Electrostatic effects upon adsorption and desorption of polylysines on the surface of lipid membranes of different composition

Electrokinetic measurements are carried out in suspensions of liposomes made from mixtures of charged (cardiolipin, CL) and neutral (phosphatidylcholine, PC) lipids in the presence of lysine and lysine-based polypeptides. Neither monolysine nor polylysines adsorbed on neutral (PC) membranes. In the case of negatively charged membranes (CL/PC) all polypeptides showed a sharp dependence of liposome electrophoretic mobility on the amount of polymer added to the cell. In suspension of cardiolipin liposomes the position of zero charge point coincided for all high-molecular polylysines; thus, pentalysine neutralizes the membrane surface, whereas polycations with a higher polymerization degree change a sign of the surface charge. Electrophoretic mobility of liposomes in plateau range depended on the molecular weight of polylysines and composition of liposomes; for large macromolecules the absolute value came close to its value for the initial liposomes. Adsorption of polycations on planar bilayer lipid membranes (BLM) resulted in alteration of the boundary potential measured by the method of intramembranous field compensation (IFC). The electrokinetic measurements and IFC method gave close results in the case of lysine monomers; their surface concentration could be fitted by an isotherm of the molecule distribution between the membrane surface and solution. Considerable differences of the surface and boundary potentials found in the case of pentalysine, correspond to changes in the dipole component of boundary potential induced by the adsorbed molecules. Using the IFC method, the kinetics of the adsorption process before saturation was studied. The adsorption of polylysines was markedly slower (more than hour) than that of pentalysine (tens of min) or monolysine (minutes). Washout experiments showed that adsorption of penta-and monolysine on planar BLM was reversible, while that of high-molecular polylysines was practically irreversible.     

Electrokinetic Properties of the Sarcoplasmic Reticulum Membrane Obtained from Reconstitution Studies

Electrophoretic mobility data of SR vesicles reconstituted with uncharged and two mixtures of charged and uncharged lipids (Brethes, D., Dulon, D., Johannin, G., Arrio, B., Gulik-Krzywicki, T., Chevallier, J. 1986. Study of the electrokinetic properties of reconstituted sarcoplasmic reticulum vesicles. Arch. Biochem. Biophys. 246:355–356) were analyzed in terms of four models of the membrane-water interface: (I) a smooth, negatively charged surface; (II) a negatively charged surface of lipid bilayer covered with an electrically neutral surface frictional layer; (III) an electrically neutral lipid bilayer covered with a neutral frictional layer containing a sheet of negative charge at some distance above the surface of the bilayer; (IV) an electrically neutral lipid bilayer covered with a homogeneously charged frictional layer. The electrophoretic mobility was predicted from the numerical integration of Poisson-Boltzmann and Navier-Stokes equations. Experimental results were consistent only with predictions based on Model-III with charged sheet about 4 nm above the bilayer and frictional layer about 10 nm thick. Assuming that the charge of the SR membrane is solely due to that on Ca⁺⁺-ATPase pumps, the dominant SR protein, the mobility data of SR and reconstituted SR vesicles are consistent with 12 electron charges/ATPase. This value compares well to the net charge of the cytoplasmic portion of ATPase estimated from the amino acid sequence (-11e). The position of the charged sheet suggests that the charge on the ATPase is concentrated in the middle of the cytoplasmic portion. The frictional layer of SR can be also assigned to the cytoplasmic portion of Ca⁺⁺-ATPase. The layer has been characterized with hydrodynamic shielding length of 1.1 nm. Its thickness is comparable to the height of the cytoplasmic portion of Ca⁺⁺-ATPase. Received: 15 June 1998/Revised: 8 October 1998     

Electrophoretic detection of reversible chlorpromazine · HCl binding at the human erythrocyte surface

