Ion flow in the bath and flux interactions between channels.

We present an exact solution to the linearized Nernst-Planck-Poisson equation for spherically symmetric current flow. This solution differs from Levitt's solution (Levitt, D. G. 1992. Biophys. J., Eq. A5) by its dependence on an additional parameter, which is equal to the net ion flux for monovalent ion-selective channels. For ion-selective channels, this solution may provide better boundary conditions to modelling the flow in the channel pore itself, although only at low salt concentrations. We use the solution to estimate the effects of flux interaction between closely packed channels.     

Mass and Energy Transport Through Slit Pores: Application to Planar Poiseuille Flow

Abstract

We develop a simple, efficient and general statistical mechanical technique for calculating the pressure tensor and the heat flux vector in atomic fluids. The method is applied to the case of planar Poiseuille flow through a narrow slit pore and the results indicate that our technique is accurate and relatively efficient. A second method to calculate shear stress is derived from the momentum continuity equation. This mesoscopic method again is seen to be accurate with good computational efficiency.

We also find that the commonly used approximation to the Irving-Kirkwood expression for the heat flux and the pressure tensor (where the Irving-Kirkwood O_ij operator is set equal to unity-the so-called IK1 approximation), leads to incorrect results for highly inhomogeneous fluids. In such cases the pressure tensor and heat flux vector display spurious oscillations.

We calculate the spatially dependent viscosity across a narrow pore and find that it exhibits real but weak oscillations, a consequence of oscillations in the number density. Finally we point out that if the heat flux vector is coupled to the gradient of the square of the strain rate tensor such an effect will only affect the shape of the temperature profile. For planar Poiseuille flow, the temperature profile should deviate from the classical quartic form and include an additional quadratic component. The actual magnitude and shape of the heat flux vector remain exactly as they would if such a coupling did not exist.     

On the fisher and the cubic-polynomial equations for the propagation of species properties

For precise boundary conditions of biological relevance, it is proved that the steadily propagating plane-wave solution to the Fisher equation requires the unique (eigenvalue) velocity of advance 2(Df)^1/2, whereD is the diffusivity of the mutant species andf is the frequency of selection in favor of the mutant. This rigorous result shows that a so-called “wrong equation”, i.e. one which differs from Fisher's by a term that is seemingly inconsequential for certain initial conditions, cannot be employed readily to obtain approximate solutions to Fisher's, for the two equations will often have qualitatively different manifolds of exact solutions. It is noted that the Fisher equation itself may be inappropriate in certain biological contexts owing to the manifest instability of the lowerconcentration uniform equilibrium state (UES). Depicting the persistence of a mutantdeficient spatial pocket, an exact steady-state solution to the Fisher equation is presented. As an alternative and perhaps more faithful model equation for the propagation of certain species properties through a homogeneous population, we consider a reaction-diffusion equation that features a cubic-polynomial rate expression in the species concentration, with two stable UES and one intermediate unstable UES. This equation admits a remarkably simple exact analytical solution to the steadily propagating plane-wave eigenvalue problem. In the latter solution, the sign of the eigenvelocity is such that the wave propagates to yield the “preferred” stable UES (namely, the one further removed from the unstable intermediate UES) at all spatial points ast→∞. The cubic-polynomial equation also admits an exact steady-state solution for a mutant-deficient or mutant-isolated spatial pocket. Finally, the perpetuating growth of a mutant population from an arbitrary localized initial distribution, a mathematical problem analogous to that for ignition in laminar flame theory, is studied by applying differential inequality analysis, and rigorous sufficient conditions for extinction are derived here.     

