Stability of stationary distributions in a space-dependent population growth process

We consider a spatial population growth process which is described by a reaction-diffusion equation c(x)u _t = (a ²(x)u _x ) _x +f(u), c(x) >0, a(x) > 0, defined on an interval [0, 1] of the spatial variable x. First we study the stability of nonconstant stationary solutions of this equation under Neumann boundary conditions. It is shown that any nonconstant stationary solution (if it exists) is unstable if a _xx0 for all x[0, 1], and conversely ifa _xx>0 for some x[0, 1], there exists a stable nonconstant stationary solution. Next we study the stability of stationary solutions under Dirichlet boundary conditions. We consider two types of stationary solutions, i.e., a solution u ₀(x) which satisfies u ₀ x0 for all x[0, 1] (type I) and a solution u ₀(x) which satisfies u _0x = 0 at two or more points in [0, 1] (type II). It is shown that any stationary solution of type I [type II] is stable [unstable] if a _xx 0 [a _xx 0] for all x[0, 1]. Conversely, there exists an unstable [a stable] stationary solution of type I [type II] if a _xx <0 [a _xx >0] for some x[0, 1].     

Rat uterus anastomoses in a single and a double layer

The Authors display their results on microsurgical operations in rat's uteri. After having described the instruments and methods used, the surgical techniques and the differences between a single and a double layer suture are discussed. However the formation of intraoperative adherences, which can damage the functional results of the intervention, is studied. And what's more the mean number of live born foetuses is seen as an attainable parameter for future validations.     

Stability and distribution of stationary states in glycolysis

The steady-state concentration distributions of glycolytic metabolites are predicted. The dependence of distribution stability on kinetic parameters is evaluated.     

Stability and distribution of stationary concentrations in the Krebs cycle

Stable steady-state concentrations of the Krebs cycle intermediates were evaluated as functions of kinetic parameters of individual enzymes. The steady-state distributions of the intermediates are predicted.     

Mechanical double layer model for Saccharomyces Cerevisiae cell wall

The elastic modulus of the Baker’s yeast (Saccharomyces cerevisiae) cell wall reported in studies using atomic force microscopy (AFM) is two orders of magnitude lower than that obtained using whole cell compression by micromanipulation. Using finite element modelling, it is shown that Hertz-Sneddon analysis cannot be applied to AFM indentation data for single layer core–shell structures. In addition, the Reissner solution for shallow homogeneous spheres is not appropriate for thick walls such as those of yeast cells. In order to explain yeast compression measurements at different length scales, a double layer wall model is presented considering a soft external layer composed of mannoproteins, and a stiff inner layer of β-glucan fibres and chitin. Under this model, previous AFM studies using sharp indenters provide reasonable estimates of the external layer elastic modulus, while micromanipulation provides the total stiffness of the cell wall. Data from both measurements are combined to estimate the mechanical properties of the inner stiff layer.     

Behavior of a dust grain in the double layer of an electric probe in a gas-discharge plasma

Equations for the motion of an individual dust grain in the double layer of a negatively charged cylindrical probe in a glow discharge plasma are derived and solved numerically. The distribution of the electric potential near the probe is determined, and the grain charge is calculated as a function of the distance from the probe for different probe potentials. The trajectories of grains with different initial energies are traced. An analysis of the grain trajectories shows that, at a certain distance from the probe, high-energy grains may be recharged; i.e., the grain charge may change sign. The grains are found to have no direct effect on the probe current in a dusty plasma of a glow discharge.     

Probing the double layer: effect of image forces on AFM

Force probes such as AFM tips or laser trap latex beads have a dielectric constant much less than that of the water that they displace. Thus when a probe approaches a charged surface under water it will be repelled simply based upon the image forces, and these can be of nN magnitude.     

