Solubility of proteins

A theory is presented on the solubility of proteins, in the hydrated as well as in the dry state, and in water as well as in organic solvents. To this effect, colloidal stability is assimilated with the solubility of the proteins, considered as hydrated entities. By means of a surface thermodynamic approach it can be shown that an increase in size of a hydrated protein must lead to insolubility, even in the absence of any change in a protein's surface properties. This can be substantiated experimentally by comparing the surface properties of immune complexes with those of their constituent immunoglobulins, as well as by comparing some of the properties of intact tobacco mosaic virus with those of its monomeric capsid subunits. Insolubilization of proteins by means of charge interactions as well as by dehydration is studied; an explanation is given of why precipitation caused by charge interactions is more likely to lead to partial irreversible denaturation than precipitation caused by protein-protein interactions brought about by partial dehydration (e.g., by “salting-out”). A link is established between the smallness (or even the negative value) of the interfacial tension between given proteins and various solvents and their solubility in these solvents. The energy of hydration of proteins can also be measured, and the differences between the free energies of interaction of dried and hydrated proteins with water point toward the additional processes underlying the solubilization, i.e., toward the conformational change of a protein in the process of becoming hydrated. The parameter of conformational change of a protein, while becoming hydrated, appears to be more closely linked to its degree of hydration than to its hydration energy.     

The effect of translocating cylindrical particles on the ionic current through a nanopore

The electric field-induced translocation of cylindrical particles through nanopores with circular cross sections is studied theoretically. The coupled Nernst-Planck equations (multi-ion model, MIM) for the concentration fields of the ions in solution and the Stokes equation for the flow field are solved simultaneously. The predictions of the multi-ion model are compared with the predictions of two simplified models based on the Poisson-Boltzmann equation (PBM) and the Smoluchowski's slip velocity (SVM). The concentration field, the ionic current though the pore, and the particle's velocity are computed as functions of the particle's size, location, and electric charge; the pore's size and electric charge; the electric field intensity; and the bulk solution's concentration. In qualitative agreement with experimental data, the MIM predicts that, depending on the bulk solution's concentration, the translocating particle may either block or enhance the ionic current. When the thickness of the electric double layer is relatively large, the PBM and SVM predictions do not agree with the MIM predictions. The limitations of the PBM and SVM are delineated. The theoretical predictions are compared with and used to explain experimental data pertaining to the translocation of DNA molecules through nanopores.     

Modeling the hydration of proteins: prediction of structural and hydrodynamic parameters from X-ray diffraction and scattering data

The implications of protein-water interactions are of importance for understanding the solution behavior of proteins and for analyzing the fine structure of proteins in aqueous solution. Starting from the atomic coordinates, by bead modeling the scattering and hydrodynamic properties of proteins can be predicted reliably (Debye modeling, program HYDRO). By advanced modeling techniques the hydration can be taken into account appropriately: by some kind of rescaling procedures, by modeling a water shell, by iterative comparisons to experimental scattering curves (ab initio modeling) or by special hydration algorithms. In the latter case, the surface topography of proteins is visualized in terms of dot surface points, and the normal vectors to these points are used to construct starting points for placing water molecules in definite positions on the protein envelope. Bead modeling may then be used for shaping the individual atomic or amino acid residues and also for individual water molecules. Among the tuning parameters, the choice of the scaling factor for amino acid hydration and of the molecular volume of bound water turned out to be crucial. The number and position of bound water molecules created by our hydration modeling program HYDCRYST were compared with those derived from X-ray crystallography, and the capability to predict hydration, structural and hydrodynamic parameters (hydrated volume, radius of gyration, translational diffusion and sedimentation coefficients) was compared with the findings generated by the water-shell approach CRYSOL. If the atomic coordinates are unknown, ab initio modeling approaches based on experimental scattering curves can provide model structures for hydrodynamic predictions.     

Hydrodynamic characterization of the size and shape of atropinesterase from Pseudomonas putida

Atropinesterase from Pseudomonas putida has been investigated by means of different ultracentrifugation methods under native and denaturing conditions. The following quantities were determined: sedimentation coefficient, translational diffusion and friction coefficient, partial specific volume and molecular weight. From these data the size, shape and hydration of the enzyme molecule in solution were estimated. The results suggest that atropinesterase is a globular protein which consists of a single polypeptide chain with a molecular weight of about 30,000. In solution under non-denaturing conditions, it occurs mainly as a dimer which hydrodynamically behaves as a rigid impenetrable particle. Calculations based on the spheroid model indicate that this particle resembles a hydrated sphere with a diameter of 6.1 +/- 0.2 nm and a hydration of 0.4 +/- 0.1 g of H2O/g of protein rather than a significantly less hydrated ellipsoid of revolution. Under denaturing conditions dissociation into monomers takes place. The effects of sodium dodecyl sulphate (SDS) on size and shape suggest that dimerization results from side-by-side association of two elongated monomers rather than from end-to-end association. Approximately 57 molecules of SDS are bound per dimer before dissociation occurs concomitant with the additional binding of about 19 molecules of detergent.     

