Evaporation rate enhancement of water with air ions from a corona discharge

Space charges (air ions) produced by a single point-to-plane corona electrode system were used to study the enhancement in the evaporation rates of water at three ion current levels. The maximum evaporation rates of 0.019 and 0.017 g·min^?1 were observed at a 1 cm electrode gap for negative and positive air ions, respectively. The cumulative evaporation rates were linear with time and an ion-enhanced rate was about 4 times greater than the control. The current density distribution measurements agreed fairly well with those predicted from the Warburg law. The principal driving force for the observed evaporation enhancement was an ion drag phenomenon which created vortex motions in water when air ions were subjected to an externally applied electric field. Theoretical considerations from derived relationships in fluid mechanics demonstrate that the mass transfer coefficient is higher for positive than negative ions of the same current strength because of the mobility difference between the charges in the medium.     

Benchmark of different charges for prediction of the partitioning coefficient through the hydrophilic/lipophilic index

A few different theoretical methods for assigning the partial atomic charges were benchmarked for calculation of the hydrophilic/lipophilic index (HLI). The coefficients were selected to produce the best correlation of the HLI values with the experimental octanol-water partition. Different parameters were checked in calculations of partial charges to get the best performance of the HLI values obtained. Thus, four partitioning schemes (Coulson, Mulliken, Merz-Kollman, Ford-Wang) were benchmarked for calculations of atomic charges with six semiempirical methods (AM1, PM3, RM1, PM6, PM6-D3H4, PM7). Moreover, five distinct types of partial atomic charges (Mulliken, Hirshfeld, Löwdin, CHELPG, NPA), obtained at the Hartree–Fock and DFT levels of theory with three basis sets, were tested for their ability to produce the HLI values with the best correlation to experimental logP coefficients of 50 mono-charged organic anions. In the case of the semiempirical methods, the best correlation between the HLI and logP values (the correlation coefficient r?=?0.9216) was obtained with the AM1 Ford–Wang parametric electrostatic potential charges. The Mulliken and Coulson charges calculated with the PM7 method can be used as an alternative to AM1, with the r values of 0.9107 and 0.8984, respectively. In the case of the DFT, the PBE/def2-TZVP natural population analysis charges produce the best correlation (r?=?0.9220). Nevertheless, in spite of a marginally lower performance (r?=?0.9159), the NPA charges computed at the PBE/def2-SVP level are more robust and can be regarded as the optimum choice for calculating the HLI values.

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Graphical abstract The hydrophilic/lipophilic index (HLI)

     

A Cross-Sectional Analysis of Variation in Charges and Prices across California for Percutaneous Coronary Intervention

Background

Though past studies have shown wide variation in aggregate hospital price indices and specific procedures, few have documented or explained such variation for distinct and common episodes of care.

Objectives

We sought to examine the variability in charges for percutaneous coronary intervention (PCI) with a drug-eluting stent and without major complications (MS-DRG-247), and determine whether hospital and market characteristics influenced these charges.

Methods

We conducted a cross-sectional analysis of adults admitted to California hospitals in 2011 for MS-DRG-247 using patient discharge data from the California Office of Statewide Health Planning and Development. We used a two-part linear regression model to first estimate hospital-specific charges adjusted for patient characteristics, and then examine whether the between-hospital variation in those estimated charges was explained by hospital and market characteristics.

Results

Adjusted charges for the average California patient admitted for uncomplicated PCI ranged from $22,047 to $165,386 (median: $88,350) depending on which hospital the patient visited. Hospitals in areas with the highest cost of living, those in rural areas, and those with more Medicare patients had higher charges, while government-owned hospitals charged less. Overall, our model explained 43% of the variation in adjusted charges. Estimated discounted prices paid by private insurers ranged from $3,421 to $80,903 (median: $28,571).

Conclusions

Charges and estimated discounted prices vary widely between hospitals for the average California patient undergoing PCI without major complications, a common and relatively homogeneous episode of care. Though observable hospital characteristics account for some of this variation, the majority remains unexplained.     

Open channel noise. V. Fluctuating barriers to ion entry in gramicidin A channels.