The binding of chlorpromazine · HCl at the human erythrocyte surface has been detected through its effect on cellular electrophoretic mobility. Incubation of erythrocytes (approx. 5 · 10⁶/ml) in 23 μM chlorpromazine · HCl resulted in a reduction of negative electrophoretic mobility from the control value of $\text{?1.11 ± 0.01}$ (μm · s^?1)/(V · cm^?1) to $\text{?1.00 ± 0.02}$ (μm · s^?1)/(V · cm^?1) (pH 7.2, ionic strength 0.155). This mobility change was completely reversed when chlorpromazine · HCl was removed by centrifugal washing. Increasing the drug concentration to 70μM did not affect the mobility change, indicating saturation of the electrophoretically detectable drug binding sites over chlorpromazine · HCl concentration range studied here. The effect of the 23 μM chlorpromazine · HCl on electrophoretic mobility was also measured in isotonic media of reduced ionic strength. The drug-induced reduction in negative surface charge density was found to be independent of ionic strength over the range 0.155 (Debye length, 0.8 nm) to 0.00310 (Debye length, 5.7 nm).Fixation of erythrocytes with glutaraldehyde affected neither the normal electrophoretic mobility of discocytes nor the reduced electrophoretic mobility of chlorpromazine · HCl-induced stomatocytes. When these stomatocytes were first fixed with glutaraldehyde, then washed free of chlorpromazine · HCl, they retained the stomatocyte form while regaining a normal control electrophoretic mobility. Conversely, when discocytes fixed in that form were treated with chlorpromazine · HCl, they showed the same mobility change as did fixed or unfixed stomatocytes. The drug-induced mobility change is therefore independent of the shape change, but reflects a contribution to cellular surface charge density from the membrane-bound chlorpromazine · HCl molecules. From the charge reduction, it is estimated that about 10⁶ chlorpromazine · HCl molecules are bound at the electrokinetic cell surface and occupy approximately 0.4% of the total surface area.     

Thiophene Rings Improve the Device Performance of Conjugated Polymers in Polymer Solar Cells with Thick Active Layers

Developing novel materials that tolerate thickness variations of the active layer is critical to further enhance the efficiency of polymer solar cells and enable large‐scale manufacturing. Presently, only a few polymers afford high efficiencies at active layer thickness exceeding 200 nm and molecular design guidelines for developing successful materials are lacking. It is thus highly desirable to identify structural factors that determine the performance of semiconducting conjugated polymers in thick‐film polymer solar cells. Here, it is demonstrated that thiophene rings, introduced in the backbone of alternating donor–acceptor type conjugated polymers, enhance the fill factor and overall efficiency for thick (>200 nm) solar cells. For a series of fluorinated semiconducting polymers derived from electron‐rich benzo[1,2‐b:4,5‐b′]dithiophene units and electron‐deficient 5,6‐difluorobenzo[2,1,3]thiazole units a steady increase of the fill factor and power conversion efficiency is found when introducing thiophene rings between the donor and acceptor units. The increased performance is a synergistic result of an enhanced hole mobility and a suppressed bimolecular charge recombination, which is attributed to more favorable polymer chain packing and finer phase separation.     

Role of ionic strength on the relationship of biopolymer conformation,DLVO contributions,and steric interactions to bioadhesion of Pseudomonas putida KT2442

Biopolymers produced extracellularly by Pseudomonas putida KT2442 were examined via atomic force microscopy (AFM) and single molecule force spectroscopy. Surface biopolymers were probed in solutions with added salt concentrations ranging from that of pure water to 1 M KCl. By studying the physicochemical properties of the polymers over this range of salt concentrations, we observed a transition in the steric and electrostatic properties and in the conformation of the biopolymers that were each directly related to bioadhesion. In low salt solutions, the electrophoretic mobility of the bacterium was negative, and large theoretical energy barriers to adhesion were predicted from soft-particle DLVO theory calculations. The brush layer in low salt solution was extended due to electrostatic repulsion, and therefore, steric repulsion was also high (polymers extended 440 nm from surface in pure water). The extended polymer brush layer was "soft", characterized by the slope of the compliance region of the AFM approach curves (-0.014 nN/nm). These properties resulted in low adhesion between biopolymers and the silicon nitride AFM tip. As the salt concentration increased to > or =0.01 M, a transition was observed toward a more rigid and compressed polymer brush layer, and the adhesion forces increased. In 1 M KCl, the polymer brush extended 120 nm from the surface and the rigidity of the outer cell surface was greater (slope of the compliance region = -0.114 nN/nm). A compressed and more rigid polymer layer, as well as a less negative electrophoretic mobility for the bacterium, resulted in higher adhesion forces between the biopolymers and the AFM tip. Scaling theories for polyelectrolyte brushes were also used to explain the behavior of the biopolymer brush layer as a function of salt concentration.     

