Team:IIT Delhi/modelling
IntroductionOf the proteins used in our project, three of them are Cytochrome C protein, wherein Heme has a very important role to play. However, the pathway of Heme biosynthesis is extremely complicated. In fact, no one has modeled it properly till date. As heme synthesis was our fundamental problem, we put on a lot of efforts in modelling it properly. What follows next is a brief insight to all that we have done. 
Mathematical model
Pathway of heme production in E. coli (C5 pathway from glutamate):

The rest of the reactions in this pathway are assumed to proceed via HenriMichaelisMenten kinetics:
Enzyme  Km (micromol/l) 

Uroporphyrinogen decarboxylase ( hemE)  6.0 
Coproporphyrinogen iii dehydrogenase  210 
Protoporphyrinogen dehydrogenase (HemG)  7 
Ferrochelatase(hemH)  4.7 
GlutamatetRNA synthase  1.9 
Glutamate1semialdehyde 2,1aminomutase  46 
Porphobilinogen synthase  800 
Km and Vmax values of hydroxymethylbilane synthase:
Simulation
After putting in the rate laws and the values of various parameters in Copasi software, following graphs were obtained for the concentrations and rate of formation of various species involved (Copasi has been used for obtaining all graphs and mathematical equations):
Fig 1: Amount of ferroheme b formed in the cytoplasm. 
Fig 2: Amount of ferroheme transported to the periplasm 
Fig 3: rate of formation of ferroheme in the cytosol 
Fig 4: rate of transfer of ferroheme from the cytoplasm to the periplasm. 
The following are the differential equations associated with the above processes:
After production of ferroheme, the cytochrome –c protein and the ferroheme are transported to the periplasm, where they form a complex via covalent bonding. At this point the protein becomes completely active.
Interpretation
After this, the following reactions take place, depending on the protein produced:


3. Nitrous oxide reduction (NosZ protein; Km = 0.007 mM)
