Approximation method for electrolyte diffusion through a fixed charge medium

The diffusion of a binary salt through media containing uniformly dispersed immobile ions is formally equivalent to the diffusion of a nonelectrolyte with a concentration-dependent diffusion coefficient. This permits the application of a quasi-steady-state approximation, developed in a previous paper (Bull. Math. Biophysics,21, 19–32, 1959), to problems of transient diffusion. Free diffusion across an interface involving a discontinuity in immobile ion concentration is considered and expressions for the salt concentration and electrical potential at any point are developed. The dependence of electrical potential on the fixed charge density, ionic mobilities, as well as on the boundary concentrations is illustrated by a numerical example. This particular example is suggested by experiments on connective tissue.     

Analytical bounding functions for diffusion problems with michaelis-menten kinetics

Pointwise upper and lower bounds for the solution of a class of nonlinear diffusion problems with Michaelis-Menten kinetics are presented. Simple analytical bounding curves are obtained and for an illustrative case the calculated values bound the recent numerical solution of P. Hiltmann and P. Lory, 1983.Bull. math. Biol. 45, 661–664.     

Linear bulk diffusion into heterogeneous tissue

In this paper an expression is derived which describes the transient overall uptake of an inert solute by a section of tissue excised with parallel faces and placed upon an impermeable base. The approach diverges from the conventional analyses for perfused tissue (Morales and Smith,Bull. Math. Biophysics,6, 125–141, 1944;7, 47–99, 1945) because the extravascular zone is regarded as a heterogeneous diffusion medium. Account for this is taken by regarding tissue as effectively composed of two phases—a continuous (extracellular) phase similar to water, and a dispersed phase comprising cells of irregular profile. In both phases the relevant mode of uptake is taken as bulk diffusion rather than surface permeation, thus emphasizing the influence of the internal geometry of the tissue upon its overall exchange response.     

Nonlinear diffusion in metabolic systems

Some general properties of the solution of the diffusion equation are deduced for the steady-state, spherically symmetric system. On the basis of these developments some results of N. Rashevsky (Bull. Math. Biophysics,11, 15, 1949) are discussed and the results of a previous investigation (Hearon,Bull. Math. Biophysics,12, 135, 1950b) are extended to more general conditions. In particular these extensions apply to the flow of a soluteagainst its concentration gradient, the nonzero gradient of an inert metabolite, and theaccumulation or exclusion of an inert metabolite in a metabolic system. A portion of this work was performed while the author was a research participant, Oak Ridge Institute of Nuclear Studies, assigned to the Mathematics Panel, Oak Ridge National Laboratory.     

The single file model for the diffusion of ions through a membrane

The model proposed by A. L. Hodgkin and R. D. Keynes (Jour. of Physiol.,128, 61–88, 1955) for the diffusion of potassium through the nerve membrane is extended to cover an arbitrary number of species of ions with charges not necessarily the same. One type of interference is also investigated.     

Upper and lower bounds from the maximum principle. Intracellular diffusion with Michaelis-Menten kinetics

Analytical bounding functions for diffusion problems with Michaelis-Menten kinetics were recently presented by Anderson and Arthurs, 1985 (Bull. math. Biol. 47, 145–153). Their methods, successful to some extent for a small range of parameters, has the disadvantage of providing a weak upper bound. The optimal approach for the use of one-line bounding kinetics is presented. The use of two-line bounding kinetics is also shown, in order to give, sufficient accuracy in those cases where the one-line approach does not provide satisfactory results. The bounding functions provide excellent upper and lower bounds on the true solution for the entire range of kinetic and transport parameters.     

