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     

A cross-diffusion model of forest boundary dynamics

A simple mathematical model of mono-species forest with two age classes which takes into account seed production and dispersal is presented in the paper. This reaction — diffusion type model is then reduced by means of an asymptotic procedure to a lower dimensional reaction — cross-diffusion model. The existence of standing and travelling wave front solutions corresponding to the forest boundary is shown for the later model. On the basis of the analysis, possible changes in forest boundary dynamics caused by antropogenic impacts are discussed.     

Bifurcation analysis of periodic SEIR and SIR epidemic models

The bifurcations of the periodic solutions of SEIR and SIR epidemic models with sinusoidally varying contact rate are investigated. The analysis is carried out with respect to two parameters: the mean value and the degree of seasonality of the contact rate. The corresponding portraits in the two-parameter space are obtained by means of a numerical continuation method. Codimension two bifurcations (degenerate flips and cusps) are detected, and multiple stable modes of behavior are identified in various regions of the parameter space. Finally, it is shown how the parametric portrait of the SEIR model tends to that of the SIR model when the latent period tends to zero.     

Modelling the effect of treatment and behavioral change in HIV transmission dynamics

In this paper we analyze a model for the HIV-infection transmission in a male homosexual population. In the model we consider two types of infected individuals. Those that are infected but do not know their serological status and/or are not under any sort of clinical /therapeutical treatment, and those who are. The two groups of infectives differ in their incubation time, contact rate with susceptible individuals, and probability of disease transmission. The aim of this article is to study the roles played by detection and changes in sexual behavior in the incidence and prevalence of HIV. The analytical results show that there exists a unique endemic equilibrium which is globally asymptotically stable under a range of parameter values whenever a detection /treatment rate and an indirect measure of the level of infection risk are sufficiently large. However, any level of detection/ treatment rate coupled with a decrease of the transmission probability lowers the incidence rate and prevalence level in the population. In general, only significant reductions in the transmission probability (achieved through, for example, the adoption of safe sexual practices) can contain effectively the spread of the disease.     

Molecular evolution of the HSP70 multigene family

Eukaryotic genomes encode multiple 70-kDa heat-shock proteins (HSP70s). The Saccharomyces cerevisiae HSP70 family is comprised of eight members. Here we present the nucleotide sequence of the SSA3 and SSB2 genes, completing the nucleotide sequence data for the yeast HSP70 family. We have analyzed these yeast sequences as well as 29 HSP70s from 24 additional eukaryotic and prokaryotic species. Comparison of the sequences demonstrates the extreme conservation of HSP70s; proteins from the most distantly related species share at least 45% identity and more than one-sixth of the amino acids are identical in the aligned region (567 amino acids) among all proteins analyzed. Phylogenetic trees constructed by two independent methods indicate that ancient molecular and cellular events have given rise to at least four monophyletic groups of eukaryotic HSP70 proteins. Each group of evolutionarily similar HSP70s shares a common intracellular localization and is presumed to be comprised of functional homologues; these include heat-shock proteins of the cytoplasm, endoplasmic reticulum, mitochondria, and chloroplasts. HSP70s localized in mitochondria and plastids are most similar to the DnaK HSP70 homologues in purple bacteria and cyanobacteria, respectively, which is consistent with the proposed prokaryotic origin of these organelles. The analyses indicate that the major eukaryotic HSP70 groups arose prior to the divergence of the earliest eukaryotes, roughly 2 billion years ago. In some cases, as exemplified by the SSA genes encoding the cytoplasmic HSP70s of S. cerevisiae, more recent duplication events have given rise to subfamilies within the major groups. The S. cerevisiae SSB proteins comprise a unique subfamily not identified in other species to date. This subfamily appears to have resulted from an ancient gene duplication that occurred at approximately the same time as the origin of the major eukaryotic HSP70 groups. Correspondence to: E.A. Craig     

Phylogeny and physiology of Drosophila opsins

Phylogenetic and physiological methods were used to study the evolution of the opsin gene family in Drosophila. A phylogeny based on DNA sequences from 13 opsin genes including representatives from the two major subgenera of Drosophila shows six major, well-supported clades: The blue opsin clade includes all of the Rhl and Rh2 genes and is separated into two distinct subclades of Rhl sequences and Rh2 sequences; the ultraviolet opsin clade includes all Rh3 and Rh4 genes and bifurcates into separate Rh3 and Rh4 clades. The duplications that generated this gene family most likely took place before the evolution of the subgenera Drosophila and Sophophora and their component species groups. Numerous changes have occurred in these genes since the duplications, including the loss and/or gain of introns in the different genes and even within the Rhl and Rh4 clades. Despite these changes, the spectral sensitivity of each of the opsins has remained remarkably fixed in a sample of four species representing two species groups in each of the two subgenera. All of the strains that were investigated had R1-6 (Rhl) spectral sensitivity curves that peaked at or near 480 nm, R7 (Rh3 and Rh4) peaks in the ultraviolet range, and ocellar (Rh2) peaks near 420 nm. Each of the four gene clades on the phylogeny exhibits very conservative patterns of amino acid replacement in domains of the protein thought to influence spectral sen sitivity, reflecting strong constraints on the spectrum of light visible to Drosophila.     

