# Team:UC Davis/Modeling

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# Equations

The equations below model the concentrations of bound transcription factors. That is, they serve to model the concentration of araC bound to pBAD and tetR bound to pTET given the concentrations of the ligands, arabinose and aTc.

The subsequent equations model the probability of active complex for each element in our circuit. P

_{BAD}represents the probability that the pBAD promoter will be unbound by araC and thus active. P

_{TET}represents the probability that the pTET promoter will be unbound by tetR and thus active. P

_{Riboswitch}expresses the probability that the riboswitch is bound by theophylline, and thus active. For simplicity, it has been modeled here as an activator-controlled promoter. P

_{Tale Binding Site}, which may be abbreviated to P

_{TBS}expresses the probability that the TALe binding site is unbound by the TAL repressor, and thus active.

The third set of equations are ordinary differential equations modeling the change in concentration over time of the riboswitch-TALe transcript, TAL repressor, GFP mRNA, GFP protein intermediate, and GFP protein. In this model we have taken into account the maturation time of GFP.