Activity coefficients of counterions in solutions of diethylaminoethyl dextran hydrochloride

Activity coefficients of counterions in solutions of diethylaminoethyl dextran hydrochloride have been determined. It has been observed that they increase with decreasing concentration of the polyelectrolyte. The experimental values have been compared with those calculated using Oosawa's theory of activity coefficients. The calculated values are higher than those observed, which suggests that the rodlike model on which Oosawa's theory is based is inadequate for the present case. Activity coefficients of counterions of some solutions containing NaCl and KC1, respectively, have also been determined. It has been found that the additivity rule for activity of counterions applies for these solutions.     

Intrinsic binding effects in mixed counterionic polyelectrolyte systems: extension of condensation theory and comparison with voltammetric data

Voltammetric speciation data for the potassium/zinc/polymethacrylate system, recently obtained for various charge densities of the polyelectrolyte (Díaz-Cruz et al., Anal. Chim. Acta, 264 (1992) 163) and for different concentrations of monovalent counterions (van den Hoop and van Leeuwen, Anal. Chim. Acta, 273 (1993) 275), are compared with theoretical predictions computed according to a new thermodynamic model developed by Paoletti et al. (Biophys. Chem., 41 (1991) 73) and recently extended by Benegas and Paoletti (in preparation). The model allows: (i) the simultaneous condensation of both monovalent and divalent counterions and (ii) can account for a certain specific affinity of the polyelectrolyte for one type of the counterion over the other. For various charge densities of the polyelectrolyte, experimentally obtained speciation data for the K/Zn/PMA system agree well with theoretical predictions by considering an extra reduced molar affinity energy of -4RT for the Zn(2+) polyelectrolyte binding. The agreement between experimental and theoretical values for the distribution of Zn(2+) ions over the free and bound state becomes less perfect for relatively high concentrations of monovalent counterions.     

Interactions of DNA with divalent metal ions. III. Extent of metal binding: Experiment and theory

DNA with Mn²⁺ as the only counterion has been prepared, and the extent of the Mn²⁺ binding was determined under a variety of conditions through measurements of the proton relaxation enhancement of water. The total extent of Mn²⁺ binding per DNA phosphate is found to be 0.43 ± 0.04, independent of the metal ion concentration in the experimental range of 2.8 × 10^?5 to 2.1 × 10^?3M. The predictions of Manning's condensation theory and those obtained from solution of the generalized Poisson-Boltzmann equation regarding the extent of divalent ion binding to polyelectrolytes, in the presence and absence of monovalent counterions, are compared with one another and with the experimental results. Good agreement between the two theoretical approaches is found, with less than 14% variance in the predicted extent of binding over a large range of mono- and divalent ion concentrations. While the predictions of both theoretical approaches generally agree with the experimental results, some discrepancies are noted and their possible origins discussed.     

中国生命周期评价理论与实践研究进展及对策分析

主要分析了我国生命周期评价的理论与实践研究进展与数据库构建现状,针对当前我国生命周期评价理论与应用研究的关键薄弱环节即不确定性分析、本土化数据库构建、本土化生命周期环境影响评价模型构建,指出了利用泰勒系列展开模型进行符合我国产业链生产现状的精确、完整、具有代表性、具有时空动态特征的生命周期数据库构建的必要性;并指出需要根据我国国情(例如:环境、地理、人口、暴露等)来构建生命周期环境影响评价模型的紧迫性。     

Applying ecological models to communities of genetic elements: the case of neutral theory

A promising recent development in molecular biology involves viewing the genome as a mini‐ecosystem, where genetic elements are compared to organisms and the surrounding cellular and genomic structures are regarded as the local environment. Here, we critically evaluate the prospects of ecological neutral theory (ENT), a popular model in ecology, as it applies at the genomic level. This assessment requires an overview of the controversy surrounding neutral models in community ecology. In particular, we discuss the limitations of using ENT both as an explanation of community dynamics and as a null hypothesis. We then analyse a case study in which ENT has been applied to genomic data. Our central finding is that genetic elements do not conform to the requirements of ENT once its assumptions and limitations are made explicit. We further compare this genome‐level application of ENT to two other, more familiar approaches in genomics that rely on neutral mechanisms: Kimura's molecular neutral theory and Lynch's mutational‐hazard model. Interestingly, this comparison reveals that there are two distinct concepts of neutrality associated with these models, which we dub ‘fitness neutrality’ and ‘competitive neutrality’. This distinction helps to clarify the various roles for neutral models in genomics, for example in explaining the evolution of genome size.     

