Gadolinium-Based NMR Spin Relaxation Measurements of Near-Surface Electrostatic Potentials of Biomolecules

NMR spectroscopy is an important tool for the measurement of the electrostatic properties of biomolecules. To this point, paramagnetic relaxation enhancements (PREs) of 1H nuclei arising from nitroxide cosolutes in biomolecular solutions have been used to measure effective near-surface electrostatic potentials (ϕENS) of proteins and nucleic acids. Here, we present a gadolinium (Gd)-based NMR method, exploiting Gd chelates with different net charges, for measuring ϕENS values and demonstrate its utility through applications to a number of biomolecular systems. The use of Gd-based cosolutes offers several advantages over nitroxides for ϕENS measurements. First, unlike nitroxide compounds, Gd chelates enable electrostatic potential measurements on oxidation-sensitive proteins that require reducing agents. Second, the large electron spin quantum number of Gd (7/2) results in notably larger PREs for Gd chelates when used at the same concentrations as nitroxide radicals. Thus, it is possible to measure ϕENS values exclusively from + and – charged compounds even for highly charged biomolecules, avoiding the use of neutral cosolutes that, as we further establish here, limits the accuracy of the measured electrostatic potentials. In addition, the smaller concentrations of cosolutes required minimize potential binding to sites on macromolecules. Fourth, the closer proximity of the paramagnetic center and charged groups within Gd chelates, in comparison to the corresponding nitroxide compounds, enables more accurate predictions of ϕENS potentials for cross-validation of the experimental results. The Gd-based method described here, thus, broadens the applicability of studies of biomolecular electrostatics using solution NMR spectroscopy.

in the main text.All grid points are used in the evaluation of Eq. [5] where i is the electrostatic potential at grid point i (from APBS or DelPhi output); ri is the distance from the 1 H nucleus of interest to a grid point i; and i is a factor that represents the accessibility of grid point i and is either 1 (accessible) or 0 (inaccessible).A value of 0 was assigned to i when dmin < rvdw + rpc, where dmin is the distance from grid point i to the closest atom in the macromolecule; rvdw is the van der Waals radius of the closest atom (the value indicated in the PQRformat file); and rpc is the effective radius that defines the accessibility of the paramagnetic center.The interval for the grid space used in calculations was 0.5 Å for each dimension.As shown in Figure S2, rpc = 3.5 Å was obtained for the Gd chelates through empirical optimization.Coincidentally, despite the different chemical structures, rpc = 3.5 Å was also obtained for the PROXYL derivatives in a previous study. 1It should be noted that rpc is an effective radius and does not represent the molecular radius unless the paramagnetic center is located at the center in a spherical molecule.[5]) for ubiquitin 1 HN atoms in regions of defined secondary structure.An identical value for rpc was assumed for the two analogous compounds Gd-DOTA and Gd-DOTAM-BA.Since the RMSD minimum as a function of rpc is shallow, rpc does not have to be determined more precisely.Based on these results, rpc = 3.5 Å was used for all calculations to predict ENS potentials in the current study.  and the crystal structure (PDB 1UBQ) 5 .The structural ensemble of 2K39 includes 116 structures, which are superimposed using the secondary-structure regions.The location of L73 is colored in orange.Note that in solution, the C-terminal tail is disordered, which is also evidenced by small order parameters observed for the NH groups in the C-terminal tail. 4 (B) Crystal packing of 1UBQ, showing that the C-terminal tail is fixed by intermolecular contacts.(C) Poisson-Boltzmann theory-based prediction of the ENS potential for L73 HN for some NMR structures selected from PDB 2K39 and for the crystal structure.The charged side chains whose conformations significantly influence the effective near-surface electrostatic potential (i.e., D39, R42, R72, and R73) are shown.In the crystal structure, for which the predicted ENS potential of L73 HN is relatively small, the negatively charged carboxylate group of D39 is pointing toward L73 HN, whereas the positively charged guanidinium groups of R42, R72, and R74 are pointing away from L73 HN.

APBS inputs
The following inputs were used for nonlinear Poisson-Boltzmann equation-based calculations with APBS 2 .The output files from APBS in the "dx" format were used to predict the effective near-surface potentials ENS using Eq.[5].The MATLAB script package 'PBENS', which is available at a GitHub webpage (https://github.com/IwaharaLab/PBENS),was used for the calculations.

1a. APBS input to calculate electrostatic potentials of ubiquitin
The PQR file, 1ubq.pqr, was generated from the PDB file1ubq using the PDB2PQR program 6 along with PROPKA 7 -based selection of titration states at pH 7.5 and the AMBER force field parameters.The ion concentrations (0.024 M) and the temperature (298.15K) were set based on the experimental conditions.The 3D space is 128 Å  128 Å  128 Å with an interval of 0.5 Å (257 points along each dimension).The dielectric constants were set to 2.0 for the interior of the protein and to 78.54 for the solvent.

