Electronic Polarization is Essential for the Stabilization and Dynamics of Buried Ion Pairs in Staphylococcal Nuclease Mutants

Abstract

Buried charged residues play important roles in the modulation of protein stabilities, conformational dynamics and make crucial contributions to protein functions. Considering the generally non-polar nature of protein interior, a key question concerns the contribution of electronic polarization to the stabilization and properties of buried charges. We answer this question by conducting free energy simulations using the latest polarizable CHARMM force field based on Drude oscillators for a series of Staphylococcal Nuclease mutants that involve a buried Glu-Lys pair in different titration states and orientations. While a non-polarizable model suggests that the ionized form of the buried Glu-Lys pair is more than 40 kcal/mol less stable than the charge-neutral form, the two titration states are comparable in stability when electronic polarization is included explicitly, a result better reconcilable with available experimental data. Analysis of free energy components suggests that additional stabilization of the ionized Glu-Lys pair has contributions from both the enhanced salt-bridge strength and stronger interaction between the ion-pair and surrounding protein residues and penetrated water. Despite the stronger direct interaction between Glu and Lys, the ion-pair exhibits considerably larger and faster structural fluctuations when polarization is included, due to compensation of interactions in the cavity. Collectively, observations from this work provide compelling evidence that electronic polarization is essential to the stability, hydration, dynamics and therefore function of buried charges in proteins. Therefore, our study advocates for the explicit consideration of electronic polarization for mechanistic and engineering studies that implicate buried charged residues, such as enzymes and ion transporters.

Graphical Abstract

1. Introduction

It has been long established that proteins feature a considerable number of buried charges in their interior.^1,2 For example, a survey and continuum electrostatic analysis suggested that there are approximately 4 charged residues buried per 100 amino acids in an average protein.³ Since it is energetically demanding to bury charges in the generally non-polar protein interior, the fact that they emerge in naturally evolved proteins suggests that these buried charges play important biological functions. Indeed, buried charges are found to participate in acid-base catalysis⁴ and/or to stabilize high-energy intermediates in enzymes,⁵ to mediate the translocation of protons^6–8 and metal ions⁹ in transporters, and to facilitate conformational transitions in ion channels¹⁰ and biomolecular motors¹¹ (Fig. 1). To understand the mechanism of these systems so as to ultimately engineer novel enzymes and biomolecular machines, it is therefore important to elucidate how buried charges are stabilized and how their structural and dynamic properties encode function.

Figure 1:

Buried charges and ion-pairs play important roles in protein functions, such as (a) participating in acid-base catalysis (ATP hydrolysis in myosin), (b-c) mediating and gating long-range proton transfers in ion transporters (cytochrome c oxidase and complex I) and (d) facilitating conformational rearrangements in biomolecular motors (F₁-ATPase). In (a-b), nearby water molecules resolved in the crystal structures are shown as spheres; panels c and d are created based on data in Refs. 24 and 11, respectively. Properties of buried charges essential to their function include the ionization state, local hydration level and structural flexibility. For example, dynamics of the ion-pairs that involve (b) R481 in cytochrome c oxidase and (c) K204/E123 in complex I in response to local hydration change have been proposed to gate proton translocations,^18,24 and rearrangements of salt-bridge interactions along the “ionic track” between the γ and β subunits in F₁-ATPase facilitate the rotation of the γ subunit.¹¹ Considering the generally less polar environment of protein interior, a key question regards the importance of electronic polarization to key properties of buried ion-pairs.

To minimize the energy penalty associated with burying charges in the protein interior, buried charged residues often exist in the form of ion-pairs,^1,12,13 which are further stabilized by additional hydrogen-bonding interactions with nearby protein motifs^14,15 and water molecules that penetrate into protein cavities.^16–21 In addition to stabilization, an equally essential aspect of buried charged residues concerns their dynamics. For example, buried ion-pairs have been proposed to mediate long-range proton transfers in a number of bioenergetics systems, such as cytochrome c oxidase^7,19,22 (Fig. 1b), complex I^23,24 (Fig. 1c) and a membrane-bound hydrogenase.²⁵ To play such roles, ion-pairs need to exhibit considerable structural flexibility, as intact salt-bridges are not amenable to accept an additional proton.²⁶ In fact, modulation of conformational dynamics of buried ion-pairs through changes in local hydration level or ion occupancy has emerged as a general mechanism of gating for ion transport.⁸ In other examples, extensive reorganizations of ion-pair interaction networks is required to facilitate large-scale conformational transitions in the gating transition of ion channels¹⁰ or power stroke of molecular motors¹¹ (Fig. 1d).

While experimental techniques such as X-ray crystallography^27,28, Nuclear Magnetic Resonance (NMR)²⁹ and infrared spectroscopies³⁰ are able to provide structural characterizations of buried charges in proteins, it is generally more challenging to reveal the dynamical properties of these important residues with atomic level of details. Mutagenesis and thermodynamic measurements can be used to probe factors that contribute to the stabilization of buried charges,⁴ although the molecular level interpretation of thermodynamic data is not always straightforward due to unanticipated structural variations upon mutations; moreover, the relative importance of protein residues and penetrated water is often difficult to disentangle because internal water molecules are not easy to probe directly in experiments.^31,32 Therefore, accurate computational studies hold great promise in providing a clear understanding of molecular factors that dictate the stability of buried charges in proteins and how their structural and dynamics properties relate to function.

To accurately treat the stability and dynamics of buried charges in protein interior, we expect that an important technical issue concerns the role of electronic polarization.^33–35 In the popular molecular mechanical (MM) force fields such as CHARMM,^36,37 AMBER³⁸ and OPLS,³⁹ electronic polarization is not included explicitly for computational efficiency. Instead, the effect of electronic polarization is captured implicitly through the parameterization procedure, such as by systematically scaling up the interaction energy between a protein group and water molecule computed with quantum chemistry methods in the gas phase,³⁶ or fitting to experimental solvation free energies.⁴⁰ While this mean-field-like model appears to work empirically for describing protein structure and dynamics, it clearly has limited transferability, especially for buried charges in a poorly hydrated environment. For example, as discussed by Stuchebrukhov and co-workers,^41,42 since the dipole moment of TIP3P water is already reduced relative to the liquid phase value to empirically describe screening in the condensed phase, the standard force field parameterization strategy may describe the properties of solvent-exposed residues reasonably well, yet interactions involving buried charges likely experience considerable errors, which may lead to over-stabilized ion-pairs in protein interiors and therefore artificially damped functional dynamics.⁴³ Indeed, even for solvent-accessible salt-bridges, non-polarizable force fields were often found to overestimate the structural stability.^44–48

In recent years, substantial progress has been made in polarizable force fields in the area of biomolecular applications,⁴⁹ and among those, the most broadly tested models are the CHARMM Drude oscillator model³³ and the AMOEBA model.³⁵ These force fields have been successfully applied to highlight the importance of explicitly including electronic polarization in a number of problems, such as the binding selectivity of metal ions to proteins,^50,51 cooperative folding of protein secondary structure elements,^52,53 structural ensemble of intrinsically disordered peptides⁵⁴ and the transport mechanism of ions through ion-channels^55,56 and across lipid bilayers.⁵⁷ Polarizable force fields have also been shown to more accurately represent electric fields in enzyme active sites⁵⁸ and therefore advocated in enzyme design applications.⁵⁹ These recent advances have set the stage for explicitly probing the importance of electronic polarization to the description of buried charges in proteins, especially concerning molecular properties such as local hydration level and factors that dictate their structural dynamics. On the other hand, we note that due in part to the higher computational cost, applications of polarizable force fields to complex biomolecules are far from being routine, thus there remains the need to carefully validate polarizable models against diverse experimental observables.^49,60

In this context, a model system that we chose to focus on here is a set of mutants of Staphylococcal Nuclease (SNase), which have been thoroughly characterized experimentally for both structure and thermodynamic stability by the Garcia-Moreno group.^61,62 The reference system in this context is the Δ+PHS background, which is a highly stable variant of SNase that involves a loop (44–49) truncation and two additional mutations, G50F and V51N.⁶³ As shown in Fig. 2, these mutants (V23E/L36K, referred to as “EK”, and V23K/L36E, referred to as “KE”) incorporate a pair of titratable residues into the protein core. Their crystal structures do not exhibit any major perturbation relative to the Δ+PHS background, suggesting that Glu and Lys are sufficiently stabilized via local interactions with both protein mainchain and sidechain groups, as well as water molecules that penetrate into the cavity, although the degree of stabilization differs between the two variants in solution⁶² (vide infra). Therefore, the microenvironment of the buried Glu-Lys pair resembles those of functional ion-pairs in more complex systems in terms of limited number of local polar interactions (Fig. 1); such representative structural features, their modest size and availability of extensive experimental data make these SNase mutants ideal systems for probing the impact of electronic polarization on the description of buried charges in proteins as well as for quantitatively testing polarizable force fields.

