Equilibria in structured populations

The existence of a stable positive equilibrium state for the density of a population which is internally structured by means of a single scalar such as age, size, etc. is studied as a bifurcation problem. Using an inherent birth modulus n as a bifurcation parameter it is shown for very general nonlinear model equations, in which vital birth and growth processes depend on population density, that a global unbounded continuum of nontrivial equilibrium pairs (n, ) bifurcates from the unique (normalized) critical point (1, 0). The pairs are locally positive and conditions are given under which the continuum is globally positive. Local stability is shown to depend on the direction of bifurcation. For the important case when density dependence is a nonlinear expression involving a linear functional of density (such as total population size) it is shown how a detailed global bifurcation diagram is easily constructed in applications from the graph of a certain real valued function obtained from an invariant on the continuum. Uniqueness and nonuniqueness of positive equilibrium states are studied. The results are illustrated by several applications to models appearing in the literature.This research was done while the author was on leave at the Lehrstuhl für Biomathematik, Universität Tübingen, Auf der Morgenstelle 10, 7400 Tübingen 1, Federal Republic of Germany     

Primary production in Rattlesnake Springs,a cold desert spring-stream

Primary productivity and respiration were measured in Rattlesnake Springs, Washington, using the upstream-downstream diel pH-CO₂ curve and harvest methods.Daily P_g and P_n rates averaged 8.7 and 0.9, 0.6 and 0.3, and 9.3 and 1.2 g C m^–2 d^–1 for periphyton, watercress, and total community, respectively. Average photosynthetic efficiencies (%, P _n Lt^–1) were approximately 0.22 and 0.07 for periphyton and watercress, respectively. Annual community P_g was 2 700 g C m^–2 a^–1 and was highest for periphyton (2 526 g C m^–2 a^–1). Periphyton P_n (356 g C m^–2 a^–1) exceeded that of watercress (87 g C m^–2 a^–1). Community R was 2 257 g C m^–2 a^–1, and was highest for periphyton (2 170 g C m² a^–1).Desert streams appear to be enigmas in terms of their relationship between autotrophy and heterotrophy and their ability to be net importers or exporters of organic matter. The fact that they can be autotrophic and net importers of organic matter is probably related to the characteristic flash-flooding of desert streams, and emphasizes the necessity of examining these systems over more than a single annual cycle.     

Visual fields of orb web and single line web spiders of the family Uloboridae (Arachnida,Araneida)

Summary In the family Uloboridae, web reduction is associated with changes in web monitoring posture and prosomal features. A spider must extend its first pair of legs directly forward to monitor the signal line of a reduced web. This posture is facilitated by shifts in prosomal musculature that cause reduced web uloborids to have a narrower anterior prosoma, a reduced or absent anterior eye row, and prominent posterior lateral eye tubercles. The eye tubercles and larger posterior eyes of these uloborids suggest that web reduction may also be accompanied by ocular changes that compensate for reduction of the anterior eyes by expanding the visual fields of the posterior eyes. A comparison of the visual fields of the eight-eyed, orb web species Octonoba octonaria and a four-eyed, reduced web Miagrammopes species was made to determine if this is true. Physical and optical measurements determined the visual angles of each species' eyes and the pattern of each species' visual surveillance. Despite loss of the anterior four eyes, the Miagrammopes species has a visual coverage similar to that of O. octonaria. This is due to (1) an increase in the visual field of each of the four remaining Miagrammopes eyes, accruing from an extension of the retina and an increase in the lens' rear radius of curvature, and (2) a ventral shift of each visual axis, associated with the development of an eye tubercle and an asymmetrical expansion of the retina. Miagrammopes monitor their simple webs from twigs or moss where they are vulnerable to predation. Therefore, maintenance of visual cover may enable them to detect predators in time to assume or maintain their characteristic, cryptic posture. It may also allow them to observe approaching prey and permit them to adjust web tension or prepare to jerk their webs when prey strikes.     

