De novo determination of near-surface electrostatic potentials by NMR Binhan Yua, Channing C. Pletkaa, B. Montgomery Pettitta, and Junji Iwaharaa,1 aDepartment of Biochemistry and Molecular Biology, Sealy Center for Structural Biology and Molecular Biophysics, University of Texas Medical Branch, Galveston, TX 77555 Edited by Lewis E. Kay, University of Toronto, Toronto, Ontario, Canada, and approved May 2, 2021 (received for review March 8, 2021) Electrostatic potentials computed from three-dimensional struc- predicted with the Poisson–Boltzmann theory may be inaccurate tures of biomolecules by solving the Poisson–Boltzmann equation for zones near the first hydration layer. Electrostatic potentials are widely used in molecular biophysics, structural biology, and predicted for regions near highly charged molecular surfaces may medicinal chemistry. Despite the approximate nature of the also be inaccurate due to the assumption of linear dielectric re- Poisson–Boltzmann theory, validation of the computed electro- sponse. Nonetheless, the Poisson–Boltzmann theory can accurately static potentials around biological macromolecules is rare and predict electrostatic interactions at longer range (7). The extent of methodologically limited. Here, we present a unique and powerful validity for such electrostatic potentials near molecular surfaces NMR method that allows for straightforward and extensive com- remains to be addressed more rigorously through experiments. parison with electrostatic models for biomolecules and their com- Despite the need, experimental validation of computed elec- plexes. This method utilizes paramagnetic relaxation enhancement trostatic potentials is rather rare and methodologically limited arising from analogous cationic and anionic cosolutes whose spatial for biological macromolecules. The validity of electrostatic models distributions around biological macromolecules reflect electrostatic has been examined using pKa data on titratable side-chain moieties potentials. We demonstrate that this NMR method enables de novo (14–16), redox potentials of redox-active groups (17, 18), and determination of near-surface electrostatic potentials for individual electron–electron double resonance (19). Among them, pKa data protein residues without using any structural information. We ap- have been most commonly used for the validation, but even fun- plied the method to ubiquitin and the Antp homeodomain–DNA damentally incorrect electrostatic models can reproduce pKa data complex. The experimental data agreed well with predictions from (20). Electrostatic fields can be experimentally determined by vi- the Poisson–Boltzmann theory. Thus, our experimental results BIOPHYSICS AND COMPUTATIONAL BIOLOGY brational spectroscopy, for example, for nitrile groups that are con- clearly support the validity of the theory for these systems. How- jugated to cysteine thiol moieties of proteins (21, 22). However, the ever, our experimental study also illuminates certain weaknesses of approaches utilizing vibrational spectroscopy or electron–electron the Poisson–Boltzmann theory. For example, we found that the the- ory predicts stronger dependence of near-surface electrostatic po- double resonance provide only limited information about the ex- tentials on ionic strength than observed in the experiments. Our trinsically introduced probes, which may perturb native systems. data also suggest that conformational flexibility or structural uncer- In this paper, we present a unique and powerful method for de tainties may cause large errors in theoretical predictions of electro- novo determination of near-surface electrostatic potentials for static potentials, particularly for highly charged systems. This NMR-based method permits extensive assessment of near-surface Significance electrostatic potentials for various regions around biological macro- molecules and thereby may facilitate improvement of the computa- Electrostatic potentials are important information for our un- tional approaches for electrostatic potentials. derstanding of biomolecular functions as well as for protein engineering and drug design. Typically, electrostatic potentials electrostatics | nuclear magnetic resonance | proteins | ions | DNA around biomolecules are computed from three-dimensional structures. However, the theory behind this computation is ue to the fundamental importance of electrostatic interac- approximate with some limitations. Validation of the electro- Dtions in chemistry and biology, electrostatic potentials are static theory through experiments is therefore essential yet invaluable information for the understanding of molecular rec- remains inadequate. This paper presents a unique spectroscopic ognition, enzymatic catalysis, and other functions