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

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

Scaling Laws in Physics

Fractal Growth

Scaling in Biology

Heart Beats

Gray and White Matter

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

Complex Systems

Moore’s Law

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

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

Experimental Setup

Aggregation of dicty

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

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

Scaling of Slug Size

Aggregation at high density

Aggregation at low density

Aggregation Time

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 = bA 3/2

Density dependence of Slug size Upper critical size Lower critical size V ~ Alog(  cr )  V 0

Nearest Neighbour Model

Voronoi Model

Probability Distribution

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 /cm 2 and min. slug size

Adaptation and Weber’s Law

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

Martiel-Goldbeter-Levine Model  T – receptor density  - [ATP]  – int [cAMP]  – ext [cAMP] G – [CAR1]/  T (0)

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)?

Scaling of Velocity Distribution?

Displacement Velocity of Non-interacting Random Walkers

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

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

Velocity Scaling Data from Sawada’s Lab V ~ L a a = 4/4

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

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