Size-biased branching population measures and the multi-type xlog⁡xx\log x condition

We investigate the $x\log x$ condition for a general (Crump--Mode--Jagers) multi-type branching process with a general type space by constructing a size-biased population measure that relates to the ordinary population measure via an intrinsic martingale $W_t$. Sufficiency of the $x\log x$ condition for a non-degenerate limit of $W_t$ is proved and conditions for necessity are investigated.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ211 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Size-Biased Branching Population Measures and the Multi-Type \u3cem\u3ex\u3c/em\u3e Log \u3cem\u3ex\u3c/em\u3e Condition

We investigate the x log x condition for a general (Crump–Mode–Jagers) multi-type branching process with arbitrary type space by constructing a size-biased population measure that relates to the ordinary population measure via the intrinsic martingale Wt. Sufficiency of the x log x condition for a non-degenerate limit of Wt is proved and conditions for necessity are investigated

Can Telomere Shortening Explain Sigmoidal Growth Curves?

A general branching process model is proposed to describe the shortening of telomeres in eukaryotic chromosomes. The model is flexible and incorporates many special cases to be found in the literature. In particular, we show how telomere shortening can give rise to sigmoidal growth curves, an idea first expressed by Portugal et al. [A computational model for telomere-dependent cell-replicative aging, BioSystems 91 (2008), pp. 262–267]. We also demonstrate how other types of growth curves arise if telomere shortening is mitigated by other cellular processes. We compare our results with published data sets from the biological literature

Budding Yeast, Branching Processes, and Generalized Fibonacci Numbers

A real-world application of branching processes to a problem in cell biology where the generalized Fibonacci numbers known as k-nacci numbers play a crucial role is described. The k-nacci sequence is used to obtain asymptotics, computational formulas, and to justify certain practical simplifications. Along the way, an explicit formula for the sum of k-nacci numbers is established

A Stochastic Model of Cell Cycle Desynchronization

A general branching process model is suggested to describe cell cycle desynchronization. Cell cycle phase times are modeled as random variables and a formula for the expected fraction of cells in S phase as a function of time is established. The model is compared to data from the literature and is also compared to previously suggested deterministic and stochastic models

Modeling Growth and Telomere Dynamics in Saccharomyces Cerevisiae

A general branching process is proposed to model a population of cells of the yeast Saccharomyces cerevisiae following loss of telomerase. Previously published experimental data indicate that a population of telomerase-deficient cells regain exponential growth after a period of slowing due to critical telomere shortening. The explanation for this phenomenon is that some cells engage telomerase-independent pathways to maintain telomeres that allow them to become “survivors.” Our model takes into account random variation in individual cell cycle times, telomere length, finite lifespan of mother cells, and survivorship. We identify and estimate crucial parameters such as the probability of an individual cell becoming a survivor, and compare our model predictions to experimental data

Networked aspects of lifelong work-integrated learning: The BUFFL case

The increasingly digitalised and continuously changing working life needs a continuous lifelong professional development that preferably is networked and work-integrated. This this study builds upon university teachers' and course participants’ experiences from a technology enhanced project called BUFFL A pilot project that combines truly work-integrated learning with lifelong learning, in a strive to address the contemporary need for continuous professional development. The important aim in the BUFFL project is to develop a model for collaborative, flexible, and lifelong professional development. A new and interesting concept in the BUFFL project was to involve concept of Bringing Your Own Data for activities in course modules. The aim of this study is to describe and discuss the lifelong work-integrated learning in the BUFFL project from a networked learning perspective. Data were gathered from e-mail interviews with teachers, e-mail conversations between teachers, facilitators and course participants, and from course evaluations. Results from the data sources have been grouped into three main themes in an inductive thematic analysis. Findings show that in academia, in industry, and in the in between a potential is found in the form of collaborative learning. A networked collaboration that should involve the theories from academia, combined with real-world-problems in the workplace, to achieve a fruitful meeting between academia and the industr

Superoxide Dismutase 3 Limits Collagen-Induced Arthritis in the Absence of Phagocyte Oxidative Burst

Extracellular superoxide dismutase (SOD3), an enzyme mediating dismutation of superoxide into hydrogen peroxide, has been shown to reduce inflammation by inhibiting macrophage migration into injured tissues. In inflamed tissues, superoxide is produced by the phagocytic NOX2 complex, which consists of the catalytic subunit NOX2 and several regulatory subunits (e.g., NCF1). To analyze whether SOD3 can regulate inflammation in the absence of functional NOX2 complex, we injected an adenoviral vector overexpressing SOD3 directly into the arthritic paws of Ncf1∗/∗ mice with collagen-induced arthritis. SOD3 reduced arthritis severity in both oxidative burst-deficient Ncf1∗/∗ mice and also in wild-type mice. The NOX2 complex independent anti-inflammatory effect of SOD3 was further characterized in peritonitis, and SOD3 was found to reduce macrophage infiltration independently of NOX2 complex functionality. We conclude that the SOD3-mediated anti-inflammatory effect on arthritis and peritonitis operates independently of NOX2 complex derived oxidative burst

Differential gene expression in pristane-induced arthritis susceptible DA versus resistant E3 rats

Arthritis susceptibility genes were sought by analysis of differential gene expression between pristane-induced arthritis (PIA)-susceptible DA rats and PIA-resistant E3 rats. Inguinal lymph nodes of naïve animals and animals 8 days after pristane injection were analyzed for differential gene expression. mRNA expression was investigated by microarray and real-time PCR, and protein expression was analyzed by flow cytometry or ELISA. Twelve genes were significantly differentially expressed when analyzed by at least two independent methods, and an additional five genes showed a strong a tendency toward differential expression. In naïve DA rats IgE, the bone marrow stromal cell antigen 1 (Bst1) and the MHC class II β-chain (MhcII) were expressed at a higher level, and the immunoglobulin kappa chain (Igκ) was expressed at a lower level. In pristane-treated DA rats the MHC class II β-chain, gelatinase B (Mmp9) and the protein tyrosine phosphatase CL100 (Ptpn16) were expressed at a higher level, whereas immunoglobulins, the CD28 molecule (Cd28), the mast cell specific protease 1 (Mcpt1), the carboxylesterase precursor (Ces2), K-cadherin (Cdh6), cyclin G1 (Ccng1), DNA polymerase IV (Primase) and the tumour associated glycoprotein E4 (Tage) were expressed at a lower level. Finally, the differentially expressed mRNA was confirmed with protein expression for some of the genes. In conclusion, the results show that animal models are well suited for reproducible microarray analysis of candidate genes for arthritis. All genes have functions that are potentially important for arthritis, and nine of the genes are located within genomic regions previously associated with autoimmune disease