Figure 2:

Structural features for the cavity of interest in several SNase variants: (a)Δ+PHS background (3BDC⁶¹); (b) V23E/L36K in the Δ+PHS background (3NHH,⁶¹ referred to as EK), (c) V23K/L36E in the Δ+PHS background (6AMF,⁶² referred to as KE). Crystallographic water molecules are shown as orange spheres. Two residues, Gly20 and Thr62, which can form hydrogen bonds with either Lys/Glu or crystallographic water are also shown in purple. Hydrogen bonds are represented as dashed lines. The protein structures are represented as new cartoon. β-strands near the cavity are in tube representation for better visualization.

Several questions concerning the buried Glu-Lys pair are of particular interest and merit a thorough analysis using a polarizable force field. First, there remains ambiguity in the titration states of Glu and Lys in the buried ion-pair. Double mutant cycle⁶² and solution NMR studies⁶¹ suggested that the buried Glu and Lys are in their charge-neutral states in KE but ionized in the EK mutant (see additional discussions in Sect.3.5). However, our recent free energy simulations⁶⁴ using the CHARMM36m force field,³⁷ a popular non-polarizable MM model, strongly argued that the Glu and Lys are charge neutral in both EK and KE variants. Specifically, when the buried Glu and Lys are both charge neutral (EK_neutral/KE_neutral), the free energy results were consistent with experimental findings in terms of the relative stabilities of EK, KE and the Δ+PHS background; when both residues are ionized, EK and KE variants were computed to be highly unstable (>55 kcal/mol) relative to the Δ+PHS background, in glaring contrast to the experimental value of ~9–11 kcal/mol. Analysis of free energy components suggested that, with the CHARMM36m model, the ionized Glu-Lys experienced substantially weaker interactions in the protein cavity compared to bulk solution,⁶⁴ thus it is of great interest to examine whether including electronic polarization can better stabilize the ionized ion-pair and therefore potentially better reconcile with experimental observations; moreover, if the Glu and Lys residues are indeed ionized under physiological condition, it is important to elucidate residues and physical interactions that stabilize the pair of charges in the rather non-polar protein cavity. Second, in the CHARMM36m simulations, a significant number of water molecules (10–15) were observed⁶⁴ to penetrate into the cavity that holds the Glu-Lys pair when both residues are ionized, while crystal structures^61,62 resolved only a small number (≤3) of water molecules in the cavity. Although the difference might be due to the fact that the crystal structures were resolved under cryogenic conditions, it is possible that including electronic polarization explicitly leads to different levels of cavity hydration, as observed in recent analysis of pore hydration in ion channels using different force field models including AMOEBA.^65,66

Motivated by these considerations, we perform extensive (~500 ns) equilibrium molecular dynamics simulations and free energy calculations for the SNase mutants with the 2019 CHARMM-Drude force field model,^33,67 which includes electronic polarization explicitly. Remarkably, while the results for EK_neutral/KE_neutral are consistent with the CHARMM36m values, the ionized form of the Glu-Lys pair is substantially stabilized by the Drude model, to the degree that it is almost comparable in stability as the charge-neutral form. Somewhat unexpectedly, the level of cavity hydration from the Drude simulations is comparable to CHARMM36m simulations, thus the dramatic stabilization of the ionized form of the Glu-Lys pair is provided to a notable degree by the nearby protein residues, whose roles and polarization are analyzed explicitly. The analysis also finds that another major contribution to the stabilization of ionized Glu-Lys pair is the stronger salt-bridge interaction between these residues when electronic polarization is included; however, due to better compensation of interactions with the local environment, the ionized Glu-Lys pair is observed to undergo substantially faster and higher magnitudes of fluctuations in the Drude simulations as compared to CHARMM36m. Therefore, the current analysis strongly advocates for explicitly considering electronic polarization when dissecting the ionization, stabilization, dynamics and therefore function of buried titratable residues in proteins.

2. Computational Methods

2.1. Simulation set-up

Crystal structures for the highly stable Δ+PHS variant of SNase, its EK and KE mutants (with PDB ID: 3BDC,⁶⁸ 3NHH,⁶¹ 6AMF,⁶² respectively) are used as starting structures, including the Ca²⁺ ion, which is observed to coordinate to several surface acidic residues (Asp21, Asp40 and Glu43) and the main chain carbonyl of Thr41. Missing residues 1–6 and 142–149 are modeled with CHARMM-GUI.⁶⁹ For the EK and KE variants, simulations are carried out with the introduced Glu-Lys residues either both ionized or charge neutral; the simulations are labeled as EK/KE and EK_neutral/KE_neutral, respectively.

The systems are assembled using the CHARMM-GUI solution builder.⁶⁹ For each system, the initial structure is solvated in a rectangular TIP3Pm^70,71 water box with a 10.0 Å of edge distance under periodic boundary conditions. 150 mM KCl ions are randomly placed to neutralize the system and mimic the physiological condition. The initial simulation box size is around 76 × 76 × 76 ų. 250 ps equilibration runs at room temperature are performed in CHARMM with the CHARMM36m force field, and the last frames of the equilibration runs are put into CHARMM-GUI Drude Prepper⁷² to generate coordinates for Drude simulations. The SWM4-NDP model⁷³ is used for water. Equilibration and production runs are carried out using OpenMM7.3.1⁷⁴ with the polarizable 2019g Drude force field;⁶⁷ in the Drude force field, electronic polarization is represented explicitly with the charge-on-a-spring model for non-hydrogen atoms,⁷⁵ and bonded and non-bonded parameters were tuned based on systematic comparison to both gas phase quantum calculations and solution experimental data.^33,67 A dual-Langevin thermostat extended Lagrangian approach⁷⁶ is used for propagating and integrating the equations of motion, where the temperature is maintained at 303.15 K for real atoms and 1 K for Drude oscillators with thermostat friction coefficients of 5 and 20 ps⁻¹, respectively; it was demonstrated in previous studies^76–78 that the extended Lagrangian approach provides an efficient and accurate alternative to the iterative solution of the coupled polarization equations. The Drude hardwall constraint is set to 0.2 Å. The time step is set to be 1 fs in all simulations.

2.2. Free energy simulations and analysis of cavity dielectric constant

Since the current work focuses on the role of electronic polarization in describing buried ion-pair properties, to compute the relative thermostability of a series of related proteins (EK, KE and the Δ+PHS background), we follow the same charging free energy based thermodynamic cycles⁷⁹ used in our recent work.⁶⁴ Briefly, the partial charges on both real atoms and Drude particles on the sidechains of interest (e.g., Glu23 and Lys36 in EK) are scaled by a factor of λ in a series of independent simulations at λ=0, 0.3, 0.7 and 1.0; a smaller number of λ windows are used here compared to our previous work using CHARMM36m due to the higher computational cost of the Drude simulation. Individual λ windows are sampled for 150 ns, which are generally sufficient for equilibrating the protein structure and cavity hydration level for end states (λ = 0, 1.0); as commented in previous work,⁶⁴ intermediate λ windows might be challenging to converge due to slow water penetration, although the impact here is likely limited considering the largely linear behaviors observed for the computed free energy derivatives (Fig. S13, also see Sect.3.5.3). Trajectories from different λ windows are then used to compute the charging free energy, ΔG_Q (summarized in the Supporting Information), for the sidechains of interest in the protein environment in the framework of thermodynamic integration.⁸⁰ As discussed in Ref. 64, the differences in the charging free energies in different proteins are expected to be good approximations to the relative thermostabilities, provided that proper unfolded references are used. The unfolded states are approximated with individual blocked amino acids in solution, thus the underlying assumption is that the unfolded states do not exhibit any significant residual structure, at least not in any sequence-dependent manner for the proteins of interest. For EK_neutral and KE_neutral, the free energy contribution due to the change of titration state for Glu and Lys in solution is included.⁶⁴

