Scaling analysis of the unsteady natural convection boundary layer adjacent to an inclined plate for Pr > 1 following instantaneous heating

The unsteady natural convection boundary layer adjacent to an instantaneously heated inclined plate is investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer following instantaneous heating may be classified into three distinct stages including a start-up stage, a transitional stage and a steady state stage, which can be clearly identified in the analytical and numerical results. Major scaling relations of the velocity and thicknesses and the flow development time of the natural convection boundary layer are obtained using triple-layer integral solutions and verified by direct numerical simulations over a wide range of flow parameters.

Early childhood education : the natural starting point for environmental education

Young children are most vulnerable to, and most at risk from, environmental and sustainability challenges. Early education investments aimed at addressing such issues, until recently however, have been neglected or under-rated. Fortunately, this is changing. A groundswell of practitioner interest in early childhood environmental education/ education for sustainability is emerging, in contrast to the ‘patches of green’ that have characterised previous decades. Indeed, an international coalition for early childhood education for sustainability (ECEfS) is beginning to develop, evidenced by The Gothenburg Recommendations on Education for Sustainable Development (2008) that identifies early childhood, within a framework of lifelong learning, as a ‘natural starting point’ for all ongoing education for sustainability. This document is important as it is the first international statement to explicitly identify ECEfS as contributing to education for sustainability. The next challenge for ECEfS is for practitioner mobilisation to be matched by research activity aimed at broadening and deepening practice-based responses. This is the next exciting frontier in the legitimisation of ECEfS.

Evidence for u.v. induction of CDKN2 mutations in melanoma cell lines

The CDKN2 gene, encoding the cyclin dependent kinase inhibitor p16, is a tumour suppressor gene involved in melanoma and maps to chromosome band 9p22. Mutations or interstitial deletions of this gene have been found both in the germline of familial melanoma cases and somatically in melanoma cell lines. Previous mutation analyses of melanoma cell lines have indicated a high frequency of C:G to T:A transitions, with all of these mutations occurring at dipyrimidine sites. Including three melanoma cell lines carrying tandem CC to TT mutations, the spectrum of mutations so far reported indicates a possible role for u.v. radiation in the mutagenesis of this gene in some tumours. To further examine this hypothesis we have characterised mutations of the CDKN2 gene in 30 melanoma cell lines. Nineteen lines carried complete or partial homozygous deletions of the gene. Of the remaining cell lines, eight were shown by direct sequencing of PCR products from exon 1 and exon 2 to carry a total of nine different mutations of CDKN2. Two cell lines carried tandem CC to TT mutations and a high rate of C:G to T:A transitions was observed. This study provides further evidence for the role of u.v. light in the genesis of melanoma, with one target being the CDKN2 tumour suppressor gene.

CDKN2A/p16 is inactivated in most melanoma cell lines

The CDKN2A gene maps to chromosome 9p21-22 and is responsible for melanoma susceptibility in some families. Its product, p16, binds specifically to CDK4 and CDK6 in vitro and in vivo, inhibiting their kinase activity. CDKN2A is homozygously deleted or mutated in a large proportion of tumor cell lines and some primary tumors, including melanomas. The aim of this study was to investigate the involvement of CDKN2A and elucidate the mechanisms of p16 inactivation in a panel of 60 cell lines derived from sporadic melanomas. Twenty-six (43%) of the melanoma lines were homozygously deleted for CDKN2A, and an additional 15 (25%) lines carried missense, nonsense, or frameshift mutations. All but one of the latter group were shown by microsatellite analysis to be hemizygous for the region of 9p surrounding CDKN2A. p16 was detected by Western blotting in only five of the cell lines carrying mutations. Immunoprecipitation of p16 in these lines, followed by Western blotting to detect the coprecipitation of CDK4 and CDK6, revealed that p16 was functionally compromised in all cell lines but the one that carried a heterozygous CDKN2A mutation. In the remaining 19 lines that carried wild-type CDKN2A alleles, Western blot analysis and immunoprecipitation indicated that 11 cell lines expressed a wild-type protein. Northern blotting was performed on the remaining eight cell lines and revealed that one cell line carried an aberrantly sized RNA transcript, and two other cell lines failed to express RNA. The promoter was found to be methylated in five cell lines that expressed CDKN2A transcript but not p16. Presumably, the message seen by Northern blotting in these cell lines is the result of cross-hybridization of the total cDNA probe with the exon 1beta transcript. Microsatellite analysis revealed that the majority of these cell lines were hemi/homozygous for the region surrounding CDKN2A, indicating that the wild-type allele had been lost. In the 11 cell lines that expressed functional p16, microsatellite analysis revealed loss of heterozygosity at the markers immediately surrounding CDKN2A in five cases, and the previously characterized R24C mutation of CDK4 was identified in one of the remaining 6 lines. These data indicate that 55 of 60 (92%) melanoma cell lines demonstrated some aberration of CDKN2A or CDK4, thus suggesting that this pathway is a primary genetic target in melanoma development.

