Assessment of the Components of the Electrostatic Potential of Proteins in Solution: Comparing Experiment and Theory

Structural stability of Calmodulin-target peptide complex at different temperatures based on molecular dynamics simulation

Calmodulin (CaM) is a multifunctional protein commonly found in various eukaryotic cells that can bind Ca2+, making it highly valuable for research in agriculture, medicine, the environment, and other fields. Protein functionality is intricately linked to its structure. To understand how varying temperatures affect the structural integrity of CaM protein at the molecular level, the effect of temperature on the structural stability of CaM-peptide complex was investigated based on the molecular dynamics (MD) simulation. Some analyses including the root mean square deviation (RMSD) values, interaction energies, the decomposition of total energy of the system, the binding mechanism for Ca2+, and the secondary structure of CaM-peptide at different temperatures have been made in this work. The RMSD increased from 0.5277 nm (298 K) to 0.6949 nm (400 K), indicating a loss of structural stability. As temperature increases, the interaction energies between CaM-peptide and Ca2+ exhibit a decline, and the number of oxygen atoms in the 4 Å range around the CaM-peptide ion tends to decrease, with the average value of the number of oxygen atoms in the 4 Å range of CaM-peptide decreasing from 7.48039 (298 K) to 6.36614 (400 K) with Coulombic interactions playing a pivotal role in stabilizing Ca2+. This decline in hydrogen bonding is directly linked to a decrease in protein stability at higher temperatures, highlighting the thermal sensitivity of the protein's structural framework. The stable secondary structures, including the α-helix, are disrupted as temperatures increase, leading to the gradual unwinding of the α-helix and a loss of structural integrity. This work explores the molecular-level structural stability of CaM, enhancing our understanding of CaM protein and its potential applications.

Effects of Probe-Related Correlations on Local Electrostatic Potentials Around DNA

In this work, we perform a test of effectiveness and accuracy of using different approximations to interpret NMR paramagnetic relaxation enhancements experiment to measure local electrostatic potentials for DNA at ionic strengths from 0.138 to 0.938 M in KCl salt solution with PROXYL spin probes. Continuum Poisson-Boltzmann (PB) theory, multiscale Brownian dynamics, and all-atom molecular dynamics simulations are carried out to predict and interpret local potentials. Local potentials around DNA demonstrate strong salt dependence. Experimental results are in good agreement at 0.138 M ionic strength with continuum theory and simulation. Compared to experiment, the PB and multiscale simulation methods overestimate local potentials in magnitude at medium to high salt concentration. We find that the overestimate is mainly caused by ignoring the probe-probe and probe-ions correlations in the proximity of DNA. The probe-related correlations can be up to 0.4 kcal/mol in certain regions. Comparisons of the experiment and the calculations emphasize not only the importance of orientations of probes but also the probe-related correlations in determination of near-surface-zone potentials.

Determining the Role of Electrostatics in the Making and Breaking of the Caprin1-ATP Nanocondensate

We employ a multiscale computational approach to investigate the condensation process of the C-terminal low-complexity region of the Caprin1 protein as a function of increasing ATP concentration for three states: the initial mixed state, nanocondensate formation, and dissolution of the droplet as it reenters the mixed state. We show that upon condensation, ATP assembles via pi-pi interactions, resulting in the formation of a large cluster of stacked ATP molecules stabilized by sodium counterions. The surface of the ATP assembly interacts with the arginine-rich regions of the Caprin1 protein, particularly with its N-terminus, to promote the complete phase-separated droplet on a length scale of tens of nanometers. In order to understand droplet stability, we analyzed the near-surface electrostatic potential (NS-ESP) of Caprin1 and estimated the zeta potential of the Caprin1-ATP assemblies. We predict a positive NS-ESP at the Caprin1 surface for low ATP concentrations that defines the early mixed state, in excellent agreement with the NS-ESP obtained from NMR experiments using paramagnetic resonance enhancement. By contrast, the NS-ESP of Caprin1 at the surface of the nanocondensate at moderate levels of ATP is highly negative compared to that at the mixed state, and estimates of a large zeta potential outside the highly dense region of charge further explain the remarkable stability of this phase-separated droplet assembly. As ATP concentrations rise further, the strong electrostatic forces needed for nanocondensate stability are replaced by weaker Caprin1-ATP interactions that drive the re-entry into the mixed state that exhibits a much lower zeta potential.

