A Bounded Rate Model for Mass Action Multiple Binding Processes: Stability Analysis

  • C. Bruni
  • A. Gandolfi
  • A. Germani
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 162)


In several biological processes a multiple binding reaction occurs, between a univalent ligand L and a n-valent macromolecule M, described by the scheme:
$$\begin{array}{*{20}{c}} {M + L\underset{{{{k}_{{{{d}_{1}}}}}}}{\overset{{{{k}_{{{{a}_{1}}}}}}}{\longleftrightarrow}}ML} \\ {ML + L\underset{{{{k}_{{{{d}_{2}}}}}}}{\overset{{{{k}_{{{{a}_{2}}}}}}}{\longleftrightarrow}}M{{L}_{2}}} \\ { \cdots \cdots \cdots \cdots } \\ {M{{L}_{{n - 1}}} + L\underset{{{{k}_{{{{d}_{n}}}}}}}{\overset{{{{k}_{{{{a}_{n}}}}}}}{\longleftrightarrow}}M{{L}_{n}}} \\ \end{array}$$
where \({\text{k}}_{{\text{a}}_{\text{i}} }\) and \({\text{k}}_{{\text{d}}_{\text{i}} }\) are respectively the association and dissociation rate constants. This kind of multiple reaction may either occur in solution (like the one between oxygen and the large respiratory proteins, e.g. hemoglobin in the vertebrates or hemocyanin in the invertebrates) or on cell surface (like the one between hormones and their cell receptors or the one between antigen and antigenic receptors on lymphocyte surface).


Asymptotic Stability Settling Time Degenerate Case Dissociation Rate Constant Regular Case 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • C. Bruni
    • 1
    • 2
  • A. Gandolfi
    • 2
  • A. Germani
    • 2
  1. 1.Istituto di AutomaticaUniversità di AnconaItaly
  2. 2.C.S.S.C.C.A., C.N.R.RomaItaly

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