Team:IIT Delhi/modelling

Introduction

Three of the proteins required in the project are cytochrome c proteins (haem proteins). Hence, the heme biosynthesis pathway needs to be modelled.

Mathematical model

Pathway of heme production in E. coli (C-5 pathway from glutamate):
Also, d-Aminolevulinate (ALA) produced as an intermediate in the above reactions. -Aminolevulinate Synthase (ALA Synthase) is the committed step of the heme synthesis pathway, and is usually rate-limiting for the overall pathway. Regulation occurs through control of gene transcription. Heme functions as a feedback inhibitor, repressing transcription of the gene for -Aminolevulinate Synthase.
A non-competitive irreversible feedback inhibition model is assumed for this step with a Ki value of 0.02 mM. Hence, the following equation governs the production of ALA:



equation1

The rest of the reactions in this pathway are assumed to proceed via Henri-Michaelis-Menten kinetics:





Enzyme Km (micromol/l)
Uroporphyrinogen decarboxylase ( hemE) 6.0
Coproporphyrinogen iii dehydrogenase 210
Protoporphyrinogen dehydrogenase (HemG) 7
Ferrochelatase(hemH) 4.7
Glutamate-tRNA synthase 1.9
Glutamate-1-semialdehyde 2,1-aminomutase 46
Porphobilinogen synthase 800



Km and Vmax values of hydroxymethylbilane synthase:






Stimulation

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):

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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:
1. Nitrite reduction (nrfA protein; Km = 0.11 mM)
NO2- ----> NH3
Differential equations involved:


2. Sulphite reduction (cys1 protein; Km = 0.017 mM)

SO32- ----> H2S
Differential equations involved:

3. Nitrous oxide reduction (NosZ protein; Km = 0.007 mM)
N2O ----> N2
Differential equations involved: