Global and local Voronoi analysis of solvation shells of proteins

Dynamic Electric Field Alignment Determines the Water Rotational Motion around Protein

Water rotational dynamics in biomolecular solution is crucial to evaluating and controlling biomolecule stability. In this molecular dynamics simulation (MD) study on lysozyme solutions, we present how the exerted internal electric field determines water rotational dynamics. We find that the relaxation time of water rotation is equivalent to that of the reorientation of the exerted overall electric field for every single water molecule, regardless of its translation mode. Namely, water molecular rotation synchronizes with the exerted field reorientation. We also map the reorientation process of the electric field at fixed points relative to protein in the solution, which displays the local hydration dynamics commensurate with the reported time-dependent fluorescence Stokes shift (TDFSS) measurements. Comparing the spatial distribution of local field reorientation relaxation time with that of rotational relaxation time, we further suggest that water rotation dynamics are subject to the reorientation of the local overall field within the hydration layer. While outside the hydration layer, the relaxation time of the local electric field reorientation is short enough (subpicosecond) to assume the δ function, showing the electric force with randomly changing orientation is applied to each water molecule.

Detecting the First Hydration Shell Structure around Biomolecules at Interfaces

Understanding the role of water in biological processes remains a central challenge in the life sciences. Water structures in hydration shells of biomolecules are difficult to study in situ due to overwhelming background from aqueous environments. Biological interfaces introduce additional complexity because biomolecular hydration differs at interfaces compared to bulk solution. Here, we perform experimental and computational studies of chiral sum frequency generation (chiral SFG) spectroscopy to probe chirality transfer from a protein to the surrounding water molecules. This work reveals that chiral SFG probes the first hydration shell around the protein almost exclusively. We explain the selectivity to the first hydration shell in terms of the asymmetry induced by the protein structure and specific protein-water hydrogen-bonding interactions. This work establishes chiral SFG as a powerful technique for studying hydration shell structures around biomolecules at interfaces, presenting new possibilities to address grand research challenges in biology, including the molecular origins of life.

Convergence behaviour of solvation shells in simulated liquids

A convenient way to analyse solvent structure around a solute is to use solvation shells, whereby solvent position around the solute is discretised by the size of a solvent molecule, leading to multiple shells around the solute. The two main ways to define multiple shells around a solute are either directly with respect to the solute, called solute-centric, or locally for both solute and solvent molecules alike. It might be assumed that both methods lead to solvation shells with similar properties. However, our analysis suggests otherwise. Solvation shells are analysed in a series of simulations of five pure liquids of differing polarity. Shells are defined locally working outwards from each molecule treated as a reference molecule using two methods: the cutoff at the first minimum in the radial distribution function and the parameter-free Relative Angular Distance method (RAD). The molecular properties studied are potential energy, coordination number and coordination radius. Rather than converging to bulk values, as might be expected for pure solvents, properties are found to deviate as a function of shell index. This behaviour occurs because molecules with larger coordination numbers and radius have more neighbours, which make them more likely to be connected to the reference molecule via fewer shells. The effect is amplified for RAD because of its more variable coordination radii and for water with its more open structure and stronger interactions. These findings indicate that locally defined shells should not be thought of as directly comparable to solute-centric shells or to distance. As well as showing how box size and cutoff affect the non-convergence, to restore convergence we propose a hybrid method by defining a new set of shells with boundaries at the uppermost distance of each locally derived shell.

How proteins modify water dynamics

Much of biology happens at the protein-water interface, so all dynamical processes in this region are of fundamental importance. Local structural fluctuations in the hydration layer can be probed by ¹⁷O magnetic relaxation dispersion (MRD), which, at high frequencies, measures the integral of a biaxial rotational time correlation function (TCF)-the integral rotational correlation time. Numerous ¹⁷O MRD studies have demonstrated that this correlation time, when averaged over the first hydration shell, is longer than in bulk water by a factor 3-5. This rotational perturbation factor (RPF) has been corroborated by molecular dynamics simulations, which can also reveal the underlying molecular mechanisms. Here, we address several outstanding problems in this area by analyzing an extensive set of molecular dynamics data, including four globular proteins and three water models. The vexed issue of polarity versus topography as the primary determinant of hydration water dynamics is resolved by establishing a protein-invariant exponential dependence of the RPF on a simple confinement index. We conclude that the previously observed correlation of the RPF with surface polarity is a secondary effect of the correlation between polarity and confinement. Water rotation interpolates between a perturbed but bulk-like collective mechanism at low confinement and an exchange-mediated orientational randomization (EMOR) mechanism at high confinement. The EMOR process, which accounts for about half of the RPF, was not recognized in previous simulation studies, where only the early part of the TCF was examined. Based on the analysis of the experimentally relevant TCF over its full time course, we compare simulated and measured RPFs, finding a 30% discrepancy attributable to force field imperfections. We also compute the full ¹⁷O MRD profile, including the low-frequency dispersion produced by buried water molecules. Computing a local RPF for each hydration shell, we find that the perturbation decays exponentially with a decay "length" of 0.3 shells and that the second and higher shells account for a mere 3% of the total perturbation measured by ¹⁷O MRD. The only long-range effect is a weak water alignment in the electric field produced by an electroneutral protein (not screened by counterions), but this effect is negligibly small for ¹⁷O MRD. By contrast, we find that the ¹⁷O TCF is significantly more sensitive to the important short-range perturbations than the other two TCFs examined here.

