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 (φ_ENS). 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 φ_ENS. We show that: (a) the longitudinal sPRE rate Δ₁is heavily dependent on spectrometer field and viscosity, while the transverse sPRE rate Δ₂is 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 φ_ENSbased on Δ₂, J(0), Δ₁, or r^-6_norm. The latter is evaluated from the magnetic field dependence of Δ₁in conjunction with Δ₂. Long-range interactions dominate J(0) and Δ₂, while, at high magnetic fields, the contribution of short-range interactions becomes significant for J(ω) and hence Δ₁; the four φ_ENSquantities enable one to probe both long- A nd short-range electrostatic interactions. The experimental φ_ENSpotentials 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 φ_ENSpotentials calculated from atomic coordinates using the Poisson-Boltzmann theory with either a r^-6or r^-4dependence.