PL EN


Preferences help
enabled [disable] Abstract
Number of results
2005 | 52 | 4 | 765-780
Article title

Kinetic analysis of the transient phase and steady state of open multicyclic enzyme cascades

Content
Title variants
Languages of publication
EN
Abstracts
EN
This paper presents a kinetic analysis of the whole reaction course, i.e. of both the transient phase and the steady state, of open multicyclic enzyme cascade systems. Equations for fractional modifications are obtained which are valid for the whole reaction course. The steady state expressions for the fractional modifications were derived from the latter equations since they are not restricted to the condition of rapid equilibrium. Finally, the validity of our results is discussed and tested by numerical integration. Apart from the intrinsic value of knowing the kinetic behaviour of any of the species involved in any open multicyclic enzyme cascade, the kinetic analysis presented here can be the basis of future contributions concerning open multicyclic enzyme cascades which require the knowledge of their time course equations (e.g. evaluation of the time needed to reach the steady state, suggestion of kinetic data analysis, etc.), analogous to those already carried out for open bicyclic cascades.
Year
Volume
52
Issue
4
Pages
765-780
Physical description
Dates
published
2005
received
2004-10-14
revised
2005-03-08
accepted
2005-05-20
(unknown)
2005-08-05
References
  • Abramowitz M, Stegun IA, eds (1972) Solutions of Quartic Equations. In Handbook of Mathematical Functions with Formulas Graphs and Mathematical Tables; pp 17-18. Dover, New York.
  • Acerenza L, Sauro HM, Kacser H (1989) Control analysis of time-dependent metabolic systems. J Theor Biol 137: 423-444.
  • Ballif BA, Blenis J (2001) Molecular mechanisms mediating mammalian mitogen-activated protein kinase (MAPK) kinase (MEK)-MAPK cell survival signals. Cell Growth Differ 12: 397-408.
  • Bardwell L (2004) A walk-through of the yeast mating pheromone response pathway. Peptides 25: 1465-1476.
  • Bardwell AJ, Abdollahi M, Bardwell L (2003) Docking sites on mitogen-activated protein kinase (MAPK) kinases MAPK phosphatases and the Elk-1 transcription factor compete for MAPK binding and are crucial for enzyme activity. Biochem J 370: 1077-1085.
  • Beyer WH (1987) CRC Standard Mathematical Tables. 28th edn CRC Press Boca Raton FL.
  • Birkhoff G, Mac Lane S (1996) A survey of Modern Algebra. 5th edn. pp 107-108. Wiley, New York.
  • Boyer CB, Merzbach UC (1991) History of Mathematics. 2nd edn pp 283-287. Wiley, New York.
  • Burden R, Faires J (1985) Numerical Analysis. PWS, Boston.
  • Cárdenas ML, Cornish-Bowden A (1989) Characteristics necessary for an interconvertible enzyme cascade to generate a highly sensitive response to an effector. Biochem J 257: 339-345.
  • Cárdenas ML, Cornish-Bowden A (1990) Properties needed for the enzymes of an interconvertible cascade to generate a highly sensitive response. In Control of Metabolic Processes. Cornish-Bowden A, Cárdenas ML, eds, pp 195-208. Plenum Press, New York.
  • Cárdenas ML, Goldbeter A (1996) The glucose-induced switch between glycogen phosphorylase and glycogen synthase in the liver: outlines of a theoretical approach J Theor Biol 182: 421-426.
  • Chock PB, Stadtman ER (1977) Superiority of interconvertible enzyme cascades in metabolic regulation: analysis of multicyclic systems. Proc Natl Acad Sci USA 74: 2766-2770.
  • Chock PB, Stadtman ER (1980) Covalently interconvertible enzyme cascade systems. Methods Enzymol 64: 297-325.
  • Chock PB, Rhee SG, Stadtman ER (1980) Interconvertible enzyme cascades in cellular regulation. Annu Rev Biochem 49: 813-843.
  • Chock PB, Rhee SG, Stadtman ER (1990) Metabolic control by cyclic cascades mechanism: a study of E. coli glutamine synthetase. In Control of Metabolic Processes. Cornish-Bowden A, Cárdenas ML, eds, pp 183-194. Plenum Press, New York.
  • Cornish-Bowden A (1995) Fundamentals of Enzyme Kinetics; 2nd edn. Porland Press, Londres.
  • Cornish-Bowden A, Hofmeyr J-HS (1991) MetaModel: a program for modelling and control analysis of metabolic pathways on the IBM PC and compatibles. Comp Appl Biosci 7: 89-93
  • De Paula R, Azzariti de Pinho C, Terenzi HF, Bertolini MC (2002) Molecular and biochemical characterization of the Neurospora crassa glycogen synthase encoded by the gsn cDNA. Mol Genet Genomics 267: 241-253.
  • Edstrom RD, Meinke MH, Gurnack ME, Steinhorn DM, Yang X, Yang R, Evans DF (1990) Regulation of muscle glycogenolysis. In Control of Metabolic Processes. Cornish-Bowden A, Cárdenas ML, eds, pp 183-194. Plenum Press, New York.