Comments on the approximate solution of the diffusion equation: II

On the basis of a previous general formulation (Bull. Math. Biophysics,15, 21–29, 1953a) a discussion is given of the error in the approximation method of N. Rashevsky. This error, inherent in the method when the metabolic rate is different at each point in the cell, is discussed in detail and numerical values are presented for two particular cases: the rate proportional to the concentration and the rate a prescribed function of the spatial coordinates. It is shown that the formulation for the first case also applies to several other cases, that the error is negligible provided the rate is sufficiently small, and that the error is fairly sensitive to the cell size. If the rate depends upon the coordinatesalone a small rate is not sufficient to insure a negligible error. The relations between the exact method, the standard approximate method, an earlier approximate method (Physics,7 260, 1936), and a more recent refinement (Bull. Math. Biophysics,10, 201, 1948) of the standard method are discussed. This work was performed while the author was a research participant, Oak Ridge Institute of Nuclear Studies, assigned to the Mathematics Panel, Oak Ridge National Laboratory.     

Particle removal by the respiratory system note on the removal of airborne particulates by the human respiratory tract with particular reference to the role of diffusion

Calculations of the contribution of diffusion to lung retention given previously (W. Findeisen,Pflüg. Arch. f. d. ges. Physiol.,236, 367–379, 1935; H. D. Landahl,Bull. Math. Biophysics,12, 43–56, 1950) contained an error appreciably underestimating the role of diffusion for particles less than a few microns in diameter. In the calculations (Landahl, 1950), a schematic representation of the lungs was modified to conform to the actual resting lung volume by increasing the number of alveolar sacs. A recalculation of total deposition with this chematic model gives too large a retention for very small particles. Hence it seemed appropriate to recalculate the retention for various paricle sizes in various regions of the respiratory tract for several respiratory paterns, using the original schematic model but assuming that the estimates reflect conditions in a deflated lung. For a given tidal air the sizes of the alveolar ducts and sacs were assumed to expand so that the total volume of the model was equal to 2.5 liters plus one half of the tidal air, i.e., the mean lung volume. The results of these calculations are appreciably different from those given previously, but the differences are serious only for particles of about 0.1 micron or less. Also given is an approximation method for calculating the probability of impaction of droplets against nasal hairs.     

Impact of high-pressure processing on diffusion in polyethylene based on molecular dynamics simulation

Abstract

The impact of high-pressure processing (HPP) on dissusion of antioxidant butylated hydroxytoluene (BHT) in polyethylene (PE) was discussed via the molecular dynamics method. Furthermore, the glass transition temperatures (T_g), the accessible free volumes of PE and the diffusion coefficients of BHT in PE at different HPP treatments were calculated, and the diffusion trajectories of the BHT molecules in PE were also presented. Finally, the diffusion mechanism of BHT in PE under HPP was analyzed based on the aforementioned simulation results. The results show that the T_g of PE increases under high pressure while the fractional free volume (FFV) reduces, and the diffusion coefficient decreases with the pressure on the rise. The diffusion trajectories of BHT in PE under HPP indicate that the BHT molecules are trapped and slowly wriggle in a narrow path among PE molecular chains due to the extreme high pressure. However, the high temperature has an opposite effect on the diffusion behavior of BHT in PE compared with high pressure. As the temperature rises, the FFV of PE and the diffusion coefficient of BHT in PE are elevated. This study is helpful to the research of high-pressure food safety and packaging migration.     

Evaluation of agar diffusion bioassay for nisin quantification

The agar diffusion bioassay is the most widely used method for the quantification of nisin, due to its high sensitivity, simplicity, and cost-effectiveness. This method is based on the measurement of the inhibition zone produced in nisin-sensitive microorganisms. The size of the zone is affected by many factors, such as nisin-sensitive strain, amount of added agar and surfactant, and pre-diffusion step. This research aims to evaluate the effects of nisin-sensitive strains and pre-diffusion on the accuracy and precision of nisin quantification. Three strains of nisin-sensitive microorganisms (Micrococcus luteus, Lactobacillus sakei, Brochothrix thermosphacta) were tested along with three different incubation processes. The best combination was the method using L. sakei as an indicator strain with pre-diffusion at 4 °C for 24 h. Compared with M. luteus and B. thermosphacta, L. sakei gave more accurate and reproducible results. Moreover, the pre-diffusion step resulted in larger inhibition zones and more precise results. Finally, the best combination was validated and compared with the method that is usually used and the result showed that the method using L. sakei with pre-diffusion gave more accurate and precise results.     

