Modeling Hydration Water and its Role in Polymer Folding

The hydrophobic effect is the dominant force which drives a proteintowards its native state, but its physics has not been thoroughlyunderstood yet. We introduce an exactly solvable model of the solvation ofnon-polar molecules in water, which shows that the reduced number ofallowed configurations of water molecules when the solute is present isenough to give rise to hydrophobic behaviour. We apply our model to anon-polar homopolymer in aqueous solution, obtaining a clear evidence ofboth `cold' and `warm' collapse transitions that recall those of proteins.Finally we show how the model can be adapted to describe the solvation ofaromatic and polar molecules.     

Understanding the role of hydrogen bonds in water dynamics and protein stability

The mechanisms of cold and pressure denaturation of proteins are a matter of debate, but it is commonly accepted that water plays a fundamental role in the process. It has been proposed that the denaturation process is related to an increase of hydrogen bonds among hydration water molecules. Other theories suggest that the causes of denaturation are the density fluctuations of surface water, or the destabilization of hydrophobic contacts as a consequence of water molecule inclusions inside the protein, especially at high pressures. We review some theories that have been proposed to give insight into this problem, and we describe a coarse-grained model of water that compares well with experiments for proteins’ hydration water. We introduce its extension for a homopolymer in contact with the water monolayer and study it by Monte Carlo simulations in an attempt to understand how the interplay of water cooperativity and interfacial hydrogen bonds affects protein stability.     

Theory of lipid polymorphism: application to phosphatidylethanolamine and phosphatidylserine

We introduce a microscopic model of a lipid with a charged headgroup and flexible hydrophobic tails, a neutral solvent, and counter ions. Short-ranged interactions between hydrophilic and hydrophobic moieties are included as are the Coulomb interactions between charges. Further, we include a short-ranged interaction between charges and neutral solvent, which mimics the short-ranged, thermally averaged interaction between charges and water dipoles. We show that the model of the uncharged lipid displays the usual lyotropic phases as a function of the relative volume fraction of the headgroup. Choosing model parameters appropriate to dioleoylphosphatidylethanolamine in water, we obtain phase behavior that agrees well with experiment. Finally we choose a solvent concentration and temperature at which the uncharged lipid exhibits an inverted hexagonal phase and turn on the headgroup charge. The lipid system makes a transition from the inverted hexagonal to the lamellar phase, which is related to the increased waters of hydration correlated with the increased headgroup charge via the charge-solvent interaction. The polymorphism displayed upon variation of pH mimics that of the behavior of phosphatidylserine.     

Simulation studies of protein-induced bilayer deformations, and lipid-induced protein tilting, on a mesoscopic model for lipid bilayers with embedded proteins

Biological membranes are complex and highly cooperative structures. To relate biomembrane structure to their biological function it is often necessary to consider simpler systems. Lipid bilayers composed of one or two lipid species, and with embedded proteins, provide a model system for biological membranes. Here we present a mesoscopic model for lipid bilayers with embedded proteins, which we have studied with the help of the dissipative particle dynamics simulation technique. Because hydrophobic matching is believed to be one of the main physical mechanisms regulating lipid-protein interactions in membranes, we considered proteins of different hydrophobic length (as well as different sizes). We studied the cooperative behavior of the lipid-protein system at mesoscopic time- and lengthscales. In particular, we correlated in a systematic way the protein-induced bilayer perturbation, and the lipid-induced protein tilt, with the hydrophobic mismatch (positive and negative) between the protein hydrophobic length and the pure lipid bilayer hydrophobic thickness. The protein-induced bilayer perturbation was quantified in terms of a coherence length, xi(P), of the lipid bilayer hydrophobic thickness profile around the protein. The dependence on temperature of xi(P), and the protein tilt-angle, were studied above the main-transition temperature of the pure system, i.e., in the fluid phase. We found that xi(P) depends on mismatch, i.e., the higher the mismatch is, the longer xi(P) becomes, at least for positive values of mismatch; a dependence on the protein size appears as well. In the case of large model proteins experiencing extreme mismatch conditions, in the region next to the so-called lipid annulus, there appears an undershooting (or overshooting) region where the bilayer hydrophobic thickness is locally lower (or higher) than in the unperturbed bilayer, depending on whether the protein hydrophobic length is longer (or shorter) than the pure lipid bilayer hydrophobic thickness. Proteins may tilt when embedded in a too-thin bilayer. Our simulation data suggest that, when the embedded protein has a small size, the main mechanism to compensate for a large hydrophobic mismatch is the tilt, whereas large proteins react to negative mismatch by causing an increase of the hydrophobic thickness of the nearby bilayer. Furthermore, for the case of small, peptidelike proteins, we found the same type of functional dependence of the protein tilt-angle on mismatch, as was recently detected by fluorescence spectroscopy measurements.     

