Journal of Mathematical Chemistry

, Volume 51, Issue 2, pp 696–714 | Cite as

On the interaction of different types of ligands binding to the same molecule Part II: systems with n to 2 and n to 3 binding sites

  • Johannes W. R. Martini
  • Martin Schlather
  • G. Matthias Ullmann
Open Access
Original Paper


In the first part of this work we formulated the decoupled sites representation for two different types of ligands and highlighted special properties of the case of n binding sites for ligand L 1 and one binding site for ligand L 2. Moreover, for this case, we identified the microstate constants as unique components all decoupled molecules share. In the second part on hand, we investigate the cases with (n, 2) and (n, 3) binding sites. As it is difficult to solve the system of equations occurring when a molecule with more than one binding site for both ligands shall be decoupled, we present applicable calculation methods which exploit the special structure of the system of equations. Moreover, we investigate which unique properties all decoupled molecules share and show that for two different decoupled molecules with the same binding polynomial, not all microstate constants of a certain macrostate are permutations of the microstate constants of the other molecule.


Decoupled sites representation Protonation Binding polynomial Interaction energy Binding energy Ligand binding Electron transfer Photosynthesis Receptor 


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Copyright information

© The Author(s) 2012

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  • Johannes W. R. Martini
    • 1
  • Martin Schlather
    • 2
  • G. Matthias Ullmann
    • 3
  1. 1.Institut für Mathematische StochastikGeorg-August Universität GöttingenGöttingenGermany
  2. 2.Institut für MathematikUniversität MannheimMannheimGermany
  3. 3.Bioinformatik/StrukturbiologieUniversität BayreuthBayreuthGermany

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