Reinvestigation of the shape and state of hydration of the skeletal myosin subfragment 1 monomer in solution

Hydrodynamic calculations lead to the conclusion that chymotryptic (or ethylenediaminetetraacetic acid) myosin S1 in solution (hydrated), at 1-5 degrees C, can be modeled as a prolate ellipsoid, with an axial ratio lying between p = 1.0 and 2.5 (major axis between 100.5 A, for p = 1.0, and 162.5 A, for p = 2.5). The degree of hydration is considerable (1.24 g/g for p = 2.5 and 2.02 g/g for p = 1.0). The dehydrated myosin head is pear-shaped under the electron microscope, and its narrowest part is located near the junction with the tail [Elliott, A., & Offer, G. (1978) J. Mol. Biol. 123, 505-519]. Mendelson & Kretzschmar [Mendelson, R. A., & Kretzschmar, K.M. (1980) Biochemistry 19, 4103-4108] have shown that the pear-shaped molecule does not predict the experimental X-ray scattering curve. Nor is this model able to predict the hydrodynamic values. The three-dimensional model for S1 used by Mendelson and Kretzschmar gives a rather good fit to the experimental X-ray scattering curve, but it does not predict the hydrodynamic values. In order to try to reconcile the three models and to fit the X-ray scattering curve and the hydrodynamic data, we suggest that, in solution, the S1 monomer has the shape of a prolate ellipsoid and that an inclusion of bound water exists at one extremity of the protein. The rest of bound water surrounds the protein. As first approximation, the dry protein and the hole are assumed to have the same shape as the hydrated molecule (prolate ellipsoid; p).(ABSTRACT TRUNCATED AT 250 WORDS)     

Simulate the diffusion of hydrated ions by nanofiltration membrane process with random walk

We propose a new diffusion model describing the diffusion behaviours of hydrated ions in the process of nanofiltration (NF) based on the random walk (RW) theory when the NF membrane is uncharged or low charged. In this model, the hydration of ions and their deformation capacity are considered. The structure of the membrane is idealised into a lozenge shape and the diameter of membrane pore is defined as gapsize. A computer program named RW system in chemistry is developed to simulate based on this model. Six familiar ions Li⁺, Na⁺, Mg²⁺, Al³⁺, K⁺ and Ca²⁺ are investigated. Their characteristics are calculated by Gaussian 03, Pople, Inc., Wallingford, CT. The diffusivities of hydrated ions are calculated and discussed. The results show that the hydration of ions cannot be ignored in NF process when the membrane pore size is near the dimensions of the hydrated ions.     

Dynamic hydration numbers for biologically important ions

The role of ionized groups in biological systems is determined by their affinity for water [Biophys. J. 72 (1997) 65-76]. The tightly bound water associated with biologically important ions increases their apparent size. We define the apparent dynamic hydration number of an ion here as the number of tightly bound water molecules that must be assigned to the ion to explain its apparent molecular weight on a Sephadex G-10 size exclusion column, and report the first accurate determination of tightly bound water for 23 ions of biological significance, including H(+) and HO(-). We also calculate the radius of the equivalent hydrated sphere (r(h)) for each ion. We find that the ratio of the hydrated volumes of two ions approximates the ratio of the square of the charges of the same two ions. Since the 'ionic strength' of the solution also depends upon the square of the charges on the ions, our results suggest that ionic strength effects may largely arise from local effects related to the hydrated volume of the ion--that is, from space filling, osmotic, water activity, surface tension and hydration shell overlap effects rather than from long-range electric field effects.     

