Molecular dynamics simulation of solvated azurin: correlation between surface solvent accessibility and water residence times

Collective Spectroscopy of Solvation Phenomena: Conflicts, Challenges, and Opportunities

Different spectroscopy types reveal different aspects of molecular processes in soft matter. In particular, collective observables can provide insights into intermolecular correlations invisible to the more popular single-particle methods. In this perspective we feature the dielectric relaxation spectroscopy (DRS) with an emphasis on the proper interpretation of this complex observable aided by computational spectroscopy. While we focus on the history and recent advances of DRS in the fields of biomolecular hydration and nanoconfinement, the discussion transcends this particular field and provides a guide for how collective spectroscopy types supported by computational decomposition can be employed to further our understanding of soft matter phenomena.

Reversible processes in collagen dehydration: A molecular dynamics study

Collagen dehydration is an unavoidable damaging process that causes the lack of fibers' physical properties and it is usually irreversible. However, the identification of low hydration conditions that permit a recovering of initial collagen features after a rehydration treatment is particularly of interest. Monitoring structural changes by means of MD simulations, we investigated the hydration-dehydration-rehydration cycle of two microfibril models built on different fragments of the sequence of rat tail collagen type I. The microfibrils have different hydropathic features, to investigate the influence of amino acid composition on the whole process. We showed that with low hydration at a level corresponding to the first shell, microfibril gains in compactness and tubularity. Crucially, some water molecules remain trapped inside the fibrils, allowing, by rehydrating, a recovery of the initial collagen structural features. Water rearranges in cluster around the protein, and its first layer is more anchored to the surface. However, these changes in distribution and mobility in low hydration conditions get back with rehydration.

First-passage fingerprints of water diffusion near glutamine surfaces

The extent to which biological interfaces affect the dynamics of water plays a key role in the exchange of matter and chemical interactions that are essential for life. The density and the mobility of water molecules depend on their proximity to biological interfaces and can play an important role in processes such as protein folding and aggregation. In this work, we study the dynamics of water near glutamine surfaces-a system of interest in studies of neurodegenerative diseases. Combining molecular-dynamics simulations and stochastic modelling, we study how the mean first-passage time and related statistics of water molecules escaping subnanometer-sized regions vary from the interface to the bulk. Our analysis reveals a dynamical complexity that reflects underlying chemical and geometrical properties of the glutamine surfaces. From the first-passage time statistics of water molecules, we infer their space-dependent diffusion coefficient in directions normal to the surfaces. Interestingly, our results suggest that the mobility of water varies over a longer length scale than the chemical potential associated with the water-protein interactions. The synergy of molecular dynamics and first-passage techniques opens the possibility for extracting space-dependent diffusion coefficients in more complex, inhomogeneous environments that are commonplace in living matter.

Capturing the Effects of Explicit Waters in Implicit Electrostatics Modeling: Qualitative Justification of Gaussian-Based Dielectric Models in DelPhi

Our group has implemented a smooth Gaussian-based dielectric function in DelPhi (J. Chem. Theory Comput. 2013, 9 (4), 2126-2136) which models the solute as an object with inhomogeneous dielectric permittivity and provides a smooth transition of dielectric permittivity from surface-bound water to bulk solvent. Although it is well-understood that the protein hydrophobic core is less polarizable than the hydrophilic protein surface, less attention is paid to the polarizability of water molecules inside the solute and on its surface. Here, we apply explicit water simulations to study the behavior of water molecules buried inside a protein and on the surface of that protein and contrast it with the behavior of the bulk water. We selected a protein that is experimentally shown to have five cavities, most of which are occupied by water molecules. We demonstrate through molecular dynamics (MD) simulations that the behavior of water in the cavity is drastically different from that in the bulk. These observations were made by comparing the mean residence times, dipole orientation relaxation times, and average dipole moment fluctuations. We also show that the bulk region has a nonuniform distribution of these tempo-spatial properties. From the perspective of continuum electrostatics, we argue that the dielectric "constant" in water-filled cavities of proteins and the space close to the molecular surface should differ from that assigned to the bulk water. This provides support for the Gaussian-based smooth dielectric model for solving electrostatics in the Poisson-Boltzmann equation framework. Furthermore, we demonstrate that using a well-parametrized Gaussian-based model with a single energy-minimized configuration of a protein can also reproduce its ensemble-averaged polar solvation energy. Thus, we argue that the Gaussian-based smooth dielectric model not only captures accurate physics but also provides an efficient way of computing ensemble-averaged quantities.