The reproductive biology of female Père David's deer (Elaphurus davidianus)

Data for this study came from breeding records of 27 Père David's (Elaphurus davidianus) hinds maintained in large pastures and from estrous records of four hand-reared nulliparous hinds. The mean estrous cycle length ranged from 17.5 to 19.6 days. Standing estrus resembled that of other cervids, except that a low, moaning vocalization was given in response to contact, and activity (as measured by pedometers) did not increase. Mean gestation length was 183.38 ± SD 6.11 days (n = 21), and nearly all females conceived in the second and third years. The median interbirth interval was 362 days. The median birth date was April 8, and 80% of the births occurred over a 9.5-week period. Multiparous hinds gave birth an average of 20.5 days earlier in the season than primiparous hinds. There was no dimorphism in birth weight. The results are discussed in light of comparative data for other species.     

Modulation of 5-Hydroxytryptamine1A Receptor Density by Nonhydrolyzable GTP Analogues

Co-incubation of rat cortical membranes with 10(-4) M GTP results in a competitive inhibition of 5-hydroxytryptamine1A (5-HT1A) receptor binding sites labeled by [3H]8-hydroxy-2-(di-n-propylamino)tetralin [( 3H]8-OH-DPAT). Preincubation of cortical membranes with 10(-4) M GTP does not significantly change either KD or Bmax values, indicating that the effect of GTP is reversible. By contrast, GTP gamma S and 5'-guanylylimidodiphosphate (GppNHp) are nonhydrolyzable analogues of GTP which lengthen the time course of guanine nucleotide activation of guanine nucleotide binding proteins (G proteins) and thereby alter G protein-receptor interactions. These nonhydrolyzable GTP analogues were used to characterize the effects of persistent alterations in G proteins on [3H]8-OH-DPAT binding to 5-HT1A receptors. Co-incubation of rat cortical membranes with either 10(-4) M GTP gamma S or GppNHp results in a decrease in both the affinity and apparent density of 5-HT1A binding sites. Co-incubation with the nonhydrolyzable nucleotides reduces the affinity of [3H]8-OH-DPAT binding by 65-70% and lowers the density of the binding site by 53-61%. Similarly, preincubation of membranes with a 10(-4) M concentration of either GTP gamma S or GppNHp significantly increases the KD value and reduces the Bmax value of [3H]8-OH-DPAT binding. These results indicate that GTP gamma S and GppNHp induce persistent changes in 5-HT1A receptor-G protein interactions that are reflected as a decrease in the density of binding sites labeled by [3H]8-OH-DPAT.     

Taxol maintains organized microtubule patterns in protoplasts which lead to the resynthesis of organized cell wall microfibrils

Summary We have investigated the effects of microtubule stabilizing conditions upon microtubule patterns in protoplasts and developed a new method for producing protoplasts which have non-random cortical microtubule arrays. Segments of elongating pea epicotyl tissue were treated with the microtubule stabilizing drug taxol for 1 h before enzymatic digestion of the cell walls in the presence of the drug. Anti-tubulin immunofluorescence showed that 40 M taxol preserved regions of ordered microtubules. The microtubules in these regions were arranged in parallel arrays, although the arrays did not always show the transverse orientation seen in the intact tissue. Protoplasts prepared without taxol had microtubules which were random in distribution. Addition of taxol to protoplasts with random microtubule arrangements did not result in organized microtubule arrays. Taxol-treated protoplasts were used to determine whether or not organized microtubule arrays would affect the organization of cell wall microfibrils as new walls were regenerated. We found that protoplasts from taxol-treated tissue which were allowed to regenerate cell walls produced organized arrays of microfibrils whose patterns matched those of the underlying microtubules. Protoplasts from untreated tissue synthesized microfibrils which were disordered. The synthesis of organized microfibrils by protoplasts with ordered microtubules arrays shows that microtubule arrangements in protoplasts influence the arrangement of newly synthesized microfibrils.Abbreviations DIC differential interference contrast - DMSO dimethyl sulfoxide - FITC fluorescein isothiocyanate - IgG immunoglobulin G - PIPES piperazine-N,N-bis[2-ethane-sulfonic acid] - PBS phosphate buffered saline     