Monte Carlo and Poisson–Boltzmann calculations of the fraction of counterions bound to DNA

The counterion density and the condensation region around DNA have been examined as functions of both ion size and added-salt concentration using Metropolis Monte Carlo (MC) and Poisson–Boltzmann (PB) methods. Two different definitions of the “bound” and “free” components of the electrolyte ion atmosphere were used to compare these approaches. First, calculation of the ion density in different spatial regions around the polyelectrolyte molecule indicates, in agreement with previous work, that the PB equation does not predict an invariance of the surface concentration of counterions as electrolyte is added to the system. Further, the PB equation underestimates the counterion concentration at the DNA surface, compared to the MC results, the difference being greatest in the grooves, where ionic concentrations are highest. If counterions within a fixed radius of the helical axis are considered to be bound, then the fraction of polyelectrolyte charge neutralized by counterions would be predicted to increase as the bulk electrolyte concentration increases. A second categorization—one in which monovalent cations in regions where the average electrostatic potential is ledd than ?kT are considered to be bound—provides an informative basis for comparison of MC and PB with each other and with counterion-condensation theory. By this criterion, PB calculations on the B from of DNA indicate that the amount of bound counterion charge per phosphate group is about .67 and is independent of salt concentration. A particularly provocative observatiob is that when this binding criterion is used, MC calculations quantitatively reproduce the bound fraction predicated by counterion-condensation theory for all-atom models of B-DNA and A-DNA as well as for charged cylindera of varying lineat charge densities. For example, for B-DNA and A-DNA, the fractions of phosphate groups neutralized by 2 Å hard sphere counterions are 0.768 and .817, respectively. For theoretical studies, the rediys enclosing the region in which the electrostatic potential is calculated studies, the radius enclosing the region in which the electrostatic potential is calculated to be less than ?kT is advocated s a more suitable binding or condensation radius that enclosing the fraction of counterions given by (1 – ξ^?1). A comparsion of radii calculated using both of these definitions is presented. © 1994 John Wiley & Sons, Inc.     

A reexamination of stability in randomly varying versus deterministic environments with comments on the stochastic theory of limiting similarity

The focus of this paper is a general relationship proposed by May (Amer. Natur. 107 (1973)) between the stability properties of stochastic models incorporating environmental variation and the stability properties of the deterministic models from which they are derived. The concepts of stochastic stability underlying this conjectured relationship are discussed and compared to the standard definitions of deterministic stability as well as alternative criteria for stability in stochastic models. It is shown by example that May's qualitative stability criterion does not ensure stability in any sense unless restrictive conditions on the form of the model are satisfied. Even under these conditions, the criterion, which is based on linearization, generally provides information only about the local dynamics of multispecies models. The applicability of such information to stochastic limiting similarity theory is discussed and alternative methods of analysis are proposed.     

Scaled particle theory applied to gels of high molecular weight DNA in the ultracentrifuge

Equilibrium ultracentrifugation of high molecular weight DNA at moderate centrifuge speed leads to the formation of gel at the bottom of the centrifuge cell. The swelling pressures of the gels are strongly affected by the ionic strength of the medium and by polyvalent counterions in the medium. Scaled particle theory applied to the DNA gels gives values to the effective particle length and particle radius of the DNA. Different models for DNA conformations in the gels were required for the monovalent, the divalent, and the tetravalent cations used in this study.     

A theory of the pattern induced flight orientation of the fly Musca domestica II

In a preceding paper, Poggio and Reichardt (1973a), a phenomenological theory describing the visual orientation behaviour of fixed flying flies (Musca domestica) towards elementary patterns was presented. Some of the problems raised in this first paper are treated here in more detail. The mapping between the position dependent torque distribution — D(ψ) characteristics — associated with a given pattern and the stationary orientation distribution p(ψ), is studied taking into account that the fluctuation process (generated by the fly) is coloured gaussian noise. Under certain critical conditions this may lead to an “early symmetry breaking” in the mean values of the p(ψ) distribution. The validity of the “superposition principle” has also been examined. Although shift and superposition give the main qualitative features of the “attractiveness profile” D(ψ), associated with a 2-stripe pattern, superposition does not hold quantitatively for stripe separations up to about 80°. Evidence is presented suggesting that such an effect is due to inhibitory interactions between input channels of the fly's eye. Implications of this finding with respect to the problem of spontaneous pattern preference are also discussed.     

Evaluation of the counterion condensation theory of polyelectrolytes.