Structural and dynamical heterogeneities at glutamine-water interfaces

The behavior of water at the surfaces of solid amino acid crystals has received little attention despite its importance in nucleation processes. In this work, we take a first step to fill this gap by using molecular dynamics simulations to study the structural and dynamical properties of water near the (100), (010) and (001) surfaces of l-glutamine crystals. These highly hydrophilic surfaces serve as excellent model systems for interrogating the behavior of water. Despite having the same molecular composition, water at each surface displays characteristic structural, orientational and dynamical correlations. This behavior is tuned by how the different chemical groups of amino acids make contact with the liquid phase. All three surfaces yield a glassy layer of interfacial water which is reflected in different ways such as the presence of a rotationally arrested layer of water molecules and substantial slow down of the diffusion of water near the interface. By increasing the concentration of molecules in solution, we show that the binding of glutamine molecules to the crystal surface creates a crowded environment involving pockets of trapped water molecules altering the water dynamics in a highly non-trivial manner suggesting that the solvent dynamics may have important implications on crystal nucleation.

Protein Solvent Shell Structure Provides Rapid Analysis of Hydration Dynamics

The solvation layer surrounding a protein is clearly an intrinsic part of protein structure-dynamics-function, and our understanding of how the hydration dynamics influences protein function is emerging. We have recently reported simulations indicating a correlation between regional hydration dynamics and the structure of the solvation layer around different regions of the enzyme Candida antarctica lipase B, wherein the radial distribution function (RDF) was used to calculate the pairwise entropy, providing a link between dynamics (diffusion) and thermodynamics (excess entropy) known as Rosenfeld scaling. Regions with higher RDF values/peaks in the hydration layer (the first peak, within 6 Å of the protein surface) have faster diffusion in the hydration layer. The finding thus hinted at a handle for rapid evaluation of hydration dynamics at different regions on the protein surface in molecular dynamics simulations. Such an approach may move the analysis of hydration dynamics from a specialized venture to routine analysis, enabling an informatics approach to evaluate the role of hydration dynamics in biomolecular function. This paper first confirms that the correlation between regional diffusive dynamics and hydration layer structure (via water center of mass around protein side-chain atom RDF) is observed as a general relationship across a set of proteins. Second, it seeks to devise an approach for rapid analysis of hydration dynamics, determining the minimum amount of information and computational effort required to get a reliable value of hydration dynamics from structural data in MD simulations based on the protein-water RDF. A linear regression model using the integral of the hydration layer in the water-protein RDF was found to provide statistically equivalent apparent diffusion coefficients at the 95% confidence level for a set of 92 regions within five different proteins. In summary, RDF analysis of 10 ns of data after simulation convergence is sufficient to accurately map regions of fast and slow hydration dynamics around a protein surface. Additionally, it is anticipated that a quick look at protein-water RDFs, comparing peak heights, will be useful to provide a qualitative ranking of regions of faster and slower hydration dynamics at the protein surface for rapid analysis when investigating the role of solvent dynamics in protein function.

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 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.

Water Dynamics in the Hydration Shells of Biomolecules

The structure and function of biomolecules are strongly influenced by their hydration shells. Structural fluctuations and molecular excitations of hydrating water molecules cover a broad range in space and time, from individual water molecules to larger pools and from femtosecond to microsecond time scales. Recent progress in theory and molecular dynamics simulations as well as in ultrafast vibrational spectroscopy has led to new and detailed insight into fluctuations of water structure, elementary water motions, electric fields at hydrated biointerfaces, and processes of vibrational relaxation and energy dissipation. Here, we review recent advances in both theory and experiment, focusing on hydrated DNA, proteins, and phospholipids, and compare dynamics in the hydration shells to bulk water.

Rotational dynamics of water molecules near biological surfaces with implications for nuclear quadrupole relaxation

Based on Molecular Dynamics simulations of two different systems, the protein ubiquitin dissolved in water and an AOT reverse micelle, we present a broad analysis of the single particle rotational dynamics of water. A comprehensive connection to NQR, which is a prominent experimental method in this field, is developed, based on a reformulation of its theoretical framework. Interpretation of experimental NQR results requires a model which usually assumes that the NQR experiences retardation only in the first hydration shell. Indeed, the present study shows that this first-shell model is correct. Moreover, previous experimental retardation factors are quantitatively reproduced. All of this is seemingly contradicted by results of other methods, e.g., dielectric spectroscopy, responsible for a long-standing debate in this field. Our detailed analysis shows that NQR omits important information contained in overall water dynamics, most notably, the retardation of the water dipole axis in the electric field exerted by a biological surface.