We have measured the fluctuations in the current through gramicidin A (GA) channels in symmetrical solutions of monovalent cations of various concentrations, and compared the spectral density values with those computed using E. Frehland's theory for noise in discrete transport systems (Frehland, E. 1978. Biophys. Chem. 8:255-265). The noise for the transport of NH4+ and Na+ ions in glycerol-monooleate/squalene membranes could be accounted for entirely by "shot noise" in the process of transport through a single-filing pore with two ion binding sites. However, in confirmation of results in a previous paper (Sigworth, F. J., D. W. Urry, and K. U. Prasad. 1987. Biophys. J. 52:1055-1064) currents of Cs+ showed a substantial excess noise at low ion concentrations, as did currents of K+ and Rb+. The excess noise was increased in thicker membranes. The observations are accounted for by a theory that postulates fluctuations of the entry rates of ions into the channel on a time scale of approximately 1 microsecond. These fluctuations occur preferentially when the channel is empty; the presence of bound ions stabilizes the "high conductance" conformation of the channel. The fluctuations are sensed to different degrees by the various ion species, and their kinetics depend on membrane thickness.     

Proteins,channels and crowded ions

Ion channels are proteins with a hole down their middle that control a vast range of biological function in health and disease. Selectivity is an important biological function determined by the open channel, which does not change conformation on the biological time scale. The challenge is to predict the function—the current of ions of different types and concentrations through a variety of channels—from structure, given fundamental physical laws. Walls of ion channels, like active sites of enzymes, often contain several fixed charges. Those fixed charges demand counter ions nearby, and the density of those counter ions is very high, greater than 5 molar, because of the tiny volumes of the channel's pore. Physical chemists can now calculate the free energy per mole of salt solutions (e.g. the activity coefficient) from infinite dilution to saturation, even in ionic melts. Such calculations of a model of the L-type calcium channel show that the large energies needed to crowd charges into the channel can account for the substantial selectivity and complex properties found experimentally. The properties of such crowded charge are likely to be an important determinant of the properties of proteins in general because channels are nearly enzymes.     

Sodium-23 and potassium-39 nuclear magnetic resonance relaxation in eye lens. Examples of quadrupole ion magnetic relaxation in a crowded protein environment.

Single and multiple quantum nuclear magnetic resonance (NMR) spectroscopic techniques were used to investigate the motional dynamics of sodium and potassium ions in concentrated protein solution, represented in this study by cortical and nuclear bovine lens tissue homogenates. Both ions displayed homogeneous biexponential magnetic relaxation behavior. Furthermore, the NMR relaxation behavior of these ions in lens homogenates was consistent either with a model that assumed the occurrence of two predominant ionic populations, "free" and "bound," in fast exchange with each other or with a model that assumed an asymmetric Gaussian distribution of correlation times. Regardless of the model employed, both ions were found to occur in a predominantly "free" or "unbound" rapidly reorienting state. The fraction of "bound" 23Na+, assuming a discrete two-site model, was approximately 0.006 and 0.017 for cortical and nuclear homogenates, respectively. Corresponding values for 39K+ were 0.003 and 0.007, respectively. Estimated values for the fraction of "bound" 23Na+ or 39K+ obtained from the distribution model (tau C greater than omega L-1) were less than or equal to 0.05 for all cases examined. The correlation times of the "bound" ions, derived using either a two-site or distribution model, yielded values that were at least one order of magnitude smaller than the reorientational motion of the constituent lens proteins. This observation implies that the apparent correlation time for ion binding is dominated by processes other than protein reorientational motion, most likely fast exchange between "free" and "bound" environments. The results of NMR visibility studies were consistent with the above findings, in agreement with other studies performed by non-NMR methods. These studies, in combination with those presented in the literature, suggest that the most likely role for sodium and potassium ions in the lens appears to be the regulation of cell volume by affecting the intralenticular water chemical potential.     

Ion repulsion within membranes.