1b. APBS input to calculate electrostatic potentials of G48A Fyn SH3
The PQR file, 3cqrt_mutate2.pqr, was generated from a PDB-format file using the PDB2PQR program 6 along with PROPKA 7 -based selection of titration states at pH 6.0 and the AMBER force field parameters.The ion concentrations (0.024 M) and the temperature (283.15K) were set based on the experimental conditions.The 3D space is 128 Å  128 Å  128 Å with an interval of 0.5 Å (257 points along each dimension).The dielectric constants were set to 2.0 for the interior of the protein and to 78.54 for the solvent.The PQR file, eg15.pqr, was generated from a PDB-format file using the PDB2PQR program 6 along with PROPKA 7 -based selection of titration states at pH 7.4 and the AMBER force field parameters.The ion concentrations (0.123 M) and the temperature (298.15K) were set based on the experimental conditions.The 3D space is 160 Å  160 Å  160 Å with an interval of 0.5 Å (321 points along each dimension).The dielectric constants were set to 2.0 for the interior of DNA and to 78.54 for the solvent.

Delphi inputs
The following inputs were used for nonlinear Poisson-Boltzmann equation-based calculations with DelPhi 3 .The output files from DelPhi in the "cube" format were used to predict the effective near-surface potentials ENS using Eq.[5].The MATLAB script package 'PBENS' was used for the calculations.

2a. DelPhi input to calculate electrostatic potentials of ubiquitin
The ion concentrations (0.024 M) and the temperature (25˚C) were set based on the experimental conditions.The 3D space is 128 Å  128 Å  128 Å with an interval of 0.5 Å (257 points along each dimension).The dielectric constants were set to 2.0 for the interior of the protein and to 78.54 for the solvent.

Figure S2 :
Figure S2: Optimization of the effective radius rpc of the paramagnetic cosolutes

Figure S3 :Figure S4 :Figure S5 :Figure S8 :Figure S1 .
Figure S3: Examples of spectra recorded for the biomolecules used in the current study Figure S4: Comparison of ENS predictions with APBS and DelPhi programs Figure S5: Explanation for the discrepancy between the experimental and predicted ENS potentials for ubiquitin L73 HN Figure S6: ENS potentials measured for H and methyl 1 H nuclei of ubiquitin using the Gd chelates Figure S7: ENS potentials for RtoK CAPRIN1 measured using the positive, neutral and negative Proxyl cosolutes Figure S8: Impact of 5 mM DTT on solvent PRE rates 2 and ENS potentials APBS inputs DelPhi inputs NMR pulse program for water 1 H R1 relaxation measurement

Figure S2 .
Figure S2.Optimization of the effective radius, rpc, of the Gd-based paramagnetic cosolutes for predicting the effective near-surface electrostatic potential ENS.(A) Correlations between experimental ENS potentials and Poisson-Boltzmann-based predictions calculated with Eq. [5] for ubiquitin 1 HN atoms of regions with defined secondary structure.Results with rpc = 2.5, 3.5, and 5.5 Å are shown.(B) RMSD between the experimental ENS potentials and Poisson-Boltzmann-based predictions (Eq.[5]) for

Figure S3 .
Figure S3.Examples of heteronuclear 2D spectra recorded to measure solvent PRE rates for ubiquitin (A), CAPRIN1 (B), G48A Fyn SH3 (C), and 15-bp DNA (D).Some signals are aliased for the 15 N and 13 C dimensions.The experimental conditions are indicated in the main text.

Figure S4 .
Figure S4.Comparison of structure-based ENS predictions using electrostatic potentials calculated with APBS 2 and DelPhi 3 programs.(A) Ubiquitin at an ionic strength of 24 mM, pH 7.5, and 25˚C.(B) G48A Fyn SH3 domain at an ionic strength of 24 mM, pH 6.0, and 10˚C.(C) 15-bp DNA at an ionic strength of 123 mM, pH 7.4, and 25˚C.The input parameters for the nonlinear Poisson-Boltzmann based calculations with the APBS and DelPhi programs are given below in the sections "APBS Inputs" and "DelPhi Inputs".

Figure S5
Figure S5Differences between the flexible C-terminal tail of ubiquitin in solution and the tail immobilized by crystal packing offer an explanation for the discrepancy between the experimental ENS potential for L73 HN and that predicted from the crystal structure.(A) Ribbon representations of the NMR structures (PDB 2K39)4 and the crystal structure (PDB 1UBQ)5 .The structural ensemble of 2K39 includes 116 structures, which are superimposed using the secondary-structure regions.The location of L73 is colored in orange.Note that in solution, the C-terminal tail is disordered, which is also evidenced by small order parameters observed for the NH groups in the C-terminal tail.4 (B) Crystal packing of 1UBQ, showing that the C-terminal tail is fixed by intermolecular contacts.(C) Poisson-Boltzmann

Figure S6 .
Figure S6.Effective near-surface electrostatic potentials ENS measured for H and methyl 1 H nuclei of ubiquitin using Gd-DOTA and Gd-DOTAM-BA cosolutes.The experimental data were compared with the predictions from the Poisson-Boltzmann electrostatic potentials.The RMSDs between the experimental values and the predictions were 4.8 mV for H atoms and 3.2 mV for methyl groups in the regions of defined secondary structure.

Figure S8 .
Figure S8.Impact of 5 mM DTT on solvent 2 PRE rates (top) and on the ENS potentials (bottom) measured for H (panel A) and methyl 1 H nuclei (panel B) of ubiquitin using Gd-DOTA and Gd-DOTAM-BA as paramagnetic cosolutes.The solution conditions were the same as those for Figure 6.