Student Theses and Dissertations
Date of Award
1970
Document Type
Thesis
Degree Name
Doctor of Philosophy (PhD)
Thesis Advisor
George Nemethy
Keywords
flexible ligand binding, protein-ligand interactions, statistical mechanics, polymer adsorption, binding isotherms, configurational entropy
Abstract
In this dissertation, a theoretical model is presented for the binding of flexible ligands to proteins. The model explicitly accounts for the ability of these chain-like molecules to bind in a large number of configurations (including many in which not all segments are in contact with the protein) and therefore is quite different from the theory of multiple equilibria which commonly is used to analyze such interactions. The latter assumes that the ligands bind rigidly to point binding sites, neglecting the internal degrees of freedom of the bound molecules. Comparisons of binding data calculated using the present model with those obtained experimentally indicate that this model, rather than the theory of multiple equilibria, is the appropriate theoretical model for the interactions between flexible ligands and proteins (e.g. the nonspecific binding of substituted alkanes to proteins). Formally, the model is similar to the statistical-mechanical theories of polymer adsorption at a surface, since the protein surface is represented by a lattice, each site of which binds a single ligand segment. However, the lattice chosen has several features which make it especially suitable for the treatment of protein-ligand interactions. For example, the lattice has been folded over a closed surface by introducing a small number of irregularities in the lattice pattern, and chemically different sites (e.g. sites with ionic, polar, and nonpolar character) in various arrangements may be included. The binding sites may cover the entire protein surface or only a small part of it. The number of configurations of the bound ligands is determined by counting the possible arrangements on the lattice, regarding the placement of each ligand on the lattice as a Markov process. For chemically homogeneous binding surfaces, an alternative form of the model is possible which does not utilize a lattice for the enumeration of ligand configurations. The model allows a calculation of parameters which characterize the average configuration of each bound ligand as well as the equilibrium properties of protein-ligand systems, such as the relationship between the free ligand concentration and the average number of ligands bound per protein molecule (which may be compared to an experimental binding isotherm). Furthermore, the dependence of these quantities on the specific characteristics of the ligand and the protein surface may be determined. Among the most important of these results is that flexible ligands bind in configurations with a larger number of desorbed segments as the lattice sites on the protein become saturated. This variation in the average configuration of the bound ligands produces a change in the intrinsic affinity of the protein for the ligand, so that the Scatchard and double-reciprocal plots of binding data never can be expected to be linear for flexible molecules, even when all of the binding sites are chemically identical. For chemically homogeneous systems, the theory of multiple equilibria predicts linearity for such plots since it assumes an equal intrinsic affinity of the protein for all ligands, an assumption which is not applicable to flexible molecules. The model predicts binding data quite similar to those observed experimentally. In fact, it is found that only the present model which accounts for the flexibility of the bound ligands can explain the experimental observation that the strength of binding increases with the chain length of the ligand. Furthermore, the model allows certain correlations to be made between the chemical nature of the binding region and the general features of experimental binding data. In particular, the binding data for several substituted alkanes (long-chain anions) indicate that the binding region must include a large number of nonpolar sites (which interact with the hydrocarbon segments of the ligand) as well as ionic sites (which interact with the ionic head group). Finally, the model may be used to illustrate the limited nature of the conclusions which may be drawn from class analyses of binding data according to the theory of multiple equilibria.
License and Reuse Information
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Recommended Citation
Laiken, Nora Dawn, "A Statistical-Mechanical Model for the Binding of Flexible Ligands to Proteins" (1970). Student Theses and Dissertations. 553.
https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/553
Comments
A thesis presented to the faculty of The Rockefeller University in partial fulfillment of the requirements for the degree of Doctor of Philosophy