Modelling acidosis and the cell cycle in multicellular tumour spheroids

A partial differential equation model is developed to understand the effect that nutrient and acidosis have on the distribution of proliferating and quiescent cells and dead cell material (necrotic and apopotic) within a multicellular tumour spheroid. The rates of cell quiescence and necrosis depend upon the local nutrient and acid concentrations and quiescent cells are assumed to consume less nutrient and produce less acid than proliferating cells. Analysis of the differences in nutrient consumption and acid production by quiescent and proliferating cells shows low nutrient levels do not necessarily lead to increased acid concentration via anaerobic metabolism. Rather, it is the balance between proliferating and quiescent cells within the tumour which is important; decreased nutrient levels lead to more quiescent cells, which produce less acid than proliferating cells. We examine this effect via a sensitivity analysis which also includes a quantification of the effect that nutrient and acid concentrations have