The bulletin of mathematical biophysics

, Volume 29, Issue 1, pp 1–16 | Cite as

Bimolecular systems: I. Linear systems of complexes

  • Vojtech Ličko
Article

Abstract

A vast number of biologically important processes are based upon bimolecular systems. In these systems intermediate complexes are formed. Bimolecular systems in which no complex-complex interactions occur are called linear systems of complexes. A definition and some characteristic properties of these systems are given here. There may exist a contradiction of Onsager's principle of detailed balancing in these systems; however, no principal differences are found between the steady state behavior of an open system and that of a closed system. It is shown that the steady state behavior of a linear system of complexes of arbitrary complexity has some similarities with the steady state behavior of a simple bimolecular system, e.g., Michaelis-Menten enzymatic reaction. Multiplicity of action of the substances participating in biomolecular processes may produce some qualitative differences in the steady state behavior of the system.

Keywords

Linear System Detailed Balance Multiple Agent Negative Term Positive Term 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Brauer, A. 1946. “Limits for the Characteristic Roots of a Matrix.”Duke Math. J.,13, 387–395.MATHMathSciNetCrossRefGoogle Scholar
  2. Brown, A. J. 1902. “Enzyme Action.”Trans. Chem. Soc.,81, 373–388.CrossRefGoogle Scholar
  3. Cleland, W. W. 1963. “The Kinetics of Enzyme-Catalyzed Reactions With Two or More Substrates or Products.”Biochim. Biophys. Acta,67, 104–137.CrossRefGoogle Scholar
  4. Hearon, J. Z. 1950. “The Steady State Kinetics of Some Biological Systems. III.”Bull. Math. Biophysics,12, 57–83.Google Scholar
  5. —, 1953. “The Kinetics of Linear Systems With Special Reference to Periodic Reactions.”Bull. Math. Biophysics,15, 121–141.MathSciNetGoogle Scholar
  6. King, E. L., Altman, C. 1956. “A Schematic Method of Deriving The Rate Laws for Enzyme-Catalyzed Reactions.”J. Phys. Chem.,60, 1375–1378.CrossRefGoogle Scholar
  7. Ličko, V. 1963. “Some Notes on the Theory of Reaction Rates: Enzymatic Reactions.”Bull. Math. Biophysics,25, 141–154.Google Scholar
  8. — 1966. “Interactions in Enzymatic Reactions.”Bull. Math. Biophysics,28, 379–390.Google Scholar
  9. Minkowski, H. 1900. “Zur Theorie der Einheiten in den algebraischen Zahlkörpern.” Nachrichten der K. Gesellschaft der Wissenschaften zu Göttingen, Mathematisch physikalische Klasse. S., 90–93.Google Scholar
  10. Morrison, J. F., James, E. 1965. “The Mechanism of the Reaction Catalyzed by Adenosine Triphosphate-Creatine Phosphotransferase.”Biochem. J.,97, 37–52.Google Scholar
  11. Onsager, L. 1931. “Reciprocal Relations in Irreversible Processes I.”Phys. Rev.,37, 405–426.MATHCrossRefGoogle Scholar
  12. Schatz, A., Schalscha, E. B., Schatz, V. 1964. “Soil Organic Matter as a Natural Chelating Material. Part 2: The Occurrence and Importance of Paradoxical Concentration Effects in Biological Systems.”Compost Science,4, 30–34.Google Scholar
  13. Wong, J. T. F., Hanes, C. S. 1962. “Kinetic Formulations for Enzymic Reactions Involving Two Substrates.”Canad. J. Biochem. Physiol.,40, 763–804.Google Scholar

Copyright information

© N. Rashevsky 1967

Authors and Affiliations

  • Vojtech Ličko
    • 2
    • 1
  1. 1.Committee on Mathematical BiologyThe University of ChicagoChicago
  2. 2.Faculty of Natural SciencesComenius UniversityBratislavaCzechoslovakia

Personalised recommendations