Gas diffusion through wood: implications for oxygen supply

Living tissue in tree stems has to be supplied with oxygen, which can be transported upwards with the transpiration stream; but in times of zero sapflow, the only source is the oxygen stored or diffusing radially through bark and xylem. We measured radial and axial diffusion of oxygen against nitrogen gas in wood of coniferous (Picea abies (L.) Karst. and Taxus baccata L.), ring-porous (Quercus robur L. and Fraxinus excelsior L.) and diffuse-porous (Fagus sylvatica L. and Carpinus betulus L.) trees at different water and gas contents in the laboratory. The diffusion coefficient (D) in radial direction was mostly between 10⁻¹¹ and 10⁻⁷ m² s⁻¹ and was strongly related to the gas content. At 40% gas volume, D increased 5–13-fold in Picea, Taxus and Quercus, 36-fold in Fraxinus, and about 1000-fold in Carpinus and Fagus relative to D at 15% gas volume. In the axial direction, diffusion was 1 or 2 orders of magnitude faster. Between-species differences in diffusion velocities can largely be explained by wood structure. In general, D was lowest in conifers, highest in diffuse-porous and intermediate in ring-porous hardwoods, where the large vessels were mostly blocked by tyloses. Model calculations showed that at very high water content, radial diffusion can be too low to ensure the supply of respiring sapwood with sufficient oxygen and an important function of gas in living stems appears to be the supply of oxygen through storage and diffusion.     

Chain length and pressure dependence of lipid translational diffusion

The translational diffusion of pyrene, pyrene butyric acid and pyrene decanoic acid has been determined in phosphatidylcholine bilayers of different chain length and under pressure up to 200 bars. In the liquid crystalline phase and at a given temperature the diffusion decreases with increasing chain length. At a constant reduced temperature, T _red (about 10 K above the transition temperature), long chain lipids exhibit the fastest diffusion which is in disagreement with hydrodynamic models but favours free volume models for diffusion in lipid bilayers. The volume of activation, V _act, calculated from the decrease of the diffusion coefficient with pressure, ln D/P, depends on lipid chain length. V _act decreases with decreasing lipid chain length at a given temperature, T=65°C, and increases at the reduced temperature. These results are again in agreement with the dependence of the diffusion on lipid chain length and therefore with the free volume model.Abbreviations DLPC Dilauroylphosphatidylcholine - DMPC Dimyristoylphosphatidylcholine - DPPC Dipalmitoylphosphatidylcholine - DSPC Distearoylphosphatidylcholine - LUV Large unilamellar vesicles - SUV Small unilamellar vesicles - Tris Tris(hydroxymethyl)aminomethan     

Neurotransmitter release: Facilitation and three-dimensional diffusion of intracellular calcium

In order to account for the time courses of both evoked release and facilitation, in the framework of the Ca²⁺ hypothesis, Fogelson and Zucker (1985,Biophys. J. 48, 1003–1017) suggested treating diffusion of Ca²⁺, once it enters through the Ca²⁺ channels, as a three-dimensional process (three-dimensional diffusion model). This model is examined here as a refined version of the “Ca²⁺-theory” for neurotransmitter release. The three-dimensional model was suggested to account for both the time course of release and that of facilitation. As such, it has been examined here as to its ability to predict the dependence of the amplitude and time course of facilitation under various experimental conditions. It is demonstrated that the three-dimensional diffusion model predicts the time course of facilitation to be insensitive to temperature. It also predicts the amplitude and time course of facilitation to be independent of extracellular Ca²⁺ concentration. Moreover, it predicts that inhibition of the [Na⁺]_o↔[Ca²⁺]_i exchange does not alter facilitation. These predictions are not upheld by the experimental results. Facilitation is prolonged upon reduction in temperature. The amplitude of facilitation declines and its duration is prolonged upon increase in extracellular Ca²⁺ concentration. Finally, inhibition of the [Na⁺]_o↔[Ca²⁺]_i exchange prolongs facilitation but does not alter the time course of evoked release after an impulse.     