Proteins Take up Water Before Unfolding

Proteins perform specific biological functions that strongly depend on their three-dimensional structure. This three-dimensional structure, i.e. the way the protein folds, is strongly determined by the interaction between the protein and the water solvent. We study the dynamics of water in aqueous solutions of several globular proteins at different degrees of urea-induced unfolding, using polarization-resolved femtosecond infrared spectroscopy. We observe that a fraction of the water molecules is strongly slowed down by their interaction with the protein surface. By monitoring the slow water fraction we can directly probe the amount of water-exposed protein surface. We find that at mild denaturing conditions, the water-exposed surface increases by almost 50%, while the secondary structure is still intact. This finding indicates that protein unfolding starts with the protein structure becoming less tight, thereby allowing water to enter.

Water Determines the Structure and Dynamics of Proteins

Water is an essential participant in the stability, structure, dynamics, and function of proteins and other biomolecules. Thermodynamically, changes in the aqueous environment affect the stability of biomolecules. Structurally, water participates chemically in the catalytic function of proteins and nucleic acids and physically in the collapse of the protein chain during folding through hydrophobic collapse and mediates binding through the hydrogen bond in complex formation. Water is a partner that slaves the dynamics of proteins, and water interaction with proteins affect their dynamics. Here we provide a review of the experimental and computational advances over the past decade in understanding the role of water in the dynamics, structure, and function of proteins. We focus on the combination of X-ray and neutron crystallography, NMR, terahertz spectroscopy, mass spectroscopy, thermodynamics, and computer simulations to reveal how water assist proteins in their function. The recent advances in computer simulations and the enhanced sensitivity of experimental tools promise major advances in the understanding of protein dynamics, and water surely will be a protagonist.

Molecular Dynamics Simulations of a Powder Model of the Intrinsically Disordered Protein Tau

The tau protein, whose aggregates are involved in Alzheimer's disease, is an intrinsically disordered protein (IDP) that regulates microtubule activity in neurons. An IDP lacks a single, well-defined structure and, rather, constantly exchanges among multiple conformations. In order to study IDP dynamics, the combination of experimental techniques, such as neutron scattering, and computational techniques, such as molecular dynamics (MD) simulations, is a powerful approach. Amorphous hydrated powder samples have been very useful for studying protein internal dynamics experimentally, e.g., using neutron scattering. Thus, there is demand for realistic in silico models of hydrated protein powders. Here we present an MD simulation analysis of a powder hydrated at 0.4 g water/g protein of the IDP tau in the temperature range 20-300 K. By comparing with neutron scattering data, we identify the protein-water interface as the predominant feature determining IDP dynamics. The so-called protein dynamical transition is shown to be attenuated, but not suppressed, in the parts of the protein that are not exposed to the solvent. In addition, we find similarities in the mean-squared displacements of the core of a globular protein and "dry" clusters formed by the IDP in hydrated powders. Thus, the ps to ns dynamics of proteins in hydrated powders originate mainly from those residues in contact with solvent. We propose that by measuring the dynamics of protein assemblies, such as aggregates, one might assess qualitatively their state of hydration.

Hydration water mobility is enhanced around tau amyloid fibers

The paired helical filaments (PHF) formed by the intrinsically disordered human protein tau are one of the pathological hallmarks of Alzheimer disease. PHF are fibers of amyloid nature that are composed of a rigid core and an unstructured fuzzy coat. The mechanisms of fiber formation, in particular the role that hydration water might play, remain poorly understood. We combined protein deuteration, neutron scattering, and all-atom molecular dynamics simulations to study the dynamics of hydration water at the surface of fibers formed by the full-length human protein htau40. In comparison with monomeric tau, hydration water on the surface of tau fibers is more mobile, as evidenced by an increased fraction of translationally diffusing water molecules, a higher diffusion coefficient, and increased mean-squared displacements in neutron scattering experiments. Fibers formed by the hexapeptide (306)VQIVYK(311) were taken as a model for the tau fiber core and studied by molecular dynamics simulations, revealing that hydration water dynamics around the core domain is significantly reduced after fiber formation. Thus, an increase in water dynamics around the fuzzy coat is proposed to be at the origin of the experimentally observed increase in hydration water dynamics around the entire tau fiber. The observed increase in hydration water dynamics is suggested to promote fiber formation through entropic effects. Detection of the enhanced hydration water mobility around tau fibers is conjectured to potentially contribute to the early diagnosis of Alzheimer patients by diffusion MRI.