Acoustic emission analysis and experiments with physical model systems reveal a peculiar nature of the xylem tension

Advanced acoustic emission analysis, special microscopic examinations and experiments with physical model systems give reasons for the assumption that the tension in the water conducting system of vascular plants is caused by countless minute gas bubbles strongly adhering to the hydrophobic lignin domains of the xylem vessel walls. We ascertained these bubbles for several species of temperate deciduous trees and conifers. It is our hypothesis that the coherent bubble system of the xylem conduits operates as a force-transmitting medium that is capable of transporting water in traveling peristaltic waves. By virtue of the high elasticity of the gas bubbles, the hydro-pneumatic bubble system is capable of cyclic storing and releasing of energy. We consider the abrupt regrouping of the wall adherent bubble system to be the origin of acoustic emissions from plants. For Ulmus glabra, we recorded violent acoustic activity during both transpiration and re-hydration. The frequency spectrum and the waveforms of the detected acoustic emissions contradict traditional assumptions according to which acoustic emissions are caused by cavitation disruption of the stressed water column. We consider negative pressure in terms of the cohesion theory to be mimicked by the tension of the wall adherent bubble system.     

Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes.

We consider whether the continuum model of hydration optimized to reproduce vacuum-to-water transfer free energies simultaneously describes the hydration free energy contributions to conformational equilibria of the same solutes in water. To this end, transfer and conformational free energies of idealized hydrophobic and amphiphilic solutes in water are calculated from explicit water simulations and compared to continuum model predictions. As benchmark hydrophobic solutes, we examine the hydration of linear alkanes from methane through hexane. Amphiphilic solutes were created by adding a charge of +/-1e to a terminal methyl group of butane. We find that phenomenological continuum parameters fit to transfer free energies are significantly different from those fit to conformational free energies of our model solutes. This difference is attributed to continuum model parameters that depend on solute conformation in water, and leads to effective values for the free energy/surface area coefficient and Born radii that best describe conformational equilibrium. In light of these results, we believe that continuum models of hydration optimized to fit transfer free energies do not accurately capture the balance between hydrophobic and electrostatic contributions that determines the solute conformational state in aqueous solution.     

A coarse-grained model for PCL: conformation,self-assembly of MePEG-b-PCL amphiphilic diblock copolymers

Poly-ε-caprolactone (PCL) is a biodegradable hydrophobic polyester that has been widely used in medical devices, tissue engineering and nanoparticle-based drug delivery. Coarse-grained molecular dynamics (CGMD) has been employed to study and gain insights into the conformational, structural and self-assembly behaviour of polymers, lipids and amphiphilic macromolecules. In this work, we developed a model for PCL within the framework of the MARTINI coarse-grained force field. The non-bonded interactions were based on the existing MARTINI bead types, while the bonded interactions were mapped onto a PCL rendition obtained from atomistic simulations. The model accurately reproduces the structural and dynamic properties of the PCL homopolymer and shows very reasonable temperature and solvent transferability. We also studied self-assembly of MePEG-b-PCL linear diblock copolymers using an existing MARTINI model for MePEG (Methoxy Polyethylene glycol), by analysing the critical micelle concentration (CMC), as well as the shape, size and morphology of the nano-polymeric micelles. We obtained excellent agreement of the CMC, while the size was under-predicted compared to experimental data. This robust model paves the way for CGMD modelling of PCL and serves as a starting point for future designs of PCL-related polymeric systems .     

Bubbles, gating, and anesthetics in ion channels

We suggest that bubbles are the bistable hydrophobic gates responsible for the on-off transitions of single channel currents. In this view, many types of channels gate by the same physical mechanism—dewetting by capillary evaporation—but different types of channels use different sensors to modulate hydrophobic properties of the channel wall and thereby trigger and control bubbles and gating. Spontaneous emptying of channels has been seen in many simulations. Because of the physics involved, such phase transitions are inherently sensitive, unstable threshold phenomena that are difficult to simulate reproducibly and thus convincingly. We present a thermodynamic analysis of a bubble gate using morphometric density functional theory of classical (not quantum) mechanics. Thermodynamic analysis of phase transitions is generally more reproducible and less sensitive to details than simulations. Anesthetic actions of inert gases—and their interactions with hydrostatic pressure (e.g., nitrogen narcosis)—can be easily understood by actions on bubbles. A general theory of gas anesthesia may involve bubbles in channels. Only experiments can show whether, or when, or which channels actually use bubbles as hydrophobic gates: direct observation of bubbles in channels is needed. Existing experiments show thin gas layers on hydrophobic surfaces in water and suggest that bubbles nearly exist in bulk water.     

