On the origins of the hydrophobic effect: observations from simulations of n-dodecane in model solvents.

The importance of the small size of a water molecule as contributing to the hydrophobic effect is examined from simulations of n-dodecane in different solvents. The earlier observations of the origin of hydrophobicity, derived from cavity formations by Pratt and Pohorille (1992, Proc. Natl. Acad. Sci. USA. 89:2995-2999) and Madan and Lee (1994, Biophys. Chem, 51:279-289), are shown to be largely consistent for a hydrocarbon-induced water pocket. In effect, the small size of a water molecule limits the probability (and hence free energy) of finding an appropriate void in the fluid that will accommodate a solute. In this work a simulated collapse of an n-dodecane molecule in H2O, CCl4, and a water-like Lennard-Jones solvent indicates that the induced entropy and enthalpy changes are qualitatively similar for hydrogen-bonded and Lennard-Jones water solvents. These results suggest that a large part of the hydrophobic response of solutes in aqueous solutions is due to the small size of the solvent. Important quantitative differences between the studied water solvents indicate that the hydrogen-bonded properties for water are still needed to determine the overall hydrophobic response.     

Locating missing water molecules in protein cavities by the three-dimensional reference interaction site model theory of molecular solvation

Water molecules confined in protein cavities are of great importance in understanding the protein structure and functions. However, it is a nontrivial task to locate such water molecules in protein by the ordinary molecular simulation and modeling techniques as well as experimental methods. The present study proves that the three-dimensional reference interaction site model (3D-RISM) theory, a recently developed statistical-mechanical theory of molecular solvation, has an outstanding advantage in locating such water molecules. In this paper, we demonstrate that the 3D-RISM theory is able to reproduce the structure and the number of water molecules in cavities of hen egg-white lysozyme observed commonly in the X-ray structures of different resolutions and conditions. Furthermore, we show that the theory successfully identified a water molecule in a cavity, the existence of which has been ambiguous even from the X-ray results. In contrast, we confirmed that molecular dynamics simulation is helpless at present to find such water molecules because the results substantially depend on the initial coordinates of water molecules. Possible applications of the theory to problems in the fields of biochemistry and biophysics are also discussed.     

Entropy convergence in hydrophobic hydration: a scaled particle theory analysis

The occurrence of entropy convergence in hydrophobic hydration is verified from available experimental thermodynamic data for both noble gases and hydrocarbons. The entropy convergence phenomenon can be reproduced by means of the scaled particle theory, provided that a temperature-dependent hard sphere diameter is used for water molecules. The calculated work of cavity creation shows a non-monotonic temperature dependence with a flat maximum slightly above 100 degrees C, irrespective of the cavity size. The corresponding cavity entropy changes converge approximately 100 degrees C, in qualitative agreement with the experimental finding.     

A review about nothing: Are apolar cavities in proteins really empty?

Cavities within proteins that are strictly apolar typically appear to be empty. It has been suggested, however, that water molecules may be present within such cavities but are too disordered to be seen in conventional crystallographic analyses. In contrast, it is argued here that solvent mobility will be limited by the size of the cavity and for this reason high‐occupancy solvent in cavities of typical volume should be readily detectable using X‐ray crystallography. Recent experimental studies of cavity hydration are reviewed. Such studies are consistent with theoretical predictions that it is energetically unfavorable to have a single water molecule in an apolar cavity. As apolar cavities become larger, a point is reached where it is favorable to have the cavity occupied by a cluster of mutually H‐bonded water molecules. The exact size of such a cavity in a protein is yet to be verified.     

Studies on the interaction of water with ethylcellulose: Effect of polymer particle size

The purpose of this research was to investigate the interaction of water with ethylcellulose samples and assess the effect of particle size on the interaction. The distribution of water within coarse particle ethylcellulose (CPEC; average particle size 310 μm) and fine particle ethylcellulose (FPEC; average particle size 9.7 μm) of 7 cps viscosity grade was assessed by differential scanning calorimetry (DSC) and dynamic vapor sorption analysis. The amounts of nonfreezing and freezing water in hydrated samples were determined from melting endotherms obtained by DSC. An increase in water content resulted in an increase in the enthalpy of fusion of water for the two particle size fractions of EC. The amount of nonfreezable water was not affected by the change in particle size at low water contents. Exposure of ethylcellulose to water for 30 minutes is sufficient to achieve equilibration within the hydrated polymer at 47% wt/wt water content. The moisture sorption profiles were analyzed according to the Guggenheim-Anderson-de Boer (GAB) and Young and Nelson equations, which can help to distinguish moisture distribution in different physical forms. The amount of externally adsorbed moisture was greater in the case of FPEC. Internally absorbed moisture was evident only with the CPEC. In light of these results, and explanation is offered for the success of FPEC in wet-granulation methods where CPEC was not successful.     

