Predicting Water at the Protein Interface in Cryo-EM Structures from MD-Excess Chemical Potential

Abstract

Predicting the positions of water molecules at the protein interface remains a formidable challenge in structural biology, fueling active research in this field. Here, we present a novel approach based on molecular dynamics (MD) simulations that utilize statistical thermodynamic signatures of water at protein interfaces that can be used to improve the accuracy of water placement in maps derived by cryogenic electron microscopy (cryo-EM). We employ an analysis based on the excess chemical potential, or the Work to Transfer (WT) a water molecule from the bulk to the interface. WT is a measure of the thermodynamic balance between the interaction energy of an interfacial water molecule with the protein and its free energy of interaction with all the other solvent molecules. WT is proportional to the log ratio of the local density of water molecules at the protein interface to the bulk density. Using apoferritin as a benchmark system, we found that 85% of the top 100 water locations with the most favorable excess chemical potential values are observed in one or more structures whose locations were determined from high resolution cryo-EM maps deposited in the PDB. 70% of the top 200 water locations indexed by excess chemical potential were also observed in PDB structures derived from the cryo-EM maps. The MD simulations are performed without experimental density restraints, and yet the water positions with favorable WT values correlate strongly to their corresponding position within experimentally defined maps. This work paves the way for the development of a cryo-EM water placement and refinement tool that integrates molecular dynamics simulations of the excess chemical potential with cryo-EM data for accurate modeling of water networks.

Introduction

Water solvation plays a key role in protein structural stability and function. Water is critical for ligand pharmacology and can contribute significantly to ligand binding thermodynamics. Water displacement by a single chemical group of a bound ligand can contribute substantially to gains in binding affinity, from both enthalpic and entropic considerations(1–4). Water also plays a critical role in drug resistance. For example, displacement of waters bound within the active site of lentiviral integrases has been proposed to be the initiating step for a key mechanism of drug resistance(5,6). Many such examples exist in the literature(7–10). Thus, the proper identification of water molecules is crucial for pharmacological efforts to improve drug design. Despite their significance, accurately placing water molecules within protein structures remains a significant challenge due to technical difficulties in resolving and modeling their positions(11).

Accurate identification of water is still an ongoing area of research even in atomic resolution X-ray structures and is becoming an important focus in cryo-EM map analysis(12)^,(13). In X-ray crystallography, anomalous dispersion methods combined with computational techniques for generating omit maps can be used to distinguish between ions and ordered waters, owing to different scattering potential of these entities. In cryo-EM, omit maps can also be employed for placing water molecules, but their use typically requires resolving the map to sub-2 Å, such that density for hydrogen atoms can be discerned(14). In principle, the ability of the electron beam to differentially scatter oxygen at different spatial frequencies can be exploited to visualize water molecules, but approaches built on these ideas have not yet gained traction(15,16). The typical workflow for modeling waters into cryo-EM maps involves assigning waters into bumps of density (without the use of omit maps and, typically, at user-defined contour values for the map), refining the model against the experimental map, and validating the refined positions using knowledge of chemistry and/or tools such as Undowser in Molprobity(17). This process is iterated until a suitably high-quality model is obtained.

The experimental placement and validation of waters into cryo-EM densities remains prone to error, especially for maps derived at resolution below ~2.5 Å. Several computer-aided methods have been devised to place water into experimental densities, to simplify the above steps, and/or to improve and validate the accuracy of placement. Recent advancements involve the use of neural networks to position water molecules around proteins(18–20). The Metric Ion Classification (MIC) tool is the latest deep learning method that is derived from training data on published X-ray and cryo-EM structures and facilitates distinguishing between waters and ions(21).

Molecular dynamics (MD) based approaches have a long history of use as a tool to solvate protein and nucleic acid structures determined by X-ray crystallography, and NMR(22–25). In early work using myoglobin as a model system, hydration site consistency with MD was compared across three crystal structures (26), conceptually similar to the approach taken here using apoferritin as a model system. MD methods can provide valuable information to facilitate placing and refining waters in cryo-EM structures by offering a likelihood-based method for placing waters at key locations, validating observed densities in cryo-EM maps, and serving as an alternative when water densities are not fully distinguishable from noise, which is often the case, except at the highest resolutions. By simulating the behavior of water molecules around the macromolecule, MD can help identify probable water positions and improve the accuracy of solvent identification and refinement in cryo-EM structures. Empirical techniques based on interaction energies(27) or knowledge-based models have been widely applied to water modeling over the past few decades. However, their reliance on crude approximations—particularly the treatment of the binding energy of water without accounting for entropy—limits both their accuracy and their transferability across different chemical and physical environments(28). Papoian et al.(29) explored the complex role of water in protein folding and function, highlighting the limitations of traditional energy calculations and emphasizing the need for more detailed thermodynamic metrics. Young et al.(30) used MD simulations combined with inhomogeneous fluid solvation theory to evaluate the binding enthalpies and entropies of interfacial water molecules in protein–ligand complexes, demonstrating how the properties of water molecules that solvate confined regions of protein active sites can contribute to enhanced binding affinities. Grand canonical Monte Carlo (GCMC) methods(31) allow water molecules to fluctuate in protein cavities, but require complex and time-consuming simulations to approximate realistic conditions(32). Alternatively, free-energy methods like FEP and thermodynamic integration can calculate absolute binding free energies of water molecules(33,34), but the large number of simulations needed makes routine application challenging. Recently, Roh et. al integrated cryo-EM and molecular dynamics (MD) simulations to cross-validate ordered water molecules along the proton path of yeast V_o in cryo-EM maps(35). An MD-based framework using peak water density has also been employed to identify and place water molecules into cryo-EM maps of RNA, capturing both the static and semi-ordered hydration layers and providing a more comprehensive view of the hydration landscape(36). However, the predictions exhibited a substantial accuracy gap relative to experimental density and were structurally region-dependent(36).

