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view/download model file: SlimeSpiral.nlogo
This program simulates waves of motion and chemical relaying
in the cellular
slime mold Dictyostelium discoideum. When Dictyostelium amoebae are
starved
on an agar surface they begin to aggregate, forming complex spatial
patterns
as they do so. Aggregation leads to the formation of a multicellular
organism,
called a slug, consisting of about 10,000 to 100,000 cells, that can
move
about on the substrate for some time. Eventually, the slug develops
into a
fruiting body, a spherical stalk with a cap on top that contains spores.
Under the appropriate conditions the spores can be released and
germinate,
thus completing the cycle.
The amoebae coordinate their movement by secreting cyclic
adenosine
monophosphate (cAMP) and by moving up the resulting cAMP gradient. This
program ignores the cell motion because it is several times slower than
the cAMP wave propogation. Accordingly, the rules governing the cells'
behavior are as follows:
- if a cell senses a concentration of cAMP above the relay
threshold
(which is believed to be higher than the movement threshold), the
cell emits 100 units of cAMP and enters a "refractory" state for a
specified number of time steps
- cells that are in the refractory state are insensitive to
cAMP, thereby
disabling cAMP secretion; instead, these cells gradually break down
the cAMP in their locality, by means of an enzyme called
phosphodiesterase
With each time step, patches share 50% of their cAMP content
with the eight
neighboring patches.
The SETUP button prints a color key in the command window and
creates a
random distribution of slime mold cells, some of which release a pulse
of
cAMP into the environment.
The GO button runs the simulation according to the rules outlined above.
The DENSITY slider specifies the initial density of slime mold cells.
The NUMBER slider indicates how many cells will release cAMP
at the start
of the simulation. In reality, these cells might be starved more
severely
than the others, thus prompting them to start initiate the chemical
signal.
The THRESHOLD slider specifies the amount of cAMP needed in a
patch for the
cell to relay the signal by releasing more cAMP.
The PERIOD slider controls the length of the cells' refractory period.
Spirals of cAMP form as wave fronts are broken by density
perturbances;
accordingly, the threshold and density sliders affect the extent of wave
propogation.
Modified by B. J. MacLennan Sep. 2003 for Java StarLogo 2.0.2 and Aug. 31, 2007 for NetLogo from version by Bill Thies on Scott Camazine's "StarLogo Simulations of Self-Organized Phenomena" <http://www.scottcamazine.com/personal/selforganization/starlogo/starlogo.htm>.
patches-own [chemical ; amount of cAMP in patch
refractory] ; remaining time that patch will be refractory
TO SETUP ;-----------------------------------------------------------------------------------------
ca ; clears display, patches, and turtles
ask patches [set chemical 0] ; resets chemical to zero
ask patches [
ifelse ((random 100) < density)
[set pcolor white ; colors "density" percent of patches white
set refractory 0]
[set pcolor 4 ; colors other patches grey and sets "refractory"
set refractory -1] ; to -1, indicating that they're never receptive
]
ask patches [ ; gives a random patches 300 units of chemical,
if ((random 100) < number) ; with probability given by number
[set chemical 300]
]
end
TO GO ;--------------------------------------------------------------------------------------------
diffuse chemical 0.5 ; each patch shares 50% of its chemical w/ 8 neighbors
ask patches [
if refractory >= 0
[ifelse refractory = 0
[ifelse chemical > threshold
[set refractory period ; receptive patches that detect a threshold level of
set pcolor red ; chemical become refractory, turn red, and emit 100
set chemical chemical + 100] ; units of chemical
[set pcolor white]] ; receptive patches with chemical concentrations less
; than the threshold are colored white
[set refractory refractory - 1 ; refractory patches decrement "refractory", decrement
set pcolor brown ; chemical, and are colored grey
set chemical max list 0 (chemical - int (100 / period + 1))]]
]
end
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