JBiSE  Vol.3 No.3 , March 2010
Mathematical model for the ubiquitin activating enzyme E1
Abstract: The ubiquitin-activating enzyme E1 (EC represents the first step in the degradation of proteins by the ubiquitin proteasome pathway. E1 transfers ubiquitin from the ubiquitinated E1 to the ubiquitin carrier proteins (E2), ubiquitin-protein ligases (E3) and proteins. This process is rather complex, and known from the work of Haas, Ciechanover, Hershko, Rose and others. The occurrence of 19 hypothetical intermediate enzyme forms (EFs) and 22 different reactions were considered in the presence of ubiquitin (Ub), ATP, adenosine 5’-tetraphosphate (p4A), pyrophosphate (P2), and tripolyphosphate (P3) as substrates, and iodoacetamide (IAA) and dithioth- reitol (DTT) as inhibitors. Inspired by the work of Cha (Cha (1968) J. Biol. Chem., 243, 820-825) we have treated these reactions in two complementary ways: in rapid equilibrium and in steady state. The kinetics of both types of reactions were simulated and solved with a system of ordinary differential equations using the Mathematica Program. The ubiquitination of E1 has been also theoretically coupled to the ubiquitination of E2, E3 and proteins. This makes the model useful to predict the theoretical influence of inhibitors (or of changes in some parameters of the reaction) on the ubiquitination of proteins. The Program responds to changes in the concentration of ATP or ubiquitin and has predictive properties as shown by the influence of AMP on the synthesis of p4A, calculated theoretically and confirmed experimentally.
Cite this paper: nullLópez-Cánovas, F. , Cánovas, F. , Sillero, M. and Sillero, A. (2010) Mathematical model for the ubiquitin activating enzyme E1. Journal of Biomedical Science and Engineering, 3, 274-284. doi: 10.4236/jbise.2010.33037.

[1]   Sillero, A. and Günther Sillero, M.A. (2000) Synthesis of dinucleoside polyphosphates catalyzed by firefly luciferase and several ligases. Pharmacology and Therapeutics, 87, 91-102.

[2]   Ortiz, B., Sillero, A. and Günther Sillero, M.A. (1993) Specific synthesis of adenosine(5’)tetraphospho(5’) nucleoside and adenosine(5’)oligophospho(5’)adenosine (n > 4) catalyzed by firefly luciferase. European Journal of Biochemistry, 212, 263-270.

[3]   Günther Sillero, M.A., de Diego, A., Silles, E. and Sillero, A. (2005) Synthesis of (di)nucleoside polyphosphates by the ubiquitin activating enzyme E1. FEBS Letter, 579, 6223-6229.

[4]   Haas, A.L. and Rose, I.A. (1982) The mechanism of ubiquitin activating enzyme. A kinetic and equilibrium analysis. Journal of Biological Chemistry, 257, 10329- 10337.

[5]   Haas, A.L., Warms, J.V., Hershko, A. and Rose, I.A. (1982) Ubiquitin-activating enzyme. Mechanism and role in protein-ubiquitin conjugation. Journal of Biological Chemistry, 257, 2543-2548.

[6]   Haas, A.L., Warms, J.V. and Rose, I.A. (1983) Ubiquitin adenylate: Structure and role in ubiquitin activation. Biochemistry, 22, 4388-4394.

[7]   Hershko, A. and Ciechanover, A. (1998) The ubiquitin system. Annual review of biochemistry, 67, 425-479.

[8]   Baumeister, W., Walz, J., Zuhl, F. and Seemuller, E. (1998) The proteasome: Paradigm of a self-compart- mentalizing protease. Cell, 92, 367-380.

[9]   Ciechanover, A., Orian, A. and Schwartz, A.L. (2000) The ubiquitin-mediated proteolytic pathway: Mode of action and clinical implications. Journal of Cell Biochemistry Supply, 34, 40-51.

[10]   Glickman, M.H. and Ciechanover, A. (2002) The ubiquitin-proteasome proteolytic pathway: Destruction for the sake of construction. Physiological reviews, 82, 373–428.

[11]   Lee, I. and Schindelin, H. (2008) Structural insights into E1-catalyzed ubiquitin activation and transfer to conjugating enzymes. Cell, 134, 268-278.

[12]   Selivanov, V.A., Puigjaner, J., Sillero, A., Centelles, J.J., Ramos-Montoya, A., Lee, P.W. and Cascante, M. (2004) An optimized algorithm for flux estimation from isotopomer distribution in glucose metabolites. Bioinformatics, 20, 3387-3397.

[13]   Torrecilla, A., Marques, A.F., Buscalioni, R.D., Oliveira, J.M., Teixeira, N.A., Atencia, E.A., Günther Sillero, M.A. and Sillero, A. (2001) Metabolic fate of AMP, IMP, GMP and XMP in the cytosol of rat brain: An experimental and theoretical analysis. Journal of Neurochemistry, 76, 1291-1307.

