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.     

Stochastic prey-predator relationships: A random differential equation approach

A stochastic model describing two interacting populations is considered. The model involves a random differential equation of the form dX/dt=A(t)X+Y(t) where the random matrixA and vectorY represent the interactions and growth rates respectively andX is a (random) vector the components of which are the logarithms of the population's sizes. An expression for the solution of the above equation is obtained whence its statistical properties can be determined. Alternatively, a method based on Liouville's theorem is used to obtain the probability distribution of the solution. Application of both methods to simple cases indicates that the random solution is asymptotically stable in the mean even when the solution to the associated deterministic equation is not, viz. in the absence of self interactions.     

Velocity distribution on the membrane of a tank-treading red blood cell

The kinematics of an area-conserving tank-treading disk-shaped red blood cell membrane is studied using the stream function method suggested by Secomb and Skalak (Q. Jl Mech. appl. Math. 35, Pt 2, 233–247, 1982). Two simple area-conserving velocity fields are superimposed to satisfy the continuity condition at the curved edges of the disk. A differential equation for the trajectory of any material point of the membrane is derived. The requirement of synchrony of the cycle for all membrane points leads to an integral equation which determines a magnitude function. An approximate solution is made possible by assuming small trajectory deflections.     

A monograph of <Emphasis Type="Italic">Ascogrammitis</Emphasis>, a new genus of grammitid ferns (Polypodiaceae)

This paper describes Ascogrammitis, a new genus of grammitid ferns formerly combined under Terpsichore. Seventeen species are recognized, including five new ones: A. clavigera, A. colombiensis, A. loxensis, A. oxapampensis, and A. tungurahuae. New combinations are made for A. alan-smithii, A. anfractuosa, A. angustipes, A. athyrioides, A. clathrata, A. cuencana, A. david-smithii, A. dilatata, A. nana, A. pichinchae, A. pichinchensis, A. stuebelii, and a lectotype is chosen for Polypodium induens. A key is provided to distinguish the species, and illustrations are provided for 12 species. The genus occurs primarily in neotropical cloud forests, with the greatest diversity in the Andes. Ascogrammitis is one of two monophyletic groups of grammitid ferns that are consistently associated with Acrospermum, an epibiotic bitunicate ascomycete that produces black clavate fruiting bodies.     

Antifungal activity of a novel chromene dimer

The activity on Aspergillus spp. growth and on ochratoxin A production of two novel chromene dimers (3) was evaluated. The results of the bioassays indicate that the chromene dimer 3a inhibited mycelia growth by approximately 50% (EC₅₀) at 140.1 μmol L⁻¹ for A. niger, 384.2 μmol L⁻¹ for A. carbonarius, 69.1 μmol L⁻¹ for A. alliaceus and 559.1 μmol L⁻¹ for A. ochraceus. When applied at concentrations of 2 mmol L⁻¹, 3a totally inhibited the growth of all Aspergillus spp. tested. Furthermore, ochratoxin A production by A. alliaceus was reduced by about 94% with a 200 μmol L⁻¹ solution of this compound. A moderate inhibitory effect was observed for the analogous structure 3b on ochratoxin A production but not in mycelia growth. No inhibition was registered for compounds 2a and 2b, used as synthetic precursors of the dimeric species 3.     

Linearized oscillations in population dynamics

A linearized oscillation theorem due to Kulenović, Ladas and Meimaridou (1987,Quart. appl. Math. XLV, 155–164) and an extension of it are applied to obtain the oscillation of solutions of several equations which have appeared in population dynamics. They include the logistic equation with several delays, Nicholson's blowflies model as described by Gurney, Blythe and Nisbet (1980,Nature, Lond. 287, 17–21) and the Lasota-Wazewska model of the red blood cell supply in an animal. We also developed a linearized oscillation result for difference equations and applied it to several equations taken from the biological literature.     