Myelin Gene Expression in Immortalized Schwann Cells: Relationship to Cell Density and Proliferation

Abstract: Myelin gene expression was investigated in the immortalized S16 Schwann cell line grown in the presence and absence of serum and at different densities. Protein expression was monitored by western blotting, and message levels were determined by RNase protection assays. To study cell proliferation rates at different cell densities and serum conditions. [³H]thymidine uptake assays and cell counts were performed. Although serum deprivation decreased cell proliferation as expected, the proliferation of S16 cells was unchanged or slightly increased at high density under the conditions of our experiments in either serum-containing or serum-free medium. This increased cell division at high density appeared to be due to greater release of an autocrine growth factor to the medium by dense cell populations. For both sparse and dense cells, substantially more P₀ glycoprotein (P₀) and myelin-associated glycoprotein (MAG) per milligram of total cellular protein were expressed when the cells were proliferating slowly in defined medium in comparison with more rapidly proliferating cells in serum-containing medium. Furthermore, in both serum-containing and defined media, dense cell populations expressed more MAG and P₀ than sparse ones. P₀ mRNA and MAG mRNA levels generally paralleled protein levels. The level of mRNA for peripheral myelin protein-22 (PMP-22) was also increased at high cell density but did not change much when proliferation was decreased by serum deprivation. PMP-22 protein was not detected under any of the growth conditions. The changes in expression of these genes with growth conditions may be specific for myelin proteins, because the expression of a nonmyelin glycoprotein, L1, remained constant. The level of cyclic AMP in the cells did not change with the different growth conditions tested. The results indicate that the S16 Schwann cell line mimics primary or secondary Schwann cells by down-regulating myelin gene expression when it proliferates more rapidly in the presence of serum. Furthermore, in both the presence and absence of serum, there was greater expression of myelin genes at high cell density that was not associated with a decreased proliferative rate. Because evidence for a role of secretory factors in affecting myelin gene expression was not obtained by treating sparse S16 cells with medium conditioned by dense S16 cells, the results suggest that the higher expression of myelin genes at high density may be mediated by cell-to-cell contact.     

Differential effects of warfarin on mRNA levels of developmentally regulated vitamin K dependent proteins,osteocalcin, and matrix Gla protein in vitro

The role of the vitamin K dependent proteins, osteocalcin which is bone specific and matrix Gla protein (MGP) found in many tissues, has been studied by inhibition of synthesis of their characteristic amino acid, γ-carboxyglutamic acid (Gla) with the anticoagulant sodium warfarin. The effect of sodium warfarin on expression of these proteins, and other phenotypic markers of bone and cartilage during cellular differentiation and development of tissue extracellular matrix, was examined in several model systems. Parameters assayed include cell growth (reflected by histone gene expression) and collagen types I and II, osteopontin, alkaline phosphatase, and mineralization. Studies were carried out in calvarial bone organ cultures, normal diploid rat osteoblast and chondrocyte cultures, and rat osteosarcoma cell lines ROS 17/2.8 and 25/1. In normal diploid cells, warfarin consistently stimulated cell proliferation (twofold). In osteoblast cultures, MGP mRNA levels were generally increased (three to tenfold). Notably, MGP mRNA levels were not affected in chondrocyte cultures, either with chronic or acute warfarin treatments. Osteocalcin mRNA levels and synthesis were decreased up to 50% in ROS 17/2.8 cells and in chronically treated (1 and 5 μg/ml sodium warfarin) rat osteoblast cultures after 22 days. Early stages of osteoblast phenotype development from the proliferation period to initial tissue formation (nodules) appeared unaffected; while after day 14, further growth and mineralization of the nodule areas were significantly decreased in warfarin-treated cultures. In summary, warfarin has opposing effects on the expression of two vitamin K dependent proteins, MGP and osteocalcin, in osteoblast cultures and MGP is regulated differently between cartilage and bone as reflected by cellular mRNA levels. Additionally, warfarin effects expression of nonvitamin K dependent proteins which may reflect the influence of warfarin on endoplasmic reticulum associated enzymes. © 1994 Wiley-Liss, Inc.