Local dynamics coupled to hydration water determines DNA-sequence-dependent deformability

Molecular dynamics (MD) simulations and quasielastic neutron scattering (QENS) experiments were conducted on two hydrated DNA dodecamers with distinct deformability: 5'CGCG[under AATT]̲CGCG3' and 5'CGCG[under TTAA]̲CGCG3'. The former is known to be rigid and the latter to be flexible. The mean-square displacements of DNA dodecamers exhibit so-called dynamical transition around 200-240 K for both sequences. To investigate the DNA-sequence-dependent dynamics, the dynamics of DNA and hydration water above the transition temperature were examined using both MD simulations and QENS experiments. The fluctuation amplitude of the AATT central tetramer is smaller, and its relaxation time is longer, than that observed in TTAA, suggesting that the AT step is kinetically more stable than TA. The sequence-dependent local base pair step dynamics correlates with the kinetics of breaking the hydrogen bond between DNA and hydration water. The sequence-dependent DNA base pair step fluctuations appear above the dynamical transition temperature. Together with these results, we conclude that DNA deformability is related to the local dynamics of the base pair steps, themselves coupled to hydration water in the minor groove.

Water dynamics in protein hydration shells: the molecular origins of the dynamical perturbation

Protein hydration shell dynamics play an important role in biochemical processes including protein folding, enzyme function, and molecular recognition. We present here a comparison of the reorientation dynamics of individual water molecules within the hydration shell of a series of globular proteins: acetylcholinesterase, subtilisin Carlsberg, lysozyme, and ubiquitin. Molecular dynamics simulations and analytical models are used to access site-resolved information on hydration shell dynamics and to elucidate the molecular origins of the dynamical perturbation of hydration shell water relative to bulk water. We show that all four proteins have very similar hydration shell dynamics, despite their wide range of sizes and functions, and differing secondary structures. We demonstrate that this arises from the similar local surface topology and surface chemical composition of the four proteins, and that such local factors alone are sufficient to rationalize the hydration shell dynamics. We propose that these conclusions can be generalized to a wide range of globular proteins. We also show that protein conformational fluctuations induce a dynamical heterogeneity within the hydration layer. We finally address the effect of confinement on hydration shell dynamics via a site-resolved analysis and connect our results to experiments via the calculation of two-dimensional infrared spectra.

Molecular structure and transport dynamics in perfluoro sulfonyl imide membranes

We report a detailed and comprehensive analysis from classical molecular dynamics simulations of the nanostructure of a model of hydrated perfluoro sulfonyl imide (PFSI) membrane, a polymeric system of interest as a proton conductor in polymer electrolyte membrane fuel cells. We also report on the transport dynamics of water and hydronium ions, and water network percolation in this system. We find that the water network percolation threshold for PFSI, i.e. the threshold at which a consistent spanning water network starts to develop in the membrane, is found to occur between hydration levels (λ) 6 and 7. The higher acidity of the sulfonyl imide acid group of PFSI compared to the sulfonic acid group in Nafion, as computationally characterized in our earlier ab initio study (Idupulapati et al 2010 J. Phys. Chem. A 114 6904-12), results in a larger fraction of 'free' hydronium ions at low hydration levels in PFSI compared to Nafion. However, the calculated diffusion coefficients of the H(3)O(+) ions and H(2)O molecules as a function the hydration level are observed to be almost the same as that of Nafion, indicating similar conductivity and consistent with experimental data.

Dynamics of water clusters confined in proteins: a molecular dynamics simulation study of interfacial waters in a dimeric hemoglobin

Water confined in proteins exhibits dynamics distinct from the dynamics of water in the bulk or near the surface of a biomolecule. We examine the water dynamics at the interface of the two globules of the homodimeric hemoglobin from Scapharca inaequivalvis (HbI) by molecular dynamics (MD) simulations, with focus on water-protein hydrogen bond lifetimes and rotational anisotropy of the interfacial waters. We find that relaxation of the waters at the interface of both deoxy- and oxy-HbI, which contain a cluster of 17 and 11 interfacial waters, respectively, is well described by stretched exponentials with exponents from 0.1 to 0.6 and relaxation times of tens to thousands of picoseconds. The interfacial water molecules of oxy-HbI exhibit slower rotational relaxation and hydrogen bond rearrangement than those of deoxy-HbI, consistent with an allosteric transition from unliganded to liganded conformers involving the expulsion of several water molecules from the interface. Though the interfacial waters are translationally and rotationally static on the picosecond time scale, they contribute to fast communication between the globules via vibrations. We find that the interfacial waters enhance vibrational energy transport across the interface by ≈10%.

Evaluation of the interaction of cyclin-dependent kinase 5 with activator p25 and with p25-derived inhibitor CIP

A high-affinity inhibitor protein called CIP, produced by small truncations of p35, was experimentally identified. P35 is a physiological activator of the cyclin-dependent kinase cdk5. P25 is derived from proteolytic truncation of p35 within "stressed" neurons, and it is associated with the hyperphosphorylation of specific neuronal proteins, typically occurring in neurodegenerative diseases such as Alzheimer's. Here, we report a study of the binding mechanisms of the cdk5-p25 and cdk5-CIP complexes. This provides a better understanding of the source of the inhibitory activity of the protein CIP. We use a geometry-based technique to test the hypothesis that p25's truncation increases the flexibility of CIP and thus prevents cdk5 from reaching its active conformation. Our study is based on a geometry-based alignment algorithm, which aligns two given protein conformations with respect to their interfaces. Our results support the flexibility hypothesis and will be used as a basis for targeted molecular dynamics simulations.

