Solute-Solvent Energetics Based on Proximal Distribution Functions

Abstract

We consider the hydration structure and thermodynamic energetics of solutes in aqueous solution. On the basis of the dominant local correlation between the solvent and the chemical nature of the solute atoms, proximal distribution functions (pDF) can be used to quantitatively estimate the hydration pattern of the macromolecules. We extended this technique to study the solute-solvent energetics including the van der Waals terms representing excluded volume and tested the method with butane and propanol. Our results indicate that the pDF-reconstruction algorithm can reproduce van der Waals solute-solvent interaction energies to useful kilocalorie per mole accuracy. We subsequently computed polyalanine-water interaction energies for a variety of conformers, which also showed agreement with the simulated values.

Figure 1

Structures of alanine peptides used in this study: (a) trialanine (ala₃); (b–e) deca-alanine (ala₁₀). For ala₁₀, peptide backbones are represented with red ribbons. For convenience, we designate d, d1, d2, and d3 for the configuration of deca-alanines, respectively. Configurations are visualized using VMD.

Figure 2

pDF of solute atoms and reconstructed solute–solvent van der Waals interaction energy, compared with the values obtained via simulation: (a) pDF of butane atoms to water oxygen with (b) corresponding van der Waals interaction energies. (c) pDF of propanol atoms to water oxygen with (d) corresponding van der Waals interaction energies. CT2, CT3, HA2, HA3, O1, and HO1 are the atom types of butane and propanol. OT is the water oxygen atom label.

Figure 3

Calculated pDFs for atoms from ala₁. CT3, C, O, NH1, CT1, HA3, HN, HB1 are the atom types of alanine. OT is the water oxygen atom type.

Figure 4

van der Waals solute solvent potential atomic component difference $\mathrm{\Delta }{U}_{\mathrm{i}}^{\text{vdW}}$ of ala₃ between simulation and the pDF reconstruction. Note the difference for the solute atom–water hydrogen atoms is scaled by a factor of 20 for clarity. The horizontal axis is the atom type i.

Figure 5

Error (ε) for each atom type of deca-alanine for each conformer.

Figure 6

(a) O–OT (b) O–HT van der Waals accumulated interaction energies as functions of distance from the carbonyl oxygen to water atoms.

Figure 7

Error of each atom type in deca-alanine (configuration d) using (a) different pDF collecting resolution and (b) linear interpolation.