A model of cell firing patterns during epileptic seizures

A simplified model is presented of the dynamics of excitatory and inhibitory neurons in the cerebral cortex. A key feature of the model is that neurons may cease to fire when strongly depolarized (spike inactivation). Computer simulations for different parameters reveal five classes of solutons: a) steady states in which neither excitatory nor inhibitory cells are active, b) steady states in which one or both types of cells fire repetitively, c) states in which one type of cell fluctuates rapidly between bursts of action potentials and inactivity due to strong depolarization, d) rhythmic activity in which both types of cells fire in unison followed by a period of spike inactivation and e) states similar to d but in which the inhibitory cells never produce action potentials. Solutions b, c, d, and e qualitatively resemble the different firing patterns observed during experimental seizures. It is shown that changes in those parameters that are functions of potassium concentration can induce changes in the type of solution. It is therefore proposed that the increase in extracellular potassium concentration during seizures may be responsible for the progressive changes observed in firing patterns and particularly for the transition from tonic to clonic patterns. A method is also outlined for testing the predictions of the model.     

Revision of the genus Adorodocia Brenske 1893 (Coleoptera: Scarabaeoidea: Rutelinae: Adoretini) endemic to Madagascar

Summary. The Adoretini of the Malagasy endemic genus Adorodocia Brenske 1893 is revised. Fourteen new species and one new subspecies are described and compared with their most closely related species: A. constricta n. sp., A. cuccodoroi n. sp., A. flava n. sp., A. liliae n. sp., A. marginata n. sp., A. peyrierasi n. sp., A. pseudoconstricta n. sp., A. pseudoflava n. sp., A. pseudostrigata n. sp., A. recta n. sp., A. robusta n. sp., A. sogai n. sp., A. vadoni n. sp., A. viettei n. sp. and A. vittaticollis flavipes n. ssp. The synonymy between Adoretus strigatus Waterhouse 1878, and Pseudadorodocia aenigma Arrow 1901, is confirmed. Thus, based on the results of this study, the genus Adorodocia includes 16 species, and one of them is represented by two subspecies. Diagnostic characters to separate the species in the genus deal mostly with the shape of parameres, color of body and legs, shape of pronotum and female eighth tergite, setation of pronotum and elytra. Key to species, diagnoses and distribution for each species are provided. Endophallus and female genitalia are illustrated for the first time for this genus.     

New species of Alaus Eschscholtz, 1829 (Coleoptera: Elateridae,Agrypninae, Hemirhipini)

Four new species of Alaus Eschscholtz, 1829 are described: A. cinnamomeus n. sp., A. latlpennls n. sp., A. serlceus n. sp. and A. thoracopunctatus n. sp. Three species removed from Chalcolepldlus Eschscholtz, 1829, are transferred to this genus: A. allcll (Pjatakowa, 1941) n. comb., A. haroldl (Candèze, 1878) n.comb. and A. unlcus (Fleutiaux, 1910) n. comb. The characters of external morphology of these seven species and male and female genitalia, when available, are described and illustrated. An identification key for all species of the genus is included: A. allcll (Pjatakowa, 1941) n. comb., A. calcarlpllosus Casari, 1996, A. cinnamomeus n. sp., A. haroldl (Candèze, 1878) n. comb., A. latlpennls n. sp., A. lusclosus (Hope, 1832), A. melanops Leconte, 1863, A. myops (Fabricius, 1801), A. nobllls Sallé, 1855, A. oculatus (Linnaeus, 1758), A. patrlclus (Candèze, 1857), A. plebejus Candèze, 1874, A. serlceus n. sp., A. thoracopunctatus n. sp., A. tricolor (Olivier, 1790), A. unlcus (Fleutiaux, 1910) n. comb., A. veracruzanus Casari, 1996 and A. zunianus Casey, 1893.     

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.     

Synthesis,spectral characterization,and in vitro antibacterial and antifungal activities of novel 1,3-thiazine-2-amines comprising morpholine nucleus

A collection of 4-(4-morpholinophenyl)-6-aryl-6H-1,3-thiazin-2-amines (20–28) were synthesized and their in vitro antimicrobial activity was investigated. Compound 21 against P. aeruginosa, 23 against B. subtilis, 24 against V. cholerae and P. aeruginosa, 26 against S. aureus and B. subtilis, 27 against B. subtilis and E. coli, and 28 against all tested bacterial strains exerted excellent antibacterial activity. Compound 20 against A. flavus and Rhizopus, 21, 26 against Rhizopus, 22, 27 against Mucor, 23 against A. flavus, 24 against both A. flavus and Mucor, 25 against all tested strains, and 28 against Rhizopus and M. gypseum exerted excellent antifungal activity.     

