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 Γ 1 is heavily dependent on spectrometer field and viscosity, while the transverse sPRE rate Γ 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 ϕ ENS based on Γ 2 , J (0), Γ 1 , or ⟨ r -6 ⟩ norm . The latter is evaluated from the magnetic field dependence of Γ 1 in conjunction with Γ 2 . Long-range interactions dominate J (0) and Γ 2 , while, at high magnetic fields, the contribution of short-range interactions becomes significant for J (ω) and hence Γ 1 ; the four ϕ ENS quantities enable one to probe both long- and short-range electrostatic interactions. The experimental ϕ ENS 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 ϕ ENS potentials calculated from atomic coordinates using the Poisson-Boltzmann theory with either a r -6 or r -4 dependence.