Given the limitations of current techniques, we sought to develop a molecular simulation methodology grounded in statistical thermodynamics that is capable of rapidly and accurately determining the water locations in cryo-EM structures. The statistical thermodynamic characterization of interfacial phenomena is essential for understanding numerous biophysical and chemical events, including protein folding, ion channel gating, the membrane permeability, and the formation of protein assemblies. It also has relevance to the energy industry for applications like electrolyte transport through pores(37–40). There is a large literature reporting the use of MD simulations and companion statistical methods to analyze the structural and thermodynamic properties of water at protein interfaces(41–43). According to multiple studies, analyzing the excess chemical potential (WT, the Work to Transfer a water molecule from the bulk to the interface) is central to the problem of interpreting interfacial processes and the statistical thermodynamics of liquids(44–46). The excess chemical potential of solvent at the protein interface is expressed as the difference between the free energy of insertion of the solvent at the interface and its insertion in the bulk far from the protein. WT can also be determined by the ratio of the local density of water molecules around a protein to the bulk density. We have recently shown that designing tighter binding ligands can be aided by knowledge of the excess chemical potential of hydrating water at protein-ligand binding sites(4).

Here, we develop a procedure built on the quantitative evaluation of the excess chemical potential to assign waters at the protein interface – without any experimental density restraints – and used these signatures to identify and cross-validate the locations of waters in cryo-EM structures. The target system we employ is apoferritin (shown in Figure 1A), which plays a role in iron storage and regulation within living organisms(47). Over the last decade, apoferritin has been routinely used as one of the primary benchmark systems for developing novel methods for cryo-EM structure determination. Most of the highest atomic-resolution cryo-EM structures solved have been that of apoferritin(48,49). As an initial benchmarking exercise, we first compare water positions across nine high-resolution (better than 1.5 Å) experimental structures of apoferritin, identifying clusters of waters present in all nine structures. We use these water clusters to develop criteria for assigning water positions as “high consensus” (present in five or more high resolution structures) or “low consensus” (present between one to four high resolution structures) based on the number of high-resolution cryo-EM maps that identified water at a given location. Next, we analyze the statistical thermodynamic properties of these “high consensus” and “low consensus” interfacial water locations by evaluating their interaction energies with apoferritin and excess chemical potentials (WT). This analysis provides insights into the correlation between the strength of the excess chemical potential and the likelihood that a water location was identified in the benchmark set of apoferritin structures with high or low consensus water positions. Finally, we evaluate the excess chemical potential of water as a function of position within the first hydration shell at the protein interface and use these signatures to identify the locations of high-density interfacial waters. We then compare the de novo MD-based placement of water molecules with water locations identified in apoferritin cryo-EM structures deposited in the PDB. We investigate potential reasons for inconsistencies in the identification of water positions when comparing the high excess chemical potential sites with water positions listed in a set of apoferritin PDB structures. We speculate why some locations with highly favorable excess chemical potential are not resolved as water density in the cryo-EM maps.

Figure 1:

The quaternary structure of apoferritin and a close-up view of a single monomer (cyan). (A): Apoferritin is a protein shell consisting of 24 identical subunits (PDB ID: 7A4M). (B): Selected high consensus (red) and low-consensus (blue) waters are shown on a single apoferritin subunit (PDB ID: 7A4M).

This study contributes to the development of new tools for identifying waters in cryo-EM structures based on the principles of statistical thermodynamics in the absence of experimental density restraints. By understanding the statistical thermodynamic properties of water at the protein interface, researchers can gain deeper insights into how solvation contributes to the stability of folded proteins, the role played by solvent in protein function, as well as design better therapeutic molecules that exploit the unique environment at protein-water interfaces.

Methods

System Preparation and Molecular Dynamics Simulations

High-resolution cryo-EM structures serve as a foundation for identifying water molecules at protein interfaces. The starting structure of apoferritin for the MD simulation is derived from the cryo-EM structure (PDB 7A4M (chain A) shown in Figure 1B). The MD simulations were conducted using the GROMACS 2020.3 suite. The ff99SB force field together with the explicit TIP3P solvation model was adopted to describe the protein and the solvent effects. Apoferritin was placed at the center of a cubic box, and the distance between apoferritin and the edge of the box was set to be ≥ 1.0 nm. The final simulation box contains apoferritin, 23,038 randomly added water molecules and 5 Na⁺ ions, with a total of 71,892 atoms in the system. The procedure began with energy minimization to relax the initial configuration, followed by a 100 ps equilibration in the NVT ensemble and a 5 ns equilibration in the NPT ensemble, both with restraints on the protein heavy atoms. The production run was carried out in the NPT ensemble with all protein atoms fixed for 1 μs at a temperature of 300 K and a pressure of 1 atm. Temperature control was achieved using a modified Berendsen thermostat, while pressure was regulated to 1 bar with a compressibility of 4.5 × 10−⁵ bar using the Parrinello-Rahman barostat(50). Electrostatic interactions were treated using the particle mesh Ewald (PME)(51) method with a real-space cutoff of 1.0 nm. The MD simulations were executed with a time step of 1 fs, and trajectory files were saved every 0.2 ps. For the WT analysis, 100,000 frames were extracted from the 1 μs trajectory by selecting every 5^th frame within the 300 ns to 400 ns time window. The WT analysis was also repeated using frames from 800–900 ns, and the results were consistent with those from the first interval.