The effect of ionic strength, temperature, and pressure on the interaction potential of dense protein solutions: from nonlinear pressure response to protein crystallization

Understanding the intermolecular interaction potential, V(r), of proteins under the influence of temperature, pressure, and salt concentration is essential for understanding protein aggregation, crystallization, and protein phase behavior in general. Here, we report small-angle x-ray scattering studies on dense lysozyme solutions of high ionic strength as a function of temperature and pressure. We show that the interaction potential changes in a nonlinear fashion over a wide range of temperatures, salt, and protein concentrations. Neither temperature nor protein and salt concentration lead to marked changes in the pressure dependence of V(r), indicating that changes of the water structure dominate the pressure dependence of the intermolecular forces. Furthermore, by analysis of the temperature, pressure, and ionic strength dependence of the normalized second virial coefficient, b2, we show that the interaction can be fine-tuned by pressure, which can be used to optimize b2 values for controlled protein crystallization.     

Temperature-dependent chaperone activity and structural properties of human alphaA- and alphaB-crystallins

The chaperone activity and biophysical properties of recombinant human alphaA- and alphaB-crystallins were studied by light scattering and spectroscopic methods. While the chaperone function of alphaA-crystallin markedly improves with an increase in temperature, the activity of alphaB homopolymer appears to change very little upon heating. Compared with alphaB-crystallin, the alphaA-homopolymer is markedly less active at low temperatures, but becomes a more active species at high temperatures. At physiologically relevant temperatures, the alphaB homopolymer appears to be modestly (two times or less) more potent chaperone than alphaA homopolymer. In contrast to very similar thermotropic changes in the secondary structure of both homopolymers, alphaA- and alphaB-crystallins markedly differ with respect to the temperature-dependent surface hydrophobicity profiles. Upon heating, alphaA-crystallin undergoes a conformational transition resulting in the exposure of additional hydrophobic sites, whereas no such transition occurs for alphaB-crystallin. The correlation between temperature-dependent changes in the chaperone activity and hydrophobicity properties of the individual homopolymers supports the view that the chaperone activity of alpha-crystallin is dependent on the presence of surface-exposed hydrophobic patches. However, the present data also show that the surface hydrophobicity is not the sole determinant of the chaperone function of alpha-crystallin.     

Mechanism of ferritin iron uptake: activity of the H-chain and deletion mapping of the ferro-oxidase site. A study of iron uptake and ferro-oxidase activity of human liver, recombinant H-chain ferritins, and of two H-chain deletion mutants

To study the functional differences between human ferritin H- and L-chains and the role of the protein shell in the formation and growth of the ferritin iron core, we have compared the kinetics of iron oxidation and uptake of ferritin purified from human liver (90% L) and of the H-chain homopolymer overproduced in Escherichia coli (100% H). As a control for iron autocatalytic activity, we analyzed the effect of Fe(III) on the iron uptake reaction. The results show that the H-chain homopolymer has faster rates of iron uptake and iron oxidation than liver ferritin in all the conditions analyzed and that the difference is reduced in the conditions in which iron autocatalysis in high: i.e. at pH 7 and in presence of iron core. We have also analyzed the properties of two engineered H-chains, one lacking the last 22 amino acids at the carboxyl terminus and the other missing the first 13 residues at the amino terminus. These mutant proteins assemble in ferritin-like proteins and maintain the ability to catalyze iron oxidation. The deletion at the carboxyl terminus, however, prevents the formation of a stable iron core. It is concluded that the ferritin H-chain has an iron oxidation site which is separated from the sites of iron transfer and hydrolysis and that either the integrity of the molecule or the presence of the amino acid sequences forming the hydrophobic channel is necessary for iron core formation.     

Structure and dynamics of parallel beta-sheets, hydrophobic core, and loops in Alzheimer's A beta fibrils

We explore the relative contributions of different structural elements to the stability of Abeta fibrils by molecular-dynamics simulations performed over a broad range of temperatures (298 K to 398 K). Our fibril structures are based on solid-state nuclear magnetic resonance experiments of Abeta(1-40) peptides, with sheets of parallel beta-strands connected by loops and stabilized by interior salt bridges. We consider models with different interpeptide interfaces, and different staggering of the N- and C-terminal beta-strands along the fibril axis. Multiple 10-20 ns molecular-dynamics simulations show that fibril segments with 12 peptides are stable at ambient temperature. The different models converge toward an interdigitated side-chain packing, and present water channels solvating the interior D23/K28 salt bridges. At elevated temperatures, we observe the early phases of fibril dissociation as a loss of order in the hydrophilic loops connecting the two beta-strands, and in the solvent-exposed N-terminal beta-sheets. As the most dramatic structural change, we observe collective sliding of the N- and C-terminal beta-sheets on top of each other. The interior C-terminal beta-sheets in the hydrophobic core remain largely intact, indicating that their formation and stability is crucial to the dissociation/elongation and stability of Abeta fibrils.     

