Theory and Applications of Nitroxide-based Paramagnetic Cosolutes for Probing Intermolecular and Electrostatic Interactions on Protein Surfaces

Solvent paramagnetic relaxation enhancement (sPRE) arising from nitroxide-based cosolutes has recently been used to provide an atomic view of cosolute-induced protein denaturation and to characterize residue-specific effective near-surface electrostatic potentials (OENS). Here, we explore distinct properties of the sPRE arising from nitroxide-based cosolutes and provide new insights into the interpretation of the sPRE and sPRE-derived OENS. We show that: (a) the longitudinal sPRE rate Gamma 1 is heavily dependent on spectrometer field and viscosity, while the transverse sPRE rate Gamma 2 is much less so; (b) the spectral density J(0) is proportional to the inverse of the relative translational diffusion constant and is related to the quantity r-4 norm, a concentration-normalized equilibrium average of the electron- proton interspin separation; and (c) attractive intermolecular interactions result in a shortening of the residue-specific effective correlation time for the electron-proton vector. We discuss four different approaches for evaluating OENS based on Gamma 2, J(0), Gamma 1, or r-6 norm. The latter is evaluated from the magnetic field dependence of Gamma 1 in conjunction with Gamma 2. Long-range interactions dominate J(0) and Gamma 2, while, at high magnetic fields, the contribution of short-range interactions becomes significant for J(w) and hence Gamma 1; the four OENS quantities enable one to probe both long-and short-range electrostatic interactions. The experimental OENS potentials were evaluated using three model protein systems, two folded (ubiquitin and native drkN SH3) and one intrinsically disordered (unfolded state of drkN SH3), in relation to theoretical OENS potentials calculated from atomic coordinates using the Poisson-Boltzmann theory with either a r-6 or r-4 dependence.