Scaling Laws in Biology ? A scaling study of Slime Mould

1. Scaling Laws in Biology?A scaling study of Slime Mould 陳志強 中央研究院物理研究所 中央大學生物物理研究所 C. K. Chan Institute of Physics, Academia Sinica, Graduate Institute of Biophysics, National Central University

2. W. Chen Emilia Hsu P. Y. Lai L C. Jia

3. Scaling Laws in Physics

4. Fractal Growth

6. Scaling in Biology

7. Heart Beats

8. Gray and White Matter

10. Scaling in Protein Network H. Jeong, et al. Nature, 411,41 (2001)

11. Complex Systems

12. Moore’s Law

13. Importance of Allometric Scaling • Universal mechanism • Universal Structure Problems • Difficult to control • Difficult to compare Allometric Scaling in A Single Organism ?

14. Dictyostelium Discoideum (Slime Mould) Common in Soils Wild type – NC4 Lab type – AX2 Feed on E. Coli Single Cellular(Ameoba) Starvation Multi-cellular (Slug) Allometric Scaling in Slug and Aggregation ?

15. Experimental Setup

16. Aggregation of dicty

17. cAMP : Chemo-taxi for aggregation • secondary messenger in • cell activities • Accidental Discovery • By a graduate student ! • - Cells secret cAMP • - cAMP detector developed • - Movement towards high • cAMP concentration

19. Remarks on cAMP • cAMP function not only as secondary messenger, but also a primary messenger. • Sensitive to even one molecule? • Similar to hearing? …

20. Scaling of Slug Size

21. Aggregation at high density

22. Aggregation at low density

23. Aggregation Time

24. Distribution of Slugs • Culture with different densities • Harvest after 36 hour • Digital pictures • Population Regulation • self-similar shape • V = A*L but A = aL • V = bA3/2

25. Density dependence of Slug size Upper critical size Lower critical size V ~ Alog(r/rcr) + V0

26. Nearest Neighbour Model

27. Voronoi Model

28. Probability Distribution

32. Summary • Mean size of slug is a function of plating density (competition?) • Distribution of size of slug can be fitted to a Voronoi distribution • Mean size of slug depends logarithmically on plating density • Existence of a critical plating density of about 10-4 /cm2 and min. slug size

33. Adaptation and Weber’s Law

34. cAMP – the signal 1. sense 2. relay 3. develop Alan. Science, vol 600, 6 June.p1525-1526.(2003)

35. Martiel-Goldbeter-Levine Model rT– receptor density a - [ATP] b – int [cAMP] g – ext [cAMP] G – [CAR1]/ rT(0)

36. Questions • How do the cells know the plating density? • How do the cells determine the aggregation territory ? • What determines the aggregation time? • How important is adaptation (Global Feedback)?

37. Scaling of Velocity Distribution?

38. Displacement Velocity of Non-interacting Random Walkers

39. at 1hr at 5hr at 10hr at 15hr Aggregation at low density

40. at 1hr at 5hr at 10hr at 15hr Aggregation at high density

41. Velocity Scaling Data from Sawada’s Lab V ~ La a = 4/4

42. Questions • Is there a universal cell displacement distribution when there is no cell-cell interaction? • Why there is scaling of V with slug size?

43. Related Concepts/Tools learned in the School : • Chemotaxi/Protein Network • Signal Transduction • Adaptation/Evolution • Microfluidic devices • Micro-manipulations