[Paper Review] Bridge functional for the molecular density functional theory with consistent pressure and surface tension and its importance for solvation in water

Cédric Gageat, Luc Belloni+2 more|arXiv (Cornell University)|Sep 28, 2017

Protein Structure and Dynamics6 references3 citations

TL;DR

This paper introduces a novel coarse-grained bridge functional for molecular density functional theory (MDFT) that ensures thermodynamic consistency by correctly reproducing liquid-vapor coexistence, bulk pressure, and surface tension in water. The method achieves solvation free energies within 1 kcal/mol of experiment and accurate solvent density profiles in minutes, significantly improving upon the hypernetted-chain approximation while maintaining numerical efficiency.

ABSTRACT

We address the problem of predicting the solvation free energy and equilibrium solvent density profile in fews minutes from the molecular density functional theory beyond the usual hypernetted-chain approximation. We introduce a bridge functional of a coarse-grained, weighted solvent density. In few minutes at most, for solutes of sizes ranging from small compounds to large proteins, we produce (i) an estimation of the free energy of solvation within 1 kcal/mol of the experimental data for the hydrophobic solutes presented here, and (ii) the solvent distribution around the solute. Contrary to previous propositions, this bridge functional is thermodynamically consistent in that it produces the correct liquid-vapor coexistence and the experimental surface tension. We show this consistency to be of crucial importance for water at room temperature and pressure. This bridge functional is designed to be simple, local, and thus numerically efficient. Finally, we illustrate this new level of molecular theory of solutions with the study of the hydration shell of a protein.

Motivation & Objective

• To develop a thermodynamically consistent bridge functional for molecular density functional theory (MDFT) that correctly captures liquid-vapor coexistence and surface tension in water.
• To improve the accuracy of solvation free energy and solvent density profile predictions in MDFT beyond the hypernetted-chain (HNC) approximation.
• To reduce computational cost to minutes per solute while maintaining high accuracy, enabling application to large biomolecules like proteins.
• To ensure the bridge functional is local and numerically efficient by leveraging fast Fourier transforms in Fourier space.
• To validate the method against experimental data and reference molecular dynamics simulations for a range of solutes, including hydrophobic compounds and protein 4m7g.

Proposed method

• The bridge functional is constructed from a coarse-grained, weighted solvent density to capture non-local correlations in a numerically efficient manner.
• It is designed to be local in Fourier space, enabling fast evaluation via fast Fourier transforms (FFTs).
• The functional is integrated into the MDFT framework by minimizing the total free energy functional composed of excess, ideal, and external contributions.
• The method uses a variational approach to determine the solvent density profile, minimizing the sum of the free energy functionals with respect to the molecular density ρ(r,ω).
• The bridge functional is calibrated to reproduce the correct liquid-vapor coexistence and surface tension, ensuring thermodynamic consistency.
• The approach is validated by comparing MDFT predictions with reference molecular dynamics simulations and experimental data for solvation free energies and radial distribution functions.

Experimental results

Research questions

• RQ1 Can a bridge functional in MDFT be designed to ensure thermodynamic consistency, including correct liquid-vapor coexistence and surface tension in water?
• RQ2 Does the proposed coarse-grained bridge functional significantly improve solvation free energy predictions compared to the standard HNC approximation?
• RQ3 Can the method achieve high accuracy in solvent density profiles and solvation free energies within minutes, even for large biomolecules like proteins?
• RQ4 How does the new bridge functional compare to reference molecular dynamics simulations in predicting hydration shell structures?
• RQ5 To what extent does the bridge functional eliminate spurious prepeaks in radial distribution functions for large hydrophobic solutes?

Key findings

• The proposed bridge functional reduces the mean unsigned error (MUE) in solvation free energy predictions from 23.61 kJ/mol (HNC) to 3.88 kJ/mol, achieving agreement within 1 kcal/mol of experimental data for hydrophobic solutes.
• The method correctly reproduces the surface tension of water and the liquid-vapor coexistence, which previous bridge functionals fail to do, making it essential for accurate water solvation modeling.
• For methane, neon, argon, krypton, and xenon, the solvation free energy predictions are within 1 kcal/mol of experiment, with MUE reduced from 23.61 to 3.88 kJ/mol.
• The hydration shell of protein 4m7g, computed in 20 minutes using MDFT with the new bridge functional, shows strong agreement with a 3-day molecular dynamics simulation at the isosurface of 3× bulk density.
• The bridge functional eliminates spurious prepeaks in radial distribution functions for large hard-sphere solutes, which are common in prior MDFT-HNC approaches.
• The computational cost is reduced by four orders of magnitude compared to all-atom molecular dynamics, enabling rapid, high-accuracy solvation analysis.