Time scales of water dynamics at biological interfaces: peptides, proteins and cells

Water 2H and 17O spin relaxation is used to study water dynamics in the hydration layers of two small peptides, two globular proteins and in living cells of two microorganisms. The dynamical heterogeneity of hydration water is characterized by performing relaxation measurements over a wide temperature range, extending deeply into the supercooled regime, or by covering a wide frequency range. Protein hydration layers can be described by a power-law distribution of rotational correlation times with an exponent close to 2. This distribution comprises a small fraction of protein-specific hydration sites, where water rotation is strongly retarded, and a dominant fraction of generic hydration sites, where water rotation is as fast as in the hydration shells of small peptides. The generic dynamic perturbation factor is less than 2 at room temperature and exhibits a maximum near 260 K. The dynamic perturbation is induced by H-bond constraints that interfere with the cooperative mechanism that facilitates rotation in bulk water. Because these constraints are temperature-independent, hydration water does not follow the super-Arrhenius temperature dependence of bulk water. Water in living cells behaves as expected from studies of simpler model systems, the only difference being a larger fraction of secluded (strongly perturbed) hydration sites associated with the supramolecular organization in the cell. Intracellular water that is not in direct contact with biopolymers has essentially the same dynamics as bulk water. There is no significant difference in cell water dynamics between mesophilic and halophilic organisms, despite the high K+ and Na+ concentrations in the latter.

Dynamics at the protein-water interface from 17O spin relaxation in deeply supercooled solutions

Most of the decisive molecular events in biology take place at the protein-water interface. The dynamical properties of the hydration layer are therefore of fundamental importance. To characterize the dynamical heterogeneity and rotational activation energy in the hydration layer, we measured the (17)O spin relaxation rate in dilute solutions of three proteins in a wide temperature range extending down to 238 K. We find that the rotational correlation time can be described by a power-law distribution with exponent 2.1-2.3. Except for a small fraction of secluded hydration sites, the dynamic perturbation in the hydration layer is the same for all proteins and does not differ in any essential way from the hydration shell of small organic solutes. In both cases, the dynamic perturbation factor is <2 at room temperature and exhibits a maximum near 262 K. This maximum implies that, at low temperatures, the rate of water molecule rotation has a weaker temperature dependence in the hydration layer than in bulk water. We attribute this difference to the temperature-independent constraints that the protein surface imposes on the water H-bond network. The free hydration layer studied here differs qualitatively from confined water in solid protein powder samples.

Diffusion and residence time of hydrogen peroxide and water in crowded protein environments

Reactive oxygen species (ROS) have important functions in cell signaling and, when present at overly high levels, may cause oxidation of important biological molecules. Kinetic models to study diffusion of ROS inside of mitochondria often assume dynamics similar to that in solution. However, it is well-known that separation of proteins in the cytosol or inside of mitochondria, where ROS are most predominant, can be smaller than 1 nm. Diffusion of small molecules can be better regarded as a percolation process. In this article, we report results of diffusivity and residence of water and hydrogen peroxide in the proximity of proteins. In carrying out this study, we found some issues with the conventional way of computing residence times by means of survival time correlation functions. The main problem is that particles remaining on the surface of a protein for long times and for which one has very poor statistics contribute significantly to the short time behavior of the survival time correlation function. We mathematically describe this problem and propose methodology to overcome it.

Atomistic simulation of nafion membrane. 2. Dynamics of water molecules and hydronium ions

We have performed a detailed and comprehensive analysis of the dynamics of water molecules and hydronium ions in hydrated Nafion using classical molecular dynamics simulations with the DREIDING force field. In addition to calculating diffusion coefficients as a function of hydration level, we have also determined mean residence time of H(2)O molecules and H(3)O(+) ions in the first solvation shell of SO(3)(-) groups. The diffusion coefficient of H(2)O molecules increases with increasing hydration level and is in good agreement with experiment. The mean residence time of H(2)O molecules decreases with increasing membrane hydration from 1 ns at a low hydration level to 75 ps at the highest hydration level studied. These dynamical changes are related to the changes in membrane nanostructure reported in the first part of this work. Our results provide insights into slow proton dynamics observed in neutron scattering experiments and are consistent with the Gebel model of Nafion structure.