Interaction Energy Calculations for High- and Low-consensus Waters

The methodology for categorizing high- and low-consensus water positions (196 water clusters shown in Figure 3) is detailed in the Results section. We first incorporated 196 water molecules, one representative of each cluster, into a single apoferritin monomer (7A4M(52)), solvated the system using the TIP3P water model in a cubic box, and neutralized by adding 5 Na⁺ ions, as described in the System Preparation section. The process began with energy minimization to relax the initial configuration, followed by a 100 ps equilibration in the NVT ensemble and a subsequent 100 ps equilibration in the NPT ensemble. During the minimization step, the 196 water oxygens were harmonically restrained, while both the 196 water oxygens and protein heavy atoms were restrained during the NVT and NPT equilibration simulations. The rest of the parameters are the same as the System Preparation section. Lastly, the total interaction energy between the protein and each water was calculated using the final frame of the NPT equilibration and extracted by the gmx_energy module. Nonbonded interaction energies (Coulombic and Lennard-Jones) were computed to quantify the strength of interactions between the protein and each water.

Figure 3:

Water cluster sizes range from 1 to 9, with a size-9 cluster indicating that the water is present in all nine cryo-EM structures. The high-consensus water clusters (cluster size 5–9) are shown in red, and the low-consensus water clusters (cluster size 1–4) are shown in blue. These water molecules are within 3.25 Å of the apoferritin structure, ensuring proximity to the protein’s surface. Additionally, they are separated by a minimum distance of 1 Å from one another to maintain spatial distinction and avoid overlapping density.

WT calculations for High- and Low-Consensus Waters

The WT for the 196 unique water positions in Figure 3B is calculated as described here. In Figure 2 and Equation 1, the excess chemical potential of a water molecule can be estimated as the free energy difference ΔF(x) − ΔF(∞) or the density ratio −kT ln $\frac{\mathit{\rho }\left(\mathbf{\text{x}}\right)}{\mathit{\rho }\left(\mathit{\infty }\right)}$ (ρ(∞)=0.033Å⁻³).

$$\Delta \text{F}\left(\mathbf{\text{x}}\right)-\Delta \text{F}\left(\infty \right)=\text{WT}\left(\mathbf{\text{x}}\right)\cong -\text{kT}\text{ln}\frac{\rho \left(\mathbf{\text{x}}\right)}{\rho \left(\infty \right)}={\text{E}}_{\text{p}-\text{w}}\left(\mathbf{\text{x}}\right)+\omega \left(\mathbf{\text{x}}\right)$$ Equation 1

E_p-w(x), the direct term, is the average interaction energy of the protein with a water at x, and ω(x), the indirect term, is the contribution to the free energy difference between a water at x and a water in the bulk, due to its interactions with all of the other solvent species, water and ions in the system, interacting with the water at x relative to the corresponding interactions in the bulk(4,44,53–55). Numerically, we use −kT ln $\frac{\mathit{\rho }\left(\mathbf{\text{x}}\right)}{\mathit{\rho }\left(\mathit{\infty }\right)}$ to estimate WT (dV) by gridding space into very small cubic voxels used to calculate the density $\mathit{\rho }\left(\mathbf{\text{x}}\right)$. For calculating WT for the 196 water positions identified in the PDB structures, we created a grid around each reference oxygen position, extending 0.5 Å in the x, y, and z directions. The grid consists of fine cubic voxels with an edge length of a=0.005 Å and volume 𝑑𝑉=a³. Subsequently, we selectively compute WT using the densest fine voxels, which is the top 1% of the 8 million cubic voxels for each reference position, or n=80,000 fine voxels. The Boltzmann average WT is calculated as the sum of the exponential of all WT (dV) values (Equation 1) divided by the sum of volume of the n fine voxels (Equation 2).

Figure 2:

The excess chemical potential of a water molecule at x, can be estimated by the difference between the solvation-free energy for growing a water molecule at x, ΔF(x), and the solvation-free energy for growing a water molecule in the bulk ΔF(∞) (or the pure liquid ΔF(0)). The excess chemical potential can also be calculated by the log ratio of the local density (ρ(x)) of water molecules around a protein to the bulk density (ρ (∞): 0.033Å-3).

$$〈e^{-\beta WT\left(V\right)}〉=\frac{{\int }_0^R{e}^{-\beta WT\left(dV\right)}dV}{{\int }_0^{R}dV}\to \text{WT}\left(\text{V}\right)=-\text{RT*ln}\frac{\sum e^{-\beta WT\left(dV\right)}\cdot dV}{V}=-\text{RT*ln}\frac{\sum e^{-\beta WT\left(dV\right)}}{n}$$ Equation 2

Waters Predicted by the Excess Chemical Potential

We first search for locations of high-water density by counting all water molecules within 3.25 Å of apoferritin(56), covering the first hydration shell, from 100,000 frames of MD simulations (see System Preparation section) using a coarser grid with voxel edge length of 0.1 Å, resulting in a total of approximately 240 million coarse voxels. This grid is also used to visualize the water distribution around apoferritin. A sliding cube of 10 × 10 × 10 such voxels, with a total edge length of 1 Å, is used as a convolution window to identify the 1 Å sized regions with the most water molecules. We then filter these so that each 1 Å cube must be at least 2.2 Å apart from each other and at least 2.25 Å away from apoferritin. From 100,000 frames of MD trajectory, the average position of the waters within each qualifying 1 Å cube is calculated and set as the predicted water position. The center of each qualifying 1 Å cube is used as the reference position for the subsequent WT calculations.

