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The CPIM stand for a Lattice model mixing the Contact Process (CP)
https://github.com/jekeymer/Contact-Process
and the Ising Model (IM)
https://en.wikipedia.org/wiki/Ising_model
together in a combined model. The basic idea is to merge both models in a fair fashion in order to model the spatial biology of an Ising-like genetic network expressed in a quasi-2D colony of bacteria growing on a surface of solid agar. The genetic network consist of a bi-stable genetic system of reporter genes (RFP vs GFP) coupled by auto-inducer molecules (HSLs)
By fair we mean here using the Gillespie algorithm
https://en.wikipedia.org/wiki/Gillespie_algorithm
in the Monte Carlo method updating the Lattice. This is a fundamental requirement as there are Lattice states with two possible reactions. Lattice states are: 0: vacancy, representing an empty site suitable for colonization by its neightboors (plotted in black) 2: undifferentiated state (plotted in white) -1: spin down, representing a site expressing one reporter gene (plotted in green) +1: spin up, representing a site expressing the other reporter (plotted in magenta)
occupied sites (states: -1,2,+1) can have spin flips or differentiation reactions together with particle death reactions.
In the Gillespie algorithm we use 2 random numbers. The first one is used to decide which one of the competing reactions might take place. Then, a second random number is used to decide if the chosen reaction, indeed take place (or not). This way, the Poisson process is respected and probabilities are well defined.