Simulation studies of the protein-water interface. I. Properties at the molecular resolution

We report molecular dynamics simulations of three globular proteins: ubiquitin, apo-calbindin D(9K), and the C-terminal SH2 domain of phospholipase C-gamma1 in explicit water. The proteins differ in their overall charge and fold type and were chosen to represent to some degree the structural variability found in medium-sized proteins. The length of each simulation was at least 15 ns, and larger than usual solvent boxes were used. We computed radial distribution functions, as well as orientational correlation functions about the surface residues. Two solvent shells could be clearly discerned about charged and polar amino acids. Near apolar amino acids the water density near such residues was almost devoid of structure. The mean residence time of water molecules was determined for water shells about the full protein, as well as for water layers about individual amino acids. In the dynamic properties, two solvent shells could be characterized as well. However, by comparison to simulations of pure water it could be shown that the influence of the protein reaches beyond 6 A, i.e., beyond the first two shells. In the first shell (r < or =3.5 A), the structural and dynamical properties of solvent waters varied considerably and depended primarily on the physicochemical properties of the closest amino acid side chain, with which the waters interact. By contrast, the solvent properties seem not to depend on the specifics of the protein studied (such as the net charge) or on the secondary structure element in which an amino acid is located. While differing considerably from the neat liquid, the properties of waters in the second solvation shell (3.5< r < or =6 A) are rather uniform; a direct influence from surface amino acids are already mostly shielded.

Ultrafast solvation dynamics of human serum albumin: correlations with conformational transitions and site-selected recognition

Human serum albumin, the most abundant protein found in blood plasma, transports a great variety of ligands in the circulatory system and undergoes reversible conformational transitions over a wide range of pH values. We report here our systematic studies of solvation dynamics and local rigidity in these conformations using a single intrinsic tryptophan (W214) residue as a local molecular probe. With femtosecond resolution, we observed a robust bimodal distribution of time scales for all conformational isomers. The initial solvation occurs in several picoseconds, representing the local librational/rotational motions, followed by the dynamics, in the tens to hundreds of picoseconds, which result from the more bonded water in the tryptophan crevice. Under the physiological condition of neutral pH, we measured approximately 100 ps for the decay of the solvation correlation function and observed a large wobbling motion at the binding site that is deeply buried in a crevice, revealing the softness of the binding pocket and the large plasticity of the native structure. At acidic pH, the albumin molecule transforms to an extended conformation with a large charge distribution at the surface, and a similar temporal behavior was observed. However, at the basic pH, the protein opens the crevice and tightens its globular structure, and we observed significantly faster dynamics, 25-45 ps. These changes in the solvation dynamics are correlated with the conformational transitions and related to their structural integrity.

Characterization of the galectin-1 carbohydrate recognition domain in terms of solvent occupancy

Human galectin-1, a galactosil-terminal sugar binding soluble protein, is a potent multifunctional effector that participates in specific protein-carbohydrate and protein-protein interactions. Recent studies revealed that it plays a key role as a modulator of cellular differentiation and immunological response. In this work, we have investigated the solvation properties of the carbohydrate recognition domain of Gal-1 by means of molecular dynamics simulations. Water sites (ws) were identified in terms of radial and angular distribution functions, and properties such as water residence times, interaction energies, and free-energy contributions were evaluated for those sites. Our results allowed us to correlate the thermodynamic properties of the ws and their binding pattern with the N-acetilgalactoside ligand. These results let us further infer that the water molecules located at the ws, which exhibit much more favorable binding, are the ones replaced by -OH groups of the sugar.

Protein surface hydration mapped by site-specific mutations

Water motion at protein surfaces is fundamental to protein structure, stability, dynamics, and function. By using intrinsic tryptophans as local optical probes, and with femtosecond resolution, it is possible to probe surface-water motions in the hydration layer. Here, we report our studies of local hydration dynamics at the surface of the enzyme Staphylococcus nuclease using site-specific mutations. From these studies of the WT and four related mutants, which change local charge distribution and structure, we are able to ascertain the contribution to solvation by protein side chains as relatively insignificant. We determined the time scales of hydration to be 3-5 ps and 100-150 ps. The former is the result of local librational/rotational motions of water near the surface; the latter is a direct measure of surface hydration assisted by fluctuations of the protein. Experimentally, these hydration dynamics of the WT and the four mutants are also consistent with results of the total dynamic Stokes shifts and fluorescence emission maxima and are correlated with their local charge distribution and structure. We discuss the role of protein fluctuation on the time scale of labile hydration and suggest reexamination of recent molecular dynamics simulations.