Impact of osmotic stress on protein diffusion in Lactococcus lactis

We measured translational diffusion of proteins in the cytoplasm and plasma membrane of the Gram‐positive bacterium Lactococcus lactis and probed the effect of osmotic upshift. For cells in standard growth medium the diffusion coefficients for cytosolic proteins (27 and 582 kDa) and 12‐transmembrane helix membrane proteins are similar to those in Escherichia coli. The translational diffusion of GFP in L. lactis drops by two orders of magnitude when the medium osmolality is increased by ～ 1.9 Osm, and the decrease in mobility is partly reversed in the presence of osmoprotectants. We find a large spread in diffusion coefficients over the full population of cells but a smaller spread if only sister cells are compared. While in general the diffusion coefficients we measure under normal osmotic conditions in L. lactis are similar to those reported in E. coli, the decrease in translational diffusion upon osmotic challenge in L. lactis is smaller than in E. coli. An even more striking difference is that in L. lactis the GFP diffusion coefficient drops much more rapidly with volume than in E. coli. We discuss these findings in the light of differences in turgor, cell volume, crowding and cytoplasmic structure of Gram‐positive and Gram‐negative bacteria.     

Single-file diffusion multi-ion mechanism of permeation in paracellular epithelial channels

Summary The transepithelial fluxes, conductances and permeabilities of Li⁺, Na⁺, K⁺, Cs⁺, NH ₄ ⁺ and H₃CNH ₃ ⁺ were studied under ionic concentrations ranging from 12 to 250mm inBufo arenarum gallbladders. When these measurements are carefully corrected in order to get only the component due to the paracellular cation channels, the following results are obtained: (1) The permeability ratios (cationic/anionic) are a decreasing function of salt concentration. (2) The partial conductances through paracellular cationic channels show nonlinear saturable concentration kinetics. (3) Moreover, partial conductance kinetics of K⁺, Cs⁺ and NH ₄ ⁺ present a maximum followed, at higher concentratons, by a negative-slope region. (4) The selectivity sequences obtained from biionic potentials do not agree with those obtained from partial conductance measurements. (5) The unidirectional²²Na tracer flux (serosal to mucosal) is inhibited by 63% when the K⁺ symmetrical concentration in the bathing solutions is raised from 25 to 200mm. (6) When the unidirectional⁴²K fluxes (serosal to mucosal) at 200mm KCl Na-free solutions are compared with K⁺ partial conductance by means of the Hodgkin and Keynes (Hodgkin, A.L., Keynes, R.D. 1955.J. Physiol London 128:61–88) expression, then factor is 2.0. These results indicate that cations do not follow the independence principle and behave as in single-file diffusion multi-ion pores when crossing the paracellular cation channels ofBufo arenarum gallbladder epithelium.     

江苏水产养殖区拟态弧菌种群结构及遗传多样性

【背景】拟态弧菌(Vibrio mimicus)是一种常见的革兰氏阴性病原菌,广泛分布于水环境和水生动物体内,可导致多种水产动物和人类感染。多位点序列分型(multilocus sequence typing, MLST)已被应用于多种病原菌的分子分型,其通过分析不同菌株之间的遗传关系,监测细菌传播的时间和地理分布,确定感染和传播途径,但目前未见有关拟态弧菌MLST的报道。【目的】开发一种基于MLST的拟态弧菌分型方法,并用于江苏水产养殖区拟态弧菌的种群结构和遗传进化分析,为拟态弧菌感染所引起的疾病防治提供理论基础。【方法】选择拟态弧菌的7个管家基因dnaE、gyrB、mdh、recA、rpoD、pntA和pyrH作为靶点,对江苏水产养殖区分离的155株拟态弧菌进行PCR扩增和测序。将测序结果分配等位基因,制作等位基因谱,分配不同的序列类型(sequence type, ST),利用软件goeBURST-1.2.1和MEGA-X对分配的ST型进行克隆复合体和遗传进化树聚类分析;此外,利用Kirby-Bauer圆盘扩散法测试155株拟态弧菌的药敏特性。【结果】155株拟态弧菌被分为56个STs,其中ST11占比最高;在双位点变异(double locus variants, DLV)水平分析发现56个STs分为3个克隆复合体和3个单体;系统发育树显示,56个STs被分为3个集群(cluster I、cluster II、cluster III)。药敏结果显示,155株拟态弧菌对红霉素类抗生素的耐药性最高(88.39%, 137/155),对氯霉素类抗生素敏感性最高(91.61%, 142/155)。【结论】本研究建立的MLST方法具有良好的分辨率,可作为拟态弧菌系统发育和未来流行病学调查有用的分子分型工具。根据抗生素耐药谱结果,提示在养殖过程中可选用氟苯尼考等国家批准使用的专用抗菌药对拟态弧菌进行防治。     

