De novo determination of near-surface electrostatic potentials by NMR

Abstract

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.

Protein Electrostatics Investigated through Paramagnetic NMR for Nonpolar Groups

“…To ensure the same concentration for the paramagnetic compounds, the PROXYL derivatives were added at the final stage in the sample preparation. At this stage, a solution of 13 C, 15 N-ubiquitin in the aforementioned buffer was mixed with a stock solution of the PROXYL-derivative in the same buffer, for which the PROXYL concentration was measured, as described . Each NMR sample was sealed in a Norell 5 mm NMR tube.…”

“…Effective near-surface electrostatic potentials ϕ ENS for individual 1 H nuclei were determined from Γ 2,+ and Γ 2,– rates as follows: where Γ 2,+ and Γ 2,– are the rates for 1 H transverse PRE arising from the aminomethyl-PROXYL (cationic) and carboxy-PROXYL (anionic), respectively, k B is the Boltzmann constant, T is the temperature, and e is the elementary charge. 2 e in eq is the difference between the charges of the cationic and anionic PROXYL derivatives.…”

“…The electrostatic potential (ϕ ENS ) determined from the PRE rates represents an effective electrostatic potential within this zone, which is referred to as the effective near-surface (ENS) zone (Figure ). Previously, we showed that each ϕ ENS potential approximates to the average of electrostatic potentials in a zone from which the paramagnetic cosolutes make 68% contribution to ∑ r –6 . Importantly, ϕ ENS data can directly be predicted using electrostatic potentials computed from a 3-D structure (see below).…”

“…The ϕ ENS -based method is relatively easy in sample preparation, experimental procedures, and data analysis and does not require any protein modification or mutation. Unlike the p K a -based method, the comparison of ϕ ENS data with theoretical predictions is straightforward …”

“…In our current work, we examine the ϕ ENS methodology for side-chain methyl 1 H and backbone 1 H α nuclei. Previously, the ϕ ENS -based method was demonstrated only for backbone 1 H N nuclei . In general, side-chain methyl 1 H and backbone 1 H α nuclei are also convenient for protein NMR spectroscopy .…”