The spatial range of protein hydration

Proteins interact with their aqueous surroundings, thereby modifying the physical properties of the solvent. The extent of this perturbation has been investigated by numerous methods in the past half-century, but a consensus has still not emerged regarding the spatial range of the perturbation. To a large extent, the disparate views found in the current literature can be traced to the lack of a rigorous definition of the perturbation range. Stating that a particular solvent property differs from its bulk value at a certain distance from the protein is not particularly helpful since such findings depend on the sensitivity and precision of the technique used to probe the system. What is needed is a well-defined decay length, an intrinsic property of the protein in a dilute aqueous solution, that specifies the length scale on which a given physical property approaches its bulk-water value. Based on molecular dynamics simulations of four small globular proteins, we present such an analysis of the structural and dynamic properties of the hydrogen-bonded solvent network. The results demonstrate unequivocally that the solvent perturbation is short-ranged, with all investigated properties having exponential decay lengths of less than one hydration shell. The short range of the perturbation is a consequence of the high energy density of bulk water, rendering this solvent highly resistant to structural perturbations. The electric field from the protein, which under certain conditions can be long-ranged, induces a weak alignment of water dipoles, which, however, is merely the linear dielectric response of bulk water and, therefore, should not be thought of as a structural perturbation. By decomposing the first hydration shell into polarity-based subsets, we find that the hydration structure of the nonpolar parts of the protein surface is similar to that of small nonpolar solutes. For all four examined proteins, the mean number of water-water hydrogen bonds in the nonpolar subset is within 1% of the value in bulk water, suggesting that the fragmentation and topography of the nonpolar protein-water interface has evolved to minimize the propensity for protein aggregation by reducing the unfavorable free energy of hydrophobic hydration.

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.

Computational solvation analysis of biomolecules in aqueous ionic liquid mixtures : From large flexible proteins to small rigid drugs

Based on their tunable properties, ionic liquids attracted significant interest to replace conventional, organic solvents in biomolecular applications. Following a Gartner cycle, the expectations on this new class of solvents dropped after the initial hype due to the high viscosity, hydrolysis, and toxicity problems as well as their high cost. Since not all possible combinations of cations and anions can be tested experimentally, fundamental knowledge on the interaction of the ionic liquid ions with water and with biomolecules is mandatory to optimize the solvation behavior, the biodegradability, and the costs of the ionic liquid. Here, we report on current computational approaches to characterize the impact of the ionic liquid ions on the structure and dynamics of the biomolecule and its solvation layer to explore the full potential of ionic liquids.

HullRad: Fast Calculations of Folded and Disordered Protein and Nucleic Acid Hydrodynamic Properties

Hydrodynamic properties are useful parameters for estimating the size and shape of proteins and nucleic acids in solution. The calculation of such properties from structural models informs on the solution properties of these molecules and complements corresponding structural studies. Here we report, to our knowledge, a new method to accurately predict the hydrodynamic properties of molecular structures. This method uses a convex hull model to estimate the hydrodynamic volume of the molecule and is orders of magnitude faster than common methods. It works well for both folded proteins and ensembles of conformationally heterogeneous proteins and for nucleic acids. Because of its simplicity and speed, the method should be useful for the modification of computer-generated, intrinsically disordered protein ensembles and ensembles of flexible, but folded, molecules in which rapid calculation of experimental parameters is needed. The convex hull method is implemented in a Python script called HullRad. The use of the method is facilitated by a web server and the code is freely available for batch applications.

Exploring volume, compressibility and hydration changes of folded proteins upon compression

Understanding the physical basis of the structure, stability and function of proteins in solution, including extreme environmental conditions, requires knowledge of their temperature and pressure dependent volumetric properties. One physical-chemical property of proteins that is still little understood is their partial molar volume and its dependence on temperature and pressure. We used molecular dynamics simulations of aqueous solutions of a typical monomeric folded protein, staphylococcal nuclease (SNase), to study and analyze the pressure dependence of the apparent volume, Vapp, and its components by the Voronoi-Delaunay method. We show that the strong decrease of Vapp with pressure (βT = 0.95 × 10(-5) bar(-1), in very good agreement with the experimental value) is essentially due to the compression of the molecular volume, VM, ultimately, of its internal voids, V. Changes of the intrinsic volume (defined as the Voronoi volume of the molecule), the contribution of the solvent to the apparent volume, and of the contribution of the boundary voids between the protein and the solvent have also been studied and quantified in detail. The pressure dependences of the volumetric characteristics obtained are compared with the temperature dependent behavior of these quantities and with corresponding results for a natively unfolded polypeptide.

The intermolecular NOE is strongly influenced by dynamics

New fundamental insights in NOE theory concerning the significance of dynamics and range are presented, using coarse-grained MD simulations.

Solvation studies of a zinc finger protein in hydrated ionic liquids

The solvation of the zinc finger protein with the PDB-ID “5ZNF” in hydrated ionic liquids was studied at varying water content. 1-Ethyl-3-methylimidazolium and trifluoromethanesulfonate were the cation and anion, respectively. The protein stability as well as the solvation structure, the shell dynamics and the shell resolved dielectric properties were investigated by means of molecular dynamics simulations. The lengths of the respective trajectories extended up to 200 nanoseconds in order to cover the complete solvent dynamics. Considering the above mentioned properties as a function of the water content they all exhibit a maximum or minimum at the very same mole fraction. While the exact value x(H(2)O) = 0.927 depends on the underlying force field, its origin may be traced back to the competition between the van der Waals and the electrostatic energy of the protein as well as to the transition from aqueous dielectric screening to ionic charge screening with decreasing water content. The parameter-free Voronoi decomposition of space served as a basis for the analysis of most results. In particular, solvation shells were naturally inferred from this concept. In addition to the molecular analysis a mesoscopic view is given in terms of dielectric properties. Thereby, the net dielectric constant is decomposed into contributions from the protein, the first and second solvation shells as well as the bulk. Cross-terms between these components are given, too.