In the current single-topology based thermodynamic integration framework, the free energy derivative takes the specific form,

$${\langle \partial U^{\mathit{\text{elec}}}(\lambda )/\partial \lambda \rangle }_{\lambda }={\langle \frac{\partial }{\partial \lambda }\left({\lambda }^2{U}_{\mathit{\text{intra}}}^{\mathit{\text{elec}}}+\lambda U_{\mathit{\text{inter}}}^{\mathit{\text{elec}}}\right)\rangle }_{\lambda }={\langle 2\lambda U_{\mathit{\text{intra}}}^{\mathit{\text{elec}}}+U_{\mathit{\text{inter}}}^{\mathit{\text{elec}}}\rangle }_{\lambda },$$ (1)

since all partial charges in the sidechains of interest are scaled by λ in the λ window. Here, $U_{\mathit{\text{intra}}}^{\mathit{\text{elec}}}$ represents unscaled electrostatic interaction energy (including Drude particles) within the sidechains of interest (residues 23 and 36) and $U_{\mathit{\text{inter}}}^{\mathit{\text{elec}}}$ represents unscaled electrostatic interaction energy between the sidechains of interest and the protein/solvent environment. Although in principle a polarizable force field is non-additive, the Drude model is formally written in terms of pair-wise interactions involving real and Drude particles. Therefore, the free energy derivatives can be formally decomposed into contributions from different groups, such as water molecules and protein groups (see Sect.3.4), although the limitation of such decomposition should be born in mind during discussion.

Similar to the previous study,⁶⁴ we estimate the local dielectric constant of cavity water using the Kirkwood-Fröhlich model.^81,82 Since the radius of the cavity, r₁, is much smaller than the effective radius of the protein, a simplified equation is used:¹⁷

$$G=\frac{\langle \Delta M_p^2\rangle }{k_{B}T{r}_1^3}=\frac{\left({ϵ}_1-1\right)\left(1+{ϵ}_2\right)}{{ϵ}_1+2{ϵ}_2},$$ (2)

where G is the Kirkwood G factor, $\langle \Delta M_p^2\rangle$ is the fluctuation of the collective dipole moment of water molecules in the cavity computed from the Drude trajectories, k_B is the Boltzmann constant, T is the temperature. The cavity radius, r₁, is taken to be 6 Å as in Ref. 64; ϵ₂ is the dielectric constant for the surrounding protein and taken to be 10 considering the proximity of the cavity to the bulk solvent; our previous study found that using a value of 20 for ϵ₂ had only a modest effect. The value of ϵ₁ is then computed based on Eq. 2.

3. Results and Discussion

In this section, we compare the Drude and CHARMM36m simulation results to elucidate the impact of explicitly including electronic polarization on the description of buried Glu-Lys pair in different titration states and orientations. We start by describing structural and dynamic properties of the Glu-Lys pair, then move on to the analysis of hydration level of the cavity that holds the pair; this is followed by the presentation of free energy results that evaluate the thermodynamic stability of the Glu-Lys pair in different titration states and orientations, as well as key interactions that provide additional stabilization when polarization is included.

3.1. Inclusion of electronic polarization leads to more dynamical Glu-Lys pairs

As shown in the Supporting Information (Figs. S1–S3), the Drude simulations generally lead to similar structural properties as CHARMM36m, especially for the Δ+PHS background and when the buried Glu and Lys residues are charge neutral. With ionized Glu-Lys pairs, EK and KE in Drude simulations exhibit RMSD values that reach beyond 3 Å when simulated longer than 300 ns, slightly higher than the values ~ 2 Å observed in CHARMM36m simulations. Distributions of radius of gyration (R_g) indicate that the structures are slightly more expanded (difference of 0.2–0.4 Å in R_g) for EK and KE in Drude simulations (Fig. S4).

The Glu-Lys pair exhibits considerably higher fluctuations in the Drude simulations than with CHARMM36m (Fig. 3a–b). The centroid distances and angular orientations (θ, see Fig. S5 for definition) characterize the ion-pair geometry and the electrostatic strength. Most favorable salt-bridge interactions feature centroid distances of 3.5 ± 0.3 Å and θ values of 104 ± 27 °, and in general salt-bridges with centroid distances shorter than 4 Å are considered as stable.¹⁴ In the Drude simulations, the centroid distance between Glu and Lys varies between ~3 and ~6 Å for both EK and KE, while they can still form stable salt-bridge interactions most of the time according to the aforementioned criteria.¹⁴ Larger fluctuations in centroid distance are observed in both EK_neutral and KE_neutral, where the distance ranges from ~4 to ~8 Å. These behaviors contrast with the observations from CHARMM36m simulations,⁶⁴ which showed generally short centroid distances comparable to the value in the corresponding crystal structure, with occasional deviations to larger values (Fig. 3a–b); the only exception was KE_neutral, which showed consistently larger fluctuations in the centroid distances (Fig. S5). Comparison of time traces of the centroid distance between Glu and Lys in Drude and CHARMM36m simulations (Figs. S5–S6) clearly highlights the differences in the lifetime of salt-bridge interactions; while salt-bridge interactions constantly break and form at the nanosecond time scale in Drude simulations, they can persist for more than hundreds of nanoseconds with CHARMM36m.

Figure 3:

Structural properties of the Glu-Lys pair in EK and KE variants from MD simulations. The distributions of the centroid distances between Glu and Lys in (a) EK and (b) KE from CHARMM36m and Drude simulations. The centroid distance is the distance between the center of geometry of atoms CD and OE1/2 in Glu and atom NZ in Lys. Compared to CHARMM36m results, the Glu-Lys pair exhibits considerably higher fluctuations in Drude simulations. Representative snapshots from Drude simulations that illustrate distinct ion-pair structures with (c) a favorable and (d) a broken salt-bridge in EK and (e) a favorable and (f) a broken salt-bridge in KE. Nearby residues interacting with the ion-pair are highlighted and colored by residue types. Negatively charged, positively charged and polar residues are shown in red, blue and green, respectively.

The more dynamical nature of the Glu-Lys pair in the Drude simulations highlights alternative ways that these sidechains are stabilized by surrounding protein and solvent. As illustrated by the snapshots in Figs. 3d, f, the Glu-Lys pair can readily break to form alternative interactions with nearby main chain (e.g., Gly20 and Asp21) or side chain groups (e.g., Thr41 and Thr62). For example, backbone of Gly20 forms hydrogen bonding interactions with the amine group of Lys36/23 with populations of 30.2% and 60.4% in EK and KE, respectively, and Lys36 in EK also forms hydrogen bonds with the hydroxyl group of Thr41 with a population of 38.5%, while Glu36 in KE forms hydrogen bonds with the sidechain amide of Asn100 with populations of 15.7% (OE1) and 32.4% (OE2), respectively. Similarly, water molecules are observed to penetrate into the cavity to solvate the ionized Glu and Lys residues (vide infra). As shown in Fig. 4, ionized Glu sidechain is better solvated than Lys in both EK and KE (also see Fig. S7 for radial distribution functions); depending on whether the Glu-Lys pair forms a salt-bridge interaction, the number of water molecules that solvate the Glu sidechain varies between 3 and 5, while the Lys sidechain interacts mostly with 2–3 water molecules.

Figure 4:

Local solvation of the Glu-Lys pair in EK and KE variants from Drude simulations. Representative snapshots illustrate water coordinations in distinct ion-pair structures with (a) a favorable and (b) a broken salt-bridge in EK and (c) a favorable and (d) a broken salt-bridge in KE. Water molecules within 2.5 Å from the Glu and Lys sidechains are shown. Protein is shown in the ribbon form in which residues are colored according to residue type (basic: blue; acidic: red; polar: green; non-polar: white). For solvent radial distribution functions around the Glu and Lys sidechains, see Fig. S7.