Physicochemical study of platelet aggregation by 3 polylysines]

The action of polylysines of various molecular weight on platelet behaviour is studied with the help of 3 techniques: photometric test, screen filtration pressure on PRP and electrophoretic mobility. Polylysines, which are polybasic substances, produce a platelet aggregation studied by photometry after a short period of latency. Aggregation, depending on the doses of poly-lysine and chiefly on the optic density, shows a "plateau" with the dose of 100 gamma/ml for poly-lysine L, of molecular weight 17000. The screen filtration pressure increases continuously in the presence of the polylysines studies. Finally, the platelet charge decreases. The results depend on the concentration of poly-lysine, and the optimal concentration which involves the more marked alterations is inversely proportional to the molecular weight of the polylysine studied.     

Thickness and Surface Density of Extracellular Polymers on Acidithiobacillus ferrooxidans

In vivo force microscopy measurements of Acidithiobacillus ferrooxidans revealed a repulsive force that was due to the presence of extracellular polymers on the bacterium's surface. Measured force-distance profiles were fit to steric force theory to estimate the density and thickness values of these exopolymers. The polymer densities were 3.4 × 10¹⁶ to 7.1 × 10¹⁶ molecules m⁻², and the equilibrium thickness was 29 nm.     

Latex phagocytosis by polymorphonuclear leukocytes: Role of sialic acid groups

Polystyrene latex particles are rapidly phagocytized by rabbit polymorphonuclear (PMN) leukocytes. The uptake is influenced by macromolecules which have the effect of altering the surface charge of the latex particle. The influence of polylysines of varying chain length on the surface charge of latex particles and of PMN cells was studied by micro-electrophoresis. Charge reversal at the latex surface was found to occur at concentrations considerably below that at which the surface charge of the PMN cells is reversed. Phagocytosis of latex by PMN cells is enhanced in the presence of low concentrations of long-chain polylysines. The enhancement of phagocytosis is strongly reduced if PMN cells are treated with neuraminidase. This suggests participation of siliac acid groups in a stage of particle-cell interaction which precedes engulfment.     

Effect of surface potential on the intramembrane electrical field measured with carotenoid spectral shift in chromatophores from Rhodopseudomonas sphaeroides

Changes in the surface potential, the electrical potential difference between the membrane surface and the bulk aqueous phase were measured with the carotenoid spectral shift which indicates the change of electrical field in the membrane. Chromatophores were prepared from a non-sulfur purple bacterium, Rhodopseudomonas sphaeroides, in a low-salt buffer. Surface potential was changed by addition of salt or by pH jump as predicted by the Gouy-Chapman diffuse double layer theory.When a salt was added at neutral pH, the shift of carotenoid spectrum to shorter wavelength, corresponding to an increase in electrical potential at the outside surface, was observed. The salts of divalent cations (MgSO₄, MgCl₂, CaCl₂) were effective at concentrations lower than those of monovalent cation salts (NaCl, KCl, Na₂SO₄) by a factor of about 50. Among the salts of monoor divalent cation used, little ionic species-dependent difference was observed in the low-concentration range except that due to the valence of cations. The pH dependence of the salt-induced carotenoid change was explained in terms of the change in surface charge density, which was about 0 at pH 5–5.5 and had negative values at higher pH values. The dependence of the pH jump-induced absorbance change on the salt concentration was also consistent with the change in the charge density. The surface potential change by the salt addition, which was calibrated by H⁺ diffusion potential, was about 90 mV at the maximum. From the difference between the effective concentrations with salts of mono- and divalent cations at pH 7.8, the surface charge density of (?1.9 ± 0.5) · 10^?3 elementary charge per Ų, and the surface potential of about ?100 mV in the presence of about 0.1 mM divalent cation or 5 mM monovalent cation were calculated.     