We compare free energies of counterion distributions in polyelectrolyte solutions predicted from the cylindrical Poisson-Boltzmann (PB) model and from the counterion condensation theories of Manning: CC1 (Manning, 1969a, b), which assumes an infinitely thin region of condensed counterions, and CC2 (Manning, 1977), which assumes a region of finite thickness. We consider rods of finite radius with the linear charge density of B-DNA in 1-1 valent and 2-2 valent salt solutions. We find that under all conditions considered here the free energy of the CC1 and the CC2 models is higher than that of the PB model. We argue that counterion condensation theory imposes nonphysical constraints and is, therefore, a poorer approximation to the underlying physics based on continuum dielectrics, point-charge small ions, Poisson electrostatics, and Boltzmann distributions. The errors in counterion condensation theory diminish with increasing distance from, or radius of, the polyion.     

Molecular dynamics simulation of human interleukin-4: comparison with NMR data and effect of pH,counterions and force field on tertiary structure stability

The human protein interleukin-4 (IL-4) has been simulated at two different pH values 2 and 6, with different amounts of counterions present in the aqueous solution, and with two different force-field parameter sets using molecular dynamics simulation with the aim of validation of force field and simulation set-up by comparison to experimental nuclear magnetic resonance data, such as proton–proton nuclear Overhauser effect (NOE) distance bounds, ³ J(HN,HC_α) coupling constants and backbone N–H order parameters. Thirteen simulations varying in the length from 3 to 7 ns are compared.

At pH 6 both force-field parameter sets used do largely reproduce the NOE's and order parameters, the GROMOS 45A3 set slightly better than the GROMOS 53A6 set. ³ J values predicted from the simulation agree less well with experimental values. At pH 2 the protein unfolds, unless counterions are explicitly present in the system, but even then the agreement with experiment is worse than at pH 6. When simulating a highly charged protein, such as IL-4 at pH 2, the inclusion of counterions in the simulation seems mandatory.     

John Warren Williams

The osmotic, sedimentation, and diffusion coefficients of sonicated sodium DNA in aqueous solutions which were rendered rigorously free of salts have been obtained in order to study the polyelectrolyte effect on these parameters. Both native and heat denatured DNA's were studied. All three parameters were found to be independent of concentration between 2 and 10 mmole/1. The osmotic coefficient gives the fraction of counterions not immobilized by the polyelectrolyte potential, under conditions of equilibrium. The value (ca. 0.18) obtained for this fraction agrees very well with that predicted by a theory of rodlike polyelectrolytes. A simplified model that permits the computation of fractions of mobile ions from sedimentation and diffusion coefficients, when applied to the experimental data, showed that under these conditions of flow between 0.5 to 0.9 of counterions are not immobilized. The experimental data also showed that for native DNA the translation frictional coefficient seems to have different values in sedimentation and diffusion, which agrees with a finding reported for another saltfree polyelectrolyte. For denatured DNA, however, the values were found to be equal: no satisfactory explanation could be found for this difference of behavior.     

The nature of the fluid boundary layer and the selection of parameters for benthic ecology

1. The nature of flow structure close to a river bed is reviewed and suggestions made as to appropriate equations to apply to given hydrodynamic regimes. 2. It is emphasized that in natural rivers the laminar sublayer observed immediately above the bed in some experimental studies is completely disrupted for flows characterized by high turbulence levels. 3. Instead of resorting to direct topographical measurement of bed undulations, the roughness of the river bed also can be quantified using hydraulic data obtained from velocity profiles. 4. Ambuhl's experimental findings of 1959 underpin modern ecological research into the nature of the benthic boundary layer. Common misconceptions concerning Ambuhl's contribution are corrected and it is shown that his results only apply to certain prescribed hydrodynamic conditions. 5. The adoption of a consistent approach to describing the benthic boundary layer is to be preferred, so that diverse studies can be usefully compared.     

Effect of different metal ions on the oxidative damage and antioxidant capacity of hyaluronic acid

Degradation and the antioxidative effect of Na-, Zn-, Co-, Cu-, and Mn-hyaluronic acid (HA) associates were studied. Our findings revealed the protective effect of certain counterions against ROS-induced HA degradation. We could also separate the antioxidative effect of certain counterions from that of the HA by examining the effect of the counterions in their free ionic forms. The result showed that metal ions with altering oxidative status (Co(2+), Cu(2+), Mn(2+)) proved to be effective in themselves or their effect added to that of HA when HA was also effective. Moreover, the effects of Co-HA against z.rad;O(2)(-) and of Mn-HA against ONOO(-) as well as the synergic effect of Zn-HA associates where Zn(2+) is of fixed oxidative status were attributed to the structure-stabilizing complex formed between certain counterions and HA. Our examination also concerned the influence of HA associates on the indirect antioxidation related to Fe(2+) chelating. The individual effects of Zn(2+), Co(2+), and Cu(2+) were only detectable, which could be explained by the competitive displacement of ferrous from its binding site.     

