3.6 A primer in morphogenesis and developmental biology

1. 3.6 A primer in morphogenesis and developmental biology

2. What are the big questions in developmental biology?

3. Phylotaxis – leafs on plants are usually arranged in specific geometries (according to the golden mean).

4. Limb development – what determines when and how limbs are formed?

5. Scaling – How come that animals always have the same proportions no matter their size?

6. Growth – How does an organism know when to stop growing (by the way note the scaling in the picture below even though it doesn‘t work physically)?

7. Morphogenesis - How do you get from a spherical egg to say a frog?

8. "It is not birth, marriage or death, but gastrulation, which is truly the most important time in your life." Lewis Wolpert

9. 3.6.1 Morphogen gradients First developmental experiments: Willhelm Roux on sea urchins

10. Driesch repeats the experiments and gets very different results

11. Spemann Mangold experiment – bringing both sides back together

12. And now for some physics: Enter Alan Turing Turing, Phil. Trans. Roy. Soc. B237, 37 (1952)

13. The activator-inhibitor system shows an instability to fluctuations.

14. An application to this may be in Phylotaxis or why do plants know the Fibonacci series.

15. In 1969 the world changed...

16. Lewis Wolpert takes up Turing‘s ideas experimentally and produces his own mathematical treatment.

17. Take a source at one end of the embryo and let the morphogen diffuse through it. Morphogen diffusion with breakdown stationary state with the solution Wolpert, Journal of theoretical biology 25, 1 (1969)

18. Once such a gradient exists, it can be used to encode positional information by increasing the expression of certain proteins.

19. But there‘s more: positional information is kept when different genes are expressed – and development is robust (sea urchins always look the same no matter what you take away from them... So there‘s scaling. How morphogens actually work we‘ll see in example 2...

20. Chick limb development: the morphogen sonic hedgehog in the early limb determines the later fate.

21. A change in morphogens can also change the orientation of a limb

22. Extremity development is crucially dependent on the right positional information at a very early stage.

23. More reaction-diffusion systems and more physics: Hans Meinhardt Gierer & Meinhardt, Kybernetik 12, 30 (1972).

24. Such activator-inhibitor systems can explain classical polarity experiments. In sea urchins Hörstadius & Wolsky, Roux‘ Archives 135 69 (1936).

25. In Hydra Müller, Differentiation 42 131 (1990).

26. Such reaction diffusion systems of three different morphogens can also lead to spatial stabilization.

27. This isn‘t just an academic plaything – the proteins MinC, MinD and MinE, which are important in the division of E. coli show exactly these oscillations. Thus leading to an accurate splitting. Raskin & de Boer, PNAS 96 4971 (1999).

28. 3.6.2 A primer in pattern formation Start with the Gierer-Meinhardt equations as an example: For simplicity, we set ka = sh = 0

29. dimensionless variables: gives simpler equations:

30. Solve them for the homogeneous steady state (i.e. D = 0 and t = 0): Then perturb this state with a harmonic function and only keep terms linear in da0 and dh0:

31. This gives the linear system of equations: with

32. There is only a solution with non-zero da and dh if the discriminant of the Matrix is zero: with

33. The fluctuations only grow if the real part of w > 0. The critical value is thus given by Re(w) = 0. If w has complex values (i.e. b > (a/2)2), the real part is given by a/2 and hence the condition is a = 0. Thus

34. On the other hand, if w is real valued, then it is only zero if b = 0. This yields: A spatial pattern can therefore only develop in an embryo, if ist size exceeds Lc. As long as the length is close to Lc, this also implies a polarity, since the cosine does not recover on this length scale.

35. We can do this more generally by assuming that k is continuous. Then we look at which wave number disturbance grows fastest: while Re(w) > 0

36. Again we start with the case that w is complex: then Re(w) = -a/2 and the fastest growing wavenumber is k = 0. The fact that w is complex and that Re(w) > 0 lead to conditions for m where we are in this case of a growing homogeneous state that oscillates.

37. If w is real, we obtain: and w is is positive if:

38. All of this is summarized in the Stability diagram: growing, inhomogeneouspattern Homogeneous, static pattern Oscillating, homogeneous pattern

39. Another set of differential equations describes a threshold switch

40. Simulation of animal coatings using reaction diffusion and a switch

41. Simulation results for pigmentation lepard giraffe cheeta

42. 3.6.3 An example: The anterio- posterior axis in Drosophila. Nüsslein-Vollhard & Wieschaus, Nature 287 795 (1980).

43. Three different sets of genes Nüsslein-Vollhard & Wieschaus, Nature 287 795 (1980).

44. So there‘s a hierarchy of genes and proteins in the early development

47. Reminder – where are we in the developmental stages...

48. Lets have a closer look at the gap-genes – their positions determine the stripes of the pair-rule genes

49. Interactions (as transcription factors) of the different gap genes

50. This can be visualised using fluorescence probes in vivo....