A derivation of a rote learning curve from the total uncertainty of a task

The derivation of H. D. Landahl’s learning curve (1941,Bull. Math. Biophysics,3, 71–77) from a single information-theoretical assumption obtained previously (Rapoport, 1956,Bull. Math. Biophysics,18, 317–21) is extended to obtain the entire family of such curves with the number of stimuliM (to each of which one ofN responses is to be associated) as a parameter. No additional assumptions are required. The entire family thus appears as a function of a single free parameter,k, all other parameters being experimentally determined. The theory is compared with a set of experiments involving the learning of artificial languages. An alternative quasi-neurological model leading to the same equation is offered.     

The growth analysis of water hyacinth,Eichhornia crasipes solms,in different water temperature conditions

A 40-day culture experiment of water hyacinth was made in 4 different water temperatures, 15, 20, 25 and 30°C, which were combined with 4 levels of concentration of culture solution, 1/3, 1, 3 and 9-fold of the standard solution containing 28 ppm of totalN and 7.7 ppm of totalP. The optimum condition for obtaining the maximum plant growth shifted from 30°C: 3-fold condition in the early stage to 20–25°C: 3-fold condition in the later stages of the experiment. The relation between the fresh weight biomass per 100-l tank,w, and the concentration of culture solution,f, was expressed successfully by a reciprocal equation,1/w=A F/f+A F ^′f/(1-f/C F)+B F, in whichA f,A f′, andB f are time dependent coefficients andC f is the upper limit of the concentration to permit plant growth which can change with time. The relation betweenw and water temperature,T, was expressed by another reciprocal equation,1/w=A T/e ^aT+A T^′e^bT+B T, in whicha andb are constants andAt At′ andB t are time dependent coefficients. The latter formulation shows that the temperature can be breated as an exponential factor, and it suggests the possibility of the growth coefficient of the logistic growth equation, ψ, being affected by temperature.     

Transfers to <Emphasis Type="Italic">Simsia</Emphasis> and description of <Emphasis Type="Italic">Davilanthus</Emphasis>, a new genus of Asteraceae (Heliantheae)

Taxonomic changes are made to reflect a reassessment of morphology based on the results of molecular phylogenetic studies. A new genus, Davilanthus, is described to include six species that collectively form the sister group to Simsia, and includes the following species transferred from Viguiera: Davilanthus davilae, Davilanthus hidalgoanus, Davilanthus hypargyreus, Davilanthus huajuapanus, Davilanthus purpusii, and Davilanthus sericeus. Three species formerly placed in Viguiera ser. Grammatoglossae are transferred to Simsia: Simsia benziorum, Simsia ovata, and Simsia rhombifolia.     

Evaluation of the effect of Tb(IV)-NR complex on herring sperm DNA genetic information by mean of spectroscopic

Abstract

The interaction between Tb(IV)-NR complex and herring sperm DNA in buffer solution of Tris-HCl was investigated with the use of acridine orange(AO) as a spectral probe. The binding modes and other information were provided by the UV–spectrophotometry and fluorescence spectroscopy. The thermodynamic functions expressed that the binding constants of Tb(IV)-NR complex with DNA was K^θ_298.15K = 4.03?×?10⁵?L·mol^?1, K^θ_310.15K =1.30?×?10⁷?L·mol^?1, and the Δ_rGθ m _298.15?K＝?3.20?×?10⁴ J·mol^?1. The scatchard equation suggested that the interaction mode between Tb(IV)-NR complex and herring sperm DNA is electrostatic and weak intercalation bindings. FTIR spectroscopy results also indicate that there is a specific interaction between the Tb(IV)-NR complex and the A and G bases of DNA.     