Evaluation Metrics: Precision and Recall

$$\mathit{\text{recall}}=\frac{TP}{TP+FN}\mathit{\text{precision}}=\frac{TP}{TP+FP}$$ Equation 3

True positive (TP) predictions refer to the number of predicted water molecules that match experimental water positions in apoferritin within 2.2 Å. False positive (FP) predictions represent the number of the predicted water molecules that do not match any experimental water, while false negative (FN) predictions indicate the number of experimental water molecules that are not matched to any predicted water (Equation 3). In this evaluation, each predicted water is assigned to its closest experimental water, with only one prediction counted per experimental water.

Cryo-EM Image Processing by Confidence Maps

We obtained raw movie frames from EMPIAR deposition 10424 and used 1689 movies for the entire analysis. All the data processing steps were carried out in CryoSparc v4.6(57,58). Movies were imported using an up-sampling factor of 2 and frames were grouped into 31 fractions. Movie frames were aligned using Patch Motion Correction with an output crop factor of 1/2 and B-factor of 500 for global alignment. Micrograph CTF estimation was performed using Patch CTF estimation. Particle picking was first performed using a combination of Blob Picker followed by Template Picker with suitable classes selected after 2-D classification of extracted particles. All particles were extracted using a box size of 512 pixels. All 2-D classifications have an inner and outer mask diameter of 125 and 140 Å, respectively. A total of 186,280 particles were obtained after iterative 2-D classification steps. An initial volume was generated through Ab Initio reconstruction of 158,100 particles with window inner and outer radius of 0.5 and 0.9 respectively and octahedral symmetry imposed. Using this initial volume, Euler angles were refined for the 186,280 particles using Homogeneous Refinement with iterative refinements accounting for per-particle defocus optimization, per-group CTF parameters accounting for tilt, trefoil, spherical aberration, tetrafoil and magnification anisotropy. A final refinement was performed accounting for Ewald Sphere curvature correction using positive curvature. Refined particles, volume and mask were then used for Reference-Based Motion Correction (RBMC) to optimize motion-correction of particle images and for improved dose-weighting(59,60). Finally, unbinned particles obtained from RBMC were re-refined to obtain a map at 1.33 Å global resolution. Random subsets of 180,000, 90,000, 45,000, 22,500, 11,250, 6,000, 3,000, 1,500, 750 and 200 particles were selected using the Particle Subsets tool and subjected to Homogeneous reconstructions to obtain maps resolved to progressively lower global resolutions as a function of decreasing particle number. Maps obtained from these reconstructions were used as inputs to derive Confidence Maps within the CCPEM software suite(61,62). A noise box of 192 pixels was used with an input pixel size of 0.228 and a box size of 1024. Correction method of FDR-BY was employed using a two-sided test procedure. The rest of the parameters were default. Positions of waters were assessed at 0.1, 1 and 5% FDR. All visualizations were performed in Chimera or ChimeraX (UCSF)(63,64).

Results

In this section, we first compare water positions across nine high-resolution experimental apoferritin structures. We then present the development and evaluation of a method for predicting water positions around the apoferritin structure, based on calculating the excess chemical potential (WT).

High- and Low-consensus Water Positions Derived from the Comparison of Nine High-Resolution Experimental Apoferritin Structures

Prior to analyzing the statistical thermodynamic properties of interfacial water molecules, we compared the water positions across several experimental apoferritin structures. We obtained nine structures of apoferritin that were resolved by cryo-EM to 1.5 Å or higher (PDB IDs: 8RQB(65), 7A6A(48), 8J5A(66), 7A4M(52), 6Z6U(48), 7RRP(67), 7A6B(48), 7K3V(67), and 7K3W(67)) (Table S1) from RCSB-PDB(68). We then aligned these nine PDB structures to one another and identified a total of 1,626 water molecules within 4 Å of a single apoferritin protomer when aggregated across all nine structures. We then grouped these positions into “clusters” by connecting any pair of water molecules that are less than 1 Å apart from one another and identified the disconnected sets of positions. For each cluster, the mean position of the water molecules was calculated. Clusters in which the mean position was more than 3.25 Å away from the apoferritin structure—the cutoff for the first hydration shell—were discarded, resulting in 196 unique water locations. The distribution of the number of clusters as a function of the number of water molecules per cluster is shown in Figure 3. Water positions identified in five or more high-resolution cryo-EM structures were designated as high-consensus water positions, while those found in only one to four structures were classified as low-consensus water positions. Select high-consensus (red) and low-consensus waters (blue) are shown on the surface of the apoferritin monomer (Figure 1B). A higher proportion of low-consensus waters are located near the more flexible regions of apoferritin compared to the high-consensus waters.

Statistical Thermodynamics of High- and Low-Consensus Waters

To elucidate whether the differences between high-consensus and low-consensus water positions can be attributed to the strength of the protein-water interactions, we calculated the total interaction energy of each of these water molecules with apoferritin. As shown in Figure 4A, the interaction energies of the high-consensus and low-consensus water positions overlap, i.e. they are not well separated as a function of the interaction energy with the protein, which indicates that interaction energy with the protein alone does not sufficiently distinguish between these two groups. This underscores the need for alternative approaches to differentiate between high- and low-consensus water positions more effectively.

