Correspondence of real life scales and simulation scales
 

1. Real life scales for bacteria colonies

For Bacillus subtilis strain 168, from experiment measurements and reasonable estimations.
 

For reference, see "Cooperative self-organization of microorganisms", Advances in Physics, Vol. 49, No, 4, 395-554 (2000) and'Modeling branching and chiral colonial patterning of lubricating bacteria" [Mathematical Models for Biological Pattern Formation, 2001.]
 

Bacterium:

Area:~ 1mm2
Velocityu:~1-10mm/s
Tumbling time t:~ 1-5 s

Weight:~ 1pg = 10-12 g

Diffusivity Db (at low concentration) = u2t~10-8-10-5cm2/s ~1-103mm2/s

Reproduction time tR:<25min=1500s

Threshold energy:Eth~3pg=3´10-12g

Metabolism rate:~1pg/25min~2/3´10-15(including movement)

Maximum consumption rate: ~3pg/25min~2´10-15
 
 

Bacteria Colony:

Growth in Petri-Dish:1-2 days~105s

Growth velocity:<1.5mm/hour~0.41 mm/s

Initial Stage:~105 bacteria (5ml)

Final Stage:~109 bacteria
 
 

Petri Dish:

Diameter:9cm~105mm
 
 

Peptone:

Concentration:0.1-10 g/l

Volume:~20-30ml

Diffusivity Dc:10-4-10-6cm2/s=104-102mm2/s (almost same scale as that of the bacteria, thus relaxation should not cause troubles).
 
 

Agar:

Concentration:1%-4%
 
 
 

2. Simulation scales for bacteria colonies in our simulation
 

Simulation box:
 

Area:5cm x 5cm

Lattice:square lattice (200 x 200)

Lattice constant (n.n distance) dx ~0.25mm=2.5´102mm

Random walkers:Nw=5´103 bacteria (each walker)

Initial number of walkers: ~20 ->105 bacteria

Final number of walkers: ~105 ->09 bacteria

Threshold energy:tT~Nw ·Eth~1.5´10-8 g (set to energy unit in simulations)

Food level P:0-30® 0-3 g/l (approximate) 

Time scale dt:~5min=300s

Maximum food eaten per time step:5min/25min=0.2 (in unit of tT)

Consumption rate (the metabolism rate):0.2/3 or so

Average jump for a walker:Sqrt(6 Db dt) (assuming Db=1.5mm2/s)~50mm~0.2dx

Diffusivity of pepton:D=Dc ·(dx2/dt) (assuming Dc~300mm2/s)=1.44