Quantifying the Entropy of Binding for Water Molecules in Protein Cavities by Computing Correlations

Protein structural analysis demonstrates that water molecules are commonly found in the internal cavities of proteins. Analysis of experimental data on the entropies of inorganic crystals suggests that the entropic cost of transferring such a water molecule to a protein cavity will not typically be greater than 7.0 cal/mol/K per water molecule, corresponding to a contribution of approximately +2.0 kcal/mol to the free energy. In this study, we employ the statistical mechanical method of inhomogeneous fluid solvation theory to quantify the enthalpic and entropic contributions of individual water molecules in 19 protein cavities across five different proteins. We utilize information theory to develop a rigorous estimate of the total two-particle entropy, yielding a complete framework to calculate hydration free energies. We show that predictions from inhomogeneous fluid solvation theory are in excellent agreement with predictions from free energy perturbation (FEP) and that these predictions are consistent with experimental estimates. However, the results suggest that water molecules in protein cavities containing charged residues may be subject to entropy changes that contribute more than +2.0 kcal/mol to the free energy. In all cases, these unfavorable entropy changes are predicted to be dominated by highly favorable enthalpy changes. These findings are relevant to the study of bridging water molecules at protein-protein interfaces as well as in complexes with cognate ligands and small-molecule inhibitors.     

How thick is the layer of thermal volume surrounding the protein?

Investigation on the volume properties of protein hydration layers is reported. Presented results are based on combination of Monte Carlo modeling and available experimental data. Six globular proteins with known data are chosen for analysis. Analyzing the model and the experimental results we found that water molecules bound to proteins by hydrogen bond are preferentially located at the places with local depressions on the protein surface. Consequently, the hydration level is not strictly proportional to the area of charged and polar surfaces, but also depends on the shape of the molecular surface. The thickness of the thermal volume layer as calculated in the framework of the scaled particle theory is 0.6-0.65 A for chosen proteins. The obtained value is significantly lower than that presented for proteins in earlier papers (where proportionality between the hydration level and the area of charged and polar surfaces was assumed), but is close to the value published for small solute molecules. Discussion including the influence of protein size and the thermal motion of the surface is presented.     

Binding of peripheral proteins to mixed lipid membranes: effect of lipid demixing upon binding

Binding isotherms have been determined for the association of horse heart cytochrome c with dioleoyl phosphatidylglycerol (DOPG)/dioleoyl phosphatidylcholine (DOPC) bilayer membranes over a range of lipid compositions and ionic strengths. In the absence of protein, the DOPG and DOPC lipids mix nearly ideally. The binding isotherms have been analyzed using double layer theory to account for the electrostatics, either the Van der Waals or scaled particle theory equation of state to describe the protein surface distribution, and a statistical thermodynamic formulation consistent with the mass-action law to describe the lipid distribution. Basic parameters governing the electrostatics and intrinsic binding are established from the binding to membranes composed of anionic lipid (DOPG) alone. Both the Van der Waals and scaled particle equations of state can describe the effects of protein distribution on the DOPG binding isotherms equally well, but with different values of the maximum binding stoichiometry (13 lipids/protein for Van der Waals and 8 lipids/protein for scaled particle theory). With these parameters set, it is then possible to derive the association constant, Kr, of DOPG relative to DOPC for surface association with bound cytochrome c by using the binding isotherms obtained with the mixed lipid membranes. A value of Kr (DOPG:DOPC) = 3.3-4.8, depending on the lipid stoichiometry, is determined that consistently describes the binding at different lipid compositions and different ionic strengths. Using the value of Kr obtained it is possible to derive the average in-plane lipid distribution and the enhancement in protein binding induced by lipid redistribution using the statistical thermodynamic theory.     

Scaling of the equilibrium sedimentation distribution in dense DNA solutions

DNA molecules, several persistence lengths long in sedimentation equilibrium at speeds high enough to maintain fairly close packing, show a dense, sharply-bounded turbid phase and an isotropic phase (as with shorter fragments) and also an intermediate, somewhat turbid region. The concentration distribution in the isotropic phase is in satisfactory agreement with a simple extension of scaled particle theory in which semiflexible chains are equivalent to straight rods of the same length. The net intermolecular interactions, as inferred from the Zimm cluster integral, are purely repulsive. As in our previous study with short fragments, the results are compatible with a hard-core electrostatic radius, decreasing with increasing salt concentration. However, for the longer fragments it is necessary to infer either a slightly greater mass per unit length or a slightly smaller electrostatic radius for closest agreement with scaled particle theory. The properties of the solution at the boundary with the turbid, presumably strongly ordered phase are consistent with those found for shorter fragments and with theoretical scaling expectation for a hard, asymmetric particle.     