of proteins and method to experimentally determine electrostatic potentials near nucleic acids (1–4). Quantification of electrostatics is also im- the molecular surfaces without using any structural information. portant for successful protein engineering (5) and structure- This method allows for examination of theoretical electrostatic based drug design (6). Computational approaches based on the potentials for many different regions of biomolecules. Structure- Poisson–Boltzmann theory are commonly used to calculate elec- independent determination of electrostatic potentials for various trostatic potentials from three-dimensional (3D) molecular struc- biomolecular systems may lead to improvement of theoretical models, which would ultimately have broad impacts on basic tures (1, 7). Owing to available software such as Adaptive Poisson- research and pharmaceutical development. Boltzmann Solver (APBS) (8, 9) and DelPhi (10, 11), computation of the electrostatic potentials around biomolecules has gained Author contributions: J.I. designed research; B.Y. and C.C.P. performed research; B.Y. and widespread popularity in the fields of molecular biophysics, struc- J.I. analyzed data; B.M.P. provided guidance on electrostatic theory; and B.Y. and J.I. tural biology, and medicinal chemistry. wrote the paper. However, the computed electrostatic potentials may not nec- The authors declare no competing interest. essarily be accurate even if the 3D structures are precisely and This article is a PNAS Direct Submission. accurately determined. Importantly, the Poisson–Boltzmann theory This open access article is distributed under Creative Commons Attribution-NonCommercial- is approximate with known limitations. The electrostatic models NoDerivatives License 4.0 (CC BY-NC-ND). based on this theory are valid under assumptions, which simplify See online for related content such as Commentaries. the calculations (12). The lack of consideration of correlations 1To whom correspondence may be addressed. Email: [email protected]. between ions can diminish accuracy in calculations of electrostatic This article contains supporting information online at https://www.pnas.org/lookup/suppl/ potentials for systems at high ionic strength (13). Due to the as- doi:10.1073/pnas.2104020118/-/DCSupplemental. sumption of a dielectric continuum, the electrostatic potentials Published June 14, 2021. PNAS 2021 Vol. 118 No. 25 e2104020118 https://doi.org/10.1073/pnas.2104020118 | 1of7 Downloaded by guest on September 29, 2021 1 many protein residues, regardless of their side-chain types, and with respect to the H nucleus; kB is the Boltzmann constant; T is without using any chemical modifications. In this method, data of temperature; and ξ is a parameter reflecting other spin proper- NMR paramagnetic relaxation enhancement (PRE) arising from ties such as the gyromagnetic ratios. More details about Eq. 1 analogous charged paramagnetic cosolutes are analyzed for 1H and the relevant parameters are provided in SI Appendix. The nuclear magnetizations of proteins (Fig. 1). The PRE data reflect integral in Eq. 1 is conveniently discretized on a 3D lattice grid the electrostatic biases in spatial distributions of charged para- surrounding the macromolecule: magnetic cosolutes and permit the determination of near-surface U electrostatic potentials around proteins without using any struc- Γ = ξc τ ∑vr−6 [ − i ] [2] 2 P c i exp k T , tural information. The de novo determination of near-surface i B electrostatic potentials can greatly facilitate the examination of theoretical models for electrostatics of biological macromolecules. where i is the index of a grid point, and v is the volume of the voxel each grid point represents. Eq. 2 is similar to the empirical Results equation used for the so-called Otting–LeMaster approach −6 De Novo Determination of Near-Surface Electrostatic Potentials. To (24–26) but differs in that each ri term involves a Boltzmann determine the near-surface electrostatic potentials, we used two de- factor representing the bias in the spatial distribution of the coso- rivatives of 2,2,5,5-tetramethylpyrrolidine-N-oxyl nitroxide (PROXYL): lute molecule due to the effective potential Ui. When comparing namely, amino-methyl-PROXYL and carboxy-PROXYL (Fig. 1). PREs arising from the cationic and anionic PROXYL derivatives These paramagnetic compounds are analogous but differ in at the same concentration, the ratio of Γ2 rates will be as follows: charge at neutral pH: amino-methyl-PROXYL is cationic (+1e) − e whereas carboxy-PROXYL is anionic ( 1 ). For PRE arising from U U −6 +,i −6 −,i paramagnetic cosolute molecules, the PRE rate for a transverse Γ2,+ Γ2,− = ∑ri exp[ − ] ∑ri exp[ − ], [3] 1 / kBT / kBT Hmagnetization(Γ2)isgivenasfollows(23): i i