Estimation of binding parameters for the protein–protein interaction using a site-directed spin labeling and EPR spectroscopy

Abstract

Sensitivity of the electron paramagnetic resonance (CW EPR) to molecular tumbling provides potential means for studying processes of molecular association. It uses spin-labeled macromolecules, whose CW EPR spectra may change upon binding to other macromolecules. When a spin-labeled molecule is mixed with its liganding partner, the EPR spectrum constitutes a linear combination of spectra of the bound and unbound ligand (as seen in our example of spin-labeled cytochrome c ₂ interacting with cytochrome bc ₁ complex). In principle, the fraction of each state can be extracted by the numerical decomposition of the spectrum; however, the accuracy of such decomposition may often be compromised by the lack of the spectrum of the fully bound ligand, imposed by the equilibrium nature of molecular association. To understand how this may affect the final estimation of the binding parameters, such as stoichiometry and affinity of the binding, a series of virtual titration experiments was conducted. Our non-linear regression analysis considered a case in which only a single class of binding sites exists, and a case in which classes of both specific and non-specific binding sites co-exist. The results indicate that in both models, the error due to the unknown admixture of the unbound ligand component in the EPR spectrum causes an overestimation of the bound fraction leading to the bias in the dissociation constant. At the same time, the stoichiometry of the binding remains relatively unaffected, which overall makes the decomposition of the EPR spectrum an attractive method for studying protein–protein interactions in equilibrium. Our theoretical treatment appears to be valid for any spectroscopic techniques dealing with overlapping spectra of free and bound component.