Minimalist explicit solvation models for surface loops in proteins

We have performed molecular dynamics simulations of protein surface loops solvated by explicit water, where a prime focus of the study is the small numbers (e.g., ~100) of explicit water molecules employed. The models include only part of the protein (typically 500 - 1000 atoms), and the water molecules are restricted to a region surrounding the loop. In this study, the number of water molecules (N(w)) is systematically varied, and convergence with large N(w) is monitored to reveal N(w)(min), the minimum number required for the loop to exhibit realistic (fully hydrated) behavior. We have also studied protein surface coverage, as well as diffusion and residence times for water molecules as a function of N(w). A number of other modeling parameters are also tested. These include the number of environmental protein atoms explicitly considered in the model, as well as two ways to constrain the water molecules to the vicinity of the loop (where we find one of these methods to perform better when N(w) is small). The results (for RMSD and its fluctuations for four loops) are further compared to much larger, fully solvated systems (using ~10,000 water molecules under periodic boundary conditions and Ewald electrostatics), and to results for the GBSA implicit solvation model. We find that the loop backbone can stabilize with a surprisingly small number of water molecules (as low as 5 molecules per amino acid residue). The side chains of the loop require somewhat larger N(w), where the atomic fluctuations become too small if N(w) is further reduced. Thus, in general, we find adequate hydration to occur at roughly 12 water molecules per residue. This is an important result, because at this hydration level, computational times are comparable to those required for GBSA. Therefore these "minimalist explicit models" can provide a viable and potentially more accurate alternative. The importance of protein loop modeling is discussed in the context of these, and other, loop models, along with other challenges including the relevance of appropriate free energy simulation methodology for assessment of conformational stability.

Dynamics of Water Confined in the Interdomain Region of a Multidomain Protein

Molecular dynamics simulations are performed to study the dynamics of interfacial water confined in the interdomain region of a two-domain protein, BphC enzyme. The results show that near the protein surface the water diffusion constant is much smaller and the water-water hydrogen bond lifetime is much longer than that in bulk. The diffusion constant and hydrogen bond lifetime can vary by a factor of as much as 2 in going from the region near the hydrophobic domain surface to the bulk. Water molecules in the first solvation shell persist for a much longer time near local concave sites than near convex sites. Also, the water layer survival correlation time shows that on average water molecules near the extended hydrophilic surfaces have longer residence times than those near hydrophobic surfaces. These results indicate that local surface curvature and hydrophobicity have a significant influence on water dynamics.

Constrained geometric simulation of diffusive motion in proteins

We describe a new computational method, FRODA (framework rigidity optimized dynamic algorithm), for exploring the internal mobility of proteins. The rigid regions in the protein are first determined, and then replaced by ghost templates which are used to guide the movements of the atoms in the protein. Using random moves, the available conformational phase space of a 100 residue protein can be well explored in approximately 10-100 min of computer time using a single processor. All of the covalent, hydrophobic and hydrogen bond constraints are maintained, and van der Waals overlaps are avoided, throughout the simulation. We illustrate the results of a FRODA simulation on barnase, and show that good agreement is obtained with nuclear magnetic resonance experiments. We additionally show how FRODA can be used to find a pathway from one conformation to another. This directed dynamics is illustrated with the protein dihydrofolate reductase.

Secondary Structure Sensitivity of Hydrogen Bond Lifetime Dynamics in the Protein Hydration Layer

The heterogeneous nature of a protein surface plays an essential role in its biological activity and molecular recognition, and this role is mediated at least partly through the surrounding water molecules. We have performed atomistic molecular dynamics simulations of an aqueous solution of HP-36 to investigate the correlation between the dynamics of the hydration layer water molecules and the lifetimes of protein-water hydrogen bonds. The nonexponential hydrogen bond lifetime correlation functions have been analyzed by using the formalism of Luzar and Chandler, which allowed identification of the quasi-bound states in the surface and quantification of the dynamic equilibrium between quasi-bound and free water molecules in terms of time-dependent rate of interconversion. It is noticed that, irrespective of the structural heterogeneity of different segments of the protein, namely the three alpha-helices, the positively charged amino acid residues form longer-lived hydrogen bonds with water. The overall relaxation behavior of protein-water hydrogen bonds is found to differ significantly among the three helices of the protein. Study of water number density fluctuation reveals that the hydration layer of helix-3 is much less rigid, which can be correlated with faster structural relaxation of the hydrogen bonds between its residues and water. This also agrees excellently with faster translational and rotational motions of water near helix-3, and hence the lower rigidity of its hydration layer. The lower rigidity of the helix-3 hydration layer also correlates well with the biological activity of the protein, as several of the active-site residues of HP-36 are located in helix-3.