NMR-Based Measurements of Site-Specific Electrostatic Potentials of Histone Tails in Nucleosome Core Particles

Electrostatics play a dominant role in guiding many biological processes. This is especially the case in the context of chromatin, where charge interactions modulate diverse activities such as DNA repair, transcription, replication, condensation, and phase separation. Using NMR experiments quantifying solvent paramagnetic relaxation enhancements of backbone amide and side chain methyl protons in the presence of paramagnetic cosolutes and focusing on the nucleosome core particle (NCP), we report near surface electrostatic potentials of tail residues of each of the four histone components of the NCP. These are all negative, despite sequences comprising a high density of positively charged amino acids, emphasizing the strong contribution of the negatively charged DNA with which the tails interact. Changes in electrostatic potentials of as much as 60 mV between isolated histone tails and tails in the context of the NCP are calculated. Notably, the tail potentials can vary significantly from each other, with enrichment in glycine residues correlating with less negative values, highlighting differences in the interactions with DNA.

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.

Direct measurements of biomolecular electrostatics through experiments

Biomolecular electrostatics has been a subject of computational investigations based on 3D structures. This situation is changing because emerging experimental tools allow us to quantitatively investigate biomolecular electrostatics without any use of structure information. Now, electrostatic potentials around biomolecules can directly be measured for many residues simultaneously by nuclear magnetic resonance (NMR) spectroscopy. This NMR method can be used to study electrostatic aspects of various processes, including macromolecular association and liquid-liquid phase separation. Applications to structurally flexible biomolecules such as intrinsically disordered proteins are particularly useful. The new tools also facilitate examination of theoretical models and methods for biomolecular electrostatics.

Extending the Experimentally Accessible Range of Spin Dipole-Dipole Spectral Densities for Protein-Cosolute Interactions by Temperature-Dependent Solvent Paramagnetic Relaxation Enhancement Measurements

Longitudinal (Γ1) and transverse (Γ2) solvent paramagnetic relaxation enhancement (sPRE) yields field-dependent information in the form of spectral densities that provides unique information related to cosolute-protein interactions and electrostatics. A typical protein sPRE data set can only sample a few points on the spectral density curve, J(ω), within a narrow frequency window (500 MHz to ∼1 GHz). However, complex interactions and dynamics of paramagnetic cosolutes around a protein make it difficult to directly interpret the few experimentally accessible points of J(ω). In this paper, we show that it is possible to significantly extend the experimentally accessible frequency range (corresponding to a range from ∼270 MHz to 1.8 GHz) by acquiring a series of sPRE experiments at different temperatures. This approach is based on the scaling property of J(ω) originally proposed by Melchior and Fries for small molecules. Here, we demonstrate that the same scaling property also holds for geometrically far more complex systems such as proteins. Using the extended spectral densities derived from the scaling property as the reference dataset, we demonstrate that our previous approach that makes use of a non-Lorentzian Ansatz spectral density function to fit only J(0) and one to two J(ω) points allows one to obtain accurate values for the concentration-normalized equilibrium average of the electron-proton interspin separation ⟨r-6⟩norm and the correlation time τC, which provide quantitative information on the energetics and timescale, respectively, of local cosolute-protein interactions. We also show that effective near-surface potentials, ϕENS, obtained from ⟨r-6⟩norm provide a reliable and quantitative measure of intermolecular interactions including electrostatics, while ϕENS values obtained from only Γ1 or Γ2 sPRE rates can have significant artifacts as a consequence of potential variations and changes in the diffusive properties of the cosolute around the protein surface. Finally, we discuss the experimental feasibility and limitations of extracting the high-frequency limit of J(ω) that is related to ⟨r-8⟩norm and report on the extremely local intermolecular potential.

Practical considerations for the measurement of near-surface electrostatics based on solvent paramagnetic relaxation enhancements

Electrostatic interactions can play important roles in regulating various biological processes. Quantifying surface electrostatics of biomolecules is, therefore, of significant interest. Recent advances in solution NMR spectroscopy have enabled site-specific measurements of de novo near-surface electrostatic potentials (ϕ_ENS) based on a comparison of solvent paramagnetic relaxation enhancements generated from differently charged paramagnetic co-solutes with similar structures. Although the NMR-derived near-surface electrostatic potentials have been shown to agree with theoretical calculations in the context of folded proteins and nucleic acids, such benchmark comparisons may not always be possible, particularly in cases where high-resolution structural models are lacking, such as in the study of intrinsically disordered proteins. Cross-validation of ϕ_ENS potentials can be achieved by comparing values obtained using three pairs of paramagnetic co-solutes, each with a different net charge. Notably we have found cases where agreement of ϕ_ENS potentials between the three pairs is poor and herein we investigate the source of this discrepancy in some detail. We show that for the systems considered here ϕ_ENS potentials obtained from cationic and anionic co-solutes are accurate and that the use of paramagnetic co-solutes with different structures can be a viable option for validation, although the optimal choice of paramagnetic compounds depends on the system of interest.

