Instantaneous, parameter-free methods to define a solute’s hydration shell

The geometry of protein hydration

Based on molecular dynamics simulations of four globular proteins in dilute aqueous solution, with three different water models, we examine several, essentially geometrical, aspects of the protein-water interface that remain controversial or incompletely understood. First, we compare different hydration shell definitions, based on spatial or topological proximity criteria. We find that the best method for constructing monolayer shells with nearly complete coverage is to use a 5 Šwater-carbon cutoff and a 4 Šwater-water cutoff. Using this method, we determine a mean interfacial water area of 11.1 Ų which appears to be a universal property of the protein-water interface. We then analyze the local coordination and packing density of water molecules in the hydration shells and in subsets of the first shell. The mean polar water coordination number in the first shell remains within 1% of the bulk-water value, and it is 5% lower in the nonpolar part of the first shell. The local packing density is obtained from additively weighted Voronoi tessellation, arguably the most physically realistic method for allocating space between protein and water. We find that water in all parts of the first hydration shell, including the nonpolar part, is more densely packed than in the bulk, with a shell-averaged density excess of 6% for all four proteins. We suggest reasons why this value differs from previous experimental and computational results, emphasizing the importance of a realistic placement of the protein-water dividing surface and the distinction between spatial correlation and packing density. The protein-induced perturbation of water coordination and packing density is found to be short-ranged, with an exponential decay "length" of 0.6 shells. We also compute the protein partial volume, analyze its decomposition, and argue against the relevance of electrostriction.

Locally adaptive method to define coordination shell

An algorithm is presented to define a particle's coordination shell for any collection of particles. It requires only the particles' positions and no pre-existing knowledge or parameters beyond those already in the force field. A particle's shell is taken to be all particles that are not blocked by any other particle and not further away than a blocked particle. Because blocking is based on two distances and an angle for triplets of particles, it is called the relative angular distance (RAD) algorithm. RAD is applied to Lennard-Jones particles in molecular dynamics simulations of crystalline, liquid, and gaseous phases at various temperatures and densities. RAD coordination shells agree well with those from a cut-off in the radial distribution function for the crystals and liquids and are slightly higher for the gas.