On periodic cohort solutions of a size-structured population model

 We consider a size-structured population model with discontinuous reproduction and feedback through the environmental variable ‘substrate’. The model admits solutions with finitely many cohorts and in that case the problem is described by a system of ODEs involving a bifurcation parameter β. Existence of nontrivial periodic n-cohort solutions is investigated. Moreover, we discuss the question whether n cohorts (n≧2) with small size differences will tend to a periodic one-cohort solution as t→∞. Received 16 March 1995; received in revised form 7 January 1997     

Galerkin-Ritz procedures for approximate solutions to systems of reaction-diffusion equations

For any essentially nonlinear system of reaction-diffusion equations of the generic form ∂c_i/∂t=D_i∇²c_i+Q_i(c,x,t) supplemented with Robin type boundary conditions over the surface of a closed bounded three-dimensional region, it is demonstrated that all solutions for the concentration distributionn-tuple function c=(c ₁(x,t),...,c _n (x,t)) satisfy a differential variational condition. Approximate solutions to the reaction-diffusion intial-value boundary-value problem are obtainable by employing this variational condition in conjunction with a Galerkin-Ritz procedure. It is shown that the dynamical evolution from a prescribed initial concentrationn-tuple function to a final steady-state solution can be determined to desired accuracy by such an approximation method. The variational condition also admits a systematic Galerkin-Ritz procedure for obtaining approximate solutions to the multi-equation elliptic boundary-value problem for steady-state distributions c=−c(x). Other systems of phenomenological (non-Lagrangian) field equations can be treated by Galerkin-Ritz procedures based on analogues of the differential variational condition presented here. The method is applied to derive approximate nonconstant steady-state solutions for ann-species symbiosis model.     

Visualisation of xylem sap flow direction in isolated fine lateral roots and estimation of the xylem sap osmotic potential

Xylem sap outflow from fine lateral roots (FLRs) isolated from hydroponically grown young maize (Zea mays L.) plants was visualized by local brightening of test solutions contrasted with purified Indian ink particles. Flow into the vessels was indicated by the adsorption of Evans Blue in their walls. The fraction of the FLRs able to exude xylem sap in a mineral medium with 30 mM mannitol decreased with increasing incubation time. This change was strongly retarded, when the FLRs were incubated in a medium containing glucose instead of mannitol. There was a broad range of variation of the osmotic potential of the test solutions (Ψ_so), wherein the fraction of the FLRs showing an initially reversed flow of the xylem sap varied between zero and unity. A median (M) of the osmotic potential of the xylem sap in FLRs (Ψ_sx) was estimated. It represents the value of Ψ_so that was lower than Ψ_sx in half of the roots of a sample before their transfer to the test solutions (Ψ_sxo). M was dependent on the osmotic potential of the medium used for growth or pre-incubation of the FLRs. Its value was not dependent on the molecular size of the osmolytes used to adjust Ψ_so, including dextran 8, which is excluded from cell walls. In all of the studied plants, M was lower than the osmotic potential of the xylem sap collected from the root before isolation of the FLRs. To explain this finding it is assumed that FLRs with Ψ_sxo > M had a higher hydraulic conductivity and a larger volume contributed to the exuded sap than those with Ψ_sx < M.     

Time course solutions of the Sax-Markov binary eurejoining/misrejoining model of DNA double-strand breaks

The Sax-Markov binary eurejoining/misrejoining (SMBE) model is a stochastic representation of Sax’s breakage-and-reunion mechanism of misrejoining DNA double-strand breaks (DSBs). In this model, to approximate DSB misrejoining probabilities that decrease with increasing distance, the nucleus is treated as a collection ofη isolated nuclear subvolumes called sites; DSB free ends within the same site interact with a probability that is independent of distance, and DSB free ends within different sites never interact. In our previous work, SMBE steady-state solutions were used to estimateη from a combination of high-dose PFGE (pulsed-field gel electrophoresis) data and moderate-dose chromosomal aberration data. Here, analytic SMBE transient solutions (i.e., time courses of DSBs and misrejoinings) are derived and used to estimateη from various sets of misrejoining DSB kinetic data. The time courses are multiexponentials with rate constantsκ, 6κ, 15κ, ... j(2j–1)κ corresponding to different nuclear site states and not different types of DSBs. For example, theκ component corresponds to nuclear sites with two DSB free ends and thus only one possible rejoining interaction, and the 6κ component corresponds to sites with four DSB free ends and thus six (four choose two) potential rejoining interactions – four of these six potential interactions lead to a final state of two misrejoinings and the other two of six lead to a final state of correct repair (unrejoinable DSBs are not represented in the SMBE model). The SMBE time course solutions provide site number estimates that fall in the range ofη≈10–100 for premature chromosome condensation (PCC) data andη≈1000 for PFGE data. Received: 23 December 1999 / Accepted: 1 July 2000     

