Yutaka Maruyama

Solvation free energy (SFE) is a fundamental thermodynamic quantity governing biomolecular processes in solution. Although the atomic decomposition method derived from the Kirkwood charging formula enables site-resolved evaluation of SFE contributions, its application within the three-dimensional reference interaction site model (3D-RISM) theory suffers from systematic overestimation relative to benchmark values. Here, we developed the Multi-Input Linear Correction for Atomic Decomposition (MILC-AD) framework by extending the original MILC approach to the atomic decomposition scheme within 3D-RISM theory. Unlike the original MILC framework, which relies on the nondecomposable partial molar volume (PMV), the proposed method uses atomically decomposable solute–solvent interaction energies as descriptors. Validated against 628 molecules from the benchmark FreeSolv database, the framework achieves a mean absolute deviation (MAD) of 0.57 kcal/mol relative to the Bennett acceptance ratio (BAR) calculations using ensemble-averaged predictions over ten conformations per molecule. As a representative application, the method is applied to the 36-residue villin headpiece subdomain HP36, revealing the site-resolved balance between intramolecular packing, SFE, and solvation entropy underlying the cooperative assembly of its hydrophobic core. These results demonstrate the potential of the MILC-AD framework as a practical tool for quantitative, site-resolved thermodynamic analyses of complex biomacromolecular systems.

We extend the multi-input linear correction (MILC) framework to the energy representation (ER) theory to improve the accuracy and robustness of solvation free energy (SFE) predictions. While ER theory offers a computationally efficient route to SFE from solute-solvent pair interaction distributions, its standard functionals often suffer from systematic biases. Although the truncated hypernetted chain (tHNC) functional was developed to reduce these errors, it relies on an empirical truncation parameter that is temperature-dependent and difficult to define for mixed solvents. To overcome these limitations, we propose the MILC-ER scheme, which utilizes a combination of descriptors─approximate SFEs for fully charged and zero-charge states, and the average interaction energy─to capture both electrostatic and excluded-volume effects without empirical truncation. Our model achieves exceptional accuracy on the FreeSolv database (excluding carboxylic acids), yielding a mean absolute deviation (MAD) of 0.35 kcal/mol relative to Bennett acceptance ratio (BAR) values. Critically, we employ a nested cross-validation protocol to provide an unbiased assessment of the model's generalization capability. The results demonstrate that simple linear models consistently outperform complex nonlinear machine learning algorithms, such as Random Forests, confirming that the systematic errors in ER functionals scale linearly with the chosen physical descriptors. This linear framework is not only statistically robust and well-conditioned for small-data regimes but also physically interpretable as a generalized extension of conventional correction schemes. Furthermore, the MILC-ER coefficients remain transferable across different temperatures and successfully generalize to mixed-solvent environments, as demonstrated for ethanol-water systems. These findings establish MILC-ER as a high-precision, computationally efficient, and transferable tool for large-scale solvation studies.

This study introduces the multi-input linear correction (MILC) method to enhance the accuracy of solvation free energy (SFE) calculations with the three-dimensional reference interaction site model (3D-RISM) theory. While the 3D-RISM theory offers significant computational efficiency compared with molecular simulation-based methods, conventional energy functionals─such as the Singer–Chandler or Gaussian fluctuation formulas─often suffer from systematic overestimation of SFEs. In general, partial molar volume (PMV) corrections are employed to account for errors related to hydrophobic and cavity formation energies. To further improve the prediction accuracy, the MILC method employs a physically motivated data-driven approach that incorporates not only the standard SFE components but also physical quantities obtained when the solute atomic charges are set to zero. Accordingly, the method requires two independent 3D-RISM calculations per solute. The robustness and transferability of the MILC method were rigorously validated using a nested cross-validation protocol on 628 molecules in the FreeSolv database (excluding carboxylic acids). By averaging over 10 conformers per molecule, the method achieved a mean absolute deviation (MAD) of 0.38 kcal/mol relative to the benchmark Bennett acceptance ratio (BAR) method. Furthermore, we demonstrate that the MILC method outperforms conventional volume-based corrections and provides predictive performance superior or comparable to complex machine learning models while maintaining high physical interpretability. This level of accuracy and statistical reliability demonstrates that the 3D-RISM theory with the MILC method is a robust and efficient tool for high-throughput applications in drug discovery and material design.