  • Fehlberg E (1970) Classische Runge-Kutta Formeln vierter und niedrigerer Ordnung mit Schrittweitenkontrolle und ihre Anvendung auf Wärmeleitungs-probleme. Computing 6: 61-71.
  • Ferrell JE Jr, Machleder EM (1998) The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. Science 280: 895-898.
  • Gall D, Baus E, Dupont G (2000) Activation of liver glycogen phosphorylase by Ca2+ oscillations: a theoretical study. J Theor Biol 207: 445-454.
  • Gálvez J, Varón R (1981) Transient phase kinetics of enzyme reactions. J Theor Biol 89: 1-17.
  • García-Sevilla F, Garrido del Solo C, Duggleby RG, García-Cánovas F, Peyró R, Varón-Castellanos R (2000) Use of a windows program for simulation of the progress curves of reactants and intermediates involved in enzyme-catalysed reactions. BioSystems 54: 151-164.
  • Goldbeter A, Koshland DE Jr (1987) Energy expenditure in the control of biochemical systems by covalent modification. J Biol Chem 262: 4460-4471.
  • Goldbeter A, Koshland DE Jr (1990) Zero-order ultrasensitivity in interconvertible enzyme systems. In Control of Metabolic Processes. Cornish-Bowden A, Cárdenas ML, eds, pp 173-182. Plenum Press, New York.
  • Goryanin I, Hodman TC, Selkov E (1999) Mathematical simulation and analysis of cellular metabolism and regulation. Bioinformatics 15: 449-758
  • Gustin MC, Albertyn J, Alexander M, Davenport K (1998) MAP kinase pathways in the yeast Saccharomyces cervisiae. Microbiol Mol Biol Rev 62: 1264-1300.
  • Hamish MF, Christine W (2003) Angiogenesis in the corpus luteum. Reprod Biol Endocrinol 1: 88-95.
  • Hanashiro I, Roach PJ (2002) Mutations of muscle glycogen synthase that disable activation by glucose 6-phosphate. Arch Biochem Biophys 397: 286-292.
  • Havsteen BH, García-Moreno M, Valero E, Manjabacas MC, Varón R (1993) The kinetics of the enzyme systems involving activation of zymogens. Bull Math Biol 55: 561-583.
  • Hearon JZ (1963) Theorems on linear systems. Ann N Y Acad Sci 108: 36-68.
  • Heinrich R, Rapoport TA (1974) Linear steady state treatment of enzymatic chains-general properties control and effector strength. Eur J Biochem 42: 89-95
  • Jacquez JA (1996) Compartmental Analysis in Biology and Medicine; 3rd edn. BioMedware, Ann Arbor.
  • Jiang P, Peliska JA, Ninfa AJ (1998) The regulation of Escherichia coli glutamine synthetase revisited: role of 2-ketoglutarate in the regulation of glutamine synthetase adenylylation state. Biochemistry 37: 12802-12810.
  • Kacser H, Burns JA (1973) The control of flux. Symp Soc Exp Biol 27: 65-104.
  • Kalir S, McClure J, Pabbaraju K, Southward C, Ronen M, Leibler S, Surette MG, Alon U (2001) Ordering genes in a flagella pathway by analysis of expression kinetics from living bacteria. Science 292: 2080-2083.
  • Krebs EG (1972) Protein kinases. Curr Top Cell Regul 5: 99-133.
  • Labrecque L, Royal I, Surprenant DS, Patterson C, Gingras D, Béliveau R (2003) Regulation of vascular endothelial growth factor receptor-2 activity by caveolin-1 and plasma membrane cholesterol. Mol Biol Cell 14: 334-347.
  • Lamb TD (1996) Gain and kinetics of activation in the G-protein cascade of phototransduction. Proc Natl Acad Sci USA 93: 566-570.
  • Mendes P (1997) Biochemistry by numbers: simulation of biochemical pathways with Gepasi 3. Trends Biochem Sci 22: 361-363.
  • Mutalik VK, Shah P, Venkatesh KV (2003) Allosteric interactions and bifunctionality make the response of glutamine synthetase cascade system of Escherichia coli robust and ultrasensitive. J Biol Chem 278: 26327-26332.
  • Mutalik VK, Singh AP, Edwards JS, Venkatesh KV (2004) Robust global sensitivity in multiple enzyme cascade system explains how the downstream cascade structure may remain unaffected by cross-talk. FEBS Lett 558: 79-84.
  • Newsholme EA, Challiss RAJ, Crabtree B (1984) Substrate cycles: their role in improving sensitivity in metabolic control. Trends Biochem Sci 9: 277-280.
  • Ottaway JH (1988) Regulation of Enzyme Activity; p 4. IRL Press, Oxford.
  • Passonneau JV, Lowry OH (1978) In Principles of Enzymatic Analysis. Bergmeyer HU, ed, pp 86-87. Verlag Chemie Weinheim, New York.
  • Passonneau JV, Lowry OH (1993) In Enzymatic Analysis: a Practical Guide. Passonneau JV, Lowry OH, eds, pp 85-110. Humana Press, Totowa, New Jersey.
