Theoretical Evaluation of Both Unknown Substrate Concentrations and Enzyme Kinetic Constants of Metabolic Cycles

Antonio Sillero^*, Víctor García-Herrero

Departamento de Bioquímica, Facultad de Medicina, Instituto de Investigaciones Biomédicas Alberto Sols UAM/CSIC, Madrid, Spain.

DOI: 10.4236/jbise.2015.88045                

Abstract

A formula has been deduced, and named as 2ESKV, relating the concentration of two consecutive substrates of a metabolic cycle with the kinetic constants of the two enzymes involved in their synthesis and degradation. After application of formula 2ESKV to consecutive pairs of substrates and enzymes, a system of interrelated equations was obtained allowing a great variety of theoretical postulates to calculate, back and forth: bunches of unknown enzyme kinetic constants and substrate concentrations, from complementary sets of known data. This vision of a metabolic cycle is of partial application to irreversible pathways and can be useful for modeling and understanding of metabolomics data. To our knowledge, the formula 2ESKV is here described for the first time.

Keywords

Metabolic Cycles, Evaluation Substrates, Evaluation Enzymes Constants, Differential Equations, Mathematica

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Alberty, R.A. (2011) Enzyme Kinetics: Rapid-Equilibrium Enzyme Kinetics. John Wiley & Sons, Hoboken. http://dx.doi.org/10.1002/9780470940020
[2]	Goldbeter, A. (2013) Oscillatory Enzyme Reactions and Michaelis-Menten Kinetics. FEBS Letters, 587, 2778-2784. http://dx.doi.org/10.1016/j.febslet.2013.07.031
[3]	Chen, W.W., Niepel, M. and Sorger, P.K. (2010) Classic and Contemporary Approaches to Modeling Biochemical Reactions. Genes & development, 24, 1861-1875. http://dx.doi.org/10.1101/gad.1945410
[4]	Milanowski, P., Carter, T.J. and Weber, G.F. (2013) Enzyme Catalysis and the Outcome of Biochemical Reactions. Journal of Proteomics Bioinform, 6, 132-141. http://dx.doi.org/10.4172/jpb.1000271
[5]	Fell, D. (1997) Understanding the Control of Metabolism. Portland Press, Portland. Distributed by Ashgate Pub. Co. in North America, London; MiamiBrookfild, VT.
[6]	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
[7]	Alon, U. (2006) An Introduction to System Biology. Design Principles of Biological Circuits. CRC Pres, Taylor & Francis Group, London.
[8]	Günther Sillero, M.A., de Diego, A., Perez-Zuniga, F.J. and Sillero, A. (2008) Synthesis of Bisphosphonate Derivatives of ATP by T4 DNA Ligase, Ubiquitin Activating Enzyme (E1) and Other Ligases. Biochemical Pharmacology, 75, 1959-1965. http://dx.doi.org/10.1016/j.bcp.2008.02.017
[9]	López-Cánovas, F.J., Cánovas, F., Günther Sillero, M.A. and Sillero, A. (2010) Mathematical Model for the Ubiquitin Activating Enzyme E1. Journal of Biomedical Science and Engineering, 3, 274-284. http://dx.doi.org/10.4236/jbise.2010.33037
[10]	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
[11]	García-Herrero, V., López-Cánovas, F.J. and Sillero, A. (2014) A Model Metabolic Cycle Simulated with the Mathematica Program. Journal of Biomedical Science and Engineering, 7, 286-295. http://dx.doi.org/10.4236/jbise.2014.75031
[12]	Wolfram, S. (2013) Wolfram Mathematica Tutorial Collection. http://www.wolfram.com/learningcenter/tutorialcolection
[13]	Voet, D. and Voet, J.G. (2004) Biochemistry. John Wiley & Sons, Hoboken, 1482-1493.
[14]	Segel, I.H. (1975) Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady State Enzyme Systems. Wiley, New York
[15]	Bisswanger, H. (2004) Enzyme Kinetics: Principle and Methods. Wiley-VCH, Weinheim.
[16]	Albe, K.R. and Wright, B.E. (1992) Systems Analysis of the Tricarboxylic Acid Cycle in Dictyostelium discoideum. II. Control Analysis. The Journal of Biological Chemistry, 267, 3106-3114.
[17]	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: A Journal of Computational Molecular Cell Biology, 10, 57-82. http://dx.doi.org/10.1089/106652703763255679
[18]	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. The Journal of Biological Chemistry, 282, 24525-24537. http://dx.doi.org/10.1074/jbc.M701024200
[19]	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
[20]	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
[21]	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
[22]	Bachmann, C. and Colombo, J.P. (1981) Computer Simulation of the Urea Cycle: Trials for an Appropriate Model. Enzyme, 26, 259-264.
[23]	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
[24]	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