[14]   Osorio, H., Carvalho, E., del Valle, M., Günther Sillero, M.A., Moradas-Ferreira, P. and Sillero, A. (2003) H2O2, but not menadione, provokes a decrease in the ATP and an increase in the inosine levels in Saccharomyces cerevisiae. An experimental and theoretical approach. European Journal of Biochemistry, 270, 1578-1589.

[15]   Wolfram, S. (1996) The Mathematica Book. Cambridge University Press, Cambridge.

[16]   Segel, I.H. (1975) Enzyme kinetics: Behavior and analysis of rapid equilibrium and steady state enzyme systems. Wiley, New York.

[17]   Cha, S. (1968) A simple method for derivation of rate equations for enzyme-catalyzed reactions under the rapid equilibrium assumption or combined assumptions of equilibrium and steady state. Journal of Biological Chemistry, 243, 820-825.

[18]   Fell, D. (1997) Understanding the control of metabolism, Portland Press, MiamiBrookfield.

[19]   King, E.L. and Altman, C. (1956) A schematic method for deriving the rate laws for enzyme-catalyzed reactions. The Journal of Physical Chemistry, 60, 1357-1378.

[20]   Wong, J.T. and Hanes, C.S. (1962) Kinetic formulations for enzymic reactions involving two substrates. Canadian journal of biochemistry and Physiology, 40, 763-804.

[21]   Volkenstein, M.V. and Goldstein, B.N. (1966) Allosteric enzyme models and their analysis by the theory of graphs. Biochimica et Biophysica Acta, 115, 471-477.

[22]   Cornish-Bowden, A. (1995) Fundamental of enzyme kinetics. Portland Press, London.

[23]   Kulaev, I.S. and Vagabov, V.M. (1983) Polyphosphate metabolism in micro-organisms. Advances in Microbial Physiology, 24, 83-171.

[24]   Wood, H.G. and Clark. J.E. (1988) Biological aspects of inorganic polyphosphates. Annual Review of Biochemistry, 57, 235-260.

[25]   Kornberg, A., Rao, N.N. and Ault-Riche, D. (1999) Inorganic polyphosphate: A molecule of many functions. Annual Review of Biochemistry, 68, 89-125.

[26]   Günther Sillero, M.A., de Diego, A., Silles, E., Osorio, H. and Sillero, A. (2003) Polyphosphates strongly inhibit the tRNA dependent synthesis of poly(A) catalyzed by poly(A) polymerase from Saccharomyces cerevisiae. FEBS Letter, 550, 41-45.

[27]   Günther Sillero, M.A., Del Valle, M., Zaera, E., Michelena, P., Garcia, A.G. and Sillero, A. (1994) Diadenosine 5’,5’’-P1,P4-tetraphosphate (Ap4A), ATP and catecholamine content in bovine adrenal medulla, chromaffin granules and chromaffin cells. Biochimie, 76, 404-409.

[28]   Small, G.D. and Cooper, C. (1966) Studies on the occurrence and biosynthesis of adenosine tetraphosphate. Bio-chemistry, 5, 26-33.

[29]   Westhoff, T., et al. (2003) Identification and characterization of adenosine 5’-tetraphosphate in human myocardial tissue. The Journal of Biological Chemistry, 278, 17735-17740.

[30]   Pintor, J., Pelaez, T. and Peral, A. (2004) Adenosine tetraphosphate, Ap4, a physiological regulator of intraocular pressure in normotensive rabbit eyes. Journal of Pharmacology and Experimental Therapeutics, 308, 468-473.

[31]   Jakubowski, H. (1986) Sporulation of the yeast Saccharomyces cerevisiae is accompanied by synthesis of adenosine 5’-tetraphosphate and adenosine 5’-pentapho-sphate. Proceedings of the National Academy of Sciences, 83, 2378-2382.

[32]   McLennan, A.G. (2000) Dinucleoside polyphosphates-friend or foe? Pharmacology and Therapeutics, 87, 73-89.

[33]   Mc Lennan, A.G., et al. (2001) Recent progress in the study of the intracellular functions of diadenosine polyphosphates. Drug Development Research, 52, 249-259.

[34]   Lobatón, C.D., Vallejo, C.G., Sillero, A. and Sillero, M.A. (1975) Diguanosinetetraphosphatase from rat liver: Acitivity on diadenosine tetraphosphate and inhibition by adenosine tetraphosphate. European journal of Biochemistry, 50, 495-501.

[35]   Alon, U. (2006) An introduction to system biology. Design principles of biological circuits. CRC Press, Taylor & Francis Group, London.

[36]   Klipp, E., Herwig, R., Kowald, A., Wierling, C. and Lehrach, H. (2005) System biology in practice. Concepts, implementation and application, Wiley-VCH Verlag GmbH & Co., Weinhein.

[37]   Fell, D. (1997) Undersatnding the control of metabolism, Portland Press, London.

[38]   Yang, Y., et al. (2007) Inhibitors of ubiquitin-activating enzyme (E1), a new class of potential cancer therapeutics. Cancer Research, 67, 9472-9481.