Brownian dynamics study of flux ratios in sodium channels

Measurements of unidirectional fluxes in ion channels provide one of the experimental methods for studying the steps involved in ion permeation in biological pores. Conventionally, the number of ions in the pore is inferred by fitting the ratio of inward and outward currents to an exponential function with an adjustable parameter known as the flux ratio exponent. Here we investigate the relationship between the number of ions in the pore and the flux ratio exponent in a model sodium channel under a range of conditions. Brownian dynamics simulations enable us to count the precise number of ions in the channel and at the same time measure the currents flowing across the pore in both directions. We show here that the values of the flux ratio exponent n′ ranges between 1 and 3 and is highly dependent on the ionic concentrations in which measurements are made. This is a consequence of the fact that both inward and outward currents are susceptible to saturation with increasing concentration. These results indicate that measurements of the flux ratio exponent cannot be directly related to the number of ions in the pore and that interpretation of such experimental measurements requires careful consideration of the conditions in which the study is made.     

Shepherd model for knot-limited polymer ejection from a capsid

We construct a tractable model to describe the rate at which a knotted polymer is ejected from a spherical capsid via a small pore. Knots are too large to fit through the pore and must reptate to the end of the polymer for ejection to occur. The reptation of knots is described by symmetric exclusion on the line, with the internal capsid pressure represented by an additional biased particle that drives knots to the end of the chain. We compute the exact ejection speed for a finite number of knots L and find that it scales as 1/L. We establish a mapping to the solvable zero-range process. We also construct a continuum theory for many knots that matches the exact discrete theory for large L.     

MEASURING THE HYDRAULIC DIAMETER OF A PORE OR CONDUIT

A method for estimating the hydraulic diameter of a pore or conduit having a noncircular opening is presented with special reference to plant anatomy. An ellipse or a rectangle is inscribed within the opening, and the length of the short axis (a) is measured. The hydraulic diameter (D_h) is estimated for the ellipse (D_h = 1.4a) or rectangle (D_h = 2a). Use of these equations often gives a more accurate estimate of the hydraulic diameter of a pore or conduit than does averaging the lengths of the short and long axes (D_h = [a + b]/2, b is the long axis) or assuming that the opening is circular (D_h = a). A table of the error in each method is included, and the errors inherent in the use of D_h are discussed. Because fewer measurements are required, estimation based on the measurement of one axis is much faster than calculation using both the short and long axes. The equations and table should permit anatomists and physiologists to rapidly determine the best method for estimating the hydraulic diameter of a pore or conduit, and to more accurately and quickly estimate the hydraulic diameters of large numbers of openings. However, because of potential pitfalls in applying theoretical fluid dynamics equations to real-world functional anatomy, botanists must ensure that their applications of hydraulic diameter are appropriate in each case.     

Computational Approaches to Solving Equations Arising from Wound Healing

In the wound healing process, the cell movement associated with chemotaxis generally outweighs the movement associated with random motion, leading to advection-dominated mathematical models of wound healing. The equations in these models must be solved with care, but often inappropriate approaches are adopted. Two one-dimensional test problems arising from advection-dominated models of wound healing are solved using four algorithms—MATLAB’s inbuilt routine pdepe.m, the Numerical Algorithms Group routine d03pcf.f, and two finite volume methods. The first finite volume method is based on a first-order upwinding treatment of chemotaxis terms and the second on a flux limiting approach. The first test problem admits an analytic solution which can be used to validate the numerical results by analyzing two measures of the error for each method: the average absolute difference and a mass balance error. These criteria as well as the visual comparison between the numerical methods and the exact solution lead us to conclude that flux limiting is the best approach to solving advection-dominated wound healing problems numerically in one dimension. The second test problem is a coupled nonlinear three species model of wound healing angiogenesis. Measurement of the mass balance error for this test problem further confirms our hypothesis that flux limiting is the most appropriate method for solving advection-dominated governing equations in wound healing models. We also consider two two-dimensional test problems arising from wound healing, one that admits an analytic solution and a more complicated problem of blood vessels growth into a devascularized wound bed. The results from the two-dimensional test problems also demonstrate that the flux limiting treatment of advective terms is ideal for an advection-dominated problem.     

