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

Abstract

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 nearsurface 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 sPREderived 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.

The solid-state DNP effect in liquids

“…The so-called force-free hard sphere (FFHS) model, which assumes spherical molecules that contain the spins at their centers, is a more realistic yet analytically tractable model (Ayant et al, 1975;Hwang and Freed, 1975). It is universally employed in the analysis of diverse magnetic-resonance measurements, including nuclear relaxation by paramagnetic impurities (Okuno et al, 2022) and DNP via the Overhauser effect (Franck et al, 2013). The Laplace transform of the dipolar correlation function of this model is (Ayant et al, 1975, eqs.…”

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

“…The spin dipole–dipole correlation function in an isotropic liquid is given by: , C ( t ) = N normalS ⟨ P 2 false( r̂ · r̂ normalo false) r 3 false( t false) r o 3 ⟩ where r and r̂ are the length and orientation of the interspin vector r ⃗; P 2 ( x ) is the Legendre polynomial of degree 2; and N S is the number of paramagnetic cosolute molecules in the system. The subscript “o” denotes the quantity at t = 0.…”

“…For nitroxide-based paramagnetic cosolutes, the electron spin relaxation time is long ( T 1e , T 2e ≥ 1 μs) compared to the characteristic timescale of translational diffusion (ns timescale), and, therefore, Curie relaxation can be neglected . The longitudinal (Γ 1 ) and transverse (Γ 2 ) relaxation rates are related to the spectral density function J (ω) by: − normalΓ 1 = true( μ normalo 4 π true) 2 ℏ 2 γ normalH 2 γ normale 2 2 15 false[ S ( S + 1 ) { J false( ω normalH − ω normale false) + 3 J false( ω normalH false) + 6 J false( ω normalH − ω normale false) } normalΓ 2 = true( μ normalo 4 π true) 2 ℏ 2 γ normalH 2 γ normale 2 1 15 <...…”

“…In addition, the sPRE experiments in the current work are performed at high field (spectrometer frequency ≥ 500 MHz) so that J (ω H ) ≫ J (ω e ) and all of the terms involving ω e can be neglected. Under these conditions, Γ 1 and Γ 2 are given by: normalΓ 1 = 3 10 true( μ normalo 4 π true) 2 ℏ 2 γ normalH 2 γ normale 2 J ( ω H ) and normalΓ 2 = 1 5 true( μ normalo 4 π true) 2 ℏ 2 γ normalH 2 γ normale 2 ( J false( 0 false) + 3 4 J false( ω normalH false) ) It should be noted that the approximations for Γ 1 and Γ 2 given in eqs and are not valid for analyzing 1 H-Γ 1 relaxivity NMR relaxation dispersion (NMRD) data because the range of external fields extends well below 100 MHz.…”

“…Solvent paramagnetic relaxation enhancement (sPRE) − has recently attracted interest as a method for studying residue-specific effective near-surface potentials (ϕ ENS ) of proteins and nucleic acids without any requirement of knowledge regarding the three-dimensional structure of the biomolecule under investigation. − A measure of ϕ ENS is generally obtained by taking the ratios of longitudinal ( 1 H-Γ 1 ) or transverse ( 1 H-Γ 2 ) sPREs obtained using paramagnetic cosolutes of different charges. ,,− The values, however, of ϕ ENS obtained in this manner are semiquantitative in nature as the exact physical interpretations of Γ 1 or Γ 2 are not straightforward to understand. Both Γ 1 and Γ 2 consist of linear combinations of the spectral densities J (0) and J (ω H ).…”