Hydration and Dewetting near Graphite−CH3 and Graphite−COOH Plates

The dynamics of water near the nanoscale hydrophobic (graphite-CH(3)) and hydrophilic (graphite-COOH) plates has been studied in detail with molecular dynamics simulations in this paper. It is shown that these designed surfaces (by growing a layer of methyl or carboxyl groups on top of graphite) can have a significant impact on the neighboring water dynamics, with the hydrophilic carboxyl surface having even more profound effects. The water hydrogen bond lifetime is much longer near both types of surfaces than that in the bulk, while on the other hand the water diffusion constant is much smaller than that in the bulk. The difference in the diffusion constant can be as large as a factor of 8 and the difference in the hydrogen bond lifetime can be as large as a factor of 2, depending on the distance from the surface. Furthermore, the water molecules in the first solvation shell of surface atoms show a strong bias in hydroxyl group orientation near the surface, confirming some of the previous findings. Finally, the possible water dewetting transition between two graphite-CH(3) plates and the effect of the strength of the solute-solvent attractions on the water drying transition are investigated. The relationship among the dewetting transition critical distance, van der Waals potential well depth, and water contact angle on the graphite-CH(3) surface is also analyzed on the basis of a simple macroscopic theory, which can be used to predict the dewetting transition critical distance.

Dynamics and Thermodynamics of Water in PAMAM Dendrimers at Subnanosecond Time Scales

Atomistic molecular dynamics simulations are used to study generation 5 polyamidoamine (PAMAM) dendrimers immersed in a bath of water. We interpret the results in terms of three classes of water: buried water well inside of the dendrimer surface, surface water associated with the dendrimer-water interface, and bulk water well outside of the dendrimer. We studied the dynamic and thermodynamic properties of the water at three pH values: high pH with none of the primary or tertiary amines protonated, intermediate pH with only the primary amines protonated, and low pH with all amines protonated. For all pH values we find that both buried and surface water exhibit two relaxation times: a fast relaxation ( approximately 1 ps) corresponding to the libration motion of the water and a slow ( approximately 20 ps) diffusional component related to the escaping of water from one domain to another. In contrast for bulk water the fast relaxation is approximately 0.4 ps while the slow relaxation is approximately 14 ps. These results are similar to those found in biological systems, where the fast relaxation is found to be approximately 1 ps while the slow relaxation ranges from 20 to 1000 ps. We used the 2PT MD method to extract the vibrational (power) spectrum and found substantial differences for the three classes of water. The translational diffusion coefficient for buried water is 11-33% (depending on pH) of the bulk value while the surface water is about 80%. The change in rotational diffusion is quite similar: 21-45% of the bulk value for buried water and 80% for surface water. This shows that translational and rotational dynamics of water are affected by the PAMAM-water interactions as well as due to the confinement in the interior of the dendrimer. We find that the reduction of translational or rotational diffusion is accompanied by a blue shift of the corresponding libration motions ( approximately 10 cm(-1) for translation, approximately 35 cm(-1) for rotation), indicating higher local force constants for these motions. These effects are most pronounced for the lowest pH, probably because of the increased rigidity caused by the internal charges. From the vibrational density of states we also calculate the enthalpies and entropies of the various waters. We find that water molecules are enthalpically favored near the PAMAM dendrimer: energy for surface water is approximately 0.1 kcal/mol lower to that in the bulk, and approximately 0.5-0.9 kcal/mol lower for buried water. In contrast, we find that both the buried and surface water are entropically unfavored: buried water is 0.9-2.2 kcal/mol lower than the bulk while the surface water is 0.1-0.2 kcal/mol lower. The net result is a thermodynamically unfavored state of the water surrounding the PAMAM dendrimer: 0.4-1.3 kcal/mol higher for buried water and 0.1-0.2 kcal/mol for surface water. This excess free energy of the surface and buried waters is released when the PAMAM dendrimer binds to DNA or metal ions, providing an extra driving force.

The Early Steps in the Unfolding of Azurin

High-temperature molecular dynamics simulations were used to gain insight into the early steps in the unfolding pathway of azurin, a blue copper protein with a beta-barrel structure formed by two sheets arranged in a Greek key folding topology. The results reveal that unfolding of the beta-barrel in azurin is associated with dislocation of its unique alpha-helix with respect to the protein scaffold. Exposure of the hydrophobic core to solvent precedes complete disruption of secondary and tertiary structure, and modifications in the region around the active site are directly connected with this event. Denaturation of the protein initiates from the sheet coordinating the copper ion, and the other sheet maintains its topology. Results derived from the simulation were compared with experimental data obtained with different techniques, showing excellent agreement and providing a framework to understand the process of disruption and formation of the beta-barrel in azurin.