Spatial structures in a simple model of population dynamics for parasite-host interactions

Spatial patterning can be crucially important for understanding the behavior of interacting populations. Here we investigate a simple model of parasite and host populations in which parasites are random walkers that must come into contact with a host in order to reproduce. We focus on the spatial arrangement of parasites around a single host, and we derive using analytics and numerical simulations the necessary conditions placed on the parasite fecundity and lifetime for the populations long-term survival. We also show that the parasite population can be pushed to extinction by a large drift velocity, but, counterintuitively, a small drift velocity generally increases the parasite population.Comment: 6 pages, 6 figure

Recognition of Design Failure by Fourth-Grade Students During an Engineering Design Challenge

The practice of persisting and learning from design failures is essential to engineering design and offers unique ways of knowing and learning for K-12 students. To understand how students engage in the practice of persisting and learning from design failures, we must first understand how, if at all, they recognize that a design failure has occurred. We studied a classroom of fourth-grade students engaged in an engineering design challenge and examined the ways in which design failure occurred and how students recognized, neglected to recognize, or misinterpreted design failure. We found that, in addition to anticipating failure, conducting fair tests, and making focused observations, students must have an understanding and awareness of the evolving criteria and constraints of the design problem in order to recognize design failure. If lacking an understanding and awareness of criteria and constraints represents a barrier to recognizing an initial design failure, it also represents a barrier to recognizing any subsequent design failures in the design process and thus a barrier to persisting and learning from design failures

Transforming growth factor-beta (beta 1, beta 2, and beta 3) gene expression and action during pubertal development of the seminiferous tubule: potential role at the onset of spermatogenesis

The potential role of transforming growth factor-beta (TGF beta) as a mediator of cell-cell interactions during the pubertal development of the seminiferous tubule was examined. Mesenchymal-derived peritubular cells and epithelial-like Sertoli cells were isolated from prepubertal, midpubertal, and late pubertal rat testes. The developmental expression of the multiple forms of TGF beta (TGF beta 1, -beta 2, and -beta 3) in whole testis and isolated somatic cell types was determined using a nuclease protection analysis. TGF beta 1 and TGF beta 2 mRNA expression was predominant in the immature testis and decreased at the onset of puberty. TGF beta 3 mRNA expression, the most abundant form of TGF beta present, peaked at an early pubertal stage, coincident with the initiation of spermatogenesis. Peritubular and Sertoli cells expressed each isoform of TGF beta during development. Peritubular cell mRNA expression of TGF beta 1, -beta 2, and -beta 3 decreased during pubertal development upon differentiation of this cell type. Sertoli cell expression of TGF beta 1 increased slightly and plateaued during pubertal development. TGF beta 2 mRNA expression was evident only in immature prepubertal Sertoli cells. Sertoli cell mRNA expression of TGF beta 3 increased transiently at the onset of puberty, corresponding with the peak of expression observed during the analysis of whole testicular development. Immunoblot analysis indicated that both cultured peritubular and Sertoli cells can produce the proteins for TGF beta 1, -beta 2, and -beta 3. Analysis of the hormonal regulation of TGF beta expression revealed that FSH caused a dramatic decrease in Sertoli cell TGF beta 2 expression while having no effect on TGF beta 1 or TGF beta 3 expression. Potential actions of TGF beta in the seminiferous tubule were also examined. TGF beta 1 inhibited TGF alpha-induced [3H]thymidine incorporation into peritubular cell DNA with cells from each developmental stage examined. TGF beta 1 had no effect on Sertoli cell proliferation. Previously, germinal cells have been shown to be responsive to TGF beta. This study demonstrates the potential of having a unique hormone-dependent pattern of TGF beta isoform expression during postnatal organ development. Observations demonstrate that the suppression of TGF beta 2 expression, in part in response to FSH, and the transient increase in TGF beta 3 expression correlate with the onset of puberty and the induction of spermatogenesis

Transforming growth factor-α and epidermal growth factor receptor gene expression and action during pubertal development of the seminiferous tubule

