On some formulas in a partnership model from the perspective of a semi-Markov process

Many deterministic models of sexually transmitted diseases, as well as population models in general, contain elements of stochastic or statistical reasoning. An example of such a model is that of Dietz and Hadeler (1988) concerning sexually transmitted diseases in which there is partnership formation and dissolution. Among the interesting formulas in this paper, which enter into the analysis of the model, are those for the expected number of partners a male or female has during a lifetime. To a probabilist such formulas suggest the possibility that some stochastic process may be constructed so as to yield these formulas as well as others that may be of interest. The principal purpose of this paper is to demonstrate that such a stochastic process does indeed exist in the form of a three state semi-Markov process in continuous time with stationary laws of evolution and with a one-step density matrix determined by four parameters which were interpreted as constant latent risk functions in the classical theory of competing risks. This construction of a semi-Markov process not only provides a framework for the systematic derivation of the formulas of Dietz and Hadeler but also suggests pathways,for extensions to the age-dependent case.This research was partially supported by NATO Grant D.890350     

Cyanophycean blooms in the reservoir of Val Joly (northern France) and their development in downstream rivers

A study was carried out in 1992 on the Val Joly reservoir and the rivers situated downstream: the River Helpe Majeure and the canalized Sambre into which it flows 40 km below the reservoir. Each year, blooms of blue-green algae occur in the reservoir. They are dominated by species such as Aphanizomenon flos-aquae (L.) Ralfs in 1991 or Pseudanabaena tenuis Koppe and Oscillatoria pseudogeminata G. Schmid in 1992. A typical fluvial composition of the phytoplankton was mostly restored above the confluence with the Sambre. Nevertheless, significant quantities of Oscillatoria and Pseudanabaena have been observed in the River Sambre, just below its confluence with the Helpe Majeure. The environmental conditions in the River Sambre do not allow Aphanizomenon to develop, but could favour Oscillatoria blooms.     

Kinetics of leucrose formation from sucrose by dextransucrase

Leucrose formation from sucrose and fructose by dextransucrase is of practical interest. It has been investigated at different experimental conditions, including the influence of temperature on reaction rate and selectivity. Under appropriate conditions high product yield can be obtained. Furthermore, a model is presented that allows interpretation of the experimental data.     

Effects of medium carbon-to-nitrogen ratio on biofilm formation and plasmid stability

Biofilm formation and plasmid segregational instability in biofilm cultures of Escherichia coli DH5alpha (pMJR1750) were investigated under different medium-carbon-to-nitrogen (C/N) ratios. At C/N ratios of 0.07 and 1, net accumulation of both biofilm plasmid-bearing and plasmid-free cells continued through the entire experiment without attaining any apparent steady state. At C/N ratios of 5 and 10, net biofilm cell accumulation for the two populations reached apparent steady states after 84 and 72 h, respectively. At C/N ratios of 0.07 and 1, polysaccharide production increased slowly and reached about 2g alginate equivalent/cm(2) by the end of both experiments. At a C/N ratio of 5, polysaccharide increase significantly after 84 h, reaching about 7mug alginate equivalent/cm(2) prior to termination. At a C/N ratio of 10, polysaccharide increased significantly after 72 h and reached 21 mug alginate equivalent/cm(2) at 108 h. At C/N ratios of 0.07 and 1, protein production reached 6.5 and 4 mug/cm(2), respectively. At C/N ratios of 5 and 10, protein production increased slightly for the first 84 h and reached a maximum at 108 h, at 3 and 2 mug/cm(2), respectively, then decreased over the last 12 h of the experiment. Ratios of polysaccharide to protein increased with increasing C/N ratios. At C/N ratios of 0.07 and 1, the ratios between extracellular polysaccharide (EP) and protein were no more than 205 mug polysaccharide/mug protein, whereas those at C/N ratios of 5 and 10 increased to about 7 and 12 mug polysaccharide/mug protein, respectively.Probabilities of plasmid loss in the biofilm cultures increased with increasing C/N ratios. At C/N ratios of 0.07, 1, and 5, the probabilities of plasmid loss were 0.0013 +/- 0.011, 0.020 +/- 0.006 and 0.122 +/- 0.021, respectively. At a C/N ratio of 10, the probability of plasmid loss was significantly higher, reaching 0.38 +/- 0.125. The increase of probability of plasmid loss at higher C/N ratios results from competition between cell replication and extracellular polysaccharide production. (c) 1994 John Wiley & Sons, Inc.     

Gravity-regulated formation of the peg in developing cucumber seedlings

It has been proposed that peg formation in the vascular transition region (TR zone) between the hypocotyl and the root in Cucurbitaceae seedlings is a gravimorphogenetic phenomenon. Initiation of the peg became visible 36 h after imbibition when cucumber (Cucumis sativus L. cv. Burpee Hybrid II) seeds were germinated in a horizontal position at 24°C in the dark. Simultaneously, sedimented amyloplasts (putative statoliths) were apparent in the sheath cells surrounding the vascular strands, and in the cortical cells immediately adjacent to them, in the TR zone. In contrast, the other cortical cells, some of which were destined to develop into the peg, contained amyloplasts which were not sedimented. These results suggest that the graviperception mechanism for peg formation may be like that of statoliths in shoot gravitropism. By 48 h following imbibition, the cells of the TR zone still had sedimented amyloplasts but had lost their sensitivity to gravity, possibly because of their maturation.     