The adsorption of hydrophobic ions such as tetraphenylborate to thin lipid membranes is known to saturate at approximately 0.1 ion/(nm)2. This saturation can be quantitatively explained by electrostatic repulsion between the ions if they are treated as discrete, mobile particles that adsorb within the lipid at least partially removed from the aqueous phases. The electrochemical potential of the ions as a function of their surface density can be expressed as a virial expansion, which in principle exactly describes the equilibrium properties of the physical model. The first few terms of the virial expansion are calculated and an approximation is considered for higher-order terms. The model has only two adjustable parameters, the depth of the adsorption sites into the lipid and the adsorption constant in the absence of repulsion. The mobile, discrete charge model can give much better fits to the equilibrium data for tetraphenylborate adsorbed at up to 0.1 ion/(nm)2 to membranes and monolayers. (Andersen et al., 1978) than those obtainable from either the smeared charge or hexagonal lattice models.     

Physical and molecular basis of ion channel gating: Can electrostatic interactions close the ion channel?

We analyzed voltage-dependent ion channel structure and conformational changes corresponding to channel gating. During the gating, S4 segments, as well as other parts of the channel, undergo a set of conformational modifications. These changes are accompanied by complicated movements of positive charges that are mostly located in the S4 segments. These charges electrostatically interact with the ions passing through the channel. The interaction energy depends on the conformational state of the channel, i.e., on the mutual positions of the permeant ions and these charges. Analyzing and making energetical estimations, we propose a hypothesis: the closed state of the ion channel corresponds to the S4 position when electrostatic interaction between positively charged groups of the S4 segments and permeant ions is strong enough to close the pathway for these ions.     

Crystal structure of tobacco necrosis virus at 2.25 A resolution

The crystal structure of tobacco necrosis virus (TNV) has been determined by real-space averaging with 5-fold non-crystallographic symmetry, and refined to R=25.3 % for diffraction data to 2.25 A resolution. A total of 180 subunits form a T=3 virus shell with a diameter of about 280 A and a small protrusion at the 5-fold axis. In 276 amino acid residues, the respective amino terminal 86, 87 and 56 residues of the A, B and C subunits are disordered. No density for the RNA was found. The subunits have a "jelly roll" beta-barrel structure, as have the structures of the subunits of other spherical viruses. The tertiary and quaternary structures of TNV are, in particular, similar to those of southern bean mosaic virus, although they are classified in different groups. Invisible residues 1 to 56 with a high level of basic residues are considered to be located inside the particle. Sequence comparison of the coat proteins of several TNV strains showed that the sequences of the disordered segment diverge considerably as compared with those of the ordered segment, consistent with a small tertiary structural constraint being imposed on the N-terminal segment. Basic residues are localized on the subunit interfaces or inner surface of the capsid. Positive charges of the basic residues facing the interior, as well as those of the N-terminal segment, may neutralize the negative charge of the RNA inside. Five calcium ions per icosahedral asymmetric unit are located at the subunit interfaces; three are close to the exterior surface, the other two away from it. The environments of the first three are similar, and those of the other two sites are similar. These calcium ions are assumed to be responsible for the stabilization/transition of the quaternary structure of the shell. Three peptide segments ordered only in the C subunits are clustered around each 3-fold (quasi-6-fold) axis forming a beta-annulus, and may lead to quasi-equivalent interactions for the organization of the T=3 shell.     

Ion hydration: Implications for cellular function, polyelectrolytes, and protein crystallization

Only oppositely charged ions with matching absolute free energies of hydration spontaneously form inner sphere ion pairs in free solution [K.D.Collins, Ions from the Hofmeister series and osmolytes: effects on proteins in solution and in the crystallization process, Methods 34 (2004) 300-311.]. We approximate this with a Law of Matching Water Affinities which is used to examine the issues of (1) how ions are selected to be compatible with the high solubility requirements of cytosolic components; (2) how cytosolic components tend to interact weakly, so that association or dissociation can be driven by environmental signals; (3) how polyelectrolytes (nucleic acids) differ from isolated charges (in proteins); (4) how ions, osmolytes and polymers are used to crystallize proteins; and (5) how the "chelate effect" is used by macromolecules to bind ions at specific sites even when there is a mismatch in water affinity between the ion and the macromolecular ligands.     

Brownian dynamics study of ion transport in the vestibule of membrane channels.