CDKN2A is not the principal target of deletions on the short arm of chromosome 9 in neuroendocrine (Merkel cell) carcinoma of the skin

The majority of small-cell lung cancers (SCLCs) express p16 but not pRb. Given our previous study showing loss of pRb in Merkel cell carcinoma (MCC)/neuroendocrine carcinoma of the skin and the clinicopathological similarities between SCLC and MCC, we wished to determine if this was also the case in MCC. Twenty-nine MCC specimens from 23 patients were examined for deletions at 10 loci on 9p and 1 on 9q. No loss of heterozygosity (LOH) was seen in 9 patients including 2 for which tumour and cell line DNAs were examined. Four patients had LOH for all informative loci on 9p. Ten tumours showed more limited regions of loss on 9p, and from these 2 common regions of deletion were determined. Half of all informative cases had LOH at D9S168, the most telomeric marker examined, and 3 specimens showed loss of only D9S168. A second region (IFNA-D9S126) showed LOH in 10 (44%) cases, and case MCC26 showed LOH for only D9S126, implicating genes centromeric of the CDKN2A locus. No mutations in the coding regions of p16 were seen in 7 cell lines tested, and reactivity to anti-p16 antibody was seen in all 11 tumour specimens examined and in 6 of 7 cell lines from 6 patients. Furthermore, all cell lines examined reacted with anti-p14(ARF) antibody. These results suggest that neither transcript of the CDKN2A locus is the target of deletions on 9p in MCC and imply the existence of tumour-suppressor genes mapping both centromeric and telomeric of this locus.

Mutations in exon 3 of the beta-catenin gene are rare in melanoma cell lines

Mutations in exon 3 of the CTNNB1 gene encoding beta-catenin have been reported in colorectal cancer cell lines and tumours. Although one study reported mutations or deletions affecting beta-catenin in 20% of melanoma cell lines, subsequent reports detected a much lower frequency of aberrations in uncultured melanomas. To determine whether this difference in mutation frequency reflected an in vitro culturing artefact, exon 3 of CTNNB1 was screened in a panel of 62 melanoma cell lines. In addition, reverse transcription-polymerase chain reaction (RT-PCR) was performed to detect intragenic deletions affecting exon 3. One out of 62 (1.6%) cell lines was found to carry a mutation, indicating that aberration of the Wnt-1/wingless pathway through activation of beta-catenin is a rare event, even in melanoma cell lines.

PTEN inactivation is rare in melanoma tumours but occurs frequently in melanoma cell lines

Deletions detected in cytogenetic and loss of heterozygosity (LOH) studies indicate that at least one tumour suppressor gene maps to the long arm of chromosome 10. Previous deletion mapping studies have observed LOH on 10q in about 30% of melanomas analysed. The PTEN gene, mapping to chromosome band 10q23.3, encodes a protein with both lipid and protein phosphatase activity. Somatic mutations and deletions in have been detected in a variety of cell lines and tumours, including melanoma samples. We performed mutation analyses and extensive allelic loss studies to investigate the role this gene plays in melanoma pathogenesis. We found that a total of 34 out of 57 (60%) melanoma cell lines carried hemizygous deletions of chromosome 10q encompassing the PTEN locus. A further three cell lines carried smaller deletions excluding PTEN. Inactivation of both PTEN alleles by exon-specific homozygous deletion or mutation was observed in 13 out of 57 (23%) melanoma cell lines. The mutation spectrum observed does not indicate an important role for ultraviolet radiation in the genesis of these mutations, and evidence from three cell lines supports the acquisition of PTEN aberrations in culture. Ten out of 49 (20%) matched melanoma tumour/normal samples harboured hemizygous deletions of either the whole chromosome or most of the long arm. Mutations within were detected in only one of the 10 tumours demonstrating LOH at 10q23 that were analysed. These results suggest that PTEN inactivation may be important for the propagation of melanoma cells in culture, and that another chromosome 10 tumour suppressor gene may be important for melanoma pathogenesis.

