A logistic branching process for population genetics

A logistic (regulated population size) branching process population genetic model is presented. It is a modification of both the Wright-Fisher and (unconstrained) branching process models, and shares several properties including the coalescent time and shape, and structure of the coalescent process with those models. An important feature of the model is that population size fluctuation and regulation are intrinsic to the model rather than externally imposed. A consequence of this model is that the fluctuation in population size enhances the prospects for fixation of a beneficial mutation with constant relative viability, which is contrary to a result for the Wright-Fisher model with fluctuating population size. Explanation of this result follows from distinguishing between expected and realized viabilities, in addition to the contrast between absolute and relative viabilities.     

Meningitis,pathogenicity near criticality: the epidemiology of meningococcal disease as a model for accidental pathogens

We formulate and analyse a model for infectious diseases transmitted by asymptomatic carriers finding, that if harmless and pathogenic strains of the infected agent compete, frequent outbreaks of the pathogenic strains can occur. A counterintuitively high number of clustered outbreaks at low pathogenicity in our model compares well with observations in diseases with severe and often fatal results for the host, as for example in meningitis. These clustered outbreaks can be described by the typical scaling behaviour around criticality. The epidemic model is a susceptible-infected-recovered system (SIR) for the harmless infective agent, acting as a background to a mutant strain Y which occasionally creates severely affected hosts X. The full system of SIRYX is described in the master equation framework, confirming limiting assumptions about a reduced YX-system with the SIR-system in stationarity. In this limiting case we can analytically show convergence to power law scaling typical for critical states, as well as the divergence of the variance of outbreaks near criticality. These large fluctuations of outbreaks of accidental pathogens as mutants of otherwise harmless commensal organisms is the challenging new feature of our model for future epidemiology of diseases like meningococcal disease.     

Branch formation induced by microbeam irradiation ofAdiantum protonemata

Branches were induced in centrifugedAdiantum protonemal cells by partial irradiation with polarized red light. Nuclear behavior and microtubule pattern change during branch formation were investigated. A branch formed at any part where a red microbeam was focused along a long apical cell. The nucleus moved towards the irradiated area and remained there until a branch developed. The pattern of microtubules changed from parallel to oblique at the irradiated area and then a transverse arrangement of microtubules appeared on both sides of the area. It appeared as if the nucleus was suspended between two microtubule rings. This nuclear behavior and the changes in microtubule pattern were different from those observed during branch formation under whole cell irradiation. From the results of this work we suggest that there is an importance for precise control of experimental conditions.     

A branching model for the spread of infectious animal diseases in varying environments

This paper is concerned with a stochastic model, describing outbreaks of infectious diseases that have potentially great animal or human health consequences, and which can result in such severe economic losses that immediate sets of measures need to be taken to curb the spread. During an outbreak of such a disease, the environment that the infectious agent experiences is therefore changing due to the subsequent control measures taken. In our model, we introduce a general branching process in a changing (but not random) environment. With this branching process, we estimate the probability of extinction and the expected number of infected individuals for different control measures. We also use this branching process to calculate the generating function of the number of infected individuals at any given moment. The model and methods are designed using important infections of farmed animals, such as classical swine fever, foot-and-mouth disease and avian influenza as motivating examples, but have a wider application, for example to emerging human infections that lead to strict quarantine of cases and suspected cases (e.g. SARS) and contact and movement restrictions.     

Early prostate development and its association with late-life prostate disease

The development of the prostate is an emerging priority area for prostate biologists. Early changes in prostate development permanently alter prostate morphology and function and an understanding of the permanent nature of early events that may influence the onset of late-life disease is vital. Two of the inherent problems involve associating exposure in early life with outcome in late life or maturity and accounting for the influence of genetic, environmental, dietary or metabolic factors during the intervening period. Any one of these factors, alone or in combination, might lead to an explanation of the discrepancies found in the literature regarding the influence of early changes to the prostate in later life. Therefore, it is important to establish a causal link between the hormonal changes that occur during the fetal/neonatal period and that imprint the gland and the onset of late-life pathology. In order to achieve this goal, several technical challenges need to be overcome to permit the objective assessment of prostate branching morphogenesis. Stereological techniques now allow the quantification of several parameters of branching morphogenesis and the identification of specific early changes that are permanent and irreversible with a late-life outcome. This methodology provides the means to determine the action of a range of genes or hormone/growth factors that have been implicated in prostate development and disease. This study is supported by an NH&MRC program grant number 973218.     

BMP7 inhibits branching morphogenesis in the prostate gland and interferes with Notch signaling

The mouse prostate gland develops by branching morphogenesis from the urogenital epithelium and mesenchyme. Androgens and developmental factors, including FGF10 and SHH, promote prostate growth (Berman, D.M., Desai, N., Wang, X., Karhadkar, S.S., Reynon, M., Abate-Shen, C., Beachy, P.A., Shen, M.M., 2004. Roles for Hedgehog signaling in androgen production and prostate ductal morphogenesis. Dev. Biol. 267, 387-398; Donjacour, A.A., Thomson, A.A., Cunha, G.R., 2003. FGF-10 plays an essential role in the growth of the fetal prostate. Dev. Biol. 261, 39-54), while BMP4 signaling from the mesenchyme has been shown to suppresses prostate branching (Lamm, M.L., Podlasek, C.A., Barnett, D.H., Lee, J., Clemens, J.Q., Hebner, C.M., Bushman, W., 2001. Mesenchymal factor bone morphogenetic protein 4 restricts ductal budding and branching morphogenesis in the developing prostate. Dev. Biol. 232, 301-314). Here, we show that Bone Morphogenetic Protein 7 (BMP7) restricts branching of the prostate epithelium. BMP7 is expressed in the periurethral urogenital mesenchyme prior to formation of the prostate buds and, subsequently, in the prostate epithelium. We show that BMP7(lacZ/lacZ) null prostates show a two-fold increase in prostate branching, while recombinant BMP7 inhibits prostate morphogenesis in organ culture in a concentration-dependent manner. We further explore the mechanisms by which the developmental signals may be interpreted in the urogenital epithelium to regulate branching morphogenesis. We show that Notch1 activity is associated with the formation of the prostate buds, and that Notch1 signaling is derepressed in BMP7 null urogenital epithelium. Based on our studies, we propose a model that BMP7 inhibits branching morphogenesis in the prostate and limits the number of domains with high Notch1/Hes1 activity.