Figure 4:

The interaction energy and WT between the protein and the 196 waters. (A): The interaction energy between the protein and high-consensus (red) and low-consensus (blue) water positions is shown. (B): Excess chemical potential (WT) values are illustrated for the high-consensus (red) and low-consensus (blue) water positions. The grey shaded areas represent the top 60 waters, ranked by interaction energy or WT values.

One such alternative method involves calculating the “excess chemical potential” (schematic diagram shown in Figure 2), which quantifies the extent to which the presence of the protein alters the thermodynamic properties of water molecules compared to their behavior in bulk water. The excess chemical potential for a water molecule at position (x) is a statistical thermodynamic quantity that can be estimated by the difference between the solvation-free energy for growing a water molecule at (x), ΔF(x), and the solvation-free energy for growing a water molecule in the bulk ΔF(∞) (i.e. the pure liquid). The excess chemical potential is the “work to transfer” (WT) a water molecule from the bulk to the interfacial position at (x); it is proportional to the log ratio of the local density (ρ(x)) of water molecules at positions located at the interface of the protein to the bulk density (ρ(∞))(44). Details of the excess chemical potential (WT) calculations by the density ratio method are provided in the Methods.

Using the MD simulation trajectory of a single apoferritin monomer solvated by ~23,000 water molecules, we calculated the water density and the WT at the oxygen coordinates corresponding to each of the 196 unique water positions identified previously (see Methods). Our results, shown in Figure 4A and 4B, indicate that high-consensus water positions have significantly more favorable WT values compared to low-consensus water positions. This implies that waters at high-consensus positions are more localized, and therefore the water density is higher than at low-consensus positions, according to Equation 1. The WT values for high-consensus waters generally range from −3.5 to −4.8 kcal/mol, while for low-consensus waters WT values typically range from −1.2 to −3.5 kcal/mol. Of the 60 water locations with the most favorable WT values in Figure 4B (grey shadow), 6 correspond to a low-consensus water position, while 21 out of 60 water locations with the most favorable interaction energies (grey shadow in Figure 4A) correspond to low-consensus water positions. This distinction suggests that WT values are an effective metric for differentiating high-consensus waters from low-consensus waters on the surface of apoferritin.

Table S3 in the SI lists the excess chemical potential, the direct protein-water interaction energy, and the indirect free energy component for each of the top 60 water locations ordered by excess chemical potential, WT, (Figure 4B right) and by average interaction energy, Ep-w (Figure 4A left). The average chemical potential, direct interaction energy with the protein, and indirect term for the 60 experimental water locations with the most favorable excess chemical potential are: WT = −4.4 ± 0.17 kcal/mol, Ep-w = −9.6 ± 4.0 kcal/mol, and ω= +5.2 ± 4.0 kcal/mol. The corresponding values for the top 60 experimental water locations ranked by the strength of the protein water interaction energy are: WT = −3.6 ± 1.0 kcal/mol, Ep-w = −12.8 ± 2.8 kcal/mol, and ω = +9.2 ± 3.0 kcal/mol. While the average excess chemical potentials for the two sets of water locations differs by less than 1 kcal/mol, the sixty water locations with the most favorable protein-water interaction energy are associated, on average, with a significantly more repulsive indirect contribution to the excess chemical potential than the sixty water locations with the most favorable excess chemical potentials ( +9.2 kcal/mol vs. +5.2 kcal/mol). This indicates the solvent structure in the environment close to the interfacial water locations with the strongest attraction to the protein surface are more perturbed relative to the bulk. We note also that there are many high-density interfacial water locations with very favorable excess chemical potential values that interact relatively weakly with the protein. For example, at the second most dense (WT = −4.70 kcal/ mol) interfacial water location corresponding to a high consensus position, the attractive interaction energy with the protein is only −5.4 kcal/mol; the opposing indirect term is also small (ω = +0.7 kcal/mol). In contrast, some of the low consensus cryo-EM water locations are associated with locations with the strongest attractive interaction energies with the protein. The possible functional implications of these observations, as well as the implications for identifying in cryo-EM maps, water locations that are less dense but interact very strongly with the protein, remain to be investigated.

Validation of Predicted Waters by Comparison with Experimental Waters

We evaluated our method by assessing how well high- and low-consensus water positions are reproduced by calculating the distances between the WT method-predicted water positions and those observed experimentally in apoferritin structures derived from cryo-EM. These experimental structures include 9 apoferritin structures with resolutions higher than 1.5 Å (designated as Group A PDBs) and 17 apoferritin structures with resolutions between 1.5 Å and 2.0 Å (designated as Group B PDBs); details are provided in Table S1. The rationale for choosing 2.2 Å as the water match distance cutoff is severalfold: first, as shown in Figure S1, the interaction between two hydrogen-bonded water molecules with optimal orientation is highly repulsive at 2.2 Å, indicating that predicted and experimental waters can be considered the same when they are within this distance. Second, this distance is the standard default recommendation for the lower distance limit to distinguish between individual solvent peaks within experimental protein refinement software, such as Phenix. Finally, previous studies have demonstrated that the cutoff distance for matching experimentally determined and predicted water positions ranges from to 2.5 Å(18,69,70).