p53 prevents progression of nevi to melanoma predominantly through cell cycle regulation

p53 is the central member of a critical tumor suppressor pathway in virtually all tumor types, where it is silenced mainly by missense mutations. In melanoma, p53 predominantly remains wild type, thus its role has been neglected. To study the effect of p53 on melanocyte function and melanomagenesis, we crossed the 'high-p53'Mdm4+/- mouse to the well-established TP-ras0/+ murine melanoma progression model. After treatment with the carcinogen dimethylbenzanthracene (DMBA), TP-ras0/+ mice on the Mdm4+/- background developed fewer tumors with a delay in the age of onset of melanomas compared to TP-ras0/+ mice. Furthermore, we observed a dramatic decrease in tumor growth, lack of metastasis with increased survival of TP-ras0/+: Mdm4+/- mice. Thus, p53 effectively prevented the conversion of small benign tumors to malignant and metastatic melanoma. p53 activation in cultured primary melanocyte and melanoma cell lines using Nutlin-3, a specific Mdm2 antagonist, supported these findings. Moreover, global gene expression and network analysis of Nutlin-3-treated primary human melanocytes indicated that cell cycle regulation through the p21WAF1/CIP1 signaling network may be the key anti-melanomagenic activity of p53.

Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

Linear models for endocytic transformations from live cell imaging

Endocytosis is the process by which cells internalise molecules including nutrient proteins from the extracellular media. In one form, macropinocytosis, the membrane at the cell surface ruffles and folds over to give rise to an internalised vesicle. Negatively charged phospholipids within the membrane called phosphoinositides then undergo a series of transformations that are critical for the correct trafficking of the vesicle within the cell, and which are often pirated by pathogens such as Salmonella. Advanced fluorescent video microscopy imaging now allows the detailed observation and quantification of these events in live cells over time. Here we use these observations as a basis for building differential equation models of the transformations. An initial investigation of these interactions was modelled with reaction rates proportional to the sum of the concentrations of the individual constituents. A first order linear system for the concentrations results. The structure of the system enables analytical expressions to be obtained and the problem becomes one of determining the reaction rates which generate the observed data plots. We present results with reaction rates which capture the general behaviour of the reactions so that we now have a complete mathematical model of phosphoinositide transformations that fits the experimental observations. Some excellent fits are obtained with modulated exponential functions; however, these are not solutions of the linear system. The question arises as to how the model may be modified to obtain a system whose solution provides a more accurate fit.

Phenomenological modeling of cell-to-cell and beat-to-beat variability in isolated Guinea Pig ventricular myocytes

Experimental action potential (AP) recordings in isolated ventricular myoctes display significant temporal beat-to-beat variability in morphology and duration. Furthermore, significant cell-to-cell differences in AP also exist even for isolated cells originating from the same region of the same heart. However, current mathematical models of ventricular AP fail to replicate the temporal and cell-to-cell variability in AP observed experimentally. In this study, we propose a novel mathematical framework for the development of phenomenological AP models capable of capturing cell-to-cell and temporal variabilty in cardiac APs. A novel stochastic phenomenological model of the AP is developed, based on the deterministic Bueno-Orovio/Fentonmodel. Experimental recordings of AP are fit to the model to produce AP models of individual cells from the apex and the base of the guinea-pig ventricles. Our results show that the phenomenological model is able to capture the considerable differences in AP recorded from isolated cells originating from the location. We demonstrate the closeness of fit to the available experimental data which may be achieved using a phenomenological model, and also demonstrate the ability of the stochastic form of the model to capture the observed beat-to-beat variablity in action potential duration.