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
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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.
KeywordsDecoupled sites representation Protonation Binding polynomial Interaction energy Binding energy Ligand binding Electron transfer Photosynthesis Receptor
- 3.E. Bombarda, G.M. Ullmann, pH-dependent pKa values in proteins—a theoretical analysis of protonation energies with practical consequences for enzymatic reactions. J. Phys. Chem. B 114(5), 1994–2003 (2010); PMID: 20088566Google Scholar
- 4.Cantor C.R., Schimmel P.R.: Biophysical Chemistry. Part III. The Behavior of Biological Macromolecules. W. H. Freeman, San Francisco (1980)Google Scholar
- 5.Hasselbalch K.: Die Berechnung der Wasserstoffzahl des Blutes aus der freien und gebundenen Kohlensäure desselben, und die Sauerstoffbindung des Blutes als Funktion der Wasserstoffzahl. Julius Springer, Berlin (1916)Google Scholar
- 6.L.J. Henderson, The Fitness of the Environment (Macmillan Company, New York, 1913)Google Scholar
- 7.J.W.R. Martini, M. Schlather, G.M. Ullmann, On the interaction of two different types of ligands binding to the same molecule part I: basics and the transfer of the decoupled sites representation to systems with n and one binding sites. J. Math. Chem. (2012). doi: 10.1007/s10910-012-0107-5
- 8.J.W. Martini, G. Ullmann, A mathematical view on the decoupled sites representation. J. Math. Biol. 1–27 (2012). doi: 10.1007/s00285-012-0517-x
- 11.R Core Team, R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna, 2012). ISBN 3-900051-07-0Google Scholar
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