Figure 5 shows the top 200 predicted water positions based on the most favorable excess chemical potential (WT) values. Of these, 92 and 29 waters are categorized as high-consensus (red filled circles) and low-consensus (blue filled circles), respectively, with an oxygen-oxygen match distance cutoff 2.2 Å. There are also 21 waters that are within 2.2 Å of the Group B PDB water molecules (red empty diamond). The 58 remaining waters (black stars) are positioned outside the 2.2 Å cutoff of either Group A or Group B PDBs. The WT threshold was selected so that the number of predicted waters (200) closely matched the number of experimental waters (196). The 200 WT values range from −4.8 to −3.8 kcal/mol, corresponding to a density difference of less than 10-fold. However, the water density at these positions exceeds the bulk density by over 1000-fold. The large majority of the matched predicted water molecules are located within 1.0 Å of the experimental waters, as shown in Figure S2. Among the 100 water locations with the most favorable excess chemical potentials, 85% are within 2.2 Å of a water molecule location identified in a cryo-EM map of 2.0 Å or higher resolution.

Figure 5:

Among the 200 most densely populated water positions predicted by excess chemical potential (WT) from MD simulations, 92, 29, and 21 predicted waters are within a cutoff distance of 2.2 Å from high-consensus waters (red filled circle), low-consensus waters (blue filled circle), and group B PDBs (red empty diamond), respectively. The black star represents predicted waters that are not within 2.2 Å of any water molecules in group A or group B. Group A PDBs have resolutions higher than 1.5 Å, while group B PDBs have resolutions between 1.5 Å and 2.0 Å.

We calculated the precision and recall for predicted water positions across various excess chemical potential thresholds, as defined in the Methods section. Figures 6A and 6B illustrate the precision and recall for four datasets: high-consensus experimental water positions from Group A PDBs (red), low-consensus experimental water positions from Group A PDBs (blue), the sum of high-consensus and low-consensus positions from Group A PDBs (grey), and the combined water positions from both Group A and Group B PDBs (purple).

Figure 6:

Precision-recall curves (PRC) are shown for the top 200 predicted water positions based on WT values with a 2.2 Å distance cutoff. The curves for high-consensus waters, low-consensus waters, and their sum (experimental waters from group A PDBs), and the sum of all waters from group A and group B PDBs (all experimental waters) are presented in red, blue, grey, and purple, respectively.

In Figure 6, the precision is notably higher for high-consensus waters (red curve) compared to low-consensus waters (blue curve). The accuracy of the predicted waters is particularly striking: approximately 70% of the top 200 predicted water positions (purple square), indexed by WT values, align with water positions observed in experimental apoferritin structures (match distance cutoff: 2.2 Å). This precision increases to 85% if we compare the 100 most densely populated waters predicted by the excess chemical potential to experimental waters (to the left of the black vertical line in Figure 5). Additionally, as shown in Figure 6, the excess chemical potential method successfully recovers 74% of the high-consensus water positions (red square). Using a 2.2 Å cutoff distance, 62% of the experimental waters resolved from Group A PDBs (sum of high-consensus and low-consensus positions) are reproduced (grey square) when the WT threshold is set so that the number of predicted waters matches the experimental count (196).

Although most (>85%) of the predicted water positions with very favorable excess chemical potential values align with those observed in cryo-EM structures, a small subset of these waters does not correspond to experimentally observed water molecules. For example, some waters appear to be caged by side chains of various apoferritin residues (Figure 7). In the 100 ns MD trajectory, we observed that the caged waters exchange with surrounding waters at least 60 times, indicating that they are not trapped in the sites. This discrepancy may be attributed to several factors. (i) The pH, ion concentration, temperature, and other conditions during cryo-EM data collection differ from those used in the MD simulations. All these factors can contribute to protein hydration at specific locations, leading to discrepancies between experimental cryo-EM maps and MD simulations. (ii) Because a single protomer is used in our MD simulations, some predicted water molecules overlap with the side chains of adjacent protomers, and waters at the interface of two or more protomers may not be accurately predicted. (iii) Furthermore, in the MD simulations, the apoferritin protomer is fixed in position, which may impact the identification of waters near the flexible regions of the protein. (iv) There is also the possibility that the water density in the cryo-EM reconstruction is weak, leading to its omission in model building and map annotation. The Chiu lab(35) has also identified additional reasons for the absence of MD-derived waters in experimental structures: (a) limitations of the classical force field in MD simulations, which might not fully capture polarization effects, and (b) differences in time scales between the methods—cryo-EM averages multiple chemical states over milliseconds during vitrification, while MD simulations capture a single state over much shorter, nanosecond to sub-millisecond, intervals(35).

Figure 7:

Two caged waters predicted from favorable excess chemical potential values are shown within the apoferritin structure. Red dots represent the oxygen atoms of caged water molecules, pink indicates residue atoms within 5 Å of the caged waters, and grey cartoon represents the apoferritin structure.

Overall, our results demonstrate that the excess chemical potential of waters at the protein interface evaluated from MD simulations can be effectively used to predict water positions in cryo-EM structures.

Analysis of the cryo-EM Apoferritin Structure using Confidence Maps at Various Resolutions

Following the identification of high-consensus and low-consensus water positions, we next assessed how the size, shape, and number of identified water molecules changes as a function of resolution. To do this, we reprocessed a cryo-EM dataset of apoferritin (EMPIAR-10424, EMDB 11638) and reconstructed maps using incrementally fewer particle numbers, yielding reconstructions at progressively lower resolution. We then calculated confidence maps derived from cryo-EM density maps at each of the resolutions. The confidence maps can be thresholded at different false discovery rates (FDR), which define the level of stringency applied when identifying water densities in the maps. Lower FDR values (1% or less) indicate higher confidence in the observed densities, whereas higher FDR values (above 1%) indicate lower confidence. Figure S3 shows the cryo-EM apoferritin maps at various resolutions, each thresholded at the 1% FDR, as well as the density of Y168 side-chain displayed at the bottom of each respective map. This figure helps to visualize how the map features vary as a function of particle numbers used in the final reconstruction. The detailed procedure for this analysis is provided in the Methods section.

