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Construction of Model

The mathematical model is based on the ODEs and kinetic parameters outlined in Pandey et al 2011. The following are its assumptions and basis:

In vitro experiments showed that AppA inhibits the DNA-binding activity of oxidized PpsR by two mechanisms (1,2):

1. By reducing a disulfide bond in PpsR.
2. By a blue-light-dependent sequestration of PpsR proteins into transcriptionally inactive complexes.

At the first stage, the reduced form of AppA (A-) reduces a disulfide bond in oxidized PpsR (P4+), which occurs independently of the light conditions.  The molecular mechanism of this two-electron transfer is not yet clear.

Redox titration experiments have shown that both PpsR and AppA have two redox-active thiol groups that can form intramolecular disulfide bonds with a similar midpoint potential, according to this equation:




At the second level of regulation, the reduced form of AppA can form a complex with reduced PpsR. Experiments based on size exclusion chromatography have revealed that, in the complex, one AppA molecule is associated with two PpsR monomers corresponding to half of a PpsR molecule, which exists as a stable tetramer in solution (1).

The same study showed that complex formation is inhibited by high intensities of blue-light irradiation (LI ¼ 900mmol/m2s). However, a subsequent study found that AppA responds to blue light over several orders of magnitude down to 0.2 mmol/m2s  (3).

Other experiments indicate that light absorption induces a structural change in the BLUF domain of AppA (5), which results in interactions with its C-terminal part, thereby causing the dissociation of PpsR (4).


To implement the redox-sensing capabilities of AppA, we use the model proposed by Han et al. (4), according to which AppA utilizes heme as a cofactor, bound to its C-terminal domain, to sense the cytosolic redox conditions, according to this equation:



If the electron transfer from AppA to PpsR in Eq. 1 was indeed effectively irreversible (kPr -<< kPr+), as suggested by the experiments of Masuda and Bauer (1), PpsR would have to be reoxidized through an AppA-independent mechanism. To account for this possibility, the assumption is that PpsR is reoxidized proportional to the oxygen concentration as:


Finally assuming mass-action kinetics for the reactions in Eq. 1 and Eqs. 3–5 the following are the set of ordinary differential equations established:


Were the total amounts of PpsR and AppA molecules are conserved according to:


1. Masuda, S., and C. E. Bauer. 2002. AppA is a blue light photoreceptor that antirepresses photosynthesis gene expression in Rhodobacter sphaeroides. Cell. 110:613–623.
2. Bauer, C. E., S. Elsen, . , S. Masuda. 2003. Redox and light regulation of gene expression in photosynthetic prokaryotes. Philos. Trans.R. Soc. Lond. B Biol. Sci. 358:147–153, discussion 153–154.
3. Metz, S., A. Jager, and G. Klug. 2009. In vivo sensitivity of blue-light- dependent signaling mediated by AppA/PpsR or PrrB/PrrA in Rhodobacter sphaeroides. J. Bacteriol. 191:4473–4477.
4. Han, Y., M. H. F. Meyer, . , G. Klug. 2007. A heme cofactor is required for redox and light signaling by the AppA protein of Rhodobacter sphaeroides. Mol. Microbiol. 64:1090–1104.
5. Masuda, S., K. Hasegawa, and T. A. Ono. 2005. Light-induced structural changes of apoprotein and chromophore in the sensor of blue light using FAD (BLUF) domain of AppA for a signaling state.Biochemistry. 44:1215–1224.