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     

POLYPLOIDY,DYSPLOIDY, AND CHROMOSOME PAIRING IN ECHEVERIA (CRASSULACEAE) AND ITS HYBRIDS

The 140+ species of Echeveria have more than 50 gametic chromosome numbers, including every number from 12 through 34 and polyploids to n = ca. 260. With related genera, they comprise an immense comparium of 200+ species that have been interconnected in cultivation by hybrids. Some species with as many as 34 gametic chromosomes include none that can pair with each other, indicating that they are effectively diploid, but other species with fewer chromosomes test as tetraploids. Most diploid hybrids form multivalents, indicating that many translocations have rearranged segments of the chromosomes. Small, nonessential chromosomal remnants can be lost, lowering the number and suggesting that higher diploid numbers (n = 30–34) in the long dysploid series are older. These same numbers are basic to most other genera in the comparium (Pachyphytum, Graptopetalum, Sedum section Pachysedum), and many diploid intergeneric hybrids show very substantial chromosome pairing. Most polyploid hybrids here are fertile, even where the parents belong to different genera and have very different chromosome numbers. This seems possible only if corresponding chromosomes from a polyploid parent pair with each other preferentially, strong evidence for autopolyploidy. High diploid numbers here may represent old polyploids that have become diploidized by loss, mutation, or suppression of duplicate genes, but other evidence for this is lacking. Most species occur as small populations in unstable habitats in an area with a history of many rapid climatic and geological changes, presenting a model for rapid evolution.     

The role of nickel in acetyl-CoA synthesis by the bifunctional enzyme CO dehydrogenase/acetyl-CoA synthase: enzymology and model chemistry

 CO dehydrogenase/acetyl-CoA synthase (CODH/ACS) is one of the four known nickel enzymes. It is a bifunctional protein that catalyzes the oxidation of CO to CO₂ at a nickel iron-sulfur cluster (Cluster C) and a remarkable condensation reaction between a methyl group (donated from a methylated corrinoid iron-sulfur protein), carbon monoxide, and coenzyme A to form acetyl-CoA at a separate nickel iron-sulfur cluster (Cluster A). This review focuses on the current understanding of the structure and function of Cluster A and on related model chemistry. It describes studies that uncovered the first example of a biological organometallic reaction sequence. The mechanism of acetyl-CoA synthesis includes enzymebound methylnickel, iron-carbonyl, and acylmetal intermediates. Discovery of the methylnickel species constituted the first example of an alkylnickel species in biology and unveiled a new biological role for nickel. Received: 10 April 1996 / Accepted: 4 July 1996     

Cloning of PCP1, a member of a family of pollen coat protein (PCP) genes from Brassica oleracea encoding novel cysteine-rich proteins involved in pollen-stigma interactions

The pollen coatings of both Brassica oleracea and Brassica napus contain a small family of basic 6–8 kDa proteins which are released on to the stigmatic surface on pollination. Following partial amino-acid sequencing of one of these pollen coat proteins (PCPs), PCR primers were constructed to isolate the PCP sequence from anther mRNA using RT-PCR. A cDNA was obtained which, in Northern hybridization experiments, revealed a characteristic pattern of expression during late stages of anther development. Interestingly, in situ hybridization revealed expression of this sequence to be confined to the cytoplasm of the trinucleate pollen grains: no signal was detected in the tapetum. Southern hybridization experiments have shown the gene ( PCP1 ) to be a member of a large family of between 30 and 40 PCP genes in the genome of Brassica oleracea , Surprisingly, RFLP experiments showed reduced copy number (one to two copies) in some of the F₂ segregants, perhaps resulting from the clustering of PCP sequences. PCP1 contains a single intron and encodes a small, basic peptide 83 amino acids in length featuring a hydrophobic signal peptide sequence separated from the more hydrophilic, cysteine-rich mature protein. The central part and C-terminal region of the peptide contain a characteristic and invariant pattern of eight cysteines which show clear homology with a number of other anther-specific genes; the remainder of the sequence shows little similarity to other sequences on the data bases. The product of PCP1 is a member of a large family of similar proteins, some of which have been demonstrated to bind specifically to S-locus glycoproteins, but does not appear to be genetically linked to the S-locus .     

Insulin-like growth factor I levels decrease in the development of diabetes inMacaca nigra

Members of the monkey speciesMacaca nigra spontaneously develop impairments in insulin secretion and glucose clearance, and eventually become overtly diabetic. Changes in certain metabolic signals such as clearance of glucose and insulin increment secreted in an intravenous glucose tolerance test have allowed the identification of four stages in the progression from non-diabetes to diabetes in monkeys — non-diabetic, hormonally impaired, borderline diabetic, and diabetic. Recently, another metabolic stage, hyperinsulinemic, was also identified in these animals. In recent years, other factors besides those listed above have been implicated to be correlated with the metabolic progression from a nondiabetic to a diabetic state. One of these factors, is insulin like growth factor I (IGF-I). In diabetic humans who are in poor metabolic control, and in rats with streptozotocin induced ketotic diabetes, serum levels of IGF-I are lowered by as much as 40–50% of control non-diabetics. If indeed decreased IGF-I levels are correlated with the onset of diabetes then changes in IGF-I concentrations prior to the clinically diagnosed disease state would be expected. Using serum samples collected from different animals in a colony ofMacaca nigra in a variety of metabolic states, we have found that IGF-I and insulin levels decrease in each defined metabolic state as the animals progress from nondiabetic to diabetic. Since IGF-I and insulin levels decrease in a similar fashion in the progression of this disease then this maybe indicative of the coordinate expression of these two factors.     