All high-consensus water positions with strong WT values (−4.55 ~ −4.46 kcal/mol) that are consistently observed across all nine PDB structures display approximately spherical density distributions (Figure 8A–C at resolution 1.34 Å). By contrast, low-consensus water positions with weaker WT values (−3.76 ~ −3.31 kcal/mol) exhibit irregular and diffuse density distributions (Figure 8D–F at resolution 1.34 Å). High-consensus water positions remain clearly identifiable in confidence maps obtained from lower-resolution reconstructions (Figure 8A–C at resolution 2.21Å), whereas low-consensus water positions exhibit greater variability across the resolution spectrum compared to high-consensus water positions (Figure 8D–F at resolution 1.67Å and Table S2). Supplementary figure S4 includes an expanded view that shows the surrounding residues, allowing the changes in water density across resolutions and thresholds to be visualized in the context of the local chemical environment.

Figure 8:

High-consensus (A–C) and low-consensus (D–F) waters are observed in confidence maps derived from cryo-EM data across a range of resolutions (1.34 Å, 1.53 Å, … 3.84 Å). These maps are displayed at a 1% false discovery rate (FDR) threshold.

Figure 9 illustrates the number of observable waters per residue identified in the cryo-EM maps at the positions of the 196 high and low consensus waters (group A PDBs) that were thresholded at a 1% FDR, as a function of resolution. The figure also includes a red line, which shows the predicted number of water molecules by WT. To determine this value, we used the experimental cryo-EM to benchmark and validate predicted positions from WT. To enable direct comparison with experimental data, the 200 waters with the highest WT values were selected, yielding a count closely matching the experimentally resolved group A waters (196). Among these, 142 positions overlap with experimental waters (Figure 5). Normalizing this number by the total apoferritin residue count produces the red curve (~0.8) shown in Figure 9. Notably, the predicted number of water molecules per apoferritin residue is independent of experimental resolution, as simulations were conducted using the PDB apoferritin structure without applying experimental density restraints to water. Our number of ~0.8 waters per amino acid is consistent with previous estimates based on high-resolution data from the PDB. For example, Biedermannová et al suggested a water:amino acid ratio of ~0.9(71). Nittinger et al indicated a large variability in the water:amino acid content that is dependent on the protein, but also found that on average this number is ~0.75:1 (with a median value of ~1:1)(72).

Figure 9:

The number of water molecules per apoferritin residue is plotted as a function of map resolution. Data analyzed on confidence maps at 1% false discovery rate (FDR) threshold.

The inclusion of water molecules in cryo-EM models is highly dependent on the resolution of the structure. Extrapolating the curve in Figure 9, it is apparent that the resolution of the experimental structure needs to be ~1.0 Å to resolve all the 0.8 water molecules per residue in apoferritin. Again, the number of waters in the cryo-EM apoferritin model (PDB 7A4M) based on this extrapolation is consistent with estimates from deposited high-resolution X-ray crystal structures, which indicate ~0.9 ± 0.5 water molecules per protein residue(71). As the resolution of the experimental maps decreases, so does the number of confidently assigned water molecules. At the 1.34 Å resolution corresponding to our best experimental reconstruction, we observe ~0.65 water molecules per residue. At resolutions of 2.0 Å, 2.5 Å, and 3.0 Å, we observe ~0.4, ~0.2, and ~0.1 water molecules per residue, respectively. Below a resolution of ~3.25 Å, water molecules are no longer identifiable. This trend is similar to that of a prior study of apoferritin cryo-EM structures, where density associated with a water molecule is observed at 2.3 Å but not at 3.1 Å(73). The results from visualizing maps at 0.1% and 5% false discovery rate (FDR) threshold are shown in Figure S5. Despite varying levels of stringency between confidence maps visualized at 0.1%, 1%, and 5% FDR, the trends of observing progressively fewer waters with decreasing resolution are all similar. This result demonstrates quantitatively how resolution limitations can lead to ambiguities and challenges when determining positions of waters based on cryo-EM maps.

Figure 10 illustrates the reliability scores that we have derived based on confidence maps calculated from cryo-EM maps at two different resolutions: 2.7 Å and 1.3 Å. Since cryo-EM maps do not have a uniform scale for thresholding, we have used confidence maps to ensure the thresholding is uniform between maps of different resolution. Water positions at high resolution (1.3 Å) are much more likely to have a reliability score of 1, indicating that the water is clearly observed at that location in the cryo-EM map. By contrast, a reliability score of 0 indicates that the water is not observed at a false discovery rate (FDR) of 1% (see the following section), while a reliability score of 0.5 reflects ambiguous or uncertain density for that water. Similarly, Table 1 shows a strong tendency for waters to be assigned a reliability score of 1 at 1.3 Å resolution (109 out of 128 instances). At 2.7 Å resolution, however, waters are more frequently assigned a reliability score of 0 or 0.5 (104 instances) compared to a score of 1 (24 instances). These findings confirm that the number of experimentally observed water molecules strongly depends on the resolution of the cryo-EM map. We believe the excess chemical potential method described in this study can thus be a powerful resolution-agnostic tool to inform about potential water positions. In future work, we plan to explore approaches that integrate reliability scores derived from cryo-EM maps with excess chemical potential values obtained from MD simulations, to identify highly probable water positions—particularly those with intermediate reliability scores (e.g., 0.5)—in lower-resolution cryo-EM maps.