Hydrolysis of organic phosphates by corn and soybean roots

Because of the importance of organic phosphates as sources of P for plants, this work was performed to study the hydrolysis of nine organic phosphates by sterile, intact corn (Zea mays L.) and soybean (Glycine max L.) roots. Results showed that the rates of hydrolysis ofp-nitrophenyl phosphate (PNP) in buffered solutions by roots of three varieties of corn and three varieties of soybean ranged from 13 to 22 μmol PO₄−P g⁻¹ root h⁻¹ and from 2.1 to 2.2 μmol PO₄−P 0.1 g⁻¹ root h⁻¹, respectively. The average rate of hydrolysis of PNP in nonbuffered solutions was 2- to 3-fold lower for corn roots and 6- to 10-fold lower for soybean roots as compared with those obtained with buffered solutions. The orthophosphate released from hydrolysis of organic P compounds in buffered solutions during a 48-h incubation of corn roots showed that the maximum rate of hydrolysis of PNP was 4 to 6 times greater than the commonly used substrates: α- and β-glycerophosphates, phenolphthalein diphosphate, and glucose-6-phosphate. The rates of hydrolysis of glucose-6-phosphate and glucose-1-phosphate were similar and about 6- to 12-fold lower than that of PNP. Phosphoethanolamine and phosphocholine were hydrolyzed slightly, ando-carboxyphenyl phosphate was not hydrolyzed. The rates of hydrolysis of organic P compounds in nonbuffered solutions by corn and soybean roots were 1 to 3 and 1 to 10 times lower than those in buffered solutions, respectively. The trends in rates of hydrolysis by soybean roots of buffered organic P substrates were similar to those observed with corn roots, with the exception of glucose-1-phosphate and phosphoethanolamine.     

Photobiochemistry of folates: A photochemical reduction of folic acid

Exposure of deaerated folic acid solutions containing an electron donor to UV radiation (310–390 nm, I = 0.4 W m⁻²) induced formation of dihydrofolic acid (DHFA), a photoexcitation which gave tetrahydrofolic acid (THFA). Only DHFA was formed in the presence of EDTA (E′_o = +0.40 V), while the presence of stronger reductants—NADH (E′_o = −0.32 V) and boron hydride (E′_o = −0.48 V)—induced photoreduction to THFA. It was demonstrated that UV radiation had no effect on the THFA formylation, giving the coenzyme 5,10-methenyltetrahydrofolic acid and its transformation into another coenzyme, 5-formyltetrahydrofolic acid.     

Impairment of mineralization by metavanadate and decavanadate solutions in a fish bone-derived cell line

Vanadium, a trace metal known to accumulate in bone and to mimic insulin, has been shown to regulate mammalian bone formation using in vitro and in vivo systems. In the present work, short- and long-term effects of metavanadate (containing monomeric, dimeric, tetrameric and pentameric vanadate species) and decavanadate (containing decameric vanadate species) solutions on the mineralization of a fish bone-derived cell line (VSa13) were studied and compared to that of insulin. After 2 h of incubation with vanadate (10 μM in monomeric vanadate), metavanadate exhibited higher accumulation rates than decavanadate (6.85 ± 0.40 versus 3.95 ± 0.10 μg V/g of protein, respectively) in fish VSa13 cells and was also shown to be less toxic when applied for short periods. In longer treatments with both metavanadate and decavanadate solutions, similar effects were promoted: stimulation of cell proliferation and strong impairment (75%) of extracellular matrix (ECM) mineralization. The effect of both vanadate solutions (5 μM in monomeric vanadate), on ECM mineralization was increased in the presence of insulin (10 nM). It is concluded that chronic treatment with both vanadate solutions stimulated fish VSa13 cells proliferation and prevented ECM mineralization. Newly developed VSa13 fish cells appeared to be appropriate in the characterization of vanadate effects on vertebrate bone formation, representing a good alternative to mammalian systems. Daniel M. Tiago and Vincent Laizé1 contributed equally to this work.     

