### Second Set of Review Questions for Second Exam

Posted February 23, 2016

A final list of review questions for the second exam
Some of these are similar to ones that have already been posted.

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: 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? Hint: What is meant by "saddle points"?

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 double-ended arrows (like those on the web page 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?

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.
(Hint: does evolution optimize the actual angles of branching? Or can the same optimization be achieved by controling the local rules that govern longitudinal tension in 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) 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).
Hint: displacement

25) 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?

26) 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?

27) 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?

*28) 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?)

29) 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? 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.}

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.

32) What phenomenon, discovered by Hans Driesch, indicates that developmental mechanisms of echinoderms have dilation symmetry? Does Driesch's entelechy have dilation symmetry!?

33) 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.
(Hint: The chemicals need to have opposite effects on each other. For a start, ask yourself what effect increased concentration of A should have on either the synthesis or breakdown of B, and vice versa, in order to continue to have alternating peaks of substances A and B? Higher concentrations of A need to cause what effect on concentrations of B, etc.)

34) Compare and contrast the geometric pattern of Liesegang Rings with those produced by other reaction diffusion systems.

35) In the photograph of Liesegang rings 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?

HINT) The dark crystals precipitate wherever the concentration of silver ions multiplied by the concentration of bichromate ions gets higher than some threshold amount. {NOTE: 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?}

36) Does action at a distance need to occur by diffusion? What other possibilities can you invent?

37) Is there just one mechanism of amoeboid locomotion; or at least how many?

38) Be able to describe special features and differences between at least four kinds of amoeboid locomotion.

39) List and describe at least four important examples of cell locomotion being used to create anatomical structures.

40) Sketch an Amoeba proteus, label the direction and location of forward cytoplasmic flow.