Biochemical kinetics in changing volumes.

• Authors: Piotr H Pawłowski , Piotr Zielenkiewicz
• Languages of publication: EN

Abstracts

EN

The need of taking into account the change of compartment volume when developing chemical kinetics analysis inside the living cell is discussed. Literature models of a single enzymatic Michaelis-Menten process, glycolytic oscillations, and mitotic cyclin oscillations were tested with appropriate theoretical extension in the direction of volume modification allowance. Linear and exponential type of volume increase regimes were compared. Due to the above, in a growing cell damping of the amplitude, phase shift, and time pattern deformation of the metabolic rhythms considered were detected, depending on the volume change character. The perfomed computer simulations allow us to conclude that evolution of the cell volume can be an essential factor of the chemical kinetics in a growing cell. The phenomenon of additional metabolite oscillations caused by the periodic cell growth and division was theoretically predicted and mathematically described. Also, the hypothesis of the periodized state in the growing cell as the generalization of the steady-state was formulated.

Keywords

EN

glycolytic oscillations; chemical kinetics; cyclin oscillations; varying volume

• Publisher: Polish Biochemical Society
• Journal: Acta Biochimica Polonica
• Year: 2004
• Volume: 51
• Issue: 1
• Pages: 231-243

Dates

published

2004

received

2003-07-23

revised

2004-01-23

accepted

2004-01-28

Contributors

author

Piotr H Pawłowski

• Institute of Biochemistry and Biophysics, Polish Academy of Sciences, Warszawa, Poland

author

Piotr Zielenkiewicz

• Institute of Biochemistry and Biophysics, Polish Academy of Sciences, Warszawa, Poland

References

• Bier M, Bakker BM, Westerhoff HV. (2000) How yeast cells synchronize their glycolytic oscillations: a perturbation analytic treatment. Biophys J.; 78: 1087-93.
• Burns JA, Cornish-Bowden A, Groen AK, Heinrich R, Kacser H, Porteous JW, Rapoport SM, Rapoport TA, Stucki JW, Tager JM, Wanders RJA, Westerhoff HV. (1985) Control of metabolic systems. Trends Biochem Sci.; 10: 16.
• Chaplin M. (1990) Fundamentals of enzyme kinetics: Simple kinetics of enzyme action. In Enzyme Technology. Chaplin M, Bucke Ch, eds, pp 1-40. Cambridge University Press, Cambridge.
• Crabtree B, Newsholme EA, Reppas NB. (1997) Principles of regulation and control in biochemistry: a pragmatic, flux-oriented approach. In Handbook of Physiology. Hoffman FJ, Jamieson JD, eds, pp 117-80. Oxford University Press, Oxford.
• Cross AL, Armstrong RL, Gobrecht C, Paton M, Ware C. (1997) Three dimensional imaging of the Belousov-Zhabotinsky reaction using magnetic resonance. Magn Reson Imaging.; 15: 719-25.
• Cuthbertson KS, Cobbold PH. (1985) Phorbol ester and sperm activate mouse oocytes by inducing sustained oscillations in cell Ca2+ Nature.; 316: 541-2.
• Gingold MP. (1974) Expressions of the Michaelis-Menten equation when studying enzyme reactions in a variable-volume medium. Biochem J.; 143: 771-3.
• Giuseppin ML, van Riel NA. (2000) Metabolic modeling of Saccharomyces cerevisiae using the optimal control of homeostasis: a cybernetic model definition. Metab Eng.; 2: 14-33.
• Goldbeter A. (1991) A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc Natl Acad Sci USA.; 88: 9107-11.
• Kacser H, Burns JA. (1973) The control of flux. Symp Soc Exp Biol.; 27: 65-104.
• Karagiannis J, Young PG. (2001) Intracellular pH homeostasis during cell-cycle progression and growth state transition in Schizosaccharomyces pombe. J Cell Sci.; 114: 2929-41.
• Lee JM. (1992) Enzyme kinetics. In Biochemical Engineering. Englewood C, ed, pp 4-16. Prentice-Hall, New York.
• Mendes P. (1993) Gepasi: a software package for modeling the dynamics, steady states and control of biochemical and other systems. Comput Appl Biosci.; 9: 563-71.
• Mendes P. (1997) Biochemistry by numbers: simulation of biochemical pathways with Gepasi 3. Trends Biochem Sci.; 22: 361-3.
• Mendes P, Kell DB. (1998) Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics.; 14: 869-83.
• Morton-Firth CJ, Bray D. (1998) Predicting temporal fluctuations in an intracellular signaling pathway. J Theor Biol.; 192: 117-28.
• Morton-Firth CJ, Shimizu TS, Bray D. (1999) A free-energy-based stochastic simulation of the Tar receptor complex. J Mol Biol.; 286: 1059-74.
• Ni TC, Savageau MA. (1996) Application of biochemical systems theory to metabolism in human red blood cells: Signal propagation and accuracy of representation. J Biol Chem.; 271: 7927-41.
• Pojman J. (1999) Studying nonlinear chemical dynamics with numerical experiments. J Chem Educ.; 76: 1310.
• Pye EK. (1971) Periodicities in intermediary metabolism. In Biochronometry. Menaker M, ed, pp 623-36. National Acad. Sci., Washington, DC.
• Schaff J, Fink C, Slepchenko B, Carson J, Loew L. (1997) A general computational framework for modeling cellular structure and function. Biophys J.; 73: 1135-46.
• Schulz AR. (1994) Enzyme Kinetics. From Diastase to Multi-enzyme Systems. Cambridge University Press, Cambridge.
• Tomita M, Hashimoto K, Takahashi K, Shimizu TS, Matsuzaki Y, Miyoshi F, Saito K, Tanida S, Yugi K, Venter JC, Hutchison CA III. (1999) E-CELL: Software environment for whole cell simulation. Bioinformatics.; 15: 72-84.
• Woldringh CL, Huls PG, Vischer NO. (1993) Volume growth of daughter and parent cells during the cell cycle of Saccharomyces cerevisiae a/alpha as determined by image cytometry. J Bacteriol.; 175: 3174-81.