Sequestillator Model 2: A More Complicated Model

While Model 1 gave us some important results (mainly: need a low Kd for oscillations to occur) , we decided to look at more complete model that accounted for some of the dimerizations the proteins undergo:

Parameters

• a= production of NifA
• kf= binding rate of NifA and NifL
• kr= dissociation rate of NifA/NifL complex
• any d= degradation rate of that species
• kb:rate of complex formation (i.e. dimerization, formation of tetramers/hexamers)
• kb2: dissociation rate of such complexes given above
• m= represents how many subunits of NifA bind to NifHp (i.e., if we modeled NifA as a dimer [so 'i'=2], we would say m=3, since 2*3=6 (NifA is a hexamer).
• tmax: Maximal transcription rate
• tl: translation rate

Functions

• We model the production function of mRNA as a Hill-like, sigmoidal function

Variables

• mL=NifL mRNA
• L=NifL protein
• L2= NifL dimer
• A= NifA protein
• A2i= NifA complex, where i=1 is a dimer, i=4 is a tetramer, and i=6 is a hexamer

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