Excursions in the Theory of Ligand Binding

Martini, Johannes

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URL: https://ub-madoc.bib.uni-mannheim.de/36161
URN: urn:nbn:de:bsz:180-madoc-361615
Document Type: Doctoral dissertation
Year of publication: 2014
Place of publication: Mannheim
University: Universität Mannheim
Evaluator: Schlather, Martin
Date of oral examination: 25 March 2014
Publication language: English
Institution: School of Business Informatics and Mathematics > Mathematische Statistik (Schlather 2012-)
Subject: 510 Mathematics
Subject headings (SWD): Ligand , Zustandssumme , Statistische Thermodynamik , Titration
Keywords (English): Decoupled Sites Representation , Ligand , Ligand binding , Titration curve , Receptor , Stochastically independent binding , binding polynomial , partition function , interaction energy
Abstract: The work on hand deals with different topics within the theory of ligand binding. The introductory part includes a motivation and basic definitions and presents the mathematical model of equilibrium ligand binding theory, which is based on the Grand Canonical Ensemble of Statistical Mechanics. The second chapter presents an alternative derivation of the Grand Canonical Partition Function based on a Markov chain model for the ligand binding dynamics of an individual molecule. Moreover, properties of the model are discussed and briey compared to properties of another processes with the same stationary distribution. Chapter 3 deals with the decoupled sites representation (DSR, Onufriev et al. (2001)), the underlying mathematical problem and possible generalizations. Moreover, the term "decoupled molecule" is defined and properties of decoupled molecules are discussed. In Chapter 4, the DSR is transfered - as far as possible - to molecules binding two different types of ligands. Furthermore, the special structure of the system of algebraic equations which has to be solved, if a decoupled molecule shall be calculated is discussed and properties of decoupled molecules are analyzed. Moreover, algorithms to find decoupled molecules are presented. Chapter 5 transfers results of the algebraic theory of Chapters 3 and 4 to probability theory and thus relates being decoupled to stochastic independence and conditional stochastic independence of certain random variables. Chapter 6 discusses possible interpretations of complex roots (with imaginary part nonzero) of the binding polynomial and their connection to cooperative ligand binding. Finally, Chapter 7 presents examples of how ligand binding theory can be used for modeling biological regulatory processes.

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