As we have five genes and associated promoters involved, we will consider a set of five differential equations that are devised to represent the underlying biological reactions. Assuming that the interactions can be described thanks to Hill function (described below), we end up with the following set of ordinary differential equations :
where :
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Besides, we have used the following notations:
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Set of parameters providing oscillations
Example of oscillations obtained
Besides, we note that a "First In, First Out" behaviour is obtained concerning the GFP, RFP and CFP concentrations, as shown in the next picture, provided that a gene is 'ON' when it has passed a threshold of 10% of its maximum value.
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