ζ-Potential and surface charge of Thermoplasma acidophila

The surface charge density and the ζ-potential of Thermoplasma acidophila was estimated from microscopic electrophoresis experiments. The cells moved towards the positive electrode. The mobility remained constant from pH 2 to 5, and increased for pH values higher than 6. The mobility at pH 6 decreased dramatically with increased external Ca²⁺ concentration. At pH 2 and an ionic strength similar to that of the growth medium, the ζ-potential was about 8 mV, negative relative to the bulk medium; the surface charge density was 1360esu/cm^-2 which corresponds to one elementary charge per 3500 A².     

Atomic force microscope measurements of long-range forces near lipid-coated surfaces in electrolytes.

The interaction of DMPC (L-alpha-dimyristoyl-1,2-diterradecanoyl-sn-glycero-3-phosphoch oli ne, C36H72NO8P) lipid-coated Si3N4 surfaces immersed in an electrolyte was investigated with an atomic force microscope. A long-range interaction was observed, even when the Si3N4 surfaces were covered with nominally neutral lipid layers. The interaction was attributed to Coulomb interactions of charges located at the lipid surface. The experimental force curves were compared with solutions for the linearized as well as with exact solutions of the Poisson-Boltzmann equation. The comparison suggested that in 0.5 mM KCl electrolyte the DMPC lipids carried about one unit of charge per 100 lipid molecules. The presence of this surface charge made it impossible to observe an effective charge density recently predicted for dipole layers near a dielectric when immersed in an electrolyte. A discrepancy between the theoretical results and the data at short separations was interpreted in terms of a decrease in the surface charge with separation distance.     

Effect of soil compaction on root growth and uptake of phosphorus

Summary Zea mays L. andLolium rigidum Gaud. were grown for 18 and 33 days respectively in pots containing three layers of soil each weighing 1 kg. The top and bottom layers were 100 mm deep and they had a bulk density of 1200 kg m^–3, while the central layer of soil was compacted to one of 12 bulk densities between 1200 and 1750 kg m^–3. The soil was labelled with³²P and³³P so that the contribution of the different layers of soil to the phosphorus content of the plant tops could be determined. Soil water potential was maintained between –20 and –100 kPa.Total dry weight of the plant tops and total root length were slightly affected by compaction of the soil, but root distribution was greatly altered. Compaction decreased root length in the compacted soil but increased root length in the overlying soil. Where bulk density was 1550 kg m^–3, root length in the compacted soil was about 0.5 of the maximum. At that density, the penetrometer resistance of the soil was 1.25 and 5.0 MPa and air porosity was 0.05 and 0.14 at water potentials of –20 and –100 kPa respectively, and daytime oxygen concentrations in the soil atmosphere at time of harvest were about 0.1 m³m^–3. Roots failed to grow completely through the compacted layer of soil at bulk densities 1550 kg m^–3. No differences were detected in the abilities of the two species to penetrate compacted soil.Ryegrass absorbed about twice as much phosphorus from uncompacted soil per unit length of root as did maize. Uptake of phosphorus from each layer of soil was related to the length of root in that layer, but differences in uptake between layers existed. Phosphorus uptake per unit length of root was higher from compacted than from uncompacted soil, particularly in the case of ryegrass at bulk densities of 1300–1500 kg m^–3.     