The energy representation (ER) theory is a type of classical density-functional theory that provides a framework for calculating solvation free energy (SFE) using molecular simulations. A key feature is the use of solute-solvent pair-energy distribution functions and approximate functionals, which eliminate the need for intermediate-state simulations. This enables the application of the ER theory to diverse systems, from small molecules to proteins, polymers, interfaces, and membranes. A strong correlation between SFE and solute-solvent interaction energy (SSIE) has been observed empirically in ER calculations, particularly for proteins with multiple conformations, while the linear interaction energy (LIE) method analytically derives the same relationship for the electrostatic component, both with a coefficient of 1/2. In this study, we derived the same coefficient within the ER framework, where SSIE includes both electrostatic and van der Waals (vdW) contributions. Using 159 conformations of 20-residue Trp-cage protein, we numerically examined the relationship between SFE, SSIE, components of SSIE, and excluded volume. The vdW contribution was much smaller than the electrostatic one, yet its inclusion improved correlations within groups of structurally similar conformations. Moreover, we showed that while the electrostatic component achieves sufficient accuracy with a single reference point, the SSIE can be further improved by introducing multiple reference points. These results clarify the theoretical basis of the SFE-SSIE relationship in the ER theory and highlight its utility for analyzing biomolecular solvation, particularly in systems where direct SFE calculations are computationally demanding.

This study introduces the truncated hypernetted chain (tHNC) approximation for calculating solvation free energy (SFE) within the energy representation (ER) theory, demonstrating its improved accuracy. Conventional ER theory employs a hybrid functional that combines the hypernetted chain approximation for attractive interactions and the Percus-Yevick approximation for repulsive ones. However, this functional tends to overestimate SFEs in water, particularly for hydrophobic molecules such as alkanes and alcohols, due to unphysical solute-solvent overlap in the repulsive energy region. To address this, we introduce an energy cutoff parameter E_t, which truncates contributions from the high-energy interaction. This cutoff plays a role analogous to partial molar volume or hardsphere corrections proposed in other theoretical frameworks, effectively mitigating overestimation. Applied to the FreeSolv database (excluding 14 carboxylic acids), the tHNC functional achieved a mean absolute deviation of 0.37 kcal/mol relative to the benchmark Bennett acceptance ratio (BAR) method. The method notably improves predictions for hydrophobic molecules and maintains robust accuracy across variations in molecular size, polarity, and functional groups. The tHNC approximation thus offers a significant advance in accurate and efficient SFE calculation, supporting broader applications in solution-phase chemical and biological studies.

ERmod‐OpenACC is a GPU‐accelerated implementation of a calculation package for the solvation free energy. In the implementation, the most computationally intensive processes—the calculation of the pair energies and the construction of the correlation function—have been optimized for GPUs. ERmod‐OpenACC also supports single precision to maximize performance on RTX series GPUs, which are commonly used in molecular dynamics simulations. A common problem with OpenACC is data transfer between the CPU and GPU. By minimizing data transfer, the package's performance has been significantly improved. Compared to a single Xeon core (3.1 GHz), ERmod‐OpenACC achieves a speedup of up to approximately when running on RTX 4080 SUPER. The package also supports multiple GPUs via MPI, achieving a speedup of with 2 GPUs and approximately with 16 GPUs. The only external library required to compile ERmod‐ACC is NVIDIA HPC SDK. The package is available at https://github.com/drmaruyama/ermod‐openacc.

