Abstract
Yates-Pardee-type metabolic pathways in a heterogenous cell milieu are modeled as a system of coupled non-linear partial differential equations. A numerical solution to this systmm is described and some properties of such a physiological system are studied. Confinement with and without a membrane is considered and it is shown how confinement results in an increase in the stability of the metabolite concentrations. These results suggest that the enzyme organization may contribute to the stability of the cellular metabolism.
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References
Batke, J. 1991. Channelling by loose enzyme complexesin situ is likely, though physiological significance is open for speculation.J. Theor. Biol. 152, 41–46.
Burger, J. and C. Machbub. 1991. Comparison of numerical solutions of a one-dimensional nonlinear heat equation.Communications in Applied Numerical Methods,7, 233–240.
Chauvet, G. 1993. Hierarchical functional organization of formal biological systems: a dynamical approach. I. The increase in complexity by self-association increases the domain of stability of a biological system.Philos. Trans. Soc. London Ser. B 339, 425–444.
Costalat, R., J.-P. Morillon and J. Burger. 1993. Effect of self-organization on the stability of metabolic units.European Congress on Artificial Life. J. L. Deneubourg (Ed), pp. 236–244. Bruxelles.
Dibrov, B. F., A. M. Zhabotinskii and B. N. Kholodenko. 1981a. Dynamic stability of metabolic chain with one feedback loop.Biophysics 26, 598–604.
Dibrov, B. F., A. M. Zhabotinskii and B. N. Kholodenko. 1981b. Dynamic stability and parametric stabilization of the steady states of unbranched metabolic pathways.Biophysics 26, 804–810.
Goldbeter, A. 1973. Patterns of spatiotemporal organization in an allosteric enzyme model.Proc. Nat. Acad. Sci. U.S.A. 70, 3255–3259.
Goodwin, B. C. 1976.Analytical Physiology of Cells and Developing Organisms. London: Academic Press.
Marmillot, Ph., J.-F. Hervagault and G. R. Welch. 1992. Patterns of spatiotemporal organization in an “ambiquitous” enzyme model.Proc. Nat. Acad. Sci. U.S.A. 89, 12103–12107.
Monod, J., J.-P. Changeux and F. Jacob, 1963. Allosteric proteins and cellular control systems.J. Mol. Biol. 6, 306–329.
Morillon, J.-P., R. Costalat, N. Burger and J. Burger. 1994. Modelling two associated biochemical pathways.MATHMOD Conference, Proceedings of the IMACS Symposium on Mathematical Modelling, Vol. 3. I. Troch and F. Breitenecker (Eds). Vienna, Austria.
Ovádi, J. 1991. Physiological significance of metabolic channelling.,J. Theor. Biol. 152, 1–22.
Rapp, P. 1976. Analysis of biochemical phase shift oscillators by a harmonic balancing technique.J. Math. Biol. 3, 203–224.
Rapp, P. 1980. Biological applications of control theory. InMathematical Models in Molecular and Cellular Biology. L. A. Segel (Ed), pp. 146–247. Cambridge: Cambridge University Press.
Raviart, P. A. and J.-M. Thomas. 1988.Introduction à l'Analyse Numérique des Équations aux Dérivées Partielles. Paris: Masson.
Savageau, M. A. 1976.Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology. Reading, MA: Addison-Wesley.
Segel, L. A. 1988. On the validity of the steady state assumption of the enzyme kinetics.Bull. Math. Biol. 50, 579–593.
Umbarger, J. E. 1956. Evidence for a negative-feedback mechanism in the biosynthesis of isoleucine.Science 123, 848.
Viniegra-Gonzalez, G. 1973. Stability properties of metabolic pathways with feedback interactions. InBiological and Biochemical Oscillators.Proceedings of Two Symposia, Prague, Czechoslovakia. B. Chance (Ed.), pp. 41–59. New York: Academic Press.
Walter, C. F. 1969a. Stability of controlled biological systems.J. Theor. Biol. 23, 23–38.
Walter, C. F. 1969b. The absolute stability of certain types of controlled biological systems.J. Theor. Biol. 23, 39–52.
Walter, C.F. 1970. The occurrence and the significance of limit cycle behavior in controlled biochemical systems.J. Theor. Biol. 27, 259–272.
Walter, C. F. 1972. Kinetic and thermodynamic aspects of biological and biochemical control mechanisms. InBiochemical Regulatory Mechanisms in Eukaryotic Cells. Kun, Ernest and Santiago Grisolia (Eds). pp. 355–489. New York: Wiley-Interscience.
Walter, C. F. 1974. Some dynamic properties of linear, hyperbolic and sigmoidal multienzyme systems with feedback control.J. Theor. Biol. 44, 219–240.
Walter, G. G. 1980. Stability and structure of compartmental models of ecosystems.Math. Biosci. 51, 1–10.
Walter, G. G. 1983. Some equivalent compartmental models.Math. Biosci. 64, 273–293.
Welch, G. R. 1977. On the role of organized multienzyme systems in cellular metabolism: a general synthesis.Prog. Biophys. Molec. Biol. 32, 103–191.
Welch, G. R., T. Keleti and B. Vértessy. 1988. The control of cell metabolism for homogenous vs. heterogeneous enzyme systems.J. Theor. Biol. 130, 407–422.
Westerhoff, H. V. and G. R. Welch. 1992. Enzyme organization and the direction of metabolic flow: physicochemical considerations.Current Topics in Cellular Regulation 33, 361–389.
Yates, P. A. and A. B. Pardee. 1956. Control of pyrimidine biosynthesis inescherichia coli by a feed-back mechanism.J. Biol. Chem. 221, 757–770.
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Costalat, R., Burger, J. Effect of enzyme organization on the stability of Yates-Pardee pathways. Bltn Mathcal Biology 58, 719–737 (1996). https://doi.org/10.1007/BF02459479
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DOI: https://doi.org/10.1007/BF02459479