Nanosecond structural dynamics of intrinsically disordered β-casein micelles by neutron spectroscopy

β-casein undergoes a reversible endothermic self-association, forming protein micelles of limited size. In its functional state, a single β-casein monomer is unfolded, which creates a high structural flexibility, which is supposed to play a major role in preventing the precipitation of calcium phosphate particles. We characterize the structural flexibility in terms of nanosecond molecular motions, depending on the temperature by quasielastic neutron scattering. Our major questions are: Does the self-association reduce the chain flexibility? How does the dynamic spectrum of disordered caseins differ from a compactly globular protein? How does the dynamic spectrum of β-casein in solution differ from that of a protein in hydrated powder states? We report on two relaxation processes on a nanosecond and a sub-nanosecond timescale for β-casein in solution. Both processes are analyzed by Brownian oscillator model, by which the spring constant can be defined in the isotropic parabolic potential. The slower process, which is analyzed by neutron spin echo, seems a characteristic feature of the unfolded structure. It requires bulk solvent and is not seen in hydrated protein powders. The faster process, which is analyzed by neutron backscattering, has a smaller amplitude and requires hydration water, which is also observed with folded proteins in the hydrated state. The self-association had no significant influence on internal relaxation, and thus, a β-casein protein monomer flexibility is preserved in the micelle. We derive spring constants of the faster and slower motions of β-caseins in solution and compared them with those of some proteins in various states (folded or hydrated powder).     

Hydrogen exchange of lysozyme powders. Hydration dependence of internal motions

The rate of exchange of the labile hydrogens of lysozyme was measured by out-exchange of tritium from the protein in solution and from powder samples of varied hydration level, for pH 2, 3, 5, 7, and 10 at 25 degrees C. The dependence of exchange of powder samples on the level of hydration was the same for all pHs. Exchange increased strongly with increased hydration until reaching a rate of exchange that is constant above 0.15 g of H2O/g of protein (120 mol of H2O/mol of protein). This hydration level corresponds to coverage of less than half the protein surface with a monolayer of water. No additional hydrogen exchange was observed for protein powders with higher water content. Considered in conjunction with other lysozyme hydration data [Rupley, J. A., Gratton, E., & Careri, G. (1983) Trends Biochem. Sci. (Pers. Ed.) 8, 18-22], this observation indicates that internal protein dynamics are not strongly coupled to surface properties. The use of powder samples offers control of water activity through regulation of water vapor pressure. The dependence of the exchange rate on water activity was about fourth order. The order was pH independent and was constant from 114 to 8 mol of hydrogen remaining unexchanged/mol of lysozyme. These results indicate that the rate-determining step for protein hydrogen exchange is similar for all backbone amides and involves few water molecules. Powder samples were hydrated either by isopiestic equilibration, with a half-time for hydration of about 1 h, or by addition of solvent to rapidly reach final hydration. Samples hydrated slowly by isopiestic equilibration exhibited more exchange than was observed for samples of the same water content that had been hydrated rapidly by solvent addition. This difference can be explained by salt and pH effects on the nearly dry protein. Such effects would be expected to contribute more strongly during the isopiestic equilibration process. Solution hydrogen exchange measurements made for comparison with the powder measurements are in good agreement with published data. Rank order was proven the same for all pHs by solution pH jump experiments. The effect of ionic strength on hydrogen exchange was examined at pH 2 and pH 5 for protein solutions containing up to 1.0 M added salt. The influence of ionic strength was similar for both pHs and was complex in that the rate increased, but not monotonically, with increased ionic strength.     

Solubility of proteins

A theory is presented on the solubility of proteins, in the hydrated as well as in the dry state, and in water as well as in organic solvents. To this effect, colloidal stability is assimilated with the solubility of the proteins, considered as hydrated entities. By means of a surface thermodynamic approach it can be shown that an increase in size of a hydrated protein must lead to insolubility, even in the absence of any change in a protein's surface properties. This can be substantiated experimentally by comparing the surface properties of immune complexes with those of their constituent immunoglobulins, as well as by comparing some of the properties of intact tobacco mosaic virus with those of its monomeric capsid subunits. Insolubilization of proteins by means of charge interactions as well as by dehydration is studied; an explanation is given of why precipitation caused by charge interactions is more likely to lead to partial irreversible denaturation than precipitation caused by protein-protein interactions brought about by partial dehydration (e.g., by salting-out). A link is established between the smallness (or even the negative value) of the interfacial tension between given proteins and various solvents and their solubility in these solvents. The energy of hydration of proteins can also be measured, and the differences between the free energies of interaction of dried and hydrated proteins with water point toward the additional processes underlying the solubilization, i.e., toward the conformational change of a protein in the process of becoming hydrated. The parameter of conformational change of a protein, while becoming hydrated, appears to be more closely linked to its degree of hydration than to its hydration energy.     