3.2. Inclusion of electronic polarization leads to similar cavity hydration levels but higher local dielectric constants

A property of considerable interest concerns the number of water molecules that penetrate into the protein core to stabilize the Glu-Lys pair. In previous CHARMM36m simulations, the cavity remained dry (less than 3) in the EK_neutral/KE_neutral simulations, similar to the crystal structures (Fig. 2), while the level of hydration elevated relatively quickly (after ~10 ns) with the ionized Glu-Lys pair to the average value of 9.3±2.3 for EK and 5.6±1.4 for KE. With the Drude model, it is a priori difficult to predict whether the hydration level should be higher or lower than the CHARMM36m results (see discussions below in Sect.3.5). Therefore, it is interesting to observe that the simulation results are generally comparable to the CHARMM36m values, except that KE features slightly higher level of hydration in the Drude simulations; as shown in Fig. 5, the average number of cavity water is 11.3±2.4, 1.7±1.4, 10.5±2.7, and 2.8±1.3 in EK, EK_neutral, KE, and KE_neutral, respectively.

Figure 5:

Cavity hydration levels as functions of simulation time in Drude simulations for (a) EK and (b) KE variants. Ionized Glu-Lys pairs lead to higher hydration levels in the protein cavity. The average number of water is 11.3±2.4, 1.7±1.4, 10.5±2.7, and 2.8±1.3 in EK, EK_neutral, KE, and KE_neutral, respectively. For comparison, the numbers of cavity water molecules in CHARMM36m simulations are EK: 9.3±2.3; EK_neutral: 0.7±0.7; KE: 5.6±1.4; KE_neutral: 0.1±0.3. Tracing the identity of cavity water molecules suggests that water exchange between cavity and the bulk occurs rapidly at the time scale of ~6 ps for EKneutral/KEneutral and ~12–18 ps for EK and KE.

While the level of cavity hydration is generally similar between Drude and CHARMM36m, we expect a higher degree of dipole variations in the Drude simulations due to the polarizable nature of water therein. Water in the Drude force field has shown the ability to probe and respond to the complex electric environment in the proximity of protein moieties with different dielectric properties, even though only a small difference in the dipole moment distributions compared to those of bulk water was observed.⁸³ This is confirmed here by the distribution of water dipole moment in the protein cavity (Fig. 6). As expected, the distribution is tilted towards higher values in the presence of ionized Glu and Lys, although a significant fraction of water is observed to exhibit substantially higher dipole moments than TIP3P even in the cavity of EK_neutral and KE_neutral; nevertheless, compared to the dipole moment distribution from the bulk water, the cavity water molecules do not feature any extremely large values. In the case of EK_neutral, a smaller peak at reduced water dipole is observed, which is likely due to water molecules trapped between hydrophobic moieties or protein backbone groups in the cavity. Overall, the average dipole moment for the cavity water is higher than TIP3P in ionized EK and KE, but more comparable in EK_neutral and KE_neutral.

Figure 6:

Dipole moment of individual water molecules in the cavity during Drude simulations of the SNase variants shows modest polarization of SWM4-NDP water compared to TIP3P water. (a) Density estimates of the dipole moment distributions using Gaussian kernels for each system and (b) average values of water dipole moments for the systems. The bulk distribution of SWM4-NDP water is shown in (a) as a normal distribution with the mean of 2.46 D and a standard deviation of 0.16 D. Error bars in (b) are the corresponding standard deviations. Red dashed lines in both panels indicate the dipole moment of the TIP3P water model. The purple dashed line and the shaded region represent the average dipole moment of bulk SWM4-NDP water and its standard deviation, respectively.

In all variants, the collective dipole fluctuations in the cavity are higher in the Drude simulations than with CHARMM36m, leading to higher Kirkwood G-factors and therefore higher local dielectric constants (see Table 1); with ionized Glu-Lys pair, the local dielectric constant for the cavity water is in the range of 13–20, which is fairly high considering the small size (~6 Å) of the cavity.^84,85 The ratio between Drude and CHARMM36m results is close to be 2 for all cases (except for the Δ+PHS background, which contains generally 0–1 water in the cavity), which is close to the expectation based on the consideration of electronic polarization (i.e., the optical dielectric constant). The higher dielectric constants suggest that the Glu-Lys pair can be better stabilized by cavity water in the Drude simulations than the CHARMM36m model, although as discussed below, both nearby protein residues and cavity water make contributions.

Table 1:

Computed Kirkwood G factor and local dielectric constant (ϵ₁) for cavity water from Drude and CHARMM36m simulations.

	G factor		ϵ 1 a
System	Drude	CHARMM36mb	Drude	CHARMM36mb
EK	9.8	5.0	19.5	7.6
KE	7.6	3.9	13.0	5.7
EKneutral	1.9	0.6	3.1	1.7
KEneutral	1.4	0.5	2.5	1.5
Δ+PHS	0.4	0.4	1.4	1.4

^a.Calculations of ϵ₁ are conducted following Eq. 2 with ϵ₂ = 10.

^b.Results are taken from Ref. 64.

3.3. Stabilities of EK_neutral and KE_neutral are not sensitive to electronic polarization

Since free energy simulations using the CHARMM36m model strongly suggested that the buried Glu and Lys are charge neutral,⁶⁴ we first examine free energy results for EK_neutral and KE_neutral from the Drude simulations. The energy gaps sampled in different λ windows closely follow Gaussian statistics (Fig. S12b, d), suggesting that the linear response model^86,87 remains applicable when electronic polarization is included explicitly; this is supported by the λ-dependence of the free energy derivatives (Fig. S13b, d), which show linear correlation coefficients R² in the range of 0.97–0.98.

As shown in Table 2, the calculated relative thermostabilities from Drude simulations are rather close to those with the CHARMM36m model. For EK_neutral and KE_neutral, the relative stability is 0.2±0.6 and 1.1±0.6 kcal/mol with Drude and CHARMM36m, respectively, in comparison to the experimental result of 2.0±0.6 kcal/mol. Relative to the Δ+PHS background, EK_neutral is less stable by 18.6±1.6 and 15.9±0.6 kcal/mol with Drude and CHARMM36m, respectively, in comparison with the experimental value of 9.3±0.4 kcal/mol; as noted previously,⁶⁴ the agreement between computation and experiment will further improve when van der Waals contribution (~ 4 kcal/mol for CHARMM36m and ~7 kcal/mol for Drude, see Table S4) is considered.

Table 2:

Relative thermodynamical stability of SNase variants (in kcal/mol) from charging free energy simulations and experiments.^a

ΔΔGf	Drude	CHARMM36m b	Exp.c
Δ+PHS → EK	24.6±1.4 (19.6)	55.8±1.6	9.3±0.4
Δ+PHS → EKneutral	18.6±1.6 (19.5)	15.9±0.6
Δ+PHS → KE	18.5±1.0 (14.7)	58.7±1.0	11.3±0.4
Δ+PHS → KEneutral	18.8±1.7 (19.1)	17.0±0.1

^a.Individual free energy components following thermodynamic cycles shown in Ref. 64; values in parentheses are based on a linear fit of the free energy derivatives (see Table S10 and Fig. S13 in the Supporting Information). As discussed in Ref. 64, the values are further reduced by ~4 kcal/mol for CHARMM36m when the difference between EK (or KE) and VL in terms of their van der Waals interactions with the surrounding environment is included; for Drude simulations, the corresponding van der Waals contributions are ~7 kcal/mol (see Table S4).

^b.Results are taken from Ref. 64;

^c.Experimental values are the thermodynamical stabilities measured by chemical denaturation monitored by Trp fluorescence in Ref. 62; note that the experimental data do not explicitly specify the titration state of the Glu-Lys pair.