Surface electrostatics dictate RNA-binding protein CAPRIN1 condensate concentration and hydrodynamic properties

Biomolecular condensates concentrate proteins, nucleic acids, and small molecules and play an essential role in many biological processes. Their formation is tuned by a balance between energetically favorable and unfavorable contacts, with charge-charge interactions playing a central role in some systems. The positively charged intrinsically disordered carboxy-terminal region of the RNA-binding protein CAPRIN1 is one such example, phase separating upon addition of negatively charged ATP or high concentrations of sodium chloride (NaCl). Using solution NMR spectroscopy, we measured residue-specific near-surface electrostatic potentials (ϕENS) of CAPRIN1 along its NaCl-induced phase separation trajectory to compare with those obtained using ATP. In both cases, electrostatic shielding decreases ϕENS values, yet surface potentials of CAPRIN1 in the two condensates can be different, depending on the amount of NaCl or ATP added. Our results establish that even small differences in ϕENS can significantly affect the level of protein enrichment and the mechanical properties of the condensed phase, leading, potentially, to the regulation of biological processes.

Arbitrary-Shape Dielectric Particles Interacting in the Linearized Poisson-Boltzmann Framework: An Analytical Treatment

This work considers the interaction of two dielectric particles of arbitrary shape immersed into a solvent containing a dissociated salt and assuming that the linearized Poisson-Boltzmann equation holds. We establish a new general spherical re-expansion result which relies neither on the conventional condition that particle radii are small with respect to the characteristic separating distance between particles nor on any symmetry assumption. This is instrumental in calculating suitable expansion coefficients for the electrostatic potential inside and outside the objects and in constructing small-parameter asymptotic expansions for the potential, the total electrostatic energy, and forces in ascending order of Debye screening. This generalizes a recent result for the case of dielectric spheres to particles of arbitrary shape and builds for the first time a rigorous (exact at the Debye-Hückel level) analytical theory of electrostatic interactions of such particles at arbitrary distances. Numerical tests confirm that the proposed theory may also become especially useful in developing a new class of grid-free, fast, highly scalable solvers.

Measuring Local Electrostatic Potentials Around Nucleic Acids by Paramagnetic NMR Spectroscopy

Electrostatic potentials around macromolecules in the presence of mobile charges are difficult to assess especially for highly charged systems. Here, we report measurements of local electrostatic potentials around DNA by paramagnetic NMR. Through quantitative analysis of NMR paramagnetic relaxation enhancement arising from positively charged or neutral paramagnetic cosolutes, we were able to determine local electrostatic potentials around 1H nuclei at >100 sites in major and minor grooves of 13C,15N-labeled 15-bp DNA at 100 mM NaCl. Our experimental electrostatic potential data directly confirmed the Coulombic end effects of DNA. The effective near-surface electrostatic potentials from the NMR data were in good agreement with the theoretical predictions with the Poisson-Boltzmann equation. This NMR method allows for unprecedented experimental investigations into the electrostatic properties of nucleic acids.

Diffusion NMR-based comparison of electrostatic influences of DNA on various monovalent cations

Counterions are important constituents for the structure and function of nucleic acids. Using 7Li and 133Cs nuclear magnetic resonance (NMR) spectroscopy, we investigated how ionic radii affect the behavior of counterions around DNA through diffusion measurements of Li+ and Cs+ ions around a 15-bp DNA duplex. Together with our previous data on 23Na+ and 15NH4+ ions around the same DNA under the same conditions, we were able to compare the dynamics of four different monovalent ions around DNA. From the apparent diffusion coefficients at varied concentrations of DNA, we determined the diffusion coefficients of these cations inside and outside the ion atmosphere around DNA (Db and Df, respectively). We also analyzed ionic competition with K+ ions for the ion atmosphere and assessed the relative affinities of these cations for DNA. Interestingly, all cations (i.e., Li+, Na+, NH4+, and Cs+) analyzed by diffusion NMR spectroscopy exhibited nearly identical Db/Df ratios despite the differences in their ionic radii, relative affinities, and diffusion coefficients. These results, along with the theoretical relationship between diffusion and entropy, suggest that the entropy change due to the release of counterions from the ion atmosphere around DNA is also similar regardless of the monovalent ion types. These findings and the experimental diffusion data on the monovalent ions are useful for examination of computational models for electrostatic interactions or ion solvation.