Preparation of magnetic microspheres from water-in-oil emulsion stabilized by block copolymer dispersant

A new method for the preparation of magnetic microspheres is reported. The preparation involved first the dispersion of an aqueous phase, containing magnetite nanoparticles and a water-soluble homopolymer, into droplets in an organic medium using an amphiphilic block copolymer as the dispersant. This was followed by water distillation at a raised temperature from the aqueous droplets to yield polymer/magnetite particles. The structure of the particles was then locked in by a reagent being added to cross-link the water-soluble copolymer block and homopolymer. Since the hydrophobic block of the copolymer consisted of a protected polyester, the removal of the protective moieties from the coronal chains yielded poly(acrylic acid) or other functional polymers to render water dispersibility to the spheres and to enable biomolecule immobilization.     

Anti-cooperativity and cooperativity in hydrophobic interactions: Three-body free energy landscapes and comparison with implicit-solvent potential functions for proteins

Potentials of mean force (PMFs) of three-body hydrophobic association are investigated to gain insight into similar processes in protein folding. Free energy landscapes obtained from explicit simulations of three methanes in water are compared with that predicted by popular implicit-solvent effective potentials for the study of proteins. Explicit-water simulations show that for an extended range of three-methane configurations, hydrophobic association at 25 degrees C under atmospheric pressure is mostly anti-cooperative, that is, less favorable than if the interaction free energies were pairwise additive. Effects of free energy nonadditivity on the kinetic path of association and the temperature dependence of additivity are explored by using a three-methane system and simplified chain models. The prevalence of anti-cooperativity under ambient conditions suggests that driving forces other than hydrophobicity also play critical roles in protein thermodynamic cooperativity. We evaluate the effectiveness of several implicit-solvent potentials in mimicking explicit water simulated three-body PMFs. The favorability of the contact free energy minimum is found to be drastically overestimated by solvent accessible surface area (SASA). Both the SASA and a volume-based Gaussian solvent exclusion model fail to predict the desolvation barrier. However, this barrier is qualitatively captured by the molecular surface area model and a recent "hydrophobic force field." None of the implicit-solvent models tested are accurate for the entire range of three-methane configurations and several other thermodynamic signatures considered.     

Essential dynamics of the cold denaturation: pressure and temperature effects in yeast frataxin

The cold denaturation of globular proteins is a process that can be caused by increasing pressure or decreasing the temperature. Currently, the action mechanism of this process has not been clearly understood, raising an interesting debate on the matter. We have studied the process of cold denaturation using molecular dynamics simulations of the frataxin system Yfh1, which has a dynamic experimental characterization of unfolding at low and high temperatures. The frataxin model here studied allows a comparative analysis using experimental data. Furthermore, we monitored the cold denaturation process of frataxin and also investigated the effect under the high‐pressure regime. For a better understanding of the dynamics and structural properties of the cold denaturation, we also analyzed the MD trajectories using essentials dynamic. The results indicate that changes in the structure of water by the effect of pressure and low temperatures destabilize the hydrophobic interaction modifying the solvation and the system volume leading to protein denaturation. Proteins 2016; 85:125–136. © 2016 Wiley Periodicals, Inc.     

Analytical derivation of thermodynamic properties of bilayer membrane with interdigitation

We consider a model of bilayer lipid membrane with interdigitation, in which the lipid tails of the opposite monolayers interpenetrate. The interdigitation is modeled by linking tails of the hydrophobic chains in the opposite monolayers within bilayer as a first approximation. This model corresponds to the types of interdigitation that are not related with the areal “hydrophobic” dilation of the membrane. A number of essential thermodynamical characteristics are calculated analytically and compared with the ones of a regular bilayer membrane without interdigitation. Important difference between lateral pressure profiles at the layers interface for linked and regular bilayer models is found. In the linked case, the lateral pressure mid-plane peak disappears, while the entropy decreases and the free energy per chain increases. Within our model we found that in case of elongation of the chains inside a nucleus of, e.g., liquid-condensed phase, homogeneous interdigitation would be more costly for the membrane’s free energy than energy of the hydrophobic mismatch between the elongated chains and the liquid-expanded surrounding. Nonetheless, an inhomogeneous interdigitation along the nucleus boundary may occur inside a “belt” of a width that varies approximately with the hydrophobic mismatch amplitude.     