The similarity in the Drude and CHARMM36m free energy results appears to be consistent with the general understanding^41,42,88 that for charge-neutral groups, it is less critical to include electronic polarization explicitly. However, free energy components in Table 3 illustrate a more nuanced picture: compared to CHARMM36m, Δ+PHS, EK_neutral and KE_neutral are stabilized in the Drude simulations by ~12, 8 and 9 kcal/mol, respectively, which lead to merely ~2–3 kcal/mol destabilization of EK_neutral and KE_neutral relative to the Δ+PHS background upon inclusion of electronic polarization. In other words, the agreement between Drude and CHARMM36m for the relative stabilities of Δ+PHS, EK_neutral and KE_neutral in fact benefits from cancellation of similar polarization stabilizations in the three closely related proteins that differ by only two charge-neutral residues.

Table 3:

Difference between Drude and CHARMM36m simulations in charging free energy of SNase variants relative to the unfolded state in solution (in kcal/mol).

Components	EK	KE	EKneutral	KEneutral	Δ+PHS
intra a	−34.8±0.6	−28.9±0.6	−6.4±1.0	−7.2±1.0	−5.3±0.2
inter a	−7.9±1.6	−22.8±1.3	−1.9±1.3	−2.0±1.2	−6.2±0.5
total a	−42.7±1.8	−51.7±1.4	−8.3±1.6	−9.2±1.6	−11.5±0.5
total (EK/KE vs Δ+PHS)b	−31.2±1.9	−40.2±1.5	3.2±1.7	2.3±1.7

^a.The values are components of ${\left(\Delta G_Q^F-\Delta G_Q^U\right)}^{\mathit{\text{Drude}}}-{\left(\Delta G_Q^F-\Delta G_Q^U\right)}^{C36m}$; “intra” refer to the interactions within the Glu and Lys residues of interest; “inter” refer to the interactions between the Glu/Lys residues and the environment; “total” is the sum of “intra” and “inter” components. For separate Drude and CHARMM36m values, see Table S5 in the Supporting Information. Note that the “intra” component here includes the difference in self-energies of Glu/Lys residues in the protein vs. bulk solution.

^b.The difference between the EK/KE variants and the Δ+PHS background.

3.4. Electronic polarization is essential to the stabilization of ionized Glu-Lys pair

With the ionized Glu-Lys pair, the energy gaps also closely follow Gaussian statistics (Fig. S12a, c) and the linearity of the free energy derivatives with respect to λ is comparable to the cases of a charge-neutral Glu-Lys pair; nevertheless, some intermediate λ windows exhibit notable deviation from the linear relation (Fig. S13a, c), highlighting the challenge associated with sampling even with ~150 ns per λ window. Considering such deviations, the computed thermostabilities are expected to have a somewhat higher level of uncertainty as compared to the CHARMM36m results; for example, using a linear fit of the free energy derivatives leads to a difference of ~ 5 kcal/mol in charging free energy of the Glu-Lys pair in the protein Tables 2). Nevertheless, the difference between Drude and CHARMM36m results is clear and compelling, especially regarding the stability relative to the Δ+PHS background. As shown in Table 2, while ionized EK and KE are more than 55 kcal/mol less stable than Δ+PHS with CHARMM36m simulations, the difference in stability is reduced to ~20 kcal/mol with the Drude force field. In other words, the ionized and charge-neutral Glu-Lys pairs have almost comparable stabilities with the Drude force field; the stark contrast between Drude and the CHARMM36m results highlights the significance of including electronic polarization when describing the stability of buried charges in proteins.

These observations beg the question of the origins of the additional stabilization upon inclusion of electronic polarization. For example, does the extra stabilization come primarily from the cavity water or surrounding protein residues? If protein residues make a major contribution, is the additional stabilization due mainly to the enhanced interactions with induced dipoles of nearby residues, or at least in part to the altered Glu-Lys pair structural ensemble in the Drude simulations as compared to the non-polarizable CHARMM36m simulations? Below we answer these questions with detailed structural and energetic analyses.

First, when comparing Drude and CHARMM36m charging free energy differences between protein and solution cases, we note that the contribution from Glu/Lys interaction (labeled as “intra” in Table 3) is larger than that from the interaction between the Glu-Lys pair and the environment (labeled as “inter” in Table 3). For example, in EK, the “intra” contribution favors Drude by as much as 34.8 kcal/mol, while the “inter” component is only 7.9 kcal/mol. In KE, the two contributions are closer in magnitude, with the “intra” contribution being ~ 6 kcal/mol stronger, pointing to the larger “inter” polarization contribution in KE than EK.

The strengths of Glu/Lys interactions in Drude and CHARMM36m simulations are explicitly summarized also in Fig. 7 (for numerical values see, Table S6), which shows ~20 kcal/mol stronger interactions with the Drude model; the magnitudes of enhancements are different between Table 3 and S6 because the values in Table 3 account for the difference in self-energies of the Glu/Lys sidechains in the protein vs. in solution. Regardless of the method of decomposition, it is evident that the Glu/Lys interaction is substantially stronger (by at least 20 kcal/mol) with electronic polarization and this accounts for more than half of the overall stabilization of ionized Glu-Lys pair relative to a non-polarizable model (~42.7–51.7 kcal/mol, see Table 3). The stronger Glu/Lys interaction is consistent with the substantial magnitude (~0.2–0.4 Debye, see Fig. S10 in the Supporting Information) of induced dipoles of the Glu and Lys residues in both EK and KE simulations.

Figure 7:

Comparison of components for the charging free energy (in kcal/mol) in SNase variants from Drude and CHARMM36m simulations; for numerical values, see Table S6. “Glu/Lys” refers to direct interactions between the side chains of the Glu-Lys pair, and thus does not include contribution from self-energies of the Glu and Lys sidechains; “Glu-Lys/Water” refers to interactions between the side chains of the Glu-Lys pair and all water molecules in the simulation box; “Glu-Lys/Protein” refers to interactions between the side chains of the Glu-Lys pair and the rest of the protein. Note that the contributions from Asp40 and Glu43 are excluded because of the compensation from the nearby Ca²⁺; see Table S7.

For the interaction between the Glu-Lys pair and the environment, values shown in Table S6 and Fig. 7 suggest that interactions with water and protein residues are consistently stronger when electronic polarization is included. The relative importance of water and protein contributions to enhanced interactions is different in EK and KE, with EK featuring stronger interactions with the protein (~−24 kcal/mol for EK vs. ~−17 kcal/mol for KE), while KE exhibiting even stronger interactions with water (by ~−28 kcal/mol) as compared to CHARMM36m; the latter trend is consistent with the observation that the Glu-Lys pair features similar local solvent distributions in Drude and CHARMM36m simulations for EK, while it is better solvated in Drude simulations for KE (see Fig. S7).

To identify the protein groups that provide major polarization stabilization of the ionized Glu-Lys pair, in Table 4 we further compare the protein contributions from Drude and CHARMM36m simulations for EK and KE; we focus here on nearby polar/charged sidechains and main chain groups (up to 8 Å from the center of the Glu-Lys pair). For EK, nearby side chains consistently exhibit stronger interactions with the Glu-Lys pair in the Drude simulations; these include not only direct hydrogen-bonding interactions (e.g., between Lys36 and Thr41 and Thr62, see Fig. 3d) but also indirect electrostatic interactions, which can be either net-favorable (e.g., stronger attraction between Glu23 and Lys16, Lys63) or net-unfavorable (e.g., stronger repulsion between Lys36 and Arg35). A major contribution comes from Asp21, which interacts favorably with Lys36 due to spatial proximity; the interaction is stronger with Drude than with CHARMM36m, likely because Asp21 sidechain is coordinated with the surface-bound Ca²⁺ and therefore undergoes substantial polarization, as reflected by the magnitude (~0.8 Debye) of the induced dipole moment (Fig. 8c). Several backbone groups also make substantial contributions to the enhanced interaction with the Glu-Lys pair when electronic polarization is included, which leads to notable magnitudes of induced dipole moments (~0.2 Debye, Fig. 8c) and therefore larger total dipole moments (compare Fig. 8a, b) of the backbone groups; the largest contributions come from Gly20 and Asp21, which form explicit hydrogen bonding interactions with Lys36 (Fig. 3c,d).

Table 4:

Charging free energy components that represent the major interactions between the ionized Glu-Lys pair and nearby protein residues in EK and KE SNase variants (in kcal/mol) from Drude and CHARMM36m (C36) simulations.

