Extending the Experimentally Accessible Range of Spin Dipole–Dipole Spectral Densities for Protein–Cosolute Interactions by Temperature-Dependent Solvent Paramagnetic Relaxation Enhancement Measurements

Longitudinal (Γ₁) and transverse (Γ₂) solvent paramagnetic relaxation enhancement (sPRE) yields field-dependent information in the form of spectral densities that provides unique information related to cosolute–protein interactions and electrostatics. A typical protein sPRE data set can only sample a few points on the spectral density curve, J(ω), within a narrow frequency window (500 MHz to ∼1 GHz). However, complex interactions and dynamics of paramagnetic cosolutes around a protein make it difficult to directly interpret the few experimentally accessible points of J(ω). In this paper, we show that it is possible to significantly extend the experimentally accessible frequency range (corresponding to a range from ∼270 MHz to 1.8 GHz) by acquiring a series of sPRE experiments at different temperatures. This approach is based on the scaling property of J(ω) originally proposed by Melchior and Fries for small molecules. Here, we demonstrate that the same scaling property also holds for geometrically far more complex systems such as proteins. Using the extended spectral densities derived from the scaling property as the reference dataset, we demonstrate that our previous approach that makes use of a non-Lorentzian Ansatz spectral density function to fit only J(0) and one to two J(ω) points allows one to obtain accurate values for the concentration-normalized equilibrium average of the electron–proton interspin separation ⟨r^–6⟩_norm and the correlation time τ_C, which provide quantitative information on the energetics and timescale, respectively, of local cosolute–protein interactions. We also show that effective near-surface potentials, ϕ_ENS, obtained from ⟨r^–6⟩_norm provide a reliable and quantitative measure of intermolecular interactions including electrostatics, while ϕ_ENS values obtained from only Γ₁ or Γ₂ sPRE rates can have significant artifacts as a consequence of potential variations and changes in the diffusive properties of the cosolute around the protein surface. Finally, we discuss the experimental feasibility and limitations of extracting the high-frequency limit of J(ω) that is related to ⟨r^–8⟩_norm and report on the extremely local intermolecular potential.