Quantized Water Clusters Around Apolar Molecules

Abstract

In order to understand the mechanism of gas hydrate kinetics and to explore the existance of other new cavities in the hydrate structure, we have used Molecular Dynamics (MD) simulation to study a system comprising two Lennard-Jones particles and 214 water molecules. Equilibrium structure and properties of twelve cases have been investigated. Our findings were as follows: ? Apolar molecules promote spherical liquid water clusters in a hydrate-like labile cavity.

? The size of the cavity and the coordination number is dependent upon the size of the apolar molecule.

? The coordination number of water molecules is quantized in jumps of four.

? Similarities are observed between the labile cavities and cavities in solid hydrates and in other chemical structures such as Buckminsterfullerene.

? Such a simulation procedure suggests the possibility of other clusters which may exist in yet-to-be-found hydrates. A separate question involves whether such suggested cavities can be combined with other cavities into a space-filling crystal.

     

Comparative chewing efficiency in mammalian herbivores

Although the relevance of particle size reduction in herbivore digestion is widely appreciated, few studies have investigated digesta particle size across species in relation to body mass or digestive strategy. We investigated faecal particle size, which reflects the size of ingesta particles after both mastication and specialized processes such as rumination. Particle size was measured by wet sieving samples from more than 700 captive individuals representing 193 mammalian species. Using phylogenetic generalized least squares, faecal particle size scaled to body mass with an exponent of 0.22 (95% confidence interval: 0.16–0.28). In comparisons among different digestive strategies, we found that (1) equids had smaller faecal particles than other hindgut fermenters, (2) non-ruminant foregut fermenters and hindgut fermenters had similar-sized faecal particles (not significantly different), and (3) ruminants had finer faecal particles than non-ruminants. These results confirm that the relationship between chewing efficiency and body mass is modified by morphological adaptations in dental design and physiological adaptations to chewing, such as rumination. This allometric relationship should be considered when investigating the effect of body size on digestive physiology, and digestion studies should include a measure of faecal particle size.     

Adsorption of globular proteins on locally planar surfaces: models for the effect of excluded surface area and aggregation of adsorbed protein on adsorption equilibria.

Equilibrium statistical-thermodynamic models are presented for the surface adsorption of proteins modeled as regular convex hard particles. The adsorbed phase is treated as a two-dimensional fluid, and the chemical potential of adsorbed protein is obtained from scaled particle theory. Adsorption isotherms are calculated for nonassociating and self-associating adsorbing proteins. Area exclusion broadens adsorption isotherms relative to the Langmuir isotherm (negative cooperativity), whereas self-association steepens them (positive cooperativity). The calculated isotherm for adsorption of hard spheres using scaled particle theory for hard discs agrees well with that calculated from the hard disc virial expansion. As the cross section of the adsorbing protein in the plane of the surface becomes less discoidal, the apparent negative cooperativity manifested in the isotherm becomes more pronounced. The model is extended to the case of simultaneous adsorption of a tracer protein at low saturation and a competitor protein with a different size and/or shape at arbitrary fractional saturation. Area exclusion by competitor for tracer (and vice versa) is shown to substantially enhance the displacement of tracer by competitor and to qualitatively invalidate the standard interpretation of ligand competition experiments, according to which the fractional displacement of tracer by competitor is equal to the fractional saturation by competitor.     

Size effects in nonpolar solvation: lessons from two simple models

Size dependence of the solute chemical potential mu(u) is examined using the Ornstein-Zernike equation for two models of the nonpolar solute-solvent interactions. Simple Lennard-Jones interactions are assumed in the first model while the Lennard-Jones potential is distributed over the solute volume in the second model similar to the Hamaker theory for the colloid dispersion forces. In both models, while mu(u) rises asymptotically as the third power of the solute size in agreement with asymptotic solution of the scaled particle theory, it increases faster at smaller sizes. Deviations from the cubic law are more pronounced at higher solvent densities and stronger molecular interactions. Within a relatively narrow size range typical for small organic molecules, mu(u) can be approximated with a polynomial of the third or even the second power. However, the latter approximation is less accurate and cannot be employed for extrapolation to the larger size region.     

Lateral diffusion of membrane proteins in protein-rich membranes. A simple hard particle model for concentration dependence of the two-dimensional diffusion coefficient.