Figure 10:

The excess chemical potential (WT) values are plotted for two different resolutions: (A) 2.7 Å and (B) 1.3 Å. Water molecules are colored based on their reliability scores: red for waters with a score of 1 (clearly resolved density), blue for a score of 0 (no observable density), and green for a score of 0.5 (ambiguous or uncertain density). Data analyzed on confidence maps at 1% false discovery rate (FDR) threshold.

Table 1:

Number of waters identified at two different resolutions (2.7 Å and 1.3 Å) as a function of reliability score.

Reliability score	1	0	0.5	total
Density	YES	No	Noisy
2.7Å	24	19	85	128
1.3Å	109	5	14	128

Discussion

Accurate water assignment in cryo-EM maps remains error-prone, especially in cryo-EM maps that are resolved to resolutions poorer than 2 Å. Given the challenges faced by experimentalists, it is important to develop diverse tools to assign – and validate – water positions. Although deep learning approaches can help automate water assignments, distinguish waters from metal ions or other species, and provide confidence measures based on prior data, the fundamental limitation of all current approaches is reliance on accurate training data. The often “black box” nature of machine learning approaches, and their reliance on large, and potentially limiting training datasets, implies that physical insight into new positions may be missed. For instance, a recent report highlighted how treating experimental cryo-EM maps with sharpening tools based on deep neural networks can attenuate, or completely eliminate, experimental densities corresponding to ligands and solvent(74). In this regard, the major advantage of our current method is the ability to improve water identification within cryo-EM density maps in a resolution-agnostic manner, based on physical principles that are rooted in statistical thermodynamics.

Our study demonstrates the effectiveness of using statistical thermodynamic properties of water to identify interfacial waters in cryo-EM structures of apoferritin. Moreover, our findings revealed that the average interaction energy with the protein is insufficient for effectively differentiating between high- and low-consensus water positions. By utilizing WT values derived from MD simulations, we can better distinguish between high- and low-consensus water locations. We note the strong prediction performance of our method based on the evaluation of the excess chemical potential, which requires integration of the local water density over a finite volume using an ultra-fine-grained grid for the integration. At a recall rate of 55%, we achieved a precision of 71% for waters from Group A + B PDBs. At the same recall rate, our method outperforms HydraProt(18) (precision 55%). Our approach also exhibits higher precision when compared to a similar MD-based approach that attempted to identify individual positions of peak water density in a fine grained grid (ref 35), where only ~25% of waters were identified as true positives. Also, we found a strong correlation between WT values and reliability scores derived from the confidence map of a 1.3 Å reconstruction. Some waters with very favorable WT values are not observed in the experimental structures, particularly waters that appear to be “caged” by surrounding aromatic side chains. Further analysis and experimentation with variation of density thresholding may be helpful in resolving these discrepancies.

The number of observable waters in cryo-EM models strongly depends on the resolution of the structure. At resolutions below 3 Å, it becomes increasingly challenging to identify water densities, although the most tightly bound waters appear to be identifiable even down to resolutions of ~3.25 Å. At these lower resolutions, water features may either blend with noise or become entirely indistinguishable. Most cryo-EM structures are resolved to between ~2–4 Å(75). For the lower-resolution structures, water densities may thus be difficult or impossible to resolve. As shown in Figure 9, waters that are clearly visible at 1.3 Å largely disappear or become too noisy to distinguish at 2.7 Å. In such scenarios, our WT-method can provide a significant advantage by accurately predicting water positions and distinguishing water densities from noise. This approach not only aids modeling but also accelerates the placement of waters in low-resolution cryo-EM structures, offering valuable insights into structural interpretation. Furthermore, we note that our MD simulations are performed without experimental density restraints, and yet the water positions with very favorable WT values correlate strongly to their corresponding position within experimentally defined maps. This indicates that such tools would likely be useful to boost confidence in annotated water positions, and to identify new water positions and correlated networks of waters that are associated with allostery, based on physical principles and thermodynamic signatures. These ideas can also be extended to identifying and characterizing metal ions within experimental maps. As a specific case study, in maps of lentiviral intasomes, the same peak within the active site of the ligand-bound complex was identified as a chloride ion in one structure(5) but a water molecule in another analogous structure (1). By using the excess chemical potential (WT) of water calculated from molecular dynamics simulations and estimating the excess chemical potential of the ion, it may be possible to distinguish between water and ions at specific locations by comparing their WT values evaluated by a procedure involving post processing of the trajectories to assign the relative likelihood of water vs. ions being located at specific sites.

Approaches that we are developing will build upon the current framework but will also include considerations of local resolution, density restraints to guide the MD simulations, integration of information concerning water locations from cryo-EM confidence maps with maps of the solvent excess chemical potential generated from MD simulations, and iterative model building and density-guided refinement approaches, for optimally hydrating experimental cryo-EM maps.

Statement of Significance.

Predicting water molecules at protein interfaces is critical for structural biology but remains a major challenge. This study introduces a novel molecular dynamics (MD) approach based on the excess chemical potential-or “Work to Transfer”-of water. Using apoferritin as a benchmark, we demonstrate that this approach accurately predicts water positions found in high-resolution cryo-EM maps, without experimental density restraints. With 85% of top-ranked water sites matching experimental data, this work paves the way for advanced cryo-EM refinement tools that integrate MD simulations with experimental data, enabling more accurate and automated modeling of the essential water networks surrounding proteins.

Data Availability

Data are contained within the article and supplementary materials. Additional data will be shared upon reasonable request.