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- A Continuum Electrostatic Approach for Calculating The Binding Energetics of Multiple Ligands (2007)
- Complex biomolecules like proteins or nucleic acids can transiently bind various ligands, e.g., electrons, protons, ions or larger molecules. This property is the key to enzymatic catalysis, regulation and energy transduction in biological systems. Interactions between different ligand binding sites can lead to complex titration behaviors, which can be explained based on a microstate description of the system. Previous approaches to calculate the binding behavior of multiple ligand, only treated sites with one or no ligand bound by using a binary state vector to describe the system. Also only one or two ligand types, i.e., protons or electrons, were used for the calculation. In this thesis, I derive a more general formulation of the theory of ligand binding to biomolecules. For each site any number of charge forms and rotamer forms are allowed as well as any number of ligands and any number of ligand types can be bound. Charge and rotamer forms of sites can be parameterized by measurements on model reactions in solution or by quantum chemical calculations. An energy function is described, consistently combining experimentally determined contributions and those, which can be calculated by continuum electrostatics, molecular mechanics and quantum chemistry. Programs (i.e., QMPB and Perl Molecule) were developed to perform calculations based on the generalized ligand binding theory. The class library Perl Molecule was developed to write powerful Perl programs, which perform the necessary processing steps, e.g., for the conversion of a pdb-file into the input required for energy calculations. The generated input contains all experimentally determined or molecular mechanically and quantum chemically obtained parameters. The energy calculations are performed by the program QMPB, which uses other programs for the continuum electrostatics calculations to solve the linearized Poisson-Boltzmann equation. The computations scale linearly with the total number of sites of the system and can easily be performed in parallel. From the obtained energies, microscopic ligand binding probabilities can be calculated as function of chemical potentials of ligands in solution, e.g., by a Monte Carlo program. Additionally, microscopic and macroscopic equilibrium constants can be computed. The usefullness and correctness of the new approach based on a generalized ligand binding theory is demonstrated by a number of studies on diverse examples. Because various groups used Lysozyme as benchmark system for continuum electrostatics, it is chosen to test if previously obtained results can be reproduced with QMPB. Different quantum chemical approaches are applied to the benzoquinone system for parameterizing a site with several protonation and reduction forms. A complex site is also the CuB center in Cytochrome c oxidase, which is studied to decide if multiple protonation forms of the coordinating histidines are involved in the reaction mechanism. Factors influencing the reduction potential of the electron transfer protein ferredoxin are analyzed using the programs Perl Molecule and QMPB. Here, in particular conformational changes of a peptide bond in the vicinity of the [2Fe-2S] center are of interest. The protonation form of a neighboring glutamate turns out to influence the reduction potential strongly. Protonation and phosphorylation studies on the protein HPr lead to the development of a four-microstate model to explain conformational changes on a histidine, which can be observed by experiment, molecular dynamics simulation and electrostatic calculations. The phosphorylation and protonation state dependent conformational change can be related to the dual role of the protein in regulation and phosphate-transfer. The new microstate description does not only allow to analyze thermodynamic properties but also paved the road for the study of the kinetics of charge transfer.