Correlation between Solvation Free Energy and Solute-Solvent Interaction Energy in Energy Representation Theory

Area of Science:

• Computational chemistry
• Biophysics
• Statistical mechanics

Background:

• Classical density-functional theory (DFT) offers a framework for calculating solvation free energy (SFE) via molecular simulations.
• Energy Representation (ER) theory, a type of DFT, utilizes solute-solvent pair-energy distribution functions to bypass intermediate-state simulations.
• Empirical observations in ER calculations show a strong correlation between SFE and solute-solvent interaction energy (SSIE), particularly for proteins.

Purpose of the Study:

• To derive the theoretical basis for the SFE-SSIE correlation within the ER framework, including both electrostatic and van der Waals (vdW) contributions.
• To numerically investigate the relationship between SFE, SSIE, its components, and excluded volume using multiple protein conformations.
• To clarify the utility of ER theory for biomolecular solvation analysis in computationally intensive systems.

Main Methods:

• Utilized Energy Representation (ER) theory for calculating solvation free energy (SFE).
• Analyzed solute-solvent interaction energy (SSIE), including electrostatic and van der Waals (vdW) components.
• Examined 159 conformations of a 20-residue Trp-cage protein to assess correlations.

Main Results:

• Derived the theoretical coefficient of 1/2 for the SFE-SSIE relationship within the ER framework.
• Found that while vdW contributions to SSIE are smaller than electrostatic ones, they improve correlations for similar conformations.
• Demonstrated that electrostatic components of SSIE are accurate with one reference point, but multiple points enhance overall SSIE accuracy.

Conclusions:

• The study clarifies the theoretical foundation of the SFE-SSIE relationship in ER theory.
• The findings underscore the practical utility of ER theory for analyzing biomolecular solvation, especially for complex systems.
• ER theory offers a computationally efficient alternative for solvation free energy calculations in challenging biomolecular systems.