Electrostatic theory of the assembly of PAMAM dendrimers and DNA

The electrostatic interactions mediated by counterions between a cationic PAMAM dendrimer, modelized as a sphere of radius and cationic surface charge highly increasing with generation, and a DNA, modelized as an anionic elastic line, are analytically calculated in the framework of condensation theory. Under these interactions the DNA is wrapped around the sphere. For excess phosphates relative to dendrimer primary amines, the free energy of the DNA‐dendrimer complex displays an absolute minimum when the complex is weakly negatively overcharged. This overcharging opposes gene delivery. For a highly positive dendrimer and a DNA fixed by experimental conditions to a number of phosphates less than the number of dendrimer primary amines, excess amine charges, the dendrimer may at the same time bind stably DNA and interact with negative cell membranes to activate cell transfection in fair agreement with molecular simulations and experiments. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 276–286, 2016.     

The relationship between the poisson-boltzmann model and the condensation hypothesis: an analysis based on the low salt form of the Donnan coefficient

Two common models for the interaction of counterions with cylindrical polyions are considered in the context of the Donnan membrane equilibrium. General analytic expressions are obtained from the Poisson-Boltzmann equation for the Donnan coefficient in terms of the potential at the surface of the polyion or the local concentration of unbound ions at the surface. Analysis based on these expressions shows that if, and only if, the polyion charge density exceeds a certain critical value a large local concentration of ions will persist near the polyion surface at low ionic strengths. We therefore conclude that this principal hypothesis of the condensation model is consistent with the characteristics of the Poisson-Boltzmann potential at the surface of the polyion.     

Reactor Performance in the Presence of Catalyst Deactivation

The main variable of enzymatic processes is often found to be the operating temperature. An increase in temperature leads to higher rates for the catalytic transformation. However, beyond a certain temperature catalyst deactivation is winning the game. Therefore, processes should be optimized in order to determine the temperature which leads to a minimal demand of enzyme preparation. For the prediction of such optimal reactor operation, modeling of the temperature dependence of the process has to be performed. Examples of such modeling are given for the hydrolysis of lactose in UHT milk by means of three different β‐galactosidases – those from Aspergillus oryzae, Kluyveromyces lactis, and Escherichia coli. The reaction kinetics for a constant initial lactose concentration can be described by a model of two parameters, of which only one depends on temperature. For the lactase of E. coli the reaction can be described as a simple reaction with first order kinetics. The deactivation mechanism includes a reversible as well as an irreversible path of denaturation. The temperature dependent parameters follow Arrhenius' and van't Hoff's law, respectively. On the basis of their particular reaction models all three enzymes can be compared with respect to their optimum use. The models have been verified under laboratory conditions and have shown their usefulness for the prediction of optimum operating variables. Quite remarkable features have been found for the lactase of E. coli.     

A 5-nanosecond molecular dynamics trajectory for B-DNA: analysis of structure, motions, and solvation.

We report the results of four new molecular dynamics (MD) simulations on the DNA duplex of sequence d(CGCGAATTCGCG)2, including explicit consideration of solvent water, and a sufficient number of Na+ counterions to provide electroneutrality to the system. Our simulations are configured particularly to characterize the latest MD models of DNA, and to provide a basis for examining the sensitivity of MD results to the treatment of boundary conditions, electrostatics, initial placement of solvent, and run lengths. The trajectories employ the AMBER 4.1 force field. The simulations use particle mesh Ewald summation for boundary conditions, and range in length from 500 ps to 5.0 ns. Analysis of the results is carried out by means of time series for conformationalm, helicoidal parameters, newly developed indices of DNA axis bending, and groove widths. The results support a dynamically stable model of B-DNA for d(CGCGAATTCGCG)2 over the entire length of the trajectory. The MD results are compared with corresponding crystallographic and NMR studies on the d(CGCGAATTCGCG)2 duplex, and placed in the context of observed behavior of B-DNA by comparisons with the complete crystallographic data base of B-form structures. The calculated distributions of mobile solvent molecules, both water and counterions, are displayed. The calculated solvent structure of the primary solvation shell is compared with the location of ordered solvent positions in the corresponding crystal structure. The results indicate that ordered solvent positions in crystals are roughly twice as structured as bulk water. Detailed analysis of the solvent dynamics reveals evidence of the incorporation of ions in the primary solvation of the minor groove B-form DNA. The idea of localized complexation of otherwise mobile counterions in electronegative pockets in the grooves of DNA helices introduces an additional source of sequence-dependent effects on local conformational, helicoidal, and morphological structure, and may have important implications for understanding the functional energetics and specificity of the interactions of DNA and RNA with regulatory proteins, pharmaceutical agents, and other ligands.