ΔGQ	Drude		CHARMM36m
	Sidechaina	Backboneb	Sidechaina	Backboneb
EK	−29.2±1.3	−20.0±2.8 (−12.7±3.0)	−7.0±0.4	−14.0±0.3 (−10.3±0.3)
KE	6.4±1.1	−7.0±1.4 (−20.8±1.6)	0.4±0.3	−2.7±0.4 (−9.7±0.4)

Dominant residual contributionsc
ΔGQ		K16	D19	D21	K24	R35	T41	K63	D19bb	G20bb	D21bb
EK	Drude	−3.9±1.0	−5.0±0.1	−15.7±0.1	−3.3±0.7	5.0±0.1	−3.8±0.2	−3.1±0.1	0.6±0.5	−12.4±2.4	−5.6±0.5
	C36	−0.01±0.002	−1.7±0.2	−4.6±0.1	−0.01±0.011	0.6±0.1	0.3±0.1	−0.2±0.1	−0.6±0.1	−10.6±0.2	−0.4±0.1
KE	Drude	5.0±0.7	−8.8±0.2	−1.2±0.4	4.6±0.6	−0.5±0.2	−0.5±0.03	6.2±0.1	−3.3±1.0	−5.7±0.4	−0.2±0.6
	C36	0.02±0.001	−1.4±0.2	0.2±0.1	0.01±0.001	−0.8±0.1	0.1±0.1	0.3±0.1	−2.2±0.1	−0.4±0.3	−1.0±0.2

^a.Total contributions from nearby charged and polar residues; additional contributions are listed in Table S8 of the Supporting Information.

^b.Total contribution from nearest residues including Ala17, Ile18, Asp19, Gly20, Asp21,Thr 22, and Lys24; numbers in the parentheses further include residues within 8 Å from the center of geometry of NZ, OE1, and OE2; additional contributions are listed in Table S8 of the Supporting Information.

^c.For individual residual contributions, notations with ‘bb’ denote the backbone atoms of the residues; other notations represent the side chain contributions.

Figure 8:

Backbone and side chain dipole moments for residues listed in Table 4. Average total dipole moments in (a) CHARMM36m and (b) Drude simulations are in general comparable, except for a few nearby main chain groups, such as Gly20 and Asp21; (c) average induced dipole moments in Drude simulations suggest that EK and KE show similar degrees of polarization. Error bars show one standard deviation.

In KE, due to the reversed orientation of the Glu-Lys pair relative to EK, many sidechain interactions are opposite in sign as compared to EK (e.g., the net interactions between the Glu-Lys pair and Lys16, Lys24, Arg35 and Lys63; see Table 4); overall, there are fewer favorable interactions between nearby sidechains (e.g., Asn100) and the Glu-Lys pair in KE, although this is partly compensated by more favorable backbone interactions. In fact, we note different trends in EK and KE as more backbone groups are included in the interaction with the Glu-Lys pair. In Drude simulations, EK exhibits more favorable interactions (~−20 kcal/mol) between the ion-pair and nearest backbone groups than KE (~−7 kcal/mol); as more distant backbone groups are included (values in parentheses in Table 4 include all backbone groups within 8 Å), however, the ion-pair is better stabilized in KE (~−21 vs. ~−13 kcal/mol for EK). These differences reflect the importance of ion-pair orientation to the interaction with nearby protein groups. In particular, since backbone groups are structurally more constrained due to the protein structure, interactions between these groups and the ion-pair are most sensitive to the latter’s orientation; indeed, the trend that the ion-pair is better stabilized by distant mainchain groups in KE than in EK is observed with CHARMM36m as well. In terms of the degree of polarization, the induced dipole moments of nearby groups (Fig. 8c) are generally similar in EK and KE, thus the larger overall protein stabilization in EK reflects the importance of ion-pair orientation and geometry, rather than stronger polarization in EK per se.

3.5. Discussion

To understand how buried ion-pairs contribute to protein functions, it is important to properly describe their thermodynamic stabilities, dynamics and the local hydration environment. The main aim of our work is to establish to what degree electronic polarization impacts these properties using the SNase mutants as representative examples. The comparisons between Drude and CHARMM36m simulations have indeed provided valuable insights.

3.5.1. Electronic polarization contribute differently to the stabilization of buried charge-neutral and ionized groups

When the Glu and Lys adopt their charge neutral states, Drude and CHARMM36m simulations give consistent structural and energetic results, including computed thermostabilities relative to the Δ+PHS background. On one hand, this observation is consistent with the argument^41,42 that for charge-neutral groups, using TIP3P model for calibrating intermolecular interactions in non-polarizable force field developments effectively captures the effect of screening in the condensed phase environment. On the other hand, free energy components in Table 3 reveal that polarization stabilizes EK_neutral, KE_neutral and Δ+PHS by a notable but similar amount (~10 kcal/mol), thus the agreement between Drude and CHARMM36m for the stabilities of EK_neutral/KE_neutral relative to the Δ+PHS background is due in part to the cancellation of polarization effects among these similar proteins, which differ by merely two charge-neutral residues. Therefore, even for charge-neutral groups, a quantitative description of free energy difference in distinct environments (e.g., protein interior vs. bulk solution) benefits from an explicit representation of electronic polarization, although the magnitude of effect is expected to be modest and on the order of several kilocalories per mole.

For buried Glu and Lys residues in their ionized form, electronic polarization makes much larger contributions to stability. The striking observation here is that the ionized EK and KE are stabilized by more than 40 kcal/mol by the inclusion of electronic polarization (Table 3), such that they are almost comparable in thermostability to the charge-neutral states. As discussed above, the stabilization appears to be driven by both the enhanced Glu/Lys interaction and more favorable Glu-Lys/environment interactions; depending on the scheme of decomposition (Tables 3 and S6), the stronger Glu-Lys interaction accounts for at least half of the stabilization due to electronic polarization. Along this line, it is worth noting that non-bonded interactions between ionized amino acid sidechains have been carefully calibrated (i.e., NBFIX) in the development of the CHARMM 2019 Drude force field^67,89 by comparison with gas phase MP2 calculations; moreover, to avoid any over-polarization in the condensed phase, experimental osmotic pressure data for solutions containing ionic compounds (e.g., guanidinium:acetate) were used as additional calibration. Thus the enhanced Glu/Lys interaction observed in the current Drude simulations is expected to be the proper response of the buried ion-pair to the less polar nature of the cavity compared to bulk water. For the enhanced interactions between the Glu-Lys pair and the local environment, both mainchain and sidechain groups contribute in EK, while mainchain groups and cavity water make primary contributions in KE. The stronger interactions with the Drude force field than CHARMM36m (see, for example, Tables 4, S6) are likely driven by both polarization of protein groups (Fig. 8, S10) and the inclusion of lone-pairs in the Drude model, which generally lead to more reliable⁹⁰ hydrogen-bonding interactions; indeed, calculations for cluster models constructed based on snapshots from the Drude simulations observe that the Drude model describes intermolecular interactions involving the Glu-Lys pair in close agreement with B3LYP-D3, while CHARMM36m tends to systematically underestimate the strength of interactions (see Sect. 3 of the Supporting Information).

3.5.2. Electronic polarization leads to enhanced ion-pair dynamics despite stronger salt-bridge interactions

Another observation of major interest is that the Drude model leads to substantially more dynamics in the buried Glu-Lys pair (Fig. 3a–b), which samples multiple hydrogen-bonding networks that involve the Glu and Lys residues (Fig. 3c–f; Fig. 4); this observation further supports previous findings that the stability of salt-bridges in proteins tends to be overestimated by non-polarizable models.^42,45,46,48 Since the magnitude of direct interaction between ionized Glu and Lys is actually larger in magnitude with the Drude model than with CHARMM36m (Fig. 7, Table 3), the more dynamical nature of the salt-bridge is a result of compensation between the stronger Glu/Lys interaction and ion-pair/environment interactions, which involve both nearby sidechains and mainchain groups (Fig. 3, Table 4) as well as cavity water (Figs. 4, 7).

