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.