Long-range DNA-water interactions

DNA functions only in aqueous environments and adopts different conformations depending on the hydration level. The dynamics of hydration water and hydrated DNA leads to rotating and oscillating dipoles that, in turn, give rise to a strong megahertz to terahertz absorption. Investigating the impact of hydration on DNA dynamics and the spectral features of water molecules influenced by DNA, however, is extremely challenging because of the strong absorption of water in the megahertz to terahertz frequency range. In response, we have employed a high-precision megahertz to terahertz dielectric spectrometer, assisted by molecular dynamics simulations, to investigate the dynamics of water molecules within the hydration shells of DNA as well as the collective vibrational motions of hydrated DNA, which are vital to DNA conformation and functionality. Our results reveal that the dynamics of water molecules in a DNA solution is heterogeneous, exhibiting a hierarchy of four distinct relaxation times ranging from ∼8 ps to 1 ns, and the hydration structure of a DNA chain can extend to as far as ∼18 Å from its surface. The low-frequency collective vibrational modes of hydrated DNA have been identified and found to be sensitive to environmental conditions including temperature and hydration level. The results reveal critical information on hydrated DNA dynamics and DNA-water interfaces, which impact the biochemical functions and reactivity of DNA.     

Protein structure probed by polarization spectroscopy. II. A time-resolved fluorescence study of human fibrinogen

Human fibrinogen in solution was studied by monitoring the time-resolved depolarization of the fluorescence emitted by two spectroscopic labels of which the fluorescence lifetimes differ by an order of magnitude. Contrary to a long-held view, no evidence of molecular flexibility was found in the 10-1000 ns range. In addition, from the rate of the overall rotation, it is proposed that a prolate and symmetric ellipsoid of 47 X 10.5 nm may represent the time-averaged hydrodynamic size and shape of the protein in solution. This rigid and highly hydrated structure (4 g water/g protein) accommodates the latest nodular models obtained from electron microscopy, explains the singular hydrodynamics of fibrinogen and, apparently, it would perform the two main functions of the protein in haemostasis, blood coagulation and platelet aggregation, more efficiently than the flexible molecule.     

Effect of hydration on the water content of human erythrocytes.

An ideal, hydrated, nondilute pseudobinary salt-protein-water solution model of the RBC intracellular solution has been developed to describe the osmotic behavior of human erythrocytes during freezing and thawing. Because of the hydration of intracellular solutes (mostly cell proteins), our analytical results predict that at least 16.65% of the isotonic cell water content will be retained within RBCs placed in hypertonic solutions. These findings are consistent not only with the experimental measurements of the amount of isotonic cell water retained within RBCs subjected to nonisotonic extracellular solutions (20-32%) but also with the experimental evidence that all of the water within RBCs is solvent water. By modeling the RBC intracellular solution as a hydrated salt-protein-water solution, no anomalous osmotic behavior is apparent.     

Dielectric behavior of water in biological solutions: studies on myoglobin, human low-density lipoprotein, and polyvinylpyrrolidone

The dielectric behavior of the aqueous solutions of three widely differing macromolecules has been investigated: myoglobin, polyvinylpyrrolidone (PVP), and human serum low-density lipoprotein (LDL). It was not possible to interpret unambiguously the dielectric properties of the PVP solution in terms of water structure. The best interpretation of the dielectric data on the myoglobin and LDL solutions was that, in both cases, the macromolecule attracts a layer of water of hydration one or two water molecules in width. For LDL, this corresponds to a hydration factor of only 0.05 g/g, whereas for myoglobin the figure is nearer 0.6 g/g. With myoglobin, part of the water of hydration exhibits its dispersion at frequencies of a few GHz, and the rest disperses at lower frequencies, perhaps as low as 10-12 MHz. The approximate constancy of the width of the hydration shell for two molecules as dissimilar in size as LDL and myoglobin confirms that the proportion of water existing as water of hydration in a biological solution depends critically on the size of the macromolecules as well as on their concentration.     

Physical aspects of the weakly hydrated protein surface.

We review the physical properties of water on the surface of weakly hydrated proteins and present some theoretical models used to understand them. The first part concerns mainly structural properties and introduces a model for two-dimensional clusters of water molecules. The second part is devoted to dynamical properties of the hydrated protein surface. Dielectric measurements which provide an evidence for proton conductivity due to the percolation of the network of surface water molecules and for the glass dynamics of migrating protons when temperature is lowered are reviewed. These results can be associated with the concept of frustration and analyzed with two models, an Ising model to describe the proton jumps and the model of two-dimensional surface water which exhibits a glassy dynamiques of the water molecules. Biological implications of these properties of hydration water are briefly discussed.     

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.     

