JBiSE  Vol.7 No.5 , April 2014
A Model Metabolic Cycle Simulated with the Mathematica Program
ABSTRACT
A system of differential equations has been used to simulate a model metabolic cycle, containing only one initial substrate and 8 irreversible enzymes. The metabolic course of the intermediates (products/substrates) was also explored in different situations: changes in the kinetic constants of one of the enzymes of the cycle; introduction of one reversible step; consecutive increments in the Km values of each enzyme of the cycle and the presence of two initial substrates. A decrease or an increase in the Km value of one of the enzymes of the cycle promotes a decrease or an increase in the steady state level of its own substrate, respectively; by the contrary, a decrease or an increase in the Vmax value promotes, respectively, an increase or a decrease in the stationary level of the corresponding substrate. A comparison between a linear and a cyclic metabolic pathway is also presented.

Cite this paper
García-Herrero, V. , López-Cánovas, F. and Sillero, A. (2014) A Model Metabolic Cycle Simulated with the Mathematica Program. Journal of Biomedical Science and Engineering, 7, 286-295. doi: 10.4236/jbise.2014.75031.
References
[1]   López-Cánovas, F.J., Gomes, P.J. and Sillero, A. (2013) Mathematica Program: Its Use to Simulate Metabolic Irreversible Pathways and Inhibition of the First Enzyme of a Metabolic Pathway as Visuaized with the Reservoir Model. Computers in Biology and Medicine, 42, 853-864.
http://dx.doi.org/10.1016/j.compbiomed.2013.04.003

[2]   Voet, D. and Voet, J.G. (2004) Biochemistry, XV +1591, 482-493.

[3]   Cleland, W.W. (1970) Steady State Kinetics in the Enzymes. 3rd Edition, Academic Press, New York, 1-65.

[4]   Krauss, M., Schaller, S., Borchers, S., Findelsen, R., Lippert, J. and Kuepfer, L. (2012) Integrating Cellular Metabolism into a Multiscale Whole-Body Model. PLOS Computational Biology, 8, e1002750.
http://dx.doi.org/10.1371/journal.pcbi.1002750

[5]   Fell, D. (1997) Understanding the Control of Metabolism. Portland Press; Distributed by Ashgate Pub. Co. in North America, London; Miami Brookfild, VT.

[6]   Segel, I.H. (1975) Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady State Enzyme Systems. Wiley, New York.

[7]   Klipp, R., Herwig, R., Kowald, A., Wierling, C. and Lehrach, H. (2005) System Biology in Practice. Wiley-VCH Verlag GmbH &Co, Winheim (FRG).
http://dx.doi.org/10.1002/3527603603

[8]   Alberty, R.A. (2011) Enzyme Kinetics. Rapid-Equilibrium Applications of Mathematica, Hoboken.
http://dx.doi.org/10.1002/9780470940020

[9]   Alon, U. (2006) An Introduction to System Biology. Design Principles of Biological Circuits. CRC Pres, Taylor & Francis Group, London.

[10]   Wolfram, S. (2013) Wolfram Mathematica Tutorial Collection.
http://www.wolfram.com/learningcenter/tutorialcolection

[11]   Bisswanger, H. (2004) Enzyme Kinetics. Principle and Methods, Wiley-VCH, Weinheim (FRG).

[12]   Albe, K.R. and Wright, B.E. (1992) Systems Analysis of the Tricarboxylic Acid Cycle in Dictyostelium Discoideum. II. Control Analysis. Journal of Biological Chemistry, 267, 3106-3114.

[13]   Oliveira, J.S., Bailey, C.G., Jones-Oliveira, J.B., Dixon, D.A., Gull, D.W. and Chandler, M.L. (2003) A Computational Model for the Identification of Biochemical Pathways in the Krebs Cycle. Journal of Computational Biology, 10, 57-82.
http://dx.doi.org/10.1089/106652703763255679

[14]   Wu, F., Yang, F., Vinnakota, K.C. and Beard, D.A. (2007) Computer Modeling of Mitochondrial Tricarboxylic Acid Cycle, Oxidative Phosphorylation, Metabolite Transport, and Electrophysiology. Journal of Biological Chemistry, 282, 24525-24537.
http://dx.doi.org/10.1074/jbc.M701024200

[15]   Nazaret, C., Heiske, M., Thurley, K. and Mazat, J.P. (2009) Mitochondrial Energetic Metabolism: A Simplified Model of TCA Cycle with ATP Production. Journal of Theoretical Biology, 258, 455-464.
http://dx.doi.org/10.1016/j.jtbi.2008.09.037

[16]   Amador-Noguez, D., Feng, X.J., Fan, J., Roquet, N., Rabitz, H. and Rabinowitz, J.D. (2010) Systems-Level Metabolic Flux Profiling Elucidates a Complete, Bifurcated Tricarboxylic Acid Cycle in Clostridium Acetobutylicum. Journal of Bacteriology, 192, 4452-4461.
http://dx.doi.org/10.1128/JB.00490-10

[17]   Smith, A.C. and Robinson, A.J. (2011) A Metabolic Model of the Mitochondrion and Its Use in Modelling Diseases of the Tricarboxylic Acid Cycle. BMC Systems Biology, 5, 102.
http://dx.doi.org/10.1186/1752-0509-5-102

[18]   Bachmann, C. and Colombo, J.P. (1981) Computer Simulation of the Urea Cycle: Trials for an Appropriate Model. Enzyme, 26, 259-264.

[19]   Morris Jr., S.M. (2002) Regulation of Enzymes of the Urea Cycle and Arginine Metabolism. Annual Review of Nutrition, 22, 87-105.
http://dx.doi.org/10.1146/annurev.nutr.22.110801.140547

[20]   Maher, A.D., Kuchel, P.W., Ortega, F., de Atauri, P., Centelles, J. and Cascante, M. (2003) Mathematical Modelling of the Urea Cycle. A Numerical Investigation into Substrate Channelling. European Journal of Biochemistry, 270, 3953-3961.
http://dx.doi.org/10.1046/j.1432-1033.2003.03783.x

[21]   Sillero, A., Selivanov, V.A. and Cascante, M. (2006) Pentose Phosphate and Calvin Cycles: Similarities and Three-Dimensional Views. Biochemistry and Molecular Biology Education, 34, 275-277.
http://dx.doi.org/10.1002/bmb.2006.494034042627

[22]   Bogorad, I.W., Lin, T.-S. and Liao, J.C. (2013) Synthetic Non-Oxidative Glycolysis Enables Complete Carbon Conservation. Journal of Biological Chemistry, 202, 693-697.

 
 
Top