The fascinating properties of pattern creating bacteria can be translated into the language of mathematics. In this subsection we investigate the equations behind the behavior of the genetically modified organisms created in the wetlab. For this purpose, a layered approach seems appropriate. Colony level modeling employs partial differential equations to describe large cell groups which are treated as a continuum. Internal level models describe the interactions that happen within single cells. Finally the hybrid model merges the two approaches into a final description of our pattern forming cells.
Our colony layer model relies on a Keller-Segel type system of partial differential equations. These equations are simulated using finite differences.
The hybrid model represents an intermediate level of detail in between the colony level model and the internal model. Bacteria are treated as individual agents, while chemical species are modeled using partial differential equations.
Our internal model aims to simulate the internal dynamics of every cell with a system of ordinary differential equations.
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