Bilayer membranes containing the ganglioside GM1: models for electrostatic potentials adjacent to biological membranes

Although the Gouy-Chapman-Stern theory of the aqueous diffuse double layer describes well the electrostatic potential adjacent to negatively charged phospholipid bilayer membranes, it does not describe adequately the zeta potential of biological membranes: the zeta potential of an erythrocyte is about half the value predicted from the theory by using the known density of negatively charged sialic acid residues. To investigate the factors responsible for this low electrophoretic mobility, we formed membranes from mixtures of the zwitterionic lipid phosphatidylcholine, PC, and the glycolipid galactosyl-N-acetylgalactosaminyl(N-acetylneuraminyl) -galactosylglucosylceramide, GM1. This glycolipid differs from phospholipids in two respects. First, the negative charge on GM1 is located about 1 nm from the surface, which tends to increase the electrophoretic mobility of vesicles. Second, the head group of GM1 contains five sugar groups that exert a hydrodynamic drag, which tends to decrease the mobility of the vesicles. In a decimolar monovalent salt solution, where the Debye length is about 1 nm, the electrophoretic mobility of the PC-GM1 vesicles is about half the mobility of PC-phosphatidylserine or PC-phosphatidylglycerol vesicles of equivalent composition. In addition, conductance measurements with planar bilayer membranes as well as 31P nuclear magnetic resonance and fluorescence measurements with sonicated vesicles indicate that the potential at the surface of PC-GM1 membranes is about half the value measured for PC-phosphatidylserine membranes in a 0.1 M monovalent salt solution.     

Surface characterization of poly(ethylene glycol) coated human red blood cells by particle electrophoresis

Recent studies have shown that the covalent attachment of poly(ethylene glycol), abbreviated as PEG, to the surface of human red blood cells (RBC) leads to masking of membrane antigenic sites and inhibition of RBC aggregation. The effects of PEG coating on the regions near the RBC glycocalyx were thus explored using cell micro-electrophoresis. Both linear (3.35, 18.5, 35.0) and an 8-arm 35.9 kDa reactive PEG were used; in one series, thick cross-linked coats were obtained using a branched PEG amine as a cross-linker. The results indicate marked decreases of RBC mobility (up to 90%) which were affected by polymer molecular mass and geometry. Since PEG is neutral and its covalent attachment is predominantly to primary amine groups, such decreases of mobility most likely reflect structural changes near and within the RBC glycocalyx rather than decreased surface charge density. Experimental data were analyzed using a theoretical approach which allows calculation of the thickness and friction of the polymer layers: (1) for linear PEGs, thickness increased and friction decreased with polymer mass; (2) compared to linear PEGs of similar molecular mass, thickness was less and friction was greater for the branched PEG; (3) cross-linked PEG coatings were more than 50 nm thick and were insensitive to changes of ionic strength. These observations are consistent with the aggregation behavior of PEG-coated RBC and indicate the usefulness of micro-electrophoresis methods for studies of covalently-attached polymers: the resulting calculated thickness and friction factors should be of value in achieving desired cellular surface characteristics or levels of cell-cell interaction.     

Extending the diffuse layer model of surface acidity constant behaviour: IV. Diffuse layer charge/potential relationships