Evolution of discontinuous solutions to transport equations in stellarators

It was shown earlier that, in the range of rare collisions, transport equations for stellarators allow steady discontinuous solutions for the ambipolar electric field and for the plasma density and temperature gradients. Moreover, such solutions are non-single-valued; that is, their explicit form depends on the initial values of the ambipolar electric field. The time-independent transport equations are derived under the conventional quasineutrality condition; i.e., it is assumed that the electron and ion densities, N _e and N _i , are related by the relationship N _e = ZN _i (where Z is the ion charge number). In other words, the plasma charge density is assumed to be much less than the product e _i N _i . Under typical conditions, the corresponding inequality is satisfied by a large margin. However, if the electric field E has discontinuities, then it can be seen from the equation ▿·E = 4πρ that, at the discontinuity points, the charge density becomes infinite and the relationship N _e = ZN _i fails to hold, so it is necessary to replace it with N _e = ZN _i + ρ/e _e . In the transport equations, this latter replacement produces additional terms, proportional to the second radial derivative of the field E. With these additional terms, the steady solutions are modified substantially. First, the ambipolar field and the derivatives of the density and temperatures all become continuous functions of the coordinates, a result that seems to be quite obvious. The second, not-so-obvious result is that the steady solutions become single-valued, i.e., independent of the initial values of the ambipolar electric field. It turns out that, in this case, two regimes are possible, depending on the values of the plasma parameters. In the first regime, the solution is unique and is independent of the initial conditions. In the second regime, two steady solutions can exist, depending on the initial conditions. One of the solution is similar to that obtained in the first regime, and the other differs from the first one both in the ambipolar field profile and in the dependence of the density and temperatures on the minor plasma radius. It cannot be excluded that different plasma confinement modes revealed in experiments are associated with the existence of such solutions.     

The effect of the osmotic potential and specific ion concentration of the nutrient solution on the uptake and reduction of nitrate by barley seedlings

Summary Short-term absorption experiments were conducted with intact barley (Hordeum vulgare L.) seedlings to observe the effects of the osmotic potential (Ψ^π) and salt species on nitrate uptake andin vivo nitrate reduction. The experiments consisted of growing barley seedlings for 5 days in complete nutrient solutions salinized to (Ψ^π) levels of −0.6, −1.8, −3.0, −4.2, and −5.4 bars with NaCl, CaCl₂ or Na₂SO₄. After the absorption period, the seedlings were separated into shoots and roots, weighed, then analyzed for NO₃. The nutrient solutions were sampled for NO₃ analysis each day immediately before renewing the solutions. The accumulative loss of NO₃ from the solutions was considered to be uptake whereas NO₃ reduction was the difference between uptake and seedling content. Lowering the (Ψ^π) of the nutrient solutions resulted in decreased concentrations of NO₃ in the plant, little or no effect (except at the lowest (Ψ^π) level) on uptake, and increased nitrate reductase activity. Increased rates of NO₃ reduction were in particular associated with the Cl concentration of the nutrient solution.     

Comparison of different techniques for gene transfer into mature and immature tobacco pollen

The particle gun, cocultivation withAgrobacterium tumefaciens, and imbibition in DNA solutions were compared as methods to transfer DNA into mature and immature pollen ofNicotiana tabacum. Bombardment of mature pollen with the β-glucuronidase gene cloned behind the pollen-specific PA2 promoter of the chalcone isomerase gene ofPetunia hybrida resulted in the expression of the β-glucuronidase gene in 0.025% of the pollen grains. Bombardment of younger stages followed byin vitro maturation also resulted in the formation of mature pollen that expressed β-glucuronidase, although at a lower frequency. Cocultivation of pollen duringin vitro maturation orin vitro germination withAgrobacterium tumefaciens did not yeild β-glucuronidase-expressing pollen. In these cases, an intron-containing β-glucuronidase gene was used which effectively prevented β-glucuronidase expression in the bacteria. Imbibition of mature, dry pollen in various DNA solutions of the same constructs also did not lead to the formation of β-glucuronidase expressing pollen.     