The basic flow equations of electrophysiology in the presence of chemical reactions: II. A practical application concerning the pH and voltage effects accompanying the diffusion of O2 through hemoglobin solution

Previous papers by F. M. Snell (Jour. Theor. Biol.,8, 469–479, 1965) and M. A. Fox and H. D. Landahl (Bull. Math. Biophysics,27, Spec. Issue, 183–190, 1965) have found that the formulation by previous authors for the oxygen flow rates through hemoglobin solution as a function of pressure determined by E. Hemmingsen and P. F. Scholander (Science,132, 1379–1381, 1960) did not give a satisfactory quantitative fit of the curve for constant pressure difference. The suggestion of Fox and Landahl that the Bohr effect involving the shift in acidity accompanying the oxidation of Hb should give rise to voltage and pH differences in oxyhemoglobin transport is examined in more detail. In this paper, the previous expressions for the total oxygen flow rate in terms of the end point concentrations are extended to include the effects of the electrical field. Estimates of the potential difference shows it to be negligible. A derivation of a voltage-pH relation shows that the Nernst relation does not apply and a negligible voltage difference does not preclude a pH shift which is the more probable explanation of the discrepancies observed. Several other predictions suitable for experimental testing are made.     

The chemical constituents of Piper kadsura and their cytotoxic and anti-neuroinflammtaory activities

The n-hexane and CHCl₃ soluble fractions of the MeOH extract of the aerial parts of Piper kadsura were found to potently inhibit nitric oxide (NO) production in LPS-activated BV-2 cells, a microglial cell line. From the active fractions, a new stereoisomer of guaiane sesquiterpene, 1α,5β-guai-4(15)-ene-6β,10β-diol, kadsuguain A (1) and a new cyclohexadienone, kadsuketanone A (2), together with twelve known compounds (3–14) were isolated. The structures of these compounds were elucidated by extensive NMR spectral studies. The absolute configuration of 2 was determined by circular dichroism (CD) spectra. Compounds 2, 6, and 11–14 significantly inhibited both nitric oxide (NO) and prostaglandin E₂ (PGE₂) production in the LPS-activated microglia cells. In addition, compounds 4, 6, and 11–14 exhibited cytotoxicity against the A549, SK-OV-3, SK-MEL-2, and HCT15 human tumour cells.     

A synopsis of <Emphasis Type="Italic">Cohniella</Emphasis> (Orchidaceae,Oncidiinae)

A synopsis of the genus Cohniella is presented with nomenclatural updates with a discusion of diagnostic features and biogeographical data. Thirteen species and one natural hybrid are recognized. Two new species, Cohniella pendula and Cohniella biorbicularis, are described and illustrated. The following four new combinations are proposed: Cohniella binotii, Cohniella brachyphylla, Cohniella cepula, and Cohniella longifolia. Lectotypes are selected for Oncidium subulifolium, Oncidium helicanthum, Oncidium humboldtii, Oncidium jonesianum var. phaeanthum, Oncidium cepula, and Oncidium wittii. We also propose an amended lectotype for Epidendrum cebolleta and several epitypifications and new synonyms. A key to the genera of the Trichocentrum complex is presented (Appendix) as well as keys to the species of Cohniella.     

On Your Mark,Get Set…

Abstract

Eric Hill, My Pets, The Park, at Home and Up There, (Baby Bear Books), Random House: New York, 1983, unpaged, $1.95 each (board pages)

Dayar Kaur Khalsa, The Baabee Books, Tundra: Montreal, Canada, set of 4, $12.95., (board pages)

Kay Charo, Kate's Car (Box, Quilt and Snowman), Dutton: New York, 1982, unpaged, $3.95 each (boards)

Colin McNaughton, At Playschool, Philomel: New York, 1982, unpaged, $3.95 (boards)

E. H. Shepard (words by A. A. Milne), Pooh's Counting Book, Dutton: New York, 1982, unpaged, $4.95 (board cover)

Arthur Dorros, Alligator Shoes, Dutton: New York, 1982, unpaged, $3.95 (boards)

Tana Hoben, Round & Round & Round, Greenwillow: New York, 1983, unpaged, $9.50

Nicole Rubel, Me and My Kitty, Macmillan: New York, 1983, unpaged, $7.95