The competing contributions from the protein environment in the Drude simulations underscore the difference in sampled conformations when polarization is included. For example, comparison of Glu and Lys sidechain χ₁ distributions (Fig. S9) suggests that Lys36 in EK samples rather different orientations in the Drude simulations as compared to CHARMM36m. To further highlight the difference in conformational ensembles, we compare CHARMM36m interaction energies in EK using conformations collected from the Drude and CHARMM36m trajectories. As shown in Table S9, with the Drude ensemble, Glu-Lys interaction is substantially weaker while their interactions with the surrounding protein, especially mainchain groups, are stronger, compared to results using the CHARMM36m snapshots. These differences highlight that the Glu-Lys pair undergoes larger fluctuations in the Drude simulations to form more extensive interactions with nearby protein atoms, especially mainchain groups.

Therefore, the underlying mechanism for the enhanced ion-pair fluctuation in the Drude simulations is fundamentally different from the phenomenological approach of charge-scaling,^41,42,88 which considers polarization effect by scaling down electrostatic interactions with the optical dielectric constant; i.e., the magnitude of salt-bridge fluctuation is enhanced by reducing the strength of interaction⁴² within the ion-pair as well as between the ion-pair and the environment. This qualitative difference from the Drude model highlights the macroscopic nature of the charge-scaling approach,⁹¹ which is reminiscent of limitations discussed for the charge-scaling model in balancing dynamic and energetic properties of ionic liquids as solvent.^92,93 Therefore, for a consistent description of both energetic and dynamic properties of buried ion-pairs, we advocate polarizable models over the charge-scaling approach since uniformly reducing interactions involving the ion-pair may inadvertently perturb other functionally relevant properties such as the local hydration level and ion binding.²⁵

3.5.3. Electronic polarization, hydration of protein cavities and sampling challenges

Hydration level of protein cavity is of interest because it plays major roles in modulating key properties of buried charges and thus their functions.^8,16,18,19 The observation that the hydration level of the cavity remains similar when electronic polarization is included explicitly is not entirely anticipated. With explicit polarization, we generally anticipate stronger interaction between the Glu-Lys pair and nearby protein groups, which may suggest that a smaller number of cavity water molecules are required to stabilize the ion-pair. On the other hand, the interaction with water is also stronger due to electronic polarization, which may argue for an increased level of hydration relative to a non-polarizable model. It appears that the competition between these two factors leads to a comparable level of cavity hydration in our specific case, although KE features a somewhat higher level of cavity hydration in the Drude simulations than with CHARMM36m (Fig. S7); in other systems, different levels of hydration of pores in ion channels were observed with polarizable and non-polarizable models,^65,66 reflecting their differences in describing interfacial properties of water.

Compared with the crystal structures (Fig. 2), which were solved under cryogenic conditions, both Drude and CHARMM36m observe a comparably small number of cavity water for EK_neutral/KE_neutral, and a substantially higher level of hydration when the Glu-Lys pair is ionized (Fig. 5). We note that these trends in the cavity hydration level alone are not sufficient to support that the Glu-Lys pair is charge-neutral. First, only strongly bound water molecules with high occupancy were resolved in the crystal structures,⁹⁴ but not disordered ones.³¹ By contrast, MD simulations consider all water molecules accessible to the cavity, many of which undergo rapid exchange with bulk water at room temperature (Fig. 5). Second, under cryogenic conditions, the damped protein flexibility,⁹⁵ which directly impacts water penetration, may also lead to a smaller number of water molecules in the cavity relative to solution at room temperature. Due to the considerable entropic component for water penetration into small volumes, hydration of protein cavities has been suggested to be particularly susceptible to cryoartifacts.⁹⁶ Indeed, while solution NMR experiments clearly indicate that Glu23 in the V23E mutant of SNase is solvent accessible when ionized (pH > 7.8), the crystal structure (PDB ID: 3TME) at pH 8 features a very dry cavity despite the open conformation of the β₁ − β₂ region.⁹⁷

In terms of the properties of cavity water, we observe generally similar dipole distributions as compared to the bulk water; the lack of significantly polarized water even in the presence of ionized Glu-Lys pair is likely because the cavity water can readily change their orientation (in part supported by the relatively large Kirkwood G factors shown in Table 1), in contrast to cases when their orientation is significantly constrained by the local protein environment.⁹⁸ Nevertheless, we anticipate that the cavity water exhibits considerably different dynamics as found recently in a comparison of Drude and CHARMM simulations for the hydration of proteins.⁶⁰ Therefore, future vibrational spectroscopy analysis^99,100 that focuses on internal water molecules^30,98,101 can provide additional insights regarding the effect of polarization on cavity hydration.

It is worth stressing that hydration levels of internal cavities are not straightforward to sample with standard MD simulations, as the time scale of water penetration can be tens or hundreds of nanoseconds.^18,102 This is particularly the case in the context of free energy simulations, for which intermediate λ windows are challenging to equilibrate due to the reduced amount of driving force for water penetration and coupled conformational adjustments in the protein as compared to the fully charged window; the importance of a large driving force to efficient water penetration simulations was illustrated by the overcharging approach of Warshel and co-workers for the prediction of pK_a values for buried titratable residues^103,104. For example, while the hydration levels for EK and KE are comparable for the fully charged and fully decharged windows, they can be rather different for intermediate λ windows (e.g., λ = 0.7, Fig. S8) even with more than 100 ns of sampling, leading to larger uncertainties in the hydration contribution to charging free energies. Fortunately, we observe significant compensation between different interactions. For example, when evaluated separately, the free energy components (e.g., Glu/Lys interaction, Glu-Lys/water and Glu-Lys/protein interactions) tend to feature rather large statistical uncertainties (Table S6); their sums, however, exhibit much smaller statistical errors (Tables 3). Similarly, while individual free energy components may differ substantially when more approximate schemes such as the linear response model (LRA) are used (Tables S10, S11), the overall stabilization of EK and KE remains comparable in magnitude. Finally, comparing EK and KE, due to the different ion-pair orientations and geometries, the Glu-Lys pairs feature rather different interactions with nearby water, sidechains and mainchain groups; when summed together, these interactions lead to comparable degrees of stabilization due to electronic polarization in ionized EK and KE variants. Nevertheless, the differences between results from numerical integration, linear fits and a LRA model that involves only λ = 0, 1 windows highlight the need of developing efficient enhanced sampling methods for cavity hydration¹⁰⁵ as demanded by more quantitative free energy simulations involving buried charges.

3.5.4. Electronic polarization is required to better reconcile with experimental analyses of ion-pair titration state

In terms of computed thermostabilities in comparison to available experimental data, the Drude simulations have a comparable level of agreement as CHARMM36m (Table 2); the degrees of destabilization due to the replacement of V23/L36 by Glu-Lys pairs in EK and KE are overestimated compared to experimental values, although including van der Waals contributions reduces the discrepancies by ~4 kcal/mol for CHARMM36m⁶⁴ and ~7 kcal/mol for Drude (see Table S4). As discussed above, challenge in adequately sampling hydration level for intermediate λ windows is one of the factors that limit the accuracy of current Drude free energy results, which involve less sampling (in terms of both the number of λ windows and length of sampling per λ window) as compared to the CHARMM36m simulations⁶⁴ due to higher computational cost. Nevertheless, considering our entire focus on electrostatic and polarization contributions and approximations inherited to our charging free energy framework for the evaluation of protein stability,⁶⁴ it is, in fact, encouraging that the Drude free energy results approach the experimental values. In this context, we note that solution NMR analysis indicated that while EK is well-folded, the KE variant features a considerable unfolded population,⁶² which is difficult to capture using atomistic simulations. The trend that the Glu-Lys pair in EK is better stabilized by the protein environment than the Lys-Glu pair in KE is qualitatively consistent with the stronger Glu-Lys/protein interactions in EK observed in our analysis (Table 4). Nevertheless, considering the limitations in the simulated ensemble for KE, we focus further discussion of the computational results in relation to experiments on the EK variant.