Calculation of hydrodynamic properties of small nucleic acids from their atomic structure

Hydrodynamic properties (translational diffusion, sedimentation coefficients and correlation times) of short B-DNA oligonucleotides are calculated from the atomic-level structure using a bead modeling procedure in which each non-hydrogen atom is represented by a bead. Using available experimental data of hydrodynamic properties for several oligonucleotides, the best fit for the hydrodynamic radius of the atoms is found to be ~2.8 Å. Using this value, the predictions for the properties corresponding to translational motion and end-over-end rotation are accurate to within a few percent error. Analysis of NMR correlation times requires accounting for the internal flexibility of the double helix, and allows an estimation of ~0.85 for the Lipari–Szabo generalized order parameter. Also, the degree of hydration can be determined from hydrodynamics, with a result of ~0.3 g (water)/g (DNA). These numerical results are quite similar to those found for globular proteins. If the hydrodynamic model for the short DNA is simply a cylindrical rod, the predictions for overall translation and rotation are slightly worse, but the NMR correlation times and the degree of hydration, which depend more on the cross-sectional structure, are more severely affected.     

Oxygen-17 and deuterium nuclear magnetic relaxation studies of lysozyme hydration in solution: field dispersion, concentration, pH/pD, and protein activity dependences

A comparison of 17O and 2H NMR relaxation rates of water in lysozyme solutions as a function of concentration, pH/pD, and magnetic field suggests that only 17O monitors directly the hydration of lysozyme in solution. NMR measurements are for the first time extended to 11.75 T. Lysozyme hydration data are analyzed in terms of an anisotropic, dual-motion model with fast exchange of water between the "bound" and "free" states. The analysis yields 180 mol "bound" water/mol lysozyme and two correlation times of 7.4 ns ("slow") and 29 ps ("fast") for the bound water population at 27 degrees C and pH 5.1, in the absence of salt, assuming anisotropic motions of water with an order parameter value for bound water of 0.12. Under these conditions, the value of the slow correlation time of bound water (7.4 ns) is consistent with the value of 8 ns obtained by frequency-domain fluorescence techniques for the correlation time associated with the lysozyme tumbling motion in solutions without salt. In the presence of 0.1 M NaCl the hydration number increases to 290 mol/mol lysozyme at pD 4.5 and 21 degrees C. The associated correlation times at 21 degrees C in the presence of 0.1 M NaCl are 4.7 ns and 15.5 ps, respectively. The value of the slow correlation time of 4.7 ns is consistent with the calculated value (4.9 ns) for the lysozyme monomer tumbling in solution. The systematic deviations of the relaxation rates, estimated with the single-exponential approximation, from the theoretical, multiexponential nuclear (I' + 1/2) spin relaxation are evaluated at various frequencies for 17O (I = 5/2) with the first-order, linear approximation (25). All NMR relaxation data for hydrated lysozymes are affected by protein activity and are sensitive both to the ionization of protein side chains and to the state of protein aggregation.     

Molecular dynamics simulation study for diffusion of Na+ ion in water-filled carbon nanotubes at 25°C

We present results of molecular dynamics simulations for diffusion of Na⁺ ion in water-filled carbon nanotubes (CNTs) at 25°C using the extended simple point charge water potential. Simulation results indicate the general trend that the diffusion coefficients of Na⁺ ion and water molecule in CNTs decrease with an increase in water density and are larger than those in the bulk solution. The average potential energies of ion–water and water–water, the radial distribution functions, the hydration numbers and the residence times of the hydrated water molecules are discussed. The classical solventberg picture describes Na⁺ ion in water adequately for systems with the small values of diffusion coefficients.     

Concentration-dependent effects on fully hydrated DNA at terahertz frequencies

Using terahertz time-domain spectroscopy (THz-TDS), the frequency-dependent dielectric constant of deoxyribonucleic acid (DNA) in solution was measured. The response of the buffer solution is dominated by two Debye modes in this frequency range, and, from an analysis of the concentration dependence, the presence of the DNA increases the main relaxation time and dielectric constant. This reflects the fact that the water in the hydration layer is more tightly bound under the influence of the DNA molecule in comparison to bulk water. This dynamical slowing down with increasing DNA concentration is similar to what is observed with purine nucleotides, but opposite to the behavior of pyrimidine nucleotides. In addition, a suspension model was used with the concentration-dependent data to isolate the dielectric response of the hydrated DNA molecule. The data for the hydrated DNA molecule is still dominated by a Debye response. It is also possible to determine the thickness of the hydration layer, and the DNA molecule influences the surrounding water out to 16 or 17 Å, which corresponds to about six effective hydration layers.