De novo determination of near-surface electrostatic potentials by NMR

Electrostatic potentials computed from three-dimensional structures of biomolecules by solving the Poisson–Boltzmann equation are widely used in molecular biophysics, structural biology, and medicinal chemistry. Despite the approximate nature of the Poisson–Boltzmann theory, validation of the computed electrostatic potentials around biological macromolecules is rare and methodologically limited. Here, we present a unique and powerful NMR method that allows for straightforward and extensive comparison with electrostatic models for biomolecules and their complexes. This method utilizes paramagnetic relaxation enhancement arising from analogous cationic and anionic cosolutes whose spatial distributions around biological macromolecules reflect electrostatic potentials. We demonstrate that this NMR method enables de novo determination of near-surface electrostatic potentials for individual protein residues without using any structural information. We applied the method to ubiquitin and the Antp homeodomain–DNA complex. The experimental data agreed well with predictions from the Poisson–Boltzmann theory. Thus, our experimental results clearly support the validity of the theory for these systems. However, our experimental study also illuminates certain weaknesses of the Poisson–Boltzmann theory. For example, we found that the theory predicts stronger dependence of near-surface electrostatic potentials on ionic strength than observed in the experiments. Our data also suggest that conformational flexibility or structural uncertainties may cause large errors in theoretical predictions of electrostatic potentials, particularly for highly charged systems. This NMR-based method permits extensive assessment of near-surface electrostatic potentials for various regions around biological macromolecules and thereby may facilitate improvement of the computational approaches for electrostatic potentials.

Due to the fundamental importance of electrostatic interactions in chemistry and biology, electrostatic potentials are invaluable information for the understanding of molecular recognition, enzymatic catalysis, and other functions of proteins and nucleic acids (1–4). Quantification of electrostatics is also important for successful protein engineering (5) and structure-based drug design (6). Computational approaches based on the Poisson–Boltzmann theory are commonly used to calculate electrostatic potentials from three-dimensional (3D) molecular structures (1, 7). Owing to available software such as Adaptive Poisson-Boltzmann Solver (APBS) (8, 9) and DelPhi (10, 11), computation of the electrostatic potentials around biomolecules has gained widespread popularity in the fields of molecular biophysics, structural biology, and medicinal chemistry.However, the computed electrostatic potentials may not necessarily be accurate even if the 3D structures are precisely and accurately determined. Importantly, the Poisson–Boltzmann theory is approximate with known limitations. The electrostatic models based on this theory are valid under assumptions, which simplify the calculations (12). The lack of consideration of correlations between ions can diminish accuracy in calculations of electrostatic potentials for systems at high ionic strength (13). Due to the assumption of a dielectric continuum, the electrostatic potentials predicted with the Poisson–Boltzmann theory may be inaccurate for zones near the first hydration layer. Electrostatic potentials predicted for regions near highly charged molecular surfaces may also be inaccurate due to the assumption of linear dielectric response. Nonetheless, the Poisson–Boltzmann theory can accurately predict electrostatic interactions at longer range (7). The extent of validity for such electrostatic potentials near molecular surfaces remains to be addressed more rigorously through experiments.Despite the need, experimental validation of computed electrostatic potentials is rather rare and methodologically limited for biological macromolecules. The validity of electrostatic models has been examined using pK_a data on titratable side-chain moieties (14–16), redox potentials of redox-active groups (17, 18), and electron–electron double resonance (19). Among them, pK_a data have been most commonly used for the validation, but even fundamentally incorrect electrostatic models can reproduce pK_a data (20). Electrostatic fields can be experimentally determined by vibrational spectroscopy, for example, for nitrile groups that are conjugated to cysteine thiol moieties of proteins (21, 22). However, the approaches utilizing vibrational spectroscopy or electron–electron double resonance provide only limited information about the extrinsically introduced probes, which may perturb native systems.In this paper, we present a unique and powerful method for de novo determination of near-surface electrostatic potentials for many protein residues, regardless of their side-chain types, and without using any chemical modifications. In this method, data of NMR paramagnetic relaxation enhancement (PRE) arising from analogous charged paramagnetic cosolutes are analyzed for ¹H nuclear magnetizations of proteins (Fig. 1). The PRE data reflect the electrostatic biases in spatial distributions of charged paramagnetic cosolutes and permit the determination of near-surface electrostatic potentials around proteins without using any structural information. The de novo determination of near-surface electrostatic potentials can greatly facilitate the examination of theoretical models for electrostatics of biological macromolecules.Open in a separate windowFig. 1.NMR PRE arising from cationic amino-methyl-PROXYL or anionic carboxy-PROXYL reflects their spatial distribution bias due to near-surface electrostatic potentials around a biological macromolecule.