Abstract

Most current electrostatic surface complexation models describing ionic binding at the particle/water interface rely on the use of Poisson–Boltzmann (PB) theory for relating diffuse layer charge densities to diffuse layer electrostatic potentials. PB theory is known to contain a number of implicit assumptions whose significance in environmental applications is largely unknown. This study seeks to better quantify the impact of these assumptions by: (1) comparing potentials obtained from planar analytical solutions to the PB with those obtained from Hypernetted Chain (HNC) theory (Attard, 2006), (2) assessing the accuracy of the Ohshima et al. (1982) spherical approximate analytical solution to the PB equation by comparison with published numerical values (Loeb et al., 1961), and (3) comparing interfacial potential estimates obtained from the spherical approximate analytical solution to the PB equation at and adjacent to the particle surface with potential estimates obtained from the Entropic Balanced Surface Potential (EB) model (Loux, 1985; Loux and Anderson, 2001) and published potential estimates obtained from the Hypernetted Chain/Mean Spherical Approximation procedure (HNC/MSA; Gonzalez-Tovar and Lozada-Cassou, 1989). EB potential estimates were obtained assuming a surface volume thickness equal to the Bjerrum length (0.357 nm in a room temperature monovalent electrolyte solution). Findings from the study included: (1) the planar, surficial HNC estimates compared favourably with planar surficial PB relationships at charge densities equal to or less than 0.05 C m^?2, (2) the Ohshima et al. (1982) approximate spherical analytical solution to the PB equation replicated the numerical charge density estimates required to obtain 72 datapoints over an e<img>/kT range of one to four with a maximum error of 3.37% and a coefficient of variation of 0.92%, (3) for a 0.1 μm radius particle in a room temperature 0.01 M (1 : 1) ionic strength solution, potential estimates over a surface charge density range of 0 to 0.3C m^?2 occurred in the following order: ψ_HNC/MSA,R >ψ_PB,R >_{ψHNC/MSA,R+0.2125nm} >ψ_PB,R+0.2nm ~ ψ_EB >ψ_{HNC/MSA,R+0.425nm} ~ _ψPB,R+0.4nm and (4) with 45 datapoints including both 1 μm and 10 nm radius particles over an ionic strength range of 1.0 to 0.001 M, the PB potential estimates 0.2 nm from the particle surface (ψ_PBR+02nm) closely tracked the corresponding EB estimates (ψ_EB) with a 5.3% coefficient of variation. If one assumes that interfacial potential values adjacent to the particle surface are most relevant for describing environmental phenomena and that a 10% coefficient of variation in potential estimates is acceptable, then presumably any of the non-surficial charge/potential relationships would be useful below an absolute charge density of 0.125 C m ^?2 (with monovalent electrolyte solutions).     

Dual polarisation interferometry characterisation of DNA immobilisation and hybridisation detection on a silanised support

Dual polarisation interferometry is an analytical technique that allows the simultaneous determination of thickness, density and mass of a biological layer on a sensing waveguide surface in real time. We evaluated, for the first time, the ability of this technique to characterise the covalent immobilisation of single stranded probe DNA and the selective detection of target DNA hybridisation on a silanised support. Two immobilisation strategies have been evaluated: direct attachment of the probe molecule and a more complex chemistry employing a 1,2 homobifunctional crosslinker molecule. With this technique we demonstrate it was possible to determine probe orientation and measure probe coverage at different stages of the immobilisation process in real time and in a single experiment. In addition, by measuring simultaneously changes in thickness and density of the probe layer upon hybridisation of target DNA, it was possible to directly elucidate the impact that probe mobility had on hybridisation efficiency. Direct covalent attachment of an amine modified 19 mer resulted in a thickness change of 0.68 nm that was consistent with multipoint attachment of the probe molecule to the surface. Blocking with BSA formed a dense layer of protein molecules that absorbed between the probe molecules on the surface. The observed hybridisation efficiency to target DNA was approximately 35%. No further significant reorientation of the probe molecule occurred upon hybridisation. The initial thickness of the probe layer upon attachment to the crosslinker molecule was 0.5 nm. Significant reorientation of the probe molecule surface normal occurred upon hybridisation to target DNA. This indicated that the probe molecule had greater mobility to hybridise to target DNA. The observed hybridisation efficiency for target DNA was approximately 85%. The results show that a probe molecule attached to the surface via a crosslinker group is better able to hybridise to target DNA due to its greater mobility.     

