Second Set of Review Questions for Second Exam   Posted February 23, 2016 i) What is contact inhibition? ii) What (abnormal and also normal) planes of reflection symmetry are possessed by the bodies of conjoined twins? (so-called "Siamese Twins") iii) When a force, or balance of forces have spherical symmetry, then what shape will they tend to remold a cell into? iv) If you see a mass of cells changing from some other shape into a sphere, then what do you tentatively conclude about the forces responsible? v) If a gene could make an internal force less symmetrical, then could that cause cells and tissues to change from one symmetry to another? Hint: of course! But please explain it enough to prove that you understand. vi) 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.) v) Are reaction-diffusion mechanisms, that Turing invented, special kinds of homeostatic mechanisms? (That stabilize geometric arrangements in addition to quantitative amounts.) vi) Is Turing's theoretical mechanism based on positive feed-back or negative feed-back? Both; but explain vii) 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. Look at your fingers and find out. Discuss why mirror images, instead of duplicates? Discuss whether this means that finger prints are not controlled by genes? (Because identical twins don't have identical finger-prints, people often say they aren't caused by genes.) Do these phenomena confirm or contradict the theory of "Positional Information". viii) 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? What about symmetries in the tension and compression stresses of an invaginating epithelial sheet? ix) During the process of mitotic cell division, what symmetries exist in the cell cortex? x) What about symmetries in a mitotic spindle? xi) Polar body formation differs from ordinary mitosis in what difference in symmetry? (In addition to some important genetic differences.) xii) 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? xiii) 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.) What planes of reflection symmetry does stiffness have? 4, but figure out why xiv) The Young-Laplace Equation P = T (1/R1 + 1/R2): Is true only for soap films? 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? Equals 3.1415926 German Mathematicians? xv) When is 1/(Radius of curvature) = Curvature? When you measure angular change in radians, instead of degrees. Pi radians = 180 degees xvi) 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? xvii) If you see a mass of cells changing from other shape into a sphere, then what do you tentatively conclude about the forces responsible? xviii) If a gene could make an internal force less symmetrical, then could that cause cells and tissues to change from one symmetry to another? xix) 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? They are assuming that all of the forces are spherically symmetrical, and behave like scalars. (but usually don't realize they are making any simplifying assumption). xx) Does Turing's (and other "Reaction-Diffusion" systems) only work for scalar variables, or can tensor variables be used also or instead? Yes; they work even better with tensor variables, It makes the math harder, but not the computer simulations. MORE TO COME...

 

back to syllabus