Small Molecule Diffusion into Swelling Iota-Carrageenan Gels: A Fluorescence Study

Abstract

Small molecule diffusion into Iota-Carrageenan gel was studied by using steady-state fluorescence (SSF) technique. Pyranine, dissolved in water was used as fluorescence probe. Fluorescence emission intensity, I_p, and scattered light intensity, I_sc, were monitored to study diffusion and swelling processes at various temperatures respectively. Fickian and Li-Tanaka models were elaborated to produce diffusion, D, and collective diffusion, D ₀, coefficients. Diffusion and swelling activation energies were also obtained and found to be 20.5 kj mol^?1 and 28.2 kj mol^?1, respectively.     

培养法检测海滨浴场细菌多样性及耐药性研究

【目的】耐药基因细菌水平基因转移导致的耐药菌数量增加引发的公共安全问题日益引起人们关注,监测环境中耐药菌变得极为重要。【方法】采集湛江3处滨海浴场的水体、沙滩土样,通过平板稀释涂布和琼脂扩散法进行浴场微生物数量、多样性和抗生素耐药性分析。【结果】3处浴场水体无机氮含量偏高,浴场微生物数量随着客流量逐渐增加,沙滩中微生物数量显著高于水体。浴场细菌分布于3门12科18属,水体中变形菌门（Proteobacteria,49.64%）占优势,沙滩则是厚壁菌门（Firmicutes,54.74%）占优势。浴场细菌对β-内酰胺类耐药率较高,青霉素、万古霉素和头孢曲松耐药率分别达到23.25%、20.53%和17.42%,耐药菌株主要分布于芽孢杆菌属（Bacillus）、弧菌属（Vibrio）、假单胞菌属（Pseudomonas）、链霉菌属（Streptomyces）和肠杆菌属（Enterobacter）,水体中多重耐药细菌数量显著高于沙滩,集中于人流量多的浴场。【结论】滨海浴场环境中细菌耐药菌种类多,需持续监测以评估对当前地区公共卫生的潜在影响。     

狐、貉源大肠杆菌分离鉴定及毒力基因检测

[背景]狐、貉肺炎频发导致养殖户遭受巨大经济损失.[目的]调查黑龙江省、吉林省、河北省、山东省等地狐、貉肺炎原因,对病原菌进行分离、鉴定及部分生物学特性研究.[方法]无菌采集患病狐、貉肺组织进行细菌分离培养;对分离菌进行革兰氏染色、生化试验、特异性基因PCR鉴定、药物纸片扩散法敏感性试验、毒力基因检测及小鼠致病性试验....     

An asymptotic solution for traveling waves of a nonlinear-diffusion Fisher's equation

We examine traveling-wave solutions for a generalized nonlinear-diffusion Fisher equation studied by Hayes [J. Math. Biol. 29, 531–537 (1991)]. The density-dependent diffusion coefficient used is motivated by certain polymer diffusion and population dispersal problems. Approximate solutions are constructed using asymptotic expansions. We find that the solution will have a corner layer (a shock in the derivative) as the diffusion coefficient approaches a step function. The corner layer at z = 0 is matched to an outer solution for z < 0 and a boundary layer for z > 0 to produce a complete solution. We show that this model also admits a new class of nonphysical solutions and obtain conditions that restrict the set of valid traveling-wave solutions. Supported by a National Science Foundation graduate fellowship. This work was performed under National Science Foundation grant DMS-9024963 and Air Force Office of Scientific Research grant AFOSR-F49620-94-1-0044.