both embryos were lined up, with heads in the same direction? What if you laid them down at right angles, one perpendicular to the other? What if you laid them down in opposite directions, with the head end of one directly above the tail end of the other embryo? What if you laid them down with the head of one over the neck of the other; or with the head over the middle of the other?

In all cases, we will assume that A and B morphogen chemicals can diffuse the short distances between parts of the embryos directly above and below each other, and will also assume that whatever "clocks" and "wave-fronts" exist will also extent their effects from one embryo to the one above or below it. Assuming that these hypothetical signals will exert effects from one embryo to the closest parts of the other embryo, then what do you expect to happen? What evidence would confirm that the signals from each embryo will sometimes change the time and locations of somite segmentation in the embryo? What do the different theories predict about these induced changes? What differences should there be in these effects, if the axes of the embryos are perpendicular? If the axes are pointed in opposite directions? If the axes are at some other angle? If one embryo is slightly older than the other?

What if you had different mutant strains, one of which formed more somites than the other? Or one of which formed somites faster than the other? ...and you plop one isolated embryo directly on top of the other. The goal is to create a situation in which the different alternative theories make sharply different predictions.

Experiments are more persuasive when you can cause something surprising to happen, the unexpectedness of which can be captured in a single photograph - like if a chick embryo could be stimulated to form somites from the posterior toward the anterior. Or along the right side sooner and faster than along the other side.
 Or more somites on the left than on the right.


back to syllabus