Characteristics of settling matter and its role in nutrient cycles in a deep oligotrophic lake

The settling flux of seston (dry weight, DW), chlorophyll a (Chl a), particulate organic carbon (POC), particulate organic nitrogen (PON), and particulate phosphorus (PP) was measured monthly in 1981–1983 at 10 different depths in Lake Chuzenji, Japan; an oligotrophic lake with a maximum depth of 163 m. The Ti concentration in entrapped matter was used to separate the sedimentation flux into allochthonous and autochthonous components. Inflow loads of dissolved nutrients (DN: 4.5, DP: 0.48 g m^-2a^-1) were almost sufficient to supply the autochthonous fluxes at 30 m (PON: 2.9, PP: 0.51 g m^-2a^-1 ), and this flux of POC (26.6 g m^-2a ^-1) was about one-third of primary production (84 g C M^-2a^-1). Sedimentation of particulate matter was the main path of losing nutrients from lake water, explaining more than 80% removal of inflow loads (TN, TP). Decomposition rates during sedimentation which were calculated from the vertical difference in the autochthonous flux agreed very closely with the results obtained by laboratory experiments of a 100-day incubation (content ratios from field observations were: POC 0.67, PON 0.65, PP 0.85; and from laboratory experiments they were: POC 0.68, PON 0.70, PP 0.94). These decomposition rates and those near the sediment interface were used to explain dissolved oxygen depletion and nitrate increase in the hypolimnion during stratification. The average sinking velocities were 1.82m d^-1 for seston and 1.16 m d^-1 for Chl a at 30m, they were influenced by Chl a content of seston.     

Differential expression of foxl2 and cyp19a1a mRNA during gonad developmental stages in great sturgeon Huso huso

This study aimed to determine the sex specificity and expression pattern of foxl2 and cyp19a1a genes in great sturgeon Huso huso gonads during gonadal sex differentiation and development. The results revealed that foxl2 and cyp19a1a mainly expressed in female gonads and during gonad development the foxl2 and cyp19a1a mRNA expression is required for ovarian development.     

Seasonal and interannual cycles of endemic cholera in Bengal 1891–1940 in relation to climate and geography

The temporal distribution of chlorophyll a (chl a), suspended matter (SM), and vertical flux of chl a and organic carbon (OC) has been investigated at three sites along the north-eastern coast of the Gulf of Aqaba during the period from January 1991 through December 1992. Highly significant temporal and interannual variations were found in chl a, and in the vertical flux of chl a and OC. The SM and its OC content did not show any significant temporal or interannual variations. The recorded levels of the forementioned variables were generally low. The temporal distribution of chl a in the water column was polymodal in 1991 with peaks in March, June, August and December, and bimodal in 1992 with peaks in May–June, and October. Maximum values of SM and its OC content occurred in July of 1991 and September of 1992. The temporal variations in the vertical flux of total particles, chl a, and OC followed those of chl a in the water column. The bulk of the sediment material was of inorganic nature, derived from desert sand carried from Wadi Araba by the prevailing northerly winds, and dust of exported raw phosphate. The temporal changes described appear to be related to the temporal variations in water stability, horizontal advection, and winds.     

Mathematical model of the simple cells in the visual cortex

A mathematical model for the spatial computations performed by simple cells in the mammalian visual cortex is derived. The construction uses as organizing principles the experimentally observed simple cell linearity and rotational symmetry breaking, together with the constraint that simple cell inputs must effectively be ganglion cell outputs. This leads to a closed form expression for the simple cellkernel in terms of Jacobi-functions. Using a-function identity, it is also shown how Gabor sampling arises as an approximation to this exact kernel for most cells. In addition, the model provides a natural mechanism for introducing the type of nonlinearity observed in some simple cells. The cell's responses to a variety of visual stimuli are calculated using the exact kernel and compared to single cell recordings. In all cases, the model's predictions are in agreement with available experimental data.Work supported by the National Science Foundation, grant PHYS86-20266Work supported by the Department of Energy, contract DE-AC02-76ERO2220     

The freshwater tidal wetland Liberty Island,CA was both a source and sink of inorganic and organic material to the San Francisco Estuary