Steady-state gel electrophoresis of long polymer molecules: a theoretical study

The velocity of long polymer molecules in a gel and the liquid flow profile in the vicinity of a molecule's surface were studied theoretically by combining the Navier-Stokes equation with the Poisson-Boltzmann equation. The electrophoretic mobility has been calculated in dependence of the ionic strength of the electrolyte solution, its viscosity, the gels' volume friction coefficient, the surface charge and the radius of the polymer molecule. The results are presented in a non-dimensional form and depend on two dimensionless parameters only. The first parameter is the radius of the polymer molecule in units of the Debye length. The second is a parameter comprising the electrolyte's viscosity and the gel density. Thus, by similarity theory, the results apply to any given experimental arrangement. Received: 10 May 1999 / Revised version: 17 November 1999 / Accepted: 6 December 1999     

Theory of the electrokinetic behavior of human erythrocytes

We develop a theory of electrophoresis of human erythrocytes that predicts mobilities significantly smaller than those based on the classical Smoluchowski relation. In the classical treatment the charge is assumed to be spread uniformly on the hydrodynamic surface. The present model takes into account that most of the charge, due mainly to sialic acid, is contained in the glycocalyx. The glycocalyx is modeled as a permeable layer of polyelectrolyte molecules anchored to the cell membrane. The charge is assumed to be uniformly distributed throughout this layer. The fluid flow in the layer is treated as being dominated by Stokes friction arising from idealized polymer segments. The Navier-Stokes equations are solved to give the dependence of electroosomotic velocity with distance from the cell surface. An expression for the electrophoretic mobility is obtained which contains two parameters (a) the thickness of the glycocalyx and (b) the mean polymer segment radius. The best fit to experimental data is obtained if these are given the values 75 A and 7 A, respectively. Deviation from experimental data at low ionic strength (less than 0.05 M) occurs. However, this deviation is in the direction one would expect if at low ionic strength the polyelectrolyte layer expands slightly due to decreased charge shielding.     

Calculation of the Electrophoretic Mobility of a Particle Bearing Bound Polyelectrolyte Using the Nonlinear Poisson-Boltzmann Equation

A numerical method for determining the electrophoretic mobility of a polyelectrolyte-coated particle is presented. The particle surface is modeled as having a permeable layer of polyelectrolyte molecules anchored to its surface. Fluid flow within the polyelectrolyte layer is subject to Stokes drag arising from the polyelectrolyte segments. The method allows arbitrary distribution of polymer segments and charge density normal to the surface to be used. The hydrodynamic plane of shear may also be varied. The potential profile is determined by a numerical solution to the nonlinearized Poisson-Boltzmann equation. The potential profile is then used in a numerical solution to the Navier-Stokes equation to give the required mobility. The use of the nonlinearized Poisson-Boltzmann equation extends the results to higher charge density/lower ionic strength conditions than previous treatments. The surface potentials and mobilities for three limiting charge distributions are compared for both the linear and nonlinear treatments to delimit the range of validity of the linear treatment. The utility of the numerical, nonlinear treatment is demonstrated by an improved fit to the electrophoretic mobility of human erythrocytes as a function of ionic strength in the range 10 to 150 mM.     

不同氮素添加量对大兴安岭冻土区泥炭地植物细根形态的影响模拟研究

为探讨氮素营养环境变化对冻土区泥炭地植物细根形态的影响,在大兴安岭泥炭地开展了不同浓度氮素添加模拟试验,添加量分别为0 g N m^-2 a^-1（CK）、6 g N m^-2 a^-1（N1）、12 g N m^-2 a^-1（N2）和24 g N m^-2 a^-1（N3）。在2020年8月和9月,利用微根管技术观测泥炭地不同深度（0-20 cm、20-40 cm）土壤中的植物细根形态,应用WinRHIZO图像分析软件分析根系特征。结果表明,在表层土壤（0-20 cm）中植物细根的总根长、总表面积、总体积和根长密度随施氮量增加而增加,其中8月份N3处理下细根总根长、总表面积、总体积和根长密度显著高于其他处理（P< 0.05）,N2处理下细根总表面积、总体积显著高于对照组和N1处理;9月份N3处理下细根总根长和根长密度显著高于对照组,总表面积和总体积显著高于对照组和N1处理。说明高浓度氮素添加在一定程度上缓解了植物氮素限制,能够显著促进表层土壤（0-20 cm）中植物细根的生长,但对亚表层土壤（20-40 cm）中细根的影响幅度小于表层土壤。