Conservation of human Y chromosome sequences among male great apes: Implications for the evolution of Y chromosomes

Nine newly described single-copy and lowcopy-number genomic DNA sequences isolated from a flow-sorted human Y chromosome library were mapped to regions of the human Y chromosome and were hybridized to Southern blots of male and female great ape genomic DNAs (Gorilla gorilla, Pan troglodytes, Pongo pygmaeus). Eight of the nine sequences mapped to the euchromatic Y long arm (Yq) in humans, and the ninth mapped to the short arm or pericentromeric region. All nine of the newly identified sequences and two additional human Yq sequences hybridized to restriction fragments in male but not female genomic DNA from the great apes, indicating Y chromosome localization. Seven of these 11 human Yq sequences hybridized to similarly-sized restriction endonuclease fragments in all the great ape species analyzed. The five human sequences that mapped to the most distal subregion of Yq (deletion of which region is associated with spermatogenic failure in humans) were hybridized to Southern blots generated by pulsed-field gel electrophoresis. These sequences define a region of approximately 1 Mb on human Yq in which HpaII tiny fragment (HTF) islands appear to be absent. The conservation of these human Yq sequences on great ape Y chromosomes indicates a greater stability in this region of the Y than has been previously described for most anonymous human Y chromosomal sequences. The stability of these sequences on great ape Y chromosomes seems remarkable given that this region of the Y does not undergo meiotic recombination and the sequences do not appear to encode genes for which positive selection might occur. Correspondence to: B. Steele Allen     

Evolution of secondary structure in the family of 7SL-like RNAs

Primate and rodent genomes are populated with hundreds of thousands copies of Alu and B1 elements dispersed by retroposition, i.e., by genomic reintegration of their reverse transcribed RNAs. These, as well as primate BC200 and rodent 4.5S RNAs, are ancestrally related to the terminal portions of 7SL RNA sequence. The secondary structure of 7SL RNA (an integral component of the signal recognition particle) is conserved from prokaryotes to distant eukaryotic species. Yet only in primates and rodents did this molecule give rise to retroposing Alu and B1 RNAs and to apparently functional BC200 and 4.5S RNAs. To understand this transition and the underlying molecular events, we examined, by comparative analysis, the evolution of RNA structure in this family of molecules derived from 7SL RNA.RNA sequences of different simian (mostly human) and prosimian Alu subfamilies as well as rodent B1 repeats were derived from their genomic consensus sequences taken from the literature and our unpublished results (prosimian and New World Monkey). RNA secondary structures were determined by enzymatic studies (new data on 4.5S RNA are presented) and/or energy minimization analyses followed by phylogenetic comparison. Although, with the exception of 4.5S RNA, all 7SL-derived RNA species maintain the cruciform structure of their progenitor, the details of 7SL RNA folding domains are modified to a different extent in various RNA groups. Novel motifs found in retropositionally active RNAs are conserved among Alu and B1 subfamilies in different genomes. In RNAs that do not proliferate by retroposition these motifs are modified further. This indicates structural adaptation of 7SL-like RNA molecules to novel functions, presumably mediated by specific interactions with proteins; these functions were either useful for the host or served the selfish propagation of RNA templates within the host genome.Abbreviations FAM fossil Alu element - FLAM free left Alu monomer - FRAM free right Alu monomer - L-Alu left Alu subunit - R-Alu right Alu subunit Correspondence to: D. LabudaDedicated to Dr. Robert Cedergren on the occasion of his 25th anniversary at the University of Montreal     

Cloning and characterization of the platypus mitochondrial genome

The vertebrate mitochondrial genome is highly conserved in size and gene content. Among the chordates there appears to be one basic gene arrangement, but rearrangements in the mitochondrial gene order of the avian lineages have indicated that the mitochondrial genome may be more variable than once thought. Different gene orders in marsupials and eutherian mammals leave the ancestral mammalian order in some doubt. We have investigated the mitochondrial gene order in the platypus (Ornithorhynchus anatinus), a representative of the third major group of mammals, to determine which mitochondrial gene arrangement is ancestral in mammals. We have found that the platypus mtDNA conforms to the basic chordate gene arrangement, common to fish, amphibians, and eutherian mammals, indicating that this arrangement was the original mammalian arrangement, and that the unusual rearrangements observed in the avians and marsupials are probably lineage-specific. Correspondence to: N.J. Gemmell     

Polymorphisms in the α-amy1 gene of wild and cultivated barley revealed by the polymerase chain reaction

-Amylases are the key enzymes involved in the hydrolysis of starch in plants. The polymerase chain reaction (PCR) was used to detect polymorphisms in the length of amplified sequences between the annealing sites of two primers derived from published -amy1 gene sequences in barley. These two primers (Bsw1 and Bsw7), flanking the promoter region and the first exon, amplified two PCR fragments in barley. One of the amplified products, with the expected length of 820 bp, appeared together with another shorter PCR band of around 750 bp. This 750-bp fragment seems to be derived from an -amylase gene not reported previously. Both of the PCR products could be amplified from the two-rowed barley varieties tested, including cv Himalaya from which the sequence information was obtained. Five of the six-rowed barley varieties also have the two PCR fragments whereas another two have only the long fragment. These two fragments seem to be unique to barley, neither of them could be amplified from other cereals; for example, wheat, rye or sorghum. These two -amylase fragments were mapped to the long arm of 6H, the location of the -amy1 genes, using wheat-barley addition lines. Amplification of genomic DNA from wild barley accessions with primers Bsw1 and Bsw7 indicated that both of the fragments could be present, or the long and short fragments could be present alone. The results also demonstrated that the genes specifying these two fragments could be independent from each other in barley. The conserved banding pattern of these two fragments in the two-rowed barley varieties implies that artificial selection from these genes may have played an important role in the evolution of cultivated barley from wild barley.