The potential role of transforming growth factor-alpha (TGF-alpha) as a mediator of cell-cell interactions in the growth and development of the testis was examined. Developing rat testes were collected, and preparations of mesenchymal-derived peritubular cells and epithelial-like Sertoli cells were isolated from prepubertal, midpubertal, and late pubertal rat testes. The developmental expression of TGF-alpha and its receptor, the epidermal growth factor receptor (EGFR), in whole testis and isolated cell types was determined using a nuclease protection assay. TGF-alpha and EGFR gene expression were predominant early in testis development and decreased during pubertal development. TGF-alpha expression was greatest in prepubertal peritubular cells. Sertoli cell TGF-alpha expression remained relatively constant during development, with a slight decline at the later pubertal stages. EGFR gene expression was predominant in peritublar cells throughout development. A low level of EGFR expression was detected in Sertoli cells. Scatchard analysis confirmed the presence of high affinity receptors on peritubular cells; however, no functional receptors were detected on Sertoli cells from any stage of development examined. Interestingly, low-level EGFR gene expression was also detected in pachytene spermatocytes and round spermatids. TGF-alpha was found to stimulate [3H] thymidine incorporation into DNA and increase cellular proliferation of peritubular cells from each developmental stage, while having no effect on Sertoli cells. The in vivo physiological significance of TGF-alpha was evaluated in a line of transgenic mice which overexpress TGF-alpha in the mature testis. These transgenic animals had no abnormal testicular morphology or alterations in spermatogenesis. Observations demonstrate that gene expression of TGF-alpha and its receptor is high during early pubertal stages when somatic cell growth is predominant and low at late pubertal stages when somatic cell proliferation is reduced. TGF-alpha can act as an autocrine/paracrine mitogen for the mesenchymal-derived peritubular cell, while actions on the Sertoli cell population are not evident. The observation that spermatogenic cells express the EGFR gene, although the protein remains to be identified, implies that TGF-alpha may potentially mediate Sertoli-germinal cell interactions

Structural characterization of proteoglycans produced by testicular peritubular cells and Sertoli cells

The structural characteristics of proteoglycans produced by seminiferous peritubular cells and by Sertoli cells are defined. Peritubular cells secrete two proteoglycans designated PC I and PC II. PC I is a high molecular mass protein containing chondroitin glycosaminoglycan (GAG) chains (maximum 70 kDa). PC II has a protein core of 45 kDa and also contains chondroitin GAG chains (maximum 70 kDa). Preliminary results imply that PC II may be a degraded or processed form of PC I. A cellular proteoglycan associated with the peritubular cells is described which has properties similar to those of PC I. Sertoli cells secrete two different proteoglycans, designated SC I and SC II. SC I is a large protein containing both chondroitin (maximum 62 kDa) and heparin (maximum 15 kDa) GAG chains. Results obtained suggest that this novel proteoglycan contains both chondroitin and heparin GAG chains bound to the same core protein. SC II has a 50-kDa protein core and contains chondroitin (maximum 25 kDa) GAG chains. A proteoglycan obtained from extracts of Sertoli cells is described which contains heparin (maximum 48 kDa) GAG chains. In addition, Sertoli cells secrete a sulfoprotein, SC III, which is not a proteoglycan. SC III has properties similar to those of a major Sertoli cell-secreted protein previously defined as a dimeric acidic glycoprotein. The stimulation by follicle-stimulating hormone of the incorporation of [35S]SO2(-4) into moieties secreted by Sertoli cells is shown to represent an increased production or sulfation of SC III (i.e. dimeric acidic glycoprotein), and not an increased production or sulfation of proteoglycans. Results are discussed in relation to the possible functions of proteoglycans in the seminiferous tubule

Fibronectin Synthesis is a Marker for Peritubular Cell Contaminants in Sertoli Cell-Enriched Cultures

With indirect immunofluorescent microscopic techniques, we have shown that fibronectin is distributed primarily in or along the basal lamina of the seminiferous tubule boundary tissue in sections of testes from 20-day-old rats. Purified rat Sertoli cell-enriched aggregates, maintained in culture in the presence or absence of serum, exhibit no detectable immunofluorescence with fibronectin antibody, whereas purified peritubular cells in culture do have a positive reaction to fibronectin antibody. Peritubular cells in culture incorporate [35S] methionine into fibronectin which can be immunoprecipitated with a fibronectin antiserum, but Sertoli cells do not. We have used various criteria to estimate the degree of purity of Sertoli cell-enriched preparations. The presence of peritubular myoid cells in conventional Sertoli cell-enriched aggregates, cultured in the presence or absence of serum, can be detected with transmission electron microscopic examination, by the Feulgen staining procedure, and by the immunocytochemical identification of fibronectin. We describe a technique to purify Sertoli cells in conventional Sertoli cell-enriched preparations by treatment with hyaluronidase, resulting in a lesser number of peritubular cells by the above criteria, even in preparations cultured in the presence of serum. Data presented suggest that some of the products previously attributed exclusively to Sertoli cells in Sertoli cell-enriched preparations, particularly those cultured in the presence of serum, may have been contributed by peritubular cells