Solvent plays an essential role in a variety of chemical, physical, and biological processes that occur in the solution phase. The reference interaction site model (RISM) and its three‐dimensional extension (3D‐RISM) serve as powerful computational tools for modeling solvation effects in chemical reactions, biological functions, and structure formations. We present the RISM integrated calculator (RISMiCal) program package, which is based on RISM and 3D‐RISM theories with fast GPU code. RISMiCal has been developed as an integrated RISM/3D‐RISM program that has interfaces with external programs such as Gaussian16, GAMESS, and Tinker. Fast 3D‐RISM programs for single‐ and multi‐GPU codes written in CUDA would enhance the availability of these hybrid methods because they require the performance of many computationally expensive 3D‐RISM calculations. We expect that our package can be widely applied for chemical and biological processes in solvent. The RISMiCal package is available athttps://rismical-dev.github.io.

Proteins that do not fold into their functional native state have been linked to diseases. In this study, the influence of the main and side chains of individual amino acids on the folding of the tryptophan cage (Trp-cage), a designed 20-residue miniprotein, was analyzed. For this purpose, we calculated the solvation free energy (SFE) contributions of individual atoms by using the 3D-reference interaction site model with the atomic decomposition method. The mechanism by which the Trp-cage is stabilized during the folding process was examined by calculating the total energy, which is the sum of the conformational energy and SFE. The folding process of the Trp-cage resulted in a stable native state, with a total energy that was 62.4 kcal/mol lower than that of the unfolded state. The solvation entropy, which is considered to be responsible for the hydrophobic effect, contributed 31.3 kcal/mol to structural stabilization. In other words, the contribution of the solvation entropy accounted for approximately half of the total contribution to Trp-cage folding. The hydrophobic core centered on Trp6 contributed 15.6 kcal/mol to the total energy, whereas the solvation entropy contribution was 6.3 kcal/mol. The salt bridge formed by the hydrophilic side chains of Asp9 and Arg16 contributed 10.9 and 5.0 kcal/mol, respectively. This indicates that not only the hydrophobic core but also the salt bridge of the hydrophilic side chains gain solvation entropy and contribute to stabilizing the native structure of the Trp-cage.

We apply moving root-mean-square deviation (mRMSD), which does not require a reference structure, as a method for analyzing protein dynamics. This method can be used to calculate the root-mean-square deviation (RMSD) of structure between two specified time points and to analyze protein dynamics behavior through time series analysis. We applied this method to the Trp-cage trajectory calculated by the Anton supercomputer and found that it shows regions of stable states as well as the conventional RMSD. In addition, we extracted a characteristic structure in which the side chains of Asp1 and Arg16 form hydrogen bonds near the most stable structure of the Trp-cage. We also determined that ≥20 ns is an appropriate time interval to investigate protein dynamics using mRMSD. Applying this method to NuG2 protein, we found that mRMSD can be used to detect regions of metastable states in addition to the stable state. This method can be applied to molecular dynamics simulations of proteins whose stable structures are unknown.

The binding process of angiotensin-converting enzyme 2 (ACE2) to the receptor-binding domain (RBD) of the severe acute respiratory syndrome-like coronavirus 2 spike protein was investigated using molecular dynamics simulation and the three-dimensional reference interaction-site model theory. The results suggested that the protein-binding process consists of a protein-protein approaching step, followed by a local structural rearrangement step. In the approaching step, the interprotein interaction energy decreased as the proteins approached each other, whereas the solvation free energy increased. As the proteins approached, the glycan of ACE2 first established a hydrogen bond with the RBD. Thereafter, the number of interprotein hydrogen bonds increased rapidly. The solvation free energy increased because of the desolvation of the protein as it approached its partner. The spatial distribution function of the solvent revealed the presence of hydrogen bonds bridged by water molecules on the RBD-ACE2 interface. Finally, principal component analysis revealed that ACE2 showed a pronounced conformational change, whereas there was no significant change in RBD.