Abstract
Cell metabolism is able to respond to changes in both internal parameters and boundary constraints. The time any system variable takes to make this response has relevant implications for understanding the evolutionary optimization of metabolism as well as for biotechnological applications. This work is focused on estimating the magnitude of the average time taken by any observable of the system to reach a new state when either a perturbation or a persistent variation occurs. With this aim, a new variable, called characteristic time, based on geometric considerations, is introduced. It is stressed that this new definition is completely general, being useful for evaluating the response time, even in complex transitions involving periodic behavior. It is shown that, in some particular situations, this magnitude coincides with previously defined transition times but differs drastically in others. Finally, to illustrate the applicability of this approach, a model of a reaction mediated by an allosteric enzyme is analyzed.
Full Text
The Full Text of this article is available as a PDF (188.8 KB).
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Acerenza L., Kacser H. Enzyme kinetics and metabolic control. A method to test and quantify the effect of enzymic properties on metabolic variables. Biochem J. 1990 Aug 1;269(3):697–707. doi: 10.1042/bj2690697. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Bailey J. E. Toward a science of metabolic engineering. Science. 1991 Jun 21;252(5013):1668–1675. doi: 10.1126/science.2047876. [DOI] [PubMed] [Google Scholar]
- Cascante M., Lloréns M., Meléndez-Hevia E., Puigjaner J., Montero F., Martí E. The metabolic productivity of the cell factory. J Theor Biol. 1996 Oct 7;182(3):317–325. doi: 10.1006/jtbi.1996.0170. [DOI] [PubMed] [Google Scholar]
- Cascante M., Meléndez-Hevia E., Kholodenko B., Sicilia J., Kacser H. Control analysis of transit time for free and enzyme-bound metabolites: physiological and evolutionary significance of metabolic response times. Biochem J. 1995 Jun 15;308(Pt 3):895–899. doi: 10.1042/bj3080895. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Chance B., Hess B., Betz A. DPNH oscillations in a cell-free extract of S. carlsbergensis. Biochem Biophys Res Commun. 1964 Jun 1;16(2):182–187. doi: 10.1016/0006-291x(64)90358-4. [DOI] [PubMed] [Google Scholar]
- Easterby J. S. A generalized theory of the transition time for sequential enzyme reactions. Biochem J. 1981 Oct 1;199(1):155–161. doi: 10.1042/bj1990155. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Easterby J. S. Coupled enzyme assays: a general expression for the transient. Biochim Biophys Acta. 1973 Feb 15;293(2):552–558. doi: 10.1016/0005-2744(73)90362-8. [DOI] [PubMed] [Google Scholar]
- Easterby J. S. The effect of feedback on pathway transient response. Biochem J. 1986 Feb 1;233(3):871–875. doi: 10.1042/bj2330871. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Goldbeter A., Lefever R. Dissipative structures for an allosteric model. Application to glycolytic oscillations. Biophys J. 1972 Oct;12(10):1302–1315. doi: 10.1016/S0006-3495(72)86164-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Heinrich R., Rapoport T. A. Mathematical analysis of multienzyme systems. II. Steady state and transient control. Biosystems. 1975 Jul;7(1):130–136. doi: 10.1016/0303-2647(75)90050-7. [DOI] [PubMed] [Google Scholar]
- Hess B., Wurster B. Transient time of the pyruvate kinase-lactate dehydrogenase system of rabbit muscle in vitro. FEBS Lett. 1970 Jul 29;9(2):73–77. doi: 10.1016/0014-5793(70)80316-7. [DOI] [PubMed] [Google Scholar]
- Lloréns M., Nuño J. C., Montero F. Transient times in linear metabolic pathways under constant affinity constraints. Biochem J. 1997 Oct 15;327(Pt 2):493–498. doi: 10.1042/bj3270493. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Meléndez-Hevia E., Sicilia J., Ramos M. T., Canela E. I., Cascante M. Molecular bureaucracy: who controls the delays? Transient times in branched pathways and their control. J Theor Biol. 1996 Oct 7;182(3):333–339. doi: 10.1006/jtbi.1996.0172. [DOI] [PubMed] [Google Scholar]
- Meléndez-Hevia E., Torres N. V., Sicilia J., Kacser H. Control analysis of transition times in metabolic systems. Biochem J. 1990 Jan 1;265(1):195–202. doi: 10.1042/bj2650195. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Pye K., Chance B. Sustained sinusoidal oscillations of reduced pyridine nucleotide in a cell-free extract of Saccharomyces carlsbergensis. Proc Natl Acad Sci U S A. 1966 Apr;55(4):888–894. doi: 10.1073/pnas.55.4.888. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Rapoport T. A., Heinrich R. Mathematical analysis of multienzyme systems. I. Modelling of the glycolysis of human erythrocytes. Biosystems. 1975 Jul;7(1):120–129. doi: 10.1016/0303-2647(75)90049-0. [DOI] [PubMed] [Google Scholar]
- Storer A. C., Cornish-Bowden A. The kinetics of coupled enzyme reactions. Applications to the assay of glucokinase, with glucose 6-phosphate dehydrogenase as coupling enzyme. Biochem J. 1974 Jul;141(1):205–209. doi: 10.1042/bj1410205. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Torres N. V., Mateo F., Riol-Cimas J. M., Meléndez-Hevia E. Control of glycolysis in rat liver by glucokinase and phosphofructokinase: influence of glucose concentration. Mol Cell Biochem. 1990 Mar 5;93(1):21–26. doi: 10.1007/BF00223488. [DOI] [PubMed] [Google Scholar]
- Torres N. V., Meléndez-Hevia E. Transition time control analysis of a glycolytic system under different glucose concentrations. Control of transition time versus control of flux. Mol Cell Biochem. 1992 Jun 26;112(2):109–115. doi: 10.1007/BF00227567. [DOI] [PubMed] [Google Scholar]
- Torres N. V., Sicilia J., Meléndez-Hevia E. Analysis and characterization of transition states in metabolic systems. Transition times and the passivity of the output flux. Biochem J. 1991 May 15;276(Pt 1):231–236. doi: 10.1042/bj2760231. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Werner A., Heinrich R. A kinetic model for the interaction of energy metabolism and osmotic states of human erythrocytes. Analysis of the stationary "in vivo" state and of time dependent variations under blood preservation conditions. Biomed Biochim Acta. 1985;44(2):185–212. [PubMed] [Google Scholar]