Brownian dynamics simulations have been carried out to study the transport of ions in a vestibular geometry, which offers a more realistic shape for membrane channels than cylindrical tubes. Specifically, we consider a torus-shaped channel, for which the analytical solution of Poisson's equation is possible. The system is composed of the toroidal channel, with length and radius of the constricted region of 80 A and 4 A, respectively, and two reservoirs containing 50 sodium ions and 50 chloride ions. The positions of each of these ions executing Brownian motion under the influence of a stochastic force and a systematic electric force are determined at discrete time steps of 50 fs for up to 2.5 ns. All of the systematic forces acting on an ion due to the other ions, an external electric field, fixed charges in the channel protein, and the image charges induced at the water-protein boundary are explicitly included in the calculations. We find that the repulsive dielectric force arising from the induced surface charges plays a dominant role in channel dynamics. It expels an ion from the vestibule when it is deliberately put in it. Even in the presence of an applied electric potential of 100 mV, an ion cannot overcome this repulsive force and permeate the channel. Only when dipoles of a favorable orientation are placed along the sides of the transmembrane segment can an ion traverse the channel under the influence of a membrane potential. When the strength of the dipoles is further increased, an ion becomes detained in a potential well, and the driving force provided by the applied field is not sufficient to drive the ion out of the well. The trajectory of an ion navigating across the channel mostly remains close to the central axis of the pore lumen. Finally, we discuss the implications of these findings for the transport of ions across the membrane.     

Monte Carlo simulation of the water in a channel with charges.

A Monte Carlo simulation of water in a channel with charges suggests the existence of water in immobile, high density, essentially glasslike form near the charges. The channel model has a conical section with an opening through which water molecules can pass, at the narrow end of the cone, and a cylindrical section at the other end. When the charges are placed near the narrow section of the model, the "glass" effectively blocks the channel; with the charges removed, the channel opens. The effect can be determined from the rate of passage of the water molecules through the pore, from the average orientation of the water molecule, and from distortion of the distribution of molecules. In the simulations carried out to date, no external ions have been considered. In addition to the energy, the Helmholtz free energy has been calculated.     

Granulysin crystal structure and a structure-derived lytic mechanism

Our crystal structure of granulysin suggests a mechanism for lysis of bacterial membranes by granulysin, a 74-residue basic protein from human cytolytic T lymphocyte and natural killer cells. We determined the initial crystal structure of selenomethionyl granulysin by MAD phasing at 2A resolution. We present the structure model refined using native diffraction data to 0.96A resolution. The five-helical bundle of granulysin resembles other "saposin folds" (such as NK-lysin). Positive charges distribute in a ring around the granulysin molecule, and one face has net positive charge. Sulfate ions bind near the segment of the molecule identified as most membrane-lytic and of highest hydrophobic moment. The ion locations may indicate granulysin's orientation of initial approach towards the membrane. The crystal packing reveals one way to pack a sheet of granulysin molecules at the cell surface for a concerted lysis effort. The energy of binding granulysin charges to the bacterial membrane could drive the subsequent lytic processes. The loosely packed core facilitates a hinge or scissors motion towards exposure of hydrophobic surface that we propose tunnels the granulysin into the fracturing target membrane.     

Surface charging by large multivalent molecules. Extending the standard Gouy-Chapman treatment.

Traditionally, Gouy-Chapman theory has been used to calculate the distribution of ions in the diffuse layer next to a charged surface. In recent years, the same theory has found application to adsorption (incorporation, partitioning) of charged peptides, hormones, or drugs at the membrane-water interface. Empirically it has been found that an effective charge, smaller than the physical charge, must often be used in the Gouy-Chapman formula. In addition, the large size of these molecules can be expected to influence their adsorption isotherms. To improve evaluation techniques for such experiments, comparatively simple extensions of the standard Gouy-Chapman formalism have been studied which are based on a discrete charge virial expansion. The model allows for the mobility of charged groups at the interface. It accounts for finite size of the adsorbed macromolecules and for discrete charge effects arising from pair interactions in the interface plane. In contrast to previous discrete charge treatments this model nearly coincides with the Gouy-Chapman formalism in the case where the adsorbing molecules are univalent. Large discrepancies are found for multivalent molecules. This could explain the reduced effective charges needed in the standard Gouy-Chapman treatment. The reduction factor can be predicted. The model is mainly limited to low surface coverage, typical for the adsorption studies in question.     