It is hypothesized that perennial freshwater tidal wetland habitat exports inorganic and organic material needed to support the estuarine food web and to create favorable habitat for aquatic organisms in San Francisco Estuary. It is also hypothesized that most of the material flux in this river-dominated region is controlled by river flow. The production and export of material by Liberty Island were measured and compared using discrete monthly and continuous (15 min) measurements of a suite of inorganic and organic materials and flow between 2004 and 2005. Seasonal material flux was estimated from monthly discrete data for inorganic nutrients, suspended solids and salts, organic carbon and nitrogen and phytoplankton and zooplankton group carbon and chlorophyll a and pheophytin pigment. Estimates of material flux from monthly values were compared with measured daily material flux values for chlorophyll a concentration, salt and suspended solids obtained from continuous measurements (15 min) using YSI water quality sondes. Phytoplankton carbon produced within the wetland was estimated by in situ primary productivity. Most inorganic and organic materials were exported from the wetland on an annual basis, but the magnitude and direction varied seasonally. Dissolved inorganic nutrients such as nitrate, soluble phosphorus, total phosphorus and silica as well as total suspended solids were exported in the summer while total and dissolved organic carbon were exported in the winter. Salts like chloride and bromide were exported in the fall. Chlorophyll a and pheophytin were exported in the fall and associated with diatom and cyanobacteria carbon. Mesozooplankton carbon was dominated by calanoid copepods and exported most of the year except summer. Continuous sampling revealed high hourly and daily variation in chlorophyll a, salt and total suspended solids flux due to high frequency changes in concentration and tidal flow. In fact, tidal flow rather than river discharge was responsible for 90% or more of the material flux of the wetland. These studies indicate that freshwater tidal wetlands can be a source of inorganic and organic material but the export of material is highly variable spatially and temporally, varies most closely with tidal flow and requires high frequency measurements of both tidal flow and material concentration for accurate estimates.     

Aryl hydrocarbon receptor-dependent induction of the NADPH oxidase subunit NCF1/p47 expression leading to priming of human macrophage oxidative burst

Polycyclic aromatic hydrocarbons such as benzo(a)pyrene (BaP) are toxic environmental contaminants known to regulate gene expression through activation of the aryl hydrocarbon receptor (AhR). In the present study, we demonstrated that acute treatment by BaP markedly increased expression of the NADPH oxidase subunit gene neutrophil cytosolic factor 1 (NCF1)/p47^phox in primary human macrophages; NCF1 was similarly up-regulated in alveolar macrophages from BaP-instilled rats. NCF1 induction in BaP-treated human macrophages was prevented by targeting AhR, through its chemical inhibition or small interference RNA-mediated down-modulation of its expression. BaP moreover induced activity of the NCF1 promoter sequence, containing a consensus AhR-related xenobiotic-responsive element (XRE), and electrophoretic mobility shift assays and chromatin immunoprecipitation experiments indicated that BaP-triggered binding of AhR to this XRE. Finally, we showed that BaP exposure resulted in p47^phox protein translocation to the plasma membrane and in potentiation of phorbol myristate acetate (PMA)-induced superoxide anion production in macrophages. This BaP priming effect toward NADPH oxidase activity was inhibited by the NADPH oxidase specific inhibitor apocynin and the chemical AhR inhibitor α-naphtoflavone. These results indicated that BaP induced NCF1/p47^phox expression and subsequently enhanced superoxide anion production in PMA-treated human macrophages, in an AhR-dependent manner; such an NCF1/NADPH oxidase regulation by polycyclic aromatic hydrocarbons may participate in deleterious effects toward human health triggered by these environmental contaminants, including atherosclerosis and smoking-related diseases.     

