Volumetric Properties of Hydrated Peptides: Voronoi–Delaunay Analysis of Molecular Simulation Runs

Abstract

The study of hydration, folding, and interaction of proteins by volumetric measurements has been promoted by recent advances in the development of highly sensitive instrumentations. However, the separation of the measured apparent volumes into contributions from the protein and the hydration water, V(app) = V(int) + ΔV, is still challenging, even with the detailed microscopic structural information from molecular simulations. By the examples of the amyloidogenic polypeptides hIAPP and Aβ42 in aqueous solution, we analyze molecular dynamics simulation runs for different temperatures, using the Voronoi-Delaunay tessellation method. This method allows a parameter free determination of the intrinsic volume V(int) of complex solute molecules without any additional assumptions. For comparison, we also use fused sphere calculations, which deliver van der Waals and solute accessible surface volumes as special cases. The apparent volume V(app) of the solute molecules is calculated by different approaches, using either a traditional distance based selection of hydration water or the construction of sequential Voronoi shells. We find an astonishing coincidence with the predictions of a simple empirical approach, which is based on experimentally determined amino acid side chain contributions (Biophys. Chem.1999, 82, 35). The intrinsic volumes of the polypeptides are larger than their apparent volumes and also increase with temperature. This is due to a negative contribution of the hydration water ΔV to the apparent volume. The absolute value of this contribution is less than 10% of the intrinsic volume for both molecules and decreases with temperature. Essential volumetric differences between hydration water and bulk water are observed in the nearest neighborhood of the solute only, practically in the first two Delaunay sublayers of the first Voronoi shell. This also helps to understand the pressure dependence of the partial molar volumes of proteins.

Biomolecular hydration dynamics: a jump model perspective

“…All the water polyhedra in contact with a biomolecule polyhedron are then considered to be in the first shell (see e.g. 20,21 ).…”

Molecular dynamics study of the volumetric and hydrophobic properties of the amphiphilic molecule C8E6

“…3 shows the behavior of the apparent volume V app (R) of C 8 E 6 molecule calculated by the discussed method (we call it traditional method [15]). The required value is defined by the asymptote of this function.…”

“…It is possible to avoid this problem, if we use another method, called combined [15]. The only difference of this approach from the traditional one is the calculation of V(R) with the help of Voronoi cells.…”

“…But for a molecule the observed increase in the solution volume has contributions from both the solute molecule and the changing of the solvent structure around the solute. Thereby, the observed apparent volume can be written as [12][13][14][15]:…”

pyMolDyn: Identification, structure, and properties of cavities in condensed matter and molecules

“…This approach has been used to analyze defect structures in simulations of radiation damage [CL85] and the motion of vacancies in colloids [LAC13], although the coordination number (the number of faces of the Voronoi cell) is not necessarily a convenient measure of their positions [LAC13]. Similar techniques have been applied to the distinction between solute and solvent in a liquid, such as hydrated peptide molecules [Vetal11].…”