The meaning of the decoupled sites representation in terms of statistical mechanics and stochastics
Johannes W. R. Martini, G. Matthias Ullmann, Martin Schlather · 2013
The investigation of thermodynamic properties of ligand binding is a classical field of (bio)chemistry and (bio)physics. Commonly, an algebraic description using polynomials (e.g. the binding polynomial) and rational functions (e.g. titration curves) is used to characterize systems of molecules and their ligand(s). However, the algebraic model is a result of the probabilistic setup of statistical mechanics and its concept of the Grand Canonical Partition Function. In this work, we reconsider the decoupled sites representation (DSR), a theoretical tool to regard an overall titration curve as sum of classical Henderson-Hasselbalch ligand binding curves from a stochastic point of view. Our work closes the circle from the initial stochastic model, to an algebraic description in which the DSR was developed and analyzed, back to its meaning in statistical mechanics and stochastics. In this regard, we translate results in the periphery of the DSR which were derived within the algebraic model into stochastics. The shifted point of view facilitates some proofs and physical interpretations and provides the basis for future work which might investigate how certain "phenomenona of the algebraic concept can be interpreted stochastically.