Formation and decomposition of vacuoles inBotryococcus in relation to the trans-Golgi network

Summary The formation and the decomposition of vacuoles in a member of Xanthophyceae,Botryococcus braunii, were examined by light and electron microscopy. Particles around the nucleus were identified as vacuoles from their stainability with neutral red. These particles disappeared during cell division. They reacted positively in an activity test for acid phosphatase. Electron microscopy revealed the presence of spherical vacuoles around the nucleus. During cell division, these vacuoles seemed to be decomposed by the ER which surrounded the vacuoles. Soon after this decomposition, many immature multivesicular bodies (MVBs) appeared to develop from the trans-Golgi network (TGN) and were pinched off from the TGN. These immature MVBs took up small vesicles in them as they grew into the mature MVBs. Mature MVBs took up and digested the surrounding cytoplasm, fused with one another, and eventually became the vacuoles.Abbreviations MVB multivesicular body - TGN trans-Golgi network     

Protein synthesis is not required for the inhibitory effect of selenite on cell colony formation and RNA synthesis

Selenite has been shown to undergo intracellular metabolism that results in its conversion to other low molecular weight Secontaining species and also to its incorporation into a selenocysteine residue in selenoprotein. In order to investigate whether the incorporation into protein is required for the cytotoxic effects of selenite, we have examined whether inhibition of protein synthesis prevents the inhibitory effect of selenite on the ability of cells to form colonies or to synthesize RNA. We have found that treatment of HeLa cells with cycloheximide inhibited protein synthesis by >90% but had no effect on the inhibitory effect of selenite on cell colony formation or RNA synthesis. Since protein synthesis is not necessary for these cytotoxic effects of selenite they are unlikely to result from an increase in the synthesis of selenoproteins.     

Structural organization and differential expression of three stilbene synthase genes located on a 13 kb grapevine DNA fragment

A 13 kb DNA fragment was isolated from a grapevine (Vitis var. Optima) genomic library by hybridizing with elicitor-induced stilbene synthase cDNA as a probe. After fragmentation with Eco RI, subcloning and sequencing, two full-size stilbene synthase genes (Vst1 and Vst2) and the 3 end of a third stilbene synthase gene (Vst3) were located within the 13 kb fragment. Vst1 and Vst2, differing only slightly in the coding region, are distinguished in the intron size and in the structure of the promoter region. The 5 flanking region of gene Vst1 contains a TATAA box at nucleotide –48. The substantial structural differences found for the promoters of the two genes are paralleled by a striking difference in the expression of the two genes in elicitor-treated cells. Moreover, the accumulation upon elicitation of six different stilbene synthase mRNAs was studied and found to differ by two orders of magnitude.     

Micropropagation of horseradish hairy root by means of adventitious shoot primordia

Adventitious shoot primordia were formed on horseradish hairy root cultured in dark. Plantlet formation frequency from the primordia was higher than that from root fragments. Culture for 26 days provided the adventitious shoot primordia, which had the highest potential for plantlet formation (53% explants at 40 days). Benzyladenine supplementation in the dark caused primordium enlargement, but did not increase the number of primordia formed. After adventitious shoot primordia were encapsulated with calcium alginate, kinetin supplementation (2.0–4.0 M) increased the shoot formation frequency (65–80% explants at 20 days) in the light, but also promoted the undesirable formattion of multiple shoots. Supplementation with naphthaleneacetic acid (0.27–5.4 M) in the calcium alginate beads in light enhanced the root emergence from primordia without inhibition of plantlet formation when the encapsulated beads were put on the agar-medium without naphthaleneacetic acid.     

Intraspecific evolution ofMicroseris pygmaea (Asteraceae,Lactuceae) analyzed by cosegregation of phenotypic characters (QTLs) and molecular markers (RAPDs)

The Chilean annual,Microseris pygmaea, has differentiated in distinct coastal and inland series of populations after long-distance dispersal from western North America. Two plants from the most diverse biotypes were crossed, a large F₂ was raised and analysed for segregation of 30 phenotypic characters. Segregation of molecular markers (47 RAPDs, 1 RFLP, 2 isozymes) was determined in a subpopulation of 45 plants which include all extremes for the phenotypic characters. 32 marker/character cosegregations were significant at the 1% level in t-tests between dominant and homozygous recessive marker genotypes. Considering linkage among markers and pleiotropy of certain marker loci, the number of independent quantitative trait loci (QTLs) is reduced to about 18. Interactions among 2 or 3 QTLs affecting one character have been characterized. The phenotypic differentiation ofM. pygmaea during its evolution from a single founder individual begins to be understood at the level of single-gene mutants.