Effect of triterpenoid glycosides on α- and β-amylase activity and total protein content in wheat seedlings

Influence of the aleanolic acid glycosides from Silphium perfoliatum L. (silphioside B, C, E and G) and their progenins on the amylase activity and total protein content in wheat seedlings was studied. Treatment of the Triticum aestivum L. seeds with 1–10 μM water solutions of mono- and diglycosides (mono- and bisdesmosines) elevated the α-amylase and total amylase activities in seedlings. Silphioside E containing three glucose moieties in its molecule did not change α-amylase activity, but it did if bis-triglycoside acetylated carbohydrate (as in silphioside C). Effects of 5–10 μM solutions of the active glycosides was comparable with that of exogenous gibberellin A₃ and 6-benzylaminopurine.     

Conformational studies of peptides representing a segment of TM7 from H+-VO-ATPase in SDS micelles

The conformation of a transmembrane peptide, sMTM7, encompassing the cytoplasmic hemi-channel domain of the seventh transmembrane section of subunit a from V-ATPase from Saccharomyces cerevisiae solubilized in SDS solutions was studied by circular dichroism (CD) spectroscopy and fluorescence spectroscopy of the single tryptophan residue of this peptide. The results show that the peptide adopts an α-helical conformation or aggregated β-sheet depending on the peptide-to-SDS ratio used. The results are compared with published data about a longer version of the peptide (i.e., MTM7). It is concluded that the bulky, positively charged arginine residue located in the center of both peptides has a destabilizing effect on the helical conformation of the SDS-solubilized peptides, leading to β-sheet formation and subsequent aggregation.     

Ion Channels Formed by NB,an Influenza B Virus Protein

The influenza B virus protein, NB, was expressed in Escherichia coli, either with a C-terminal polyhistidine tag or with NB fused to the C-terminus of glutathione S-transferase (GST), and purified by affinity chromatography. NB produced ion channel activity when added to artificial lipid bilayers separating NaCl solutions with unequal concentrations (150–500 mm cis, 50 mm trans). An antibody to a peptide mimicking the 25 residues at the C-terminal end of NB, and amantadine at high concentration (2–3 mm), both depressed ion channel activity. Ion channels had a variable conductance, the lowest conductance observed being approximately 10 picosiemens. At a pH of 5.5 to 6.5, currents reversed at positive potentials indicating that the channel was more permeable to sodium than to chloride ions (P_Na/P_Cl∼ 9). In asymmetrical NaCl solutions at a pH of 2.5, currents reversed closer to the chloride than to the sodium equilibrium potential indicating that the channel had become more permeable to chloride than to sodium ions (P_Cl/P_Na∼ 4). It was concluded that, at normal pHs, NB forms cation-selective channels. Received: 6 March 1995/Revised: 17 November 1995     

Existence of traveling wave solutions in a diffusive predator-prey model

 We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R ⁴ and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R ⁴ . The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem. Received: 25 May 2001 / Revised version: 5 August 2002 / Published online: 19 November 2002 RID="*" ID="*" Research was supported by the National Natural Science Foundations (NNSF) of China. RID="*" ID="*" Research was partially supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. On leave from the Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada. Mathematics Subject Classification (2000): 34C35, 35K57 Key words or phrases: Traveling wave solution – Wazewski set – Shooting argument – Hopf bifurcation Acknowledgements. We would like to thank the two referees for their careful reading and helpful comments.     

Biosorption of Cd, Cu, Pb, and Zn from aqueous solutions by the fruiting bodies of jelly fungi (Tremella fuciformis and Auricularia polytricha)

In this study, dried and humid fruiting bodies of Tremella fuciformis and Auricularia polytricha were examined as cost-effective biosorbents in treatment of heavy metals (Cd²⁺, Cu²⁺, Pb²⁺, and Zn²⁺) in aqueous solution. The humid T. fuciformis showed the highest capacity to adsorb the four metals in the multi-metal solutions. The Pb²⁺ adsorption rates were 85.5%, 97.8%, 84.8%, and 91.0% by dried T. fuciformis, humid T. fuciformis, dried A. polytricha, and humid A. polytricha, respectively. The adsorption amount of Pb²⁺ by dried and humid T. fuciformis in Cd²⁺ + Pb²⁺, Cu²⁺ + Pb²⁺, Pb²⁺ + Zn²⁺, Cd²⁺ + Cu²⁺ + Pb²⁺, and Cd²⁺ + Zn²⁺ + Pb²⁺ solutions were not lower than that in Pb²⁺ solutions. The results suggested that in humid T. fuciformis, Cd²⁺, Cu²⁺, and Zn²⁺ promoted the Pb²⁺ adsorption by the biomass. In the multi-metal solutions of Cd²⁺ + Cu²⁺ + Pb²⁺ + Zn²⁺, the adsorption amount and rates of the metals by all the test biosorbents were in the order of Pb²⁺ > Cu²⁺ > Zn²⁺ > Cd²⁺. Compared with the pseudo first-order model, the pseudo second-order model described the adsorption kinetics much better, indicating a two-step biosorption process. The present study confirmed that fruiting bodies of the jelly fungi should be useful for the treatment of wastewater containing Cd²⁺, Cu²⁺, Pb²⁺, and Zn²⁺.     

