The bistability of nitrite utilization by {\it Escherichia coli}: analysis of the mathematical model
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 4, pp. 110-117.

Voir la notice de l'article provenant de la source Math-Net.Ru

A mathematical model describing nitrite utilization by E. coli cells grown in a flow chemostat is analyzed. The system is of interest from the standpoint of the analysis of the mechanisms by which a cell utilizes toxic substrates in respiration. It is demonstrated that the system admits the appearance of two stationary nitrite concentrations; thus, it becomes bistable. The range of nitrite supply rate into the chemostat for which the model is bistable is determined. The model predicts the possibility of spontaneous death of the culture in transition between the stationary states.
Keywords: gene expression regulation, Escherichia coli, anaerobic respiration, modeling, bistability.
@article{SJIM_2012_15_4_a10,
     author = {N. A. Ri and T. M. Khlebodarova and V. V. Kogai and S. I. Fadeev and V. A. Likhoshvai},
     title = {The bistability of nitrite utilization by {\it {Escherichia} coli}: analysis of the mathematical model},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {110--117},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a10/}
}
TY  - JOUR
AU  - N. A. Ri
AU  - T. M. Khlebodarova
AU  - V. V. Kogai
AU  - S. I. Fadeev
AU  - V. A. Likhoshvai
TI  - The bistability of nitrite utilization by {\it Escherichia coli}: analysis of the mathematical model
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2012
SP  - 110
EP  - 117
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a10/
LA  - ru
ID  - SJIM_2012_15_4_a10
ER  - 
%0 Journal Article
%A N. A. Ri
%A T. M. Khlebodarova
%A V. V. Kogai
%A S. I. Fadeev
%A V. A. Likhoshvai
%T The bistability of nitrite utilization by {\it Escherichia coli}: analysis of the mathematical model
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2012
%P 110-117
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a10/
%G ru
%F SJIM_2012_15_4_a10
N. A. Ri; T. M. Khlebodarova; V. V. Kogai; S. I. Fadeev; V. A. Likhoshvai. The bistability of nitrite utilization by {\it Escherichia coli}: analysis of the mathematical model. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 4, pp. 110-117. http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a10/

[1] Wang H., Gunsalus R. P., “The $nrfA$ and $nirB$ nitrite reductase operons in Escherichia coli are expressed differently in response to nitrate than to nitrite”, J. Bacteriol., 182 (2000), 5813–5822 | DOI

[2] Hervagault J. F., Canu S., “Bistability and irreversible transitions in a simple substrate cycle”, J. Theor. Biol., 127 (1987), 439–449 | DOI | MR

[3] Raymond K. W., Pocker Y., “Bistability and the ordered bimolecular mechanism”, Biochem. Cell Biol., 69 (1991), 661–664 | DOI

[4] Chaudhury S., Igoshin O. A., “Dynamic disorder-driven substrate inhibition and bistability in a simple enzymatic reaction”, J. Phys. Chem. B, 113 (2009), 13421–13428 | DOI

[5] Shen P., Larter R., “Role of substrate inhibition kinetics in enzymatic chemical oscillations”, Biophys. J., 67:4 (1994), 1414–1428 | DOI

[6] Likhoshvai V., Ratushny A., “Generalized hill function method for modeling molecular processes”, J. Bioinform. Comput. Biol., 5:2B (2007), 521–531 | DOI

[7] Cole J. A., Newman B. M., White P., “Biochemical and genetic characterization of $nirB$ mutants of Escherichia coli K12 pleiotropically defective in nitrite and sulphite reduction”, J. Gen. Microbiol., 120 (1980), 475–483

[8] Kemp G. L., Clarke T. A., Marritt S. J., Lockwood C., Poock S. R., Hemmings A. M., Richardson D. J., Cheesman M. R., Butt J. N., “Kinetic and thermodynamic resolution of the interactions between sulfite and the pentahaem cytochrome $NrfA$ from Escherichia coli”, Biochem. J., 431 (2010), 73–80 | DOI

[9] Wang H., Tseng C. P., Gunsalus R. P., “The $napF$ and $narG$ nitrate reductase operons in Escherichia coli are differentially expressed in response to submicromolar concentrations of nitrate but not nitrite”, J. Bacteriol., 181 (1999), 5303–5308

[10] Talmadge K., Gilbert W., “Cellular location affects protein stability in Escherichia coli”, Proc. Natl. Acad. Sci. USA, 79:6 (1982), 1830–1833 | DOI

[11] Bendixson I., “Sur les courbes definies par des equations differentielles”, Acta Math., 24 (1901), 1–88 | DOI | MR

[12] Fadeev S. I., Pokrovskaya S. A., Berezin A. Yu., Gainova I. A., Paket programm STEP dlya chislennogo issledovaniya sistem nelineinykh uravnenii i avtonomnykh sistem obschego vida, Ucheb. posobie, 1998

[13] Kholodniok M., Klich A., Kubichek M., Marek M., Metody analiza nelineinykh dinamicheskikh modelei, Mir, M., 1991

[14] Zavyalov Yu. S., Kvasov B. I., Miroshnichenko V. L., Metody splain-funktsii, Nauka, M., 1980 | MR

[15] Mehra S., Charaniya S., Takano E., Hu W. S., “A bistable gene switch for antibiotic biosynthesis: the butyrolactone regulon in Streptomyces coelicolor”, PLoS One, 3:7 (2008), e2724 | DOI

[16] Angeli D., Ferrell J. E. (Jr.), Sontag E. D., “Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems”, Proc. Natl. Acad. Sci. USA, 101:7 (2004), 1822–1827 | DOI