A model for the effect of protein concentration on the rate of lateral diffusion of integral membrane proteins is presented, in which the proteins are represented by equivalent hard circular particles on a surface. As the density of particles increases, the probability of finding a vacancy immediately adjacent to a tracer particle into which it may diffuse decreases, resulting in a concomitant reduction of the tracer diffusion coefficient. Using scaled particle theory to calculate the concentration-dependent probabilities, a simple approximate result is obtained in closed form, that is compared with the results of previously published Monte Carlo lattice simulations and experimental observations.     

Analysis of particle strain in stirred bioreactors by drop breakage investigations

Understanding of particle strain and drop breakage is relevant for various technical applications. To analyze it, single drop experiments in a breakage cell and evolving drop size distributions in an agitated system are studied. The mechanisms for particle strain and drop breakage are assumed to be comparable for the investigated turbulent flow regime. The agitation process is simulated using a population balance model. This model provides transient prediction capacities at different scales and can be used for scale-up/down projects. The number and the size distributions of daughter fragments for single drops have been studied. The results clearly support the assumption of binary breakage. The most common assumption of a Gaussian distribution for the daughter drop size distribution could not be supported. The evolution of a breakage-dominated toluene/water system was then simulated using different daughter drop size distributions from literature. The computational results were compared with experimental values. All simulations were able to predict the transient Sauter mean diameter excellently but varied strongly in the results on the shape of the distribution. In agreement with the experimental single drop results, the use of a bimodal or a very broad bell-shaped distribution of the daughter drops is proposed for the simulations. Although these results were obtained in a particular vessel for a specific phase system, it can be applied to simulate transient multiphase systems at different scales. We would expect that the general trends observed in this study are comparable to various applications in multiphase bioreactors.     

Insertion and pore formation driven by adsorption of proteins onto lipid bilayer membrane-water interfaces

We describe the binding of proteins to lipid bilayers in the case for which binding can occur either by adsorption to the lipid bilayer membrane-water interface or by direct insertion into the bilayer itself. We examine in particular the case when the insertion and pore formation are driven by the adsorption process using scaled particle theory. The adsorbed proteins form a two-dimensional "surface gas" at the lipid bilayer membrane-water interface that exerts a lateral pressure on the lipid bilayer membrane. Under conditions of strong intrinsic binding and a high degree of interfacial converge, this pressure can become high enough to overcome the energy barrier for protein insertion. Under these conditions, a subtle equilibrium exists between the adsorbed and inserted proteins. We propose that this provides a control mechanism for reversible insertion and pore formation of proteins such as melittin and magainin. Next, we discuss experimental data for the binding isotherms of cytochrome c to charged lipid membranes in the light of our theory and predict that cytochrome c inserts into charged lipid bilayers at low ionic strength. This prediction is supported by titration calorimetry results that are reported here. We were furthermore able to describe the observed binding isotherms of the pore-forming peptides endotoxin (alpha 5-helix) and of pardaxin to zwitterionic vesicles from our theory by assuming adsorption/insertion equilibrium.     

Hydration of nucleic acid fragments: comparison of theory and experiment for high-resolution crystal structures of RNA, DNA, and DNA-drug complexes.

A computationally efficient method to describe the organization of water around solvated biomolecules is presented. It is based on a statistical mechanical expression for the water-density distribution in terms of particle correlation functions. The method is applied to analyze the hydration of small nucleic acid molecules in the crystal environment, for which high-resolution x-ray crystal structures have been reported. Results for RNA [r(ApU).r(ApU)] and DNA [d(CpG).d(CpG) in Z form and with parallel strand orientation] and for DNA-drug complexes [d(CpG).d(CpG) with the drug proflavine intercalated] are described. A detailed comparison of theoretical and experimental data shows positional agreement for the experimentally observed water sites. The presented method can be used for refinement of the water structure in x-ray crystallography, hydration analysis of nuclear magnetic resonance structures, and theoretical modeling of biological macromolecules such as molecular docking studies. The speed of the computations allows hydration analyses of molecules of almost arbitrary size (tRNA, protein-nucleic acid complexes, etc.) in the crystal environment and in aqueous solution.     

A simulation approach to understanding the masticatory process

An analysis of the reduction of food particle sizes during human mastication is presented in terms of the probability of a particle being broken (selection function) and the distribution of fragment sizes produced when it fails (breakage function). Both selection and breakage functions are defined and a general equation produced. Several feasible behaviours for these two variables that have been suggested in the literature are modelled by computer simulation and the results are compared to published breakdown patterns. The conclusions are that selection and breakage functions probably behave very simply with respect to particle size, and that these behaviours could be deduced from an analysis of food particle size distributions and the rate at which particle sizes are reduced per chew.