Water availability effects on antioxidant enzyme activities, lipid peroxidation, and reducing sugar contents of alfalfa (Medicago sativa L.)

To understand alfalfa (Medicago sativa L.) reactions to osmotic stress, solutions with −0.5, −1 and −1.5 MPa osmotic potentials using PEG (Poly ethyleneglycol) and distilled water as control were prepared. In a germination test, eleven alfalfa cultivar seeds were allowed to germinate in these solutions. M. sativa cv. Yazdi and M. sativa cv. Gharayonje, selected as tolerant and sensitive cultivars, respectively, and were used for further studies. In all PEG solutions, root and shoot dry weights decreased in both cultivars. Under different levels of osmotic stress, root to shoot ratio increased significantly in Yazdi, whereas this parameter showed no significant differences in Gharayonje. Yazdi cultivar also showed higher activities of SOD (Superoxide dismutase), APX (Ascorbate peroxidase), CAT (Catalase), POD (Peroxidase), and higher reducing sugar contents of leaves in comparison with Gharayonje. These higher antioxidant activities help the tolerant cultivar to decrease oxidative damages of osmotic stress to membrane lipids as compared with its sensitive counterpart. As a result, electrolyte leakage and the amounts of MDA (Malondialdehyde), were higher in Gharayonje. This study highlights the importance of enzymatic and non-enzymatic antioxidant systems in scavenging reactive oxygen species which is caused by osmotic stress. It is seems that antioxidant systems are more active in tolerant cultivars than those of sensitive ones.     

Relevance of Rheological Properties of Sodium Alginate in Solution to Calcium Alginate Gel Properties

The purpose of this study is to determine whether sodium alginate solutions’ rheological parameters are meaningful relative to sodium alginate’s use in the formulation of calcium alginate gels. Calcium alginate gels were prepared from six different grades of sodium alginate (FMC Biopolymer), one of which was available in ten batches. Cylindrical gel samples were prepared from each of the gels and subjected to compression to fracture on an Instron Universal Testing Machine, equipped with a 1-kN load cell, at a cross-head speed of 120 mm/min. Among the grades with similar % G, (grades 1, 3, and 4), there is a significant correlation between deformation work (L _E) and apparent viscosity (η _app). However, the results for the partial correlation analysis for all six grades of sodium alginate show that L _E is significantly correlated with % G, but not with the rheological properties of the sodium alginate solutions. Studies of the ten batches of one grade of sodium alginate show that η _app of their solutions did not correlate with L _E while tan δ was significantly, but minimally, correlated to L _E. These results suggest that other factors—polydispersity and the randomness of guluronic acid sequencing—are likely to influence the mechanical properties of the resultant gels. In summary, the rheological properties of solutions for different grades of sodium alginate are not indicative of the resultant gel properties. Inter-batch differences in the rheological behavior for one specific grade of sodium alginate were insufficient to predict the corresponding calcium alginate gel’s mechanical properties.     

A field theory of neural nets: I: Derivation of field equations

A model is described in which neural activity is represented by a field quantity ϕ, with the neurons as the sources of ϕ. It is shown that, with certain physically realistic assumptions, ϕ satisfies a moderately nonlinear differential equation. It is also found that this equation is isotropic and of second order if and only if the neuronal connectivity has a dependence on distance,p, of the formp ⁻¹ e ^−1/2βp .     

Stability of periodic travelling wave solutions of a nerve conduction equation

Summary Nagumo's nerve conduction equation has travelling wave solutions of pulse type and periodic wave type. We consider the stability of the latter ones. We denote byL(c) the minimum spatial period of a periodic travelling wave solution whose propagation speed isc. It is shown that this travelling wave solution is unstable ifL′(c)<0.