  • Pomerance M, Abduullah HB, Kamerji S, Corrèze C, Blondeau JP (2000) Thyroid-stimulating hormone and cyclic AMP activate p38 mitogen-activated protein kinase cascade. J Biol Chem 275: 40539-40546.
  • Rozi A, Jia Y (2003) A theoretical study of effects of cytosolic Ca2+ oscillations on activation of glycogen phosphorylase. Biophys Chem 106: 193-202.
  • Santen RJ, Song RX, McPherson R, Kumar R, Adam L, Jeng MH, Yue W (2002) The role of mitogen-activated protein (MAP) kinase in breast cancer. J Steroid Biochem Mol Biol 80: 239-256.
  • Sauro HM (1993) SCAMP: a general-purpose simulator and metabolic control analysis program. Comp Appl Biosci 9: 441-450.
  • Sauro HM (2000) JARNAC: a system for interactive metabolic analysis. In Animating the Cellular Map. Hofmeyr J-HS, Rohwer JM, Snoep JL, eds, pp 221-228. Stellenbosch University Press, Stellenbosch.
  • Schulz AR (1998) Control analysis of muscle glycogen metabolism. Arch Biochem Biophys 353: 172-180.
  • Shacter E, Chock PB, Rhee SG, Stadtman ER (1986) In The Enzymes; vol XVII, Boyer PD, Krebs EG, eds, pp 21-42. Academic Press, New York.
  • Smith DE (1994) A Source Book in Mathematics. Dover, New York.
  • Stadtman ER (1990) Discovery of glutamine synthetase cascade. Methods Enzymol 182: 793-809.
  • Stadtman ER (2001) The story of glutamine synthetase regulation. J Biol Chem 276: 44357-44364.
  • Stadtman ER, Chock PB (1977) Superiority of interconvertible enzyme cascades in metabolic regulation: analysis of monocyclic systems. Proc Nat Acad Sci USA 74: 2761-2765.
  • Stadtman ER, Chock PB (1979) Advantages of enzyme cascades in the regulation of key metabolic processes. In The Neurosciences Fourth Study Program. Schmidtt FO, ed, pp 801-817. M.I.T. Press, Cambridge.
  • Stadtman ER, Chock PB, Adler SP (1976) In Metabolic Interconversion of Enzymes. Shaltiel S, ed, pp 142-149. Springer-Verlag, New York.
  • Szedlacsek SE, Cárdenas ML, Cornish-Bowden A (1992) Response coefficients of interconvertible enzyme cascades towards effectors that act on one or both modifier enzymes. Eur J Biochem 204: 807-813.
  • Thattai M, van Oudenaarden A (2002) Attenuation of noise in ultrasensitive signaling cascades. Biophys J 82: 2943-2950.
  • Valero E, García-Carmona F (1996) Optimizing enzymatic cycling assays: spectrophotometric determination of pyruvate and l-lactate. Anal Biochem 239: 47-52.
  • Valero E, Varón R, García-Carmona F (1997) Mathematical model for the determination of enzyme activity based on enzymatic amplification by substrate cycling. Anal Chim Acta 346: 215-221.
  • Valero E, Varón R, García-Carmona F (2000) Kinetics of a self-amplifying substrate cycle: ADP-ATP cycling assay. Biochem J 350: 237-243.
  • Van den Steen P, Rudd PM, Dwek RA, Van Damme J, Opdenakker G (1998) Cytokine and protease glycosylation as a regulatory mechanism in inflammation and autoimmunity. Adv Exp Med Biol 435: 133-143.
  • Varón R, Havsteen BH (1990) Kinetics of the transient phase and steady-state of the monocyclic enzyme cascades. J Theor Biol 144: 397-413.
  • Varón R, Molina-Alarcón M, García-Moreno M, García-Sevilla F, Valero E (1994a) Kinetic analysis of the opened bicyclic enzyme cascades. Biol Chem Hoppe Seyler 375: 365-371.
  • Varón R, Havsteen BH, Molina-Alarcón M, Szedlasek SE, García-Moreno M, García-Cánovas F, (1994b) Kinetic analysis of reversible closed bicyclic enzyme cascades covering the whole course of the reaction. Int J Biochem 26: 787-797.
  • Varón R, Ruiz-Galea MM, Garrido del Solo C, García-Sevilla F, García-Moreno M, García-Cánovas F, Moya-García G, Havsteen BH (1999) Transient phase of enzyme reactions. Time course equations of the strict and the rapid equilibrium conditions and their computerized derivation. BioSystems 50: 99-126.
  • Weisstein EW (1995) QuarticEquation. From Math/World-A Wolfram Web Resource.
  • Yakar I, Melamed R, Shakhar G, Shakhar K, Rosenne E, Abudarham N, Page G, Ben-Eliyahu S (2003) Prostaglandin E2 suppresses nk activity in vivo and promotes postoperative tumor metastasis in rats. Ann Surg Oncol 10: 469-479.
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.bwnjournal-article-abpv52p765kz
Identifiers
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.