Cell Aggregation (Adhesion + Self-Generated Gradient Sensing)

Cells situated in regions of high population density secrete a chemokine and stop dividing. Adjacent cells chemotact up the local gradient, resulting in cell aggregation.

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Simulation Parameters
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Potts Model
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Simulation time: 1500 MCS
Temperature: 30
Target area: U(80, 120)
Lambda area: 1.0
Lambda perimeter: 2.0
Random force magnitude: 400
Characteristic repolarization time: 100 MCS

Adhesion Energies
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Cell - Medium: 15
Cell - Cell: 7

Mitosis
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First cycle duration: U(150, 500)
Subsequent cycle duration: U(450, 550)
Contact inhibition of cell division: None
Axis of division: Random
Note: Cells secreting chemokine do not divide.

Quorum (signalling) criteria
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Search radius: 12
Threshold for chemokine secretion: 4 cells

Reaction - Diffusion Equation
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Numerical Scheme: Forward Euler
Rate of secretion: 0.5 / MCS
Decay constant: 0.002
Diffusion constant: 0.2
Cellular uptake (receptor binding + endocytosis): None
Note: Secreting cells do not stop secreting even if cell density in local neighborhood decreases below quorum threshold.

Chemotaxis
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Lambda for secreting cells towards Medium: 20
Lambda for non-secreting cells towards Medium: 30