9-Amino-acridine as a probe of the electrical double layer associated with the chloroplast thylakoid membranes

Chloroplasts washed with monovalent cations are found to quench 9-amino-acridine fluorescence after resuspension in a cation-free medium. This quenching occurs in the absence of a high energy state and can be reversed by the addition of salts. The effectiveness of these salts is related to the charge carried by the cations and appears to be essentially independent of the associated anions. The order of effectiveness is polyvalent > divalent > monovalent, and virtually no variation is found within the groups of monovalent cations and divalent cations tested. Furthermore, choline and lysine are as effective as alkali metal cations, and lysyl-lysine is almost as effective as alkaline earth metal cations. These results are consistent with an effect mediated by the electrical double layer at the membrane surface rather than chemical bonding, and can be qualitatively explained in terms of the Gouy-Chapman theory.It appears that 9-amino-acridine acts as a diffusible monovalent cation which increases its fluorescence when displaced from the diffuse layer adjacent to the negatively charged membrane surface. The 9-amino-acridine fluorescence changes have been experimentally correlated with the cation-induced chlorophyll a fluorescence changes also observed with isolated chloroplasts.     

Stability switches and double Hopf bifurcation in a two-neural network system with multiple delays

Time delay is an inevitable factor in neural networks due to the finite propagation velocity and switching speed. Neural system may lose its stability even for very small delay. In this paper, a two-neural network system with the different types of delays involved in self- and neighbor- connection has been investigated. The local asymptotic stability of the equilibrium point is studied by analyzing the corresponding characteristic equation. It is found that the multiple delays can lead the system dynamic behavior to exhibit stability switches. The delay-dependent stability regions are illustrated in the delay-parameter plane, followed which the double Hopf bifurcation points can be obtained from the intersection points of the first and second Hopf bifurcation, i.e., the corresponding characteristic equation has two pairs of imaginary eigenvalues. Taking the delays as the bifurcation parameters, the classification and bifurcation sets are obtained in terms of the central manifold reduction and normal form method. The dynamical behavior of system may exhibit the quasi-periodic solutions due to the Neimark- Sacker bifurcation. Finally, numerical simulations are made to verify the theoretical results.     

Monte Carlo simulation of the double layer at an electrode including the effect of a dielectric boundary

Monte Carlo values of the density profiles and related properties of the double layer formed by an electrolyte near a charged electrode are reported for the cases where the electrode has a dielectric coefficient greater, equal, and smaller than that of the electrolyte that causes a surface polarization that can be represented by electrostatic images. As expected, compared to the case where there is no dielectric boundary the ions near the electrode are attracted or repelled by the electrode if the dielectric coefficient is greater or smaller, respectively, than that of the electrolyte. This effect is most pronounced near the electrode and is stronger for 2:2 electrolytes than for 1:1 electrolytes. For both monovalent and divalent ions the effect of the dielectric boundary is stronger at low concentrations.     

Effect of spatial inhomogeneity in dielectric permittivity on DNA double layer formation

In solutions of tetramethylammonium (TMA+) DNA (double stranded) without added low-molecular-weight salt, the counterion radial density is calculated using the cylindrical Poisson-Boltzmann equation with a distance-dependent quasimacroscopic dielectric permittivity. Comparisons with small-angle neutron scattering data indicate that any inhomogeneity in dielectric permittivity is confined to one or two solvent layers from the DNA surface. At least for TMA+, which may be too large to penetrate the grooves of DNA to any significant extent, dielectric inhomogeneity modeled in this way has no detectable effect on the radial distribution.     

A non-destructive culturing and cell sorting method for cardiomyocytes and neurons using a double alginate layer

A non-destructive method of collecting cultured cells after identifying their in situ functional characteristics is proposed. In this method, cells are cultivated on an alginate layer in a culture dish and released by spot application of a calcium chelate buffer that locally melts the alginate layer and enables the collection of cultured cells at the single-cell level. Primary hippocampal neurons, beating human embryonic stem (hES) cell-derived cardiomyocytes, and beating hES cell-derived cardiomyocyte clusters cultivated on an alginate layer were successfully released and collected with a micropipette. The collected cells were recultured while maintaining their physiological function, including beating, and elongated neurites. These results suggest that the proposed method may eventually facilitate the transplantation of ES- or iPS-derived cardiomyocytes and neurons differentiated in culture.     

