Development and Application of Equilibrium Thermodynamic Models Describing Coupled Protein Oligomerization and Ligand Binding

Abstract

The association and dissociation of protein oligomers is frequently coupled to the binding of ligands, facilitating the regulation of many biological processes. Equilibrium thermodynamic models are needed to describe the linkage between ligand binding and homo-oligomerization. These models must be parameterized in a way that makes physical interpretation straightforward, and allows elaborations or simplifications to be readily incorporated. We propose a systematic framework for the equilibrium analysis of ligand-linked oligomerization, treating in detail the case of a homo-oligomer with cyclic point group symmetry, where each subunit binds a ligand at a single site. Exploiting the symmetry of the oligomer, in combination with a nearest-neighbors approximation, we derive a class of site-specific ligand binding models involving only four parameters, irrespective of the size of the oligomer. The model parameters allow direct quantitative assessment of ligand binding cooperativity, and the influence of ligand binding on protein oligomerization, which are the key questions of biological interest. These models, which incorporate multiple types of linkage, are practically applicable, and we show how Markov Chain Monte Carlo (MCMC) methods can be used to characterize the agreement of the model with experimental data. Simplifications to the model emerge naturally, as its parameters take on extremal values. The nearest-neighbors approximation underpinning the model is transparent, and the model could be augmented in obvious fashion if the approximation were inadequate. The approach is generalizable, and could be used to treat more complex situations, involving more than a single kind of ligand, or a different protein symmetry.\n\nAuthor SummaryThe assembly and disassembly of protein complexes in response to the binding of ligands is a ubiquitous biological phenomenon. This is often linked, in turn, to the activation or deactivation of protein function. Methods are therefore needed to quantitate the linkage or coupling between protein assembly and effector binding, requiring the development of mathematical models describing the coupled binding processes. As proteins usually assemble in a symmetric fashion, the nature of any symmetry present has to be considered during model construction. We have developed a class of models than can effectively describe the coupling between effector binding and protein assembly into symmetric ring-like structures of any size. Despite the relatively complex mathematical form of the models, they are practically applicable. Markov Chain Monte Carlo methods, a form of Bayesian statistical analysis, can be used to analyze the fit of the models to experimental data, and recover the model parameters. This allows the direct assessment of the nature and magnitude of the coupling between effector binding and protein assembly, as well as other relevant characteristics of the system.