The Drosophila melanogaster homolog of UBE3A is not imprinted in neurons

In mammals, expression of UBE3A is epigenetically regulated in neurons and expression is restricted to the maternal copy of UBE3A. A recent report claimed that Drosophila melanogaster UBE3A homolog (Dube3a) is preferentially expressed from the maternal allele in fly brain, inferring an imprinting mechanism. However, complex epigenetic regulatory features of the mammalian imprinting center are not present in Drosophila, and allele specific expression of Dube3a has not been documented. We used behavioral and electrophysiological analysis of the Dube3a loss-of-function allele (Dube3a^15b) to investigate Dube3a imprinting in fly neurons. We found that motor impairment (climbing ability) and a newly-characterized defect in synaptic transmission are independent of parental inheritance of the Dube3a^15b allele. Furthermore, expression analysis of coding single nucleotide polymorphisms (SNPs) in Dube3a did not reveal allele specific expression differences among reciprocal crosses. These data indicate that Dube3a is neither imprinted nor preferentially expressed from the maternal allele in fly neurons.     

甘蓝型油菜热激转录因子的克隆及表达分析

以甘蓝型纯系油菜为试材,用RT-PCR和RACE方法首次从油菜种子中获得油菜热激转录因子的cDNA全长序列,命名为BnHSFA4a,GenBank登录号为HQ435241。结果表明:该cDNA长1 667bp,编码1个具有389aa的蛋白质,该基因编码的氨基酸序列与拟南芥热激转录因子AtHSFA4a编码的氨基酸序列间相似度为82%。对34条编码不同热激转录因子的氨基酸序列进行多重比对,结果在100～190aa处序列间氨基酸总相似性超过60%,显示出较高的保守性。构建原核表达载体并成功表达出预期蛋白。半定量RT-PCR结果显示,该基因的表达先于油菜肌醇半乳糖苷合成酶(BnGOLS1)基因,符合该基因调控BnGOLS1的假设。推测AtHSFA4a基因可能通过调控BnGOLS1的表达量进而在油菜种子脱水耐性获得过程中发挥一定的作用。     

Sequence,expression divergence,and complementation of homologous <Emphasis Type="Italic">ALCATRAZ</Emphasis> loci in <Emphasis Type="Italic">Brassica napus</Emphasis>

The genomic era provides new perspectives in understanding polyploidy evolution, mostly on the genome-wide scale. In this paper, we show the sequence and expression divergence between the homologous ALCATRAZ (ALC) loci in Brassica napus, responsible for silique dehiscence. We cloned two homologous ALC loci, namely BnaC.ALC.a and BnaA.ALC.a in B. napus. Driven by the 35S promoter, both the loci complemented to the alc mutation of Arabidopsis thaliana, yet only the expression of BnaC.ALC.a was detectable in the siliques of B. napus. Sequence alignment indicated that BnaC.ALC.a and BolC.ALC.a, or BnaA.ALC.a and BraA.ALC.a, possess a high level of similarity. The understanding of the sequence and expression divergence among homologous loci of a gene is of due importance for an effective gene manipulation and TILLING (or ECOTILLING) analysis for the allelic DNA variation at a given locus. S. Hua and I. H. Shamsi contributed equally to this work.     

Hydrodynamics and mass transfer in miniaturized bubble column bioreactors

Miniaturized bubble columns (MBCs) have different hydrodynamics in comparison with the larger ones, but there is a lack of scientific data on MBCs. Hence, in this study, the effect of gas hold-up, flow regimes, bubble size distribution on volumetric oxygen mass transfer coefficient at different pore size spargers and gas flow rates in MBCs in the presence and absence of microorganisms were investigated. It was found that flow regime transition occurred around low gas flow rates of 1.18 and 0.85 cm/s for small (16–40 µm) and large (40–100 µm) pore size spargers, respectively. Gas hold-up and K_La in MBC with small size sparger were higher than those with larger one, with an increasing effect in the presence of microorganisms. A comparison revealed that the wall effect on the flow regime and gas hold-up in MBCs was greater than bench-scale bubble columns. The K_La values significantly increased up to tenfold using small pore size sparger. In the MBC and stirred tank bioreactors, the maximum obtained cell concentrations were OD₆₀₀ of 41.5 and 43.0, respectively. Furthermore, it was shown that in MBCs, higher K_La and lower turbulency could be achieved at the end of bubbly flow regime.