Perturbations in the sof the double layer at an enzymic surface

The surfaces of cells are both charged and enzymically active; furthermore, mass transfer across the surface is occurring constantly. These dynamic processes are capable of perturbing the equilibrium double layer that would be present in the absence of mass transfer and reactions. This paper investigates the influence of enzymic surface reactions on the structure of the diffuse double layer, and conversely the influence of potential on concentration profiles and reaction rates. It is shown that (1) mobility differences in substrate and product can lead to more or less extended double layers and to extrema in the potential profile depending on kinetic factors such as reaction rate and ion mobility of substrate and product and (2) surface reactions can act as a surface concentration switch or amplifier wherein comparatively small variations in bulk concentration produce large variations in surface concentration. Deviations from equilibrium potentials are described by a dimensionless parameter involving reaction rate, ionic strength and the substrate-product mobility difference. Deviations from equilibrium concentrations are described by two electrostatic reaction-diffusion moduli. One of these expresses the effect of differing ion mobilities between substrate and product. Depending on the sign of this parameter, the surface substrate concentration may be either displaced above or below the case (usually hypothetical) of equal ion mobilities. The physiological significance of a reaction or mass flow perturbed surface potential is discussed.     

DNA/polyvinyl alcohol interpenetrating polymer network as stationary phase for thin layer chromatography

Natural DNA was introduced to thin layer chromatography (TLC) with an aim to separate chemicals like DNA-affinity compounds and enantiomers. By cross-linking polyvinyl alcohol (PVA) with glutaraldehyde (GA) and subsequent cross-linking DNA with a UV irradiation, a DNA/PVA interpenetrating polymer network (IPN) is formed and was used to coat the surface of the porous silica particles of the TLC. Three typical DNA-binding compounds and eight amino acid enantiomers were used as model chemicals to investigate the chromatographic behavior of the modified TLC, and high separation efficiency was observed in both classes of the chemicals. On the practical side, the DNA-modified TLC have high prospects in diverse applications, including efficacy evaluation of a medicine, toxicity assessment of a pollutant at the molecular level, as well as separation of enantiomers such as dyes, amino acids, peptides, proteins, nucleotides, and drugs.     

Comparison of double layer potentials in lipid monolayers and lipid bilayer membranes

Summary It is shown that the Gouy-Chapman double layer analysis adequately describes the variation of the surface potential of monolayers of acidic natural lipids over a wide range of surface charge density and salt concentration. It is also shown that the potential which initially appears when an electrolyte gradient is rapidly imposed across a bilayer membrane is due to a difference in the double layer potentials on the two sides of the membrane. This conclusion follows from the fact that the observed bilayer potentials arise much more rapidly than can be accounted for by charge migration across the membrane and from the observation that the bilayer membrane concentration potentials, when measured immediately after establishment of a gradient, are equal to the surface potential change observed when the subphase concentration of a monolayer of the same lipid is changed by an amount equal to the gradient across the bilayer. The bilayer potential and monolayer potential changes, so measured, agree in a number of different electrolyte solutions over a wide range of electrolyte concentrations and surface charge densities. Because of this agreement and the applicability of the Gouy theory to monolayers, initial bilayer potentials may be calculated if the composition of the mixture used to form the membrane is known, provided that the pK's and areas of such components are available. In the absence of this information, membrane potentials may be calculated from electrophoretic data on the membrane lipid mixture; the conditions under which the latter approach is possible have been determined. The experimental results indicate that the composition of monolyers and bilayers spread from the same lipid mixture in decane are very similar, that the composition of the two types of film closely resembles the composition of the solution used to generate them, and that bilayer membranes are close-packed. The evidence further indicates that if any hydrocarbon solvent remains in these bilayers, it must be so situated that it contributes little, if anything, to the surface area. The steady state potential in the bilayer membrane system is frequently not identical with the initial potential which supports the hypothesis that in many cases only a fraction of the electrical conductance of unmodified membranes is caused by the ions which constitute the bulk electrolyte. An expression for the relationship between diffusion and double layer potentials has been derived which shows that, in the absence of any intrinsic selectivity of the hydrocarbon region of the membrane for hydrogen, hydroxyl, or impurity, the two potentials should be identical.     

Oblique double layer potentials for the direct and inverse problems of electrocardiology

A mathematical analysis of a model of the cardiac bioelectric sources generating the potential field in a bounded conducting volume is carried out. A boundary integral representation of the potential is given, which shows that, if the anisotropy of the cardiac muscle is taken into account, the bioelectric sources are characterized by an “oblique” double layer on the excitation wavefront. Boundedness conditions for the potential and jump relationships across the front are investigated. Uniqueness results for the inverse problem (i.e. the determination of the wavefront surface, given the potential on the volume boundary) are established.