Most significantly, the current results have major implications to the titration state of the Glu-Lys pair in the SNase mutants, for which our CHARMM36m simulations⁶⁴ argued for a different assignment from experimental analysis.^61,62 As mentioned in the Introduction, the titration states are difficult to discern based on the corresponding crystal structures, which revealed a small (1–3) number of water molecules in the cavity. Both Drude and CHARMM36m simulations find that a low-level of hydration is only consistent with EK_neutral and KE_neutral, although as discussed above, the crystal structures were solved under cryogenic condition and resolved only strongly bound water molecules, making the comparison to MD simulations at room temperature less straightforward. In solution NMR studies,^61,97 the CBCGCO correlation spectrum for the V23E mutant under the pH condition where Glu23 is expected to be charge-neutral revealed an unusual upfield chemical shift in the Cδ resonance, which was assigned to be the protonated Glu23. This resonance was not observed in the EK mutant, and the peak assigned to Glu23 therein appeared in the normal region of the CBCGCO spectra typical for Glu residues that are solvent exposed and charged. Thus the NMR data appeared most consistent with Glu23 being charged in EK over a broad range of pH. This interpretation is consistent with the result of double mutant cycle analysis:⁶² it was found that the interaction between Glu-Lys in EK (~−4.9 kcal/mol) was substantially stronger than that between Gln-Lys (−1.5±0.3 kcal/mol) in the QK variant, where Gln served as a non-ionizable proxy for a neutral Glu; i.e., the result was interpreted to suggest that Glu and Lys are ionized in the EK variant.

With CHARMM36m simulations, we found that the EK_neutral state is substantially more stable than EK by >40 kcal/mol, in stark contrast to suggestions from solution NMR and double mutant cycle experiments; with the Drude force field, this difference is dramatically reduced to be ~0–5 kcal/mol (Table 2), which, considering the challenge in sampling as discussed above, leaves open the possibility that Glu and Lys are indeed ionized. Therefore, inclusion of electronic polarization is required to potentially reconcile computational analysis with available experimental data on the titration state of the buried Glu-Lys pair. On the other hand, it is worth pointing out that a molecular level interpretation of either the NMR data or the double mutant cycle is also not clear-cut. For example, as discussed in the Supporting Information using models constructed based on Drude simulation snapshots, the chemical shift of Glu23 could be perturbed back to the range expected for a solvated and ionized Glu by interactions with the nearby Lys or water molecule(s), even if Glu23 is, in fact, protonated (see Figs. S14, S15). Regarding the double mutant cycle result mentioned above, as discussed in Ref. 64, the stronger interaction free energy measured for Glu-Lys in EK than that for Gln-Lys in QK⁶² could also be due to differences in the microenvironment of the buried Glu-Lys vs. Gln-Lys pairs, rather than unequivocally proving the ionized nature of Glu-Lys in EK. Therefore, a firm assignment of the titration states for the Glu-Lys pair requires further analysis by, for example, systematic QM/MM chemical shift calculations,^106–108 which are beyond the scope of this work. Nevertheless, the results of our study clearly suggests that for a reliable analysis of SNase and similar problems in other systems, electronic polarization needs to be included explicitly.

Finally, we note that the Drude simulations suggest that the ionized Glu/Lys residues engage in alternative hydrogen bonding interactions with nearby polar groups (Fig. 3), thus mutations of these residues are expected to perturb the stability of the protein, while the effects are likely minimal with a charge-neutral Glu-Lys pair. Therefore, analysis of protein stability change due to additional mutations of the polar residues identified here as alternative hydrogen-bonding partners of the Glu-Lys pair can serve as a test of current simulations and potentially shed light onto the titration state of the Glu-Lys pair in EK.

3.5.5. Implications to the properties and function of buried ion-pairs in other systems

While the specific set of SNase mutants are model systems, the microenvironment of the buried Glu-Lys pair resembles those in more complex systems in terms of limited number of local polar interactions (Fig. 1). Therefore, the framework of our analysis and key findings are expected to apply to other protein systems. For example, while we do not explicitly study chemical reactions here, our findings suggest that for reactive processes that involve a significant charge redistribution in enzymes, such as those creating or annihilating a pair of formal charges, electronic polarization is likely to make a significant contribution to the computed reaction energetics. It is worth noting that our analysis highlights the difference in the conformational ensembles sampled with polarizable and non-polarizable models (see Fig. 3a–b and Table S9), thus polarization contribution can not be reliably evaluated by a perturbative approach using conformations collected from non-polarizable simulations. Therefore, the impact of electronic polarization on such reactive processes is potentially more complex than on ultrafast spectroscopies, which tend to be dominated by electronic responses at the sub-nanosecond time scales.¹⁰⁹

The current observation is also relevant to the on-going discussion of QM region size requirement in QM/MM simulations of enzymes,¹¹⁰ as a large QM region is preferable if electronic polarization of the environment is crucial to the reaction energetics. For computational efficiency consideration, especially the need of proper sampling, an attractive alternative is to treat the environment of reactive site with a polarizable force field rather than a high-level QM method,¹¹¹ an option also supported by comparing electric fields in enzyme active sites from different force fields to large-scale QM calculations.⁵⁸

As alluded to in the Introduction, the dynamic properties of buried ion-pairs, which are often modulated by the local hydration level,^8,16,18,19 are critical to the ion translocation function of many transporters and conformational transitions in ion channels and biomolecular motors. Our observation that electronic polarization contributes significantly to the dynamic and hydration properties of buried ion-pairs in SNase mutants suggests that for the analysis of these complex systems, it is preferable to include electronic polarization explicitly whenever possible; otherwise, overestimated structural stability of buried ion-pairs may limit their participation in gated ion-transport^8,26,43 and functional conformational transitions, or lead to major errors in predicted thermodynamic and kinetic parameters for these processes.^48,51 With further developments in implementation¹¹² and algorithms for efficiently computing polarization contributions,^113,114 such applications will become increasingly realistic.

4. Conclusions

Ever since the realization that proteins contain a notable number of buried charges,^1,2 considerable experimental and computational efforts have focused on characterizing the contributions of these groups to the modulation of protein stability and molecular factors that stabilize their presence in the protein interior. These studies generally highlighted balancing contributions from electrostatic interactions, desolvation penalty and favorable geometries for hydrogen-bonding and/or salt-bridge formation.^12–14,115 In this context, considering the involvement of charged groups in relatively non-polar environments, we reason that electronic polarization, which is a fundamental component of intermolecular interaction,¹¹⁶ is likely to make a significant contribution as well. Such analysis has not been possible until very recently when polarizable force field models for biomolecules have become more mature and well tested;⁴⁹ indeed, previous analysis of buried charges in proteins employed either non-polarizable models or continuum electrostatic models, in which electronic polarization was treated macroscopically. In this study, taking advantage of the latest polarizable CHARMM force field based on the Drude oscillator, we explicitly analyze at a microscopic level the contribution of electronic polarization to the properties of buried Glu-Lys pairs in a series of SNase mutants.

The results from our analysis strongly support that electronic polarization indeed plays an essential role in stabilizing buried charges in proteins. In fact, with an empirical non-polarizable model, the ionized form of the buried Glu-Lys pair in both EK and KE mutants of SNase is more than 40 kcal/mol(!) less stable than the charge neutral titration state; this is in stark contrast to the observation that the two titration states are comparable in stability when electronic polarization is included, a result better reconcilable with available experimental data on the titration state of the ion-pair. Evidently, to capture the proper ionization states of buried titratable residues, electronic polarization needs to be treated explicitly.

In addition to the ionization states, properties crucial to the function of buried charges include their local hydration environment and structural flexibility. Our analysis of the SNase mutants further highlights that electronic polarization also impacts these properties in significant ways. In terms of local hydration, although the levels of water penetration are comparable with polarizable and non-polarizable models, the cavity water provides stronger stabilization of the ionized Glu-Lys pair when electronic polarization is included explicitly. The stronger interaction between the ionized Glu/Lys and the surrounding water and protein groups leads to better energy compensation, which results in larger and faster fluctuations of the Glu-Lys pair as compared to simulations with a non-polarizable model.

Collectively, observations from our study provide compelling evidence that electronic polarization is essential to the stability, hydration and dynamics of buried charges in proteins. Therefore, particularly for enzymes catalyzing reactions that create or annihilate pairs of formal charges, ion transporters and biomolecular machines, we advocate the application of a polarizable model whenever possible.