The influence of geometry, surface character, and flexibility on the permeation of ions and water through biological pores

A hydrophobic constriction site can act as an efficient barrier to ion and water permeation if its diameter is less than the diameter of an ion's first hydration shell. This hydrophobic gating mechanism is thought to operate in a number of ion channels, e.g. the nicotinic receptor, bacterial mechanosensitive channels (MscL and MscS) and perhaps in some potassium channels (e.g. KcsA, MthK and KvAP). Simplified pore models allow one to investigate the primary characteristics of a conduction pathway, namely its geometry (shape, pore length, and radius), the chemical character of the pore wall surface, and its local flexibility and surface roughness. Our extended (about 0.1 micros) molecular dynamic simulations show that a short hydrophobic pore is closed to water for radii smaller than 0.45 nm. By increasing the polarity of the pore wall (and thus reducing its hydrophobicity) the transition radius can be decreased until for hydrophilic pores liquid water is stable down to a radius comparable to a water molecule's radius. Ions behave similarly but the transition from conducting to non-conducting pores is even steeper and occurs at a radius of 0.65 nm for hydrophobic pores. The presence of water vapour in a constriction zone indicates a barrier for ion permeation. A thermodynamic model can explain the behaviour of water in nanopores in terms of the surface tensions, which leads to a simple measure of 'hydrophobicity' in this context. Furthermore, increased local flexibility decreases the permeability of polar species. An increase in temperature has the same effect, and we hypothesize that both effects can be explained by a decrease in the effective solvent-surface attraction which in turn leads to an increase in the solvent-wall surface free energy.     

Simulating induced interdigitation in membranes

In this study we introduce a mesoscopic lipid-water-alcohol model. Dissipative particle dynamics (DPD) simulations have been used to investigate the induced interdigitation of bilayers consisting of double-tail lipids by adding alcohol molecules to the bilayer. Our simulations nicely reproduce the experimental phase diagrams. We find that alcohol can induce an interdigitated structure where the common bilayer structure changes into monolayer in which the alcohol molecules screen the hydrophobic tails from the water phase. At low concentrations of alcohol the membrane has domains of the interdigitated phase that are in coexistence with the common membrane phase. We compute the effect of the chain length of the alcohol on the phase behavior of the membrane and show that the stability of the interdigitated phase depends on the length of the alcohol. We show that we can reproduce the experimental hydrophobic thickness of the bilayer for various combinations of lipids and alcohols. We use our model to clarify some of the experimental questions related to the structure of the interdigitated phase and put forward a simple model that explains the alcohol chain length dependence of the stability of this interdigitated phase.     

Mathematical modeling of the circulation in the liver lobule

In this paper, we develop a mathematical model of blood circulation in the liver lobule. We aim to find the pressure and flux distributions within a liver lobule. We also investigate the effects of changes in pressure that occur following a resection of part of the liver, which often leads to high pressure in the portal vein. The liver can be divided into functional units called lobules. Each lobule has a hexagonal cross-section, and we assume that its longitudinal extent is large compared with its width. We consider an infinite lattice of identical lobules and study the two-dimensional flow in the hexagonal cross-sections. We model the sinusoidal space as a porous medium, with blood entering from the portal tracts (located at each of the vertices of the cross-section of the lobule) and exiting via the centrilobular vein (located in the center of the cross-section). We first develop and solve an idealized mathematical model, treating the porous medium as rigid and isotropic and blood as a Newtonian fluid. The pressure drop across the lobule and the flux of blood through the lobule are proportional to one another. In spite of its simplicity, the model gives insight into the real pressure and velocity distribution in the lobule. We then consider three modifications of the model that are designed to make it more realistic. In the first modification, we account for the fact that the sinusoids tend to be preferentially aligned in the direction of the centrilobular vein by considering an anisotropic porous medium. In the second, we account more accurately for the true behavior of the blood by using a shear-thinning model. We show that both these modifications have a small quantitative effect on the behavior but no qualitative effect. The motivation for the final modification is to understand what happens either after a partial resection of the liver or after an implantation of a liver of small size. In these cases, the pressure is observed to rise significantly, which could cause deformation of the tissue. We show that including the effects of tissue compliance in the model means that the total blood flow increases more than linearly as the pressure rises.