Protein geometry and placement in the cardiac dyad influence macroscopic properties of calcium-induced calcium release

In cardiac ventricular myocytes, events crucial to excitation-contraction coupling take place in spatially restricted microdomains known as dyads. The movement and dynamics of calcium (Ca2+) ions in the dyad have often been described by assigning continuously valued Ca2+ concentrations to one or more dyadic compartments. However, even at its peak, the estimated number of free Ca2+ ions present in a single dyad is small (approximately 10-100 ions). This in turn suggests that modeling dyadic calcium dynamics using laws of mass action may be inappropriate. In this study, we develop a model of stochastic molecular signaling between L-type Ca2+ channels (LCCs) and ryanodine receptors (RyR2s) that describes: a), known features of dyad geometry, including the space-filling properties of key dyadic proteins; and b), movement of individual Ca2+ ions within the dyad, as driven by electrodiffusion. The model enables investigation of how local Ca2+ signaling is influenced by dyad structure, including the configuration of key proteins within the dyad, the location of Ca2+ binding sites, and membrane surface charges. Using this model, we demonstrate that LCC-RyR2 signaling is influenced by both the stochastic dynamics of Ca2+ ions in the dyad as well as the shape and relative positioning of dyad proteins. Results suggest the hypothesis that the relative placement and shape of the RyR2 proteins helps to "funnel" Ca2+ ions to RyR2 binding sites, thus increasing excitation-contraction coupling gain.     

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.     

Charge calculations in molecular mechanics 6: the calculation of partial atomic charges in nucleic acid bases and the electrostatic contribution to DNA base pairing.

A previously described scheme for the direct calculation of the partial atomic charges in molecules (CHARGE2) is applied to the nucleic acid bases. It is shown that inclusion of the omega-technique for the calculation of HMO derived pi charges is of particular importance for these highly polar systems. The molecular dipole moments obtained for the resulting charges are in very good agreement with the observed values for a variety of substituted purine and pyrimidine bases. The partial atomic charges for cytosine, thymine, guanine and adenine (as the 1-methyl and 9-methyl forms) are given and compared with values calculated by a variety of molecular orbital and empirical schemes. All the schemes reproduce the same general trends, with the possible exception of those calculated by the Del Re method, though the charges given by Kollman are in general somewhat larger than the others. The electrostatic contribution to the Watson-Crick base pair interaction energies are calculated using these partial atomic charges. The electrostatic contributions obtained from the M.O. derived atomic charges are less than half the observed values, as are those obtained by the Gasteiger method. The electrostatic contributions calculated from the CHARGE2 atomic charges and those of Kollman are in reasonable agreement with the observed values. The influence of a distant-dependent dielectric constant is examined, but no clear pattern emerges.     

Lipid demixing and protein-protein interactions in the adsorption of charged proteins on mixed membranes

The adsorption free energy of charged proteins on mixed membranes, containing varying amounts of (oppositely) charged lipids, is calculated based on a mean-field free energy expression that accounts explicitly for the ability of the lipids to demix locally, and for lateral interactions between the adsorbed proteins. Minimization of this free energy functional yields the familiar nonlinear Poisson-Boltzmann equation and the boundary condition at the membrane surface that allows for lipid charge rearrangement. These two self-consistent equations are solved simultaneously. The proteins are modeled as uniformly charged spheres and the (bare) membrane as an ideal two-dimensional binary mixture of charged and neutral lipids. Substantial variations in the lipid charge density profiles are found when highly charged proteins adsorb on weakly charged membranes; the lipids, at a certain demixing entropy penalty, adjust their concentration in the vicinity of the adsorbed protein to achieve optimal charge matching. Lateral repulsive interactions between the adsorbed proteins affect the lipid modulation profile and, at high densities, result in substantial lowering of the binding energy. Adsorption isotherms demonstrating the importance of lipid mobility and protein-protein interactions are calculated using an adsorption equation with a coverage-dependent binding constant. Typically, at bulk-surface equilibrium (i.e., when the membrane surface is "saturated" by adsorbed proteins), the membrane charges are "overcompensated" by the protein charges, because only about half of the protein charges (those on the hemispheres facing the membrane) are involved in charge neutralization. Finally, it is argued that the formation of lipid-protein domains may be enhanced by electrostatic adsorption of proteins, but its origin (e.g., elastic deformations associated with lipid demixing) is not purely electrostatic.