SurfPB: A GPU-Accelerated Electrostatic Calculation and Visualization Tool for Biomolecules

Studying the Protein Thermostabilities and Folding Rates by the Interaction Energy Network in Solvent

Residue interaction networks determine various characteristics of proteins, such as the folding rate, thermostability, and allosteric process. The interactions between residues can be described by distances or energies. The former is simple but less rigorous. The latter is complicated but more precise, especially when considering the solvent effect. In this work, we apply an existing energy decomposition method based on the Poisson-Boltzmann equation solver. The calculation is especially accelerated on GPU for higher performance. In four formal applications, the constructed interaction energy (IE) network shows good results. First, it is found that the protein folding rate has a stronger correlation with the energy-based contact order than the distance-based contact order. The Pearson correlation coefficient (PCC) is 0.839 versus 0.784 on a dataset of non-two-state proteins. Second, we find that most thermophilic proteins have lower IEs than mesophilic proteins. The IE in solvent acts as an indicator to evaluate the thermostabilities of proteins. Third, we use the IE network to predict the key residues in the formation of the insulin dimer. Most key residues are in agreement with the findings in previous alanine-scanning experiments. Lastly, we propose a novel method (called APFN) to predict the allosteric pathway based on the IE network. The method gives the same allosteric pathway for CheY protein as in previous nuclear magnetic resonance spectroscopy experiments. On the whole, the IE network in the solvent has been demonstrated to be reliable in describing the characteristics embedded in protein structures.

Protein solvation: Site-specific hydrophilicity, hydrophobicity, counter ions, and interaction entropy

Solvation free energy is a driving force that plays an important role in the stability of biomolecular conformations. Currently, the implicit solvent model is widely used to calculate solvation energies of biomolecules such as proteins. However, for proteins, the implicit solvent calculation does not provide much detailed information since a protein is highly inhomogeneous on its surface. In this study, we develop an explicit solvent approach to protein solvation, which allows us to investigate detailed site-specific hydrophilicity and hydrophobicity, including the role of counter ions and intra-protein interactions. This approach facilitates the analysis of specific residue interactions with solvent molecules, extending the understanding of protein solubility to the energetic impacts of site-specific residue-solvent interactions. Our study showed that specific residue-solvent interactions are strongly influenced by the electrostatic environment created by its nearby residues, especially charged residues. In particular, charged residues on the protein surface are mainly responsible for the heterogeneity of the electrostatic environment of the protein surface, and they significantly affect the local distribution of water. In addition, counter ions change the local electrostatic environment and alter specific residue-water interactions. Neutral residues also interact with water, with polar residues being more prominent than nonpolar ones but contributing less to solvation energy than charged residues. This study illustrates an explicit solvent approach to protein solvation, which gives residue-specific contributions to protein solvation and provides detailed information on site-specific hydrophilicity and hydrophobicity.

Calculation of solvation force in molecular dynamics simulation by deep-learning method

Electrostatic calculations are generally used in studying the thermodynamics and kinetics of biomolecules in solvent. Generally, this is performed by solving the Poisson-Boltzmann equation on a large grid system, a process known to be time consuming. In this study, we developed a deep neural network to predict the decomposed solvation free energies and forces of all atoms in a molecule. To train the network, the internal coordinates of the molecule were used as the input data, and the solvation free energies along with transformed atomic forces from the Poisson-Boltzmann equation were used as labels. Both the training and prediction tasks were accelerated on GPU. Formal tests demonstrated that our method can provide reasonable predictions for small molecules when the network is well-trained with its simulation data. This method is suitable for processing lots of snapshots of molecules in a long trajectory. Moreover, we applied this method in the molecular dynamics simulation with enhanced sampling. The calculated free energy landscape closely resembled that obtained from explicit solvent simulations.