URF13, a ligand-gated,pore-forming receptor for T-toxin in the inner membrane ofcms-T mitochondria

URF13 is the product of a mitochondrial-encoded gene (T-urfl3) found only in maize plants containing the Texas male-sterile cytoplasm (cms-T), and it is thought to be responsible for both cytoplasmic male sterility and the susceptibility ofcms-T maize to the fungal pathogensBipolaris maydis race T andPhyllosticta maydis. Mitochondria isolated fromcms-T maize are uniquely sensitive to pathotoxins (T-toxin) produced by these fungi and to methomyl (a commercial insecticide). URF13 acts as a receptor that specifically binds T-toxin to produce hydrophilic pores in the inner mitochondrial membrane. When expressed inEscherichia coli cells, URF13 also forms hydrophilic pores in the plasma membrane if exposed to T-toxin or methomyl. Topological studies established that URF13 contains three membrane-spanning -helices, two of which are amphipathic and can contribute to pore formation. Chemical crosslinking of URF13 was used to demonstrate the existence of URF13 oligomers incms-T mitochondria andE. coli cells. The ability of the carboxylate-specific reagent,N,N-dicyclohexycarbodiimide, to cross-link URF13 was used in conjunction with site-directed mutagenesis to establish that the URF13 tetramer has a central core consisting of a four--helical bundle which undergoes a conformational change after interaction with T-toxin or methomyl. Overall, the experimental evidence indicates that URF13 functions as a ligand-gated, pore-forming T-toxin receptor incms-T mitochondria.     

A Cluster of Cuticle Protein Genes of Drosophila Melanogaster at 65a: Sequence, Structure and Evolution

A 36-kb genomic DNA segment of the Drosophila melanogaster genome containing 12 clustered cuticle genes has been mapped and partially sequenced. The cluster maps at 65A 5-6 on the left arm of the third chromosome, in agreement with the previously determined location of a putative cluster encompassing the genes for the third instar larval cuticle proteins LCP5, LCP6 and LCP8. This cluster is the largest cuticle gene cluster discovered to date and shows a number of surprising features that explain in part the genetic complexity of the LCP5, LCP6 and LCP8 loci. The genes encoding LCP5 and LCP8 are multiple copy genes and the presence of extensive similarity in their coding regions gives the first evidence for gene conversion in cuticle genes. In addition, five genes in the cluster are intronless. Four of these five have arisen by retroposition. The other genes in the cluster have a single intron located at an unusual location for insect cuticle genes.     

Effects of asexual reproduction on the neighborhood area of cyclical parthenogens

The habitat occupied by a subpopulation and withinwhich there is random mating is known as itsneighborhood area. Neighborhood area is dependenton dispersal rates and organisms with low rates ofdispersal are expected to have small neighborhoodareas. In the absence of evolutionary forces,neighborhood areas under sexual reproduction will beconstant in size as long as dispersal patterns do notchange. This scenario differs when reproduction is bycyclical parthenogenesis since recombination anddispersal may occur in different generations. Ingeneral, dispersal distances increase with the numberof parthenogenetic generations. We show that cyclicalparthenogenesis increases neighborhood area which,concomitantly, decreases the potential for geneticsubdivision. It is noteworthy, however, that theincrease in neighborhood area is a decreasing functionof the number of parthenogenetic generations.This mechanism may have important implications for thepopulation structure of planktonic rotifers living ina horizontally undifferentiated habitat. In suchhabitats organisms are effectively unrestricted intheir lateral movements. Because rotifers typicallyhave low dispersal rates spatial geneticdiscontinuities may develop that divide the populationinto genetically distinct subpopulations. Counteringthis tendency is the increased neighborhood areaproduced by dispersal during the parthenogeneticphase. Thus cyclical parthenogenesis in organismslike rotifers may have important and previouslyunreported effects on the population's geneticstructure.     

Insulin activation of phosphatidylinositol 3-kinase in human skeletal muscle in vivo

Hickey, Matthew S., Charles J. Tanner, D. Sean O'Neill,Lydia J. Morgan, G. Lynis Dohm, and Joseph A. Houmard. Insulin activation of phosphatidylinositol 3-kinase in human skeletal muscle invivo. J. Appl. Physiol. 83(3):718-722, 1997.The purpose of this investigation was to determinewhether insulin-stimulated phosphatidylinositol 3-kinase (PI3-kinase)activity is detectable in needle biopsies of human skeletal muscle.Sixteen healthy nonobese males matched for age, percent fat, fastinginsulin, and fasting glucose participated in one of two experimentalprotocols. During an intravenous glucose tolerance test (IVGTT)protocol, insulin-stimulated PI3-kinase activity was determined frompercutaneous needle biopsies at 2, 5, and 15 min post-insulinadministration (0.025 U/kg). In the second group, a 2-h, 100 mU · m² · min¹euglycemic hyperinsulinemic clamp was performed, and biopsies wereobtained at 15, 60, and 120 min after insulin infusion was begun.Insulin stimulated PI3-kinase activity by 1.6 ± 0.2-, 2.2 ± 0.3-, and 2.2 ± 0.4-fold at 2, 5, and 15 min, respectively, duringthe IVGTT. During the clamp protocol, PI3-kinase was elevated by 5.3 ± 1.3-, 8.0 ± 2.6-, and 2.7 ± 1.4-fold abovebasal at 15, 60, and 120 min, respectively. Insulin-stimulatedPI3-kinase activity at 15 min post-insulin administration wassignificantly greater during the clamp protocol vs. the IVGTT(P < 0.05). These observations suggest that insulin-stimulated PI3-kinase activity is detectable inneedle biopsies of human skeletal muscle, and furthermore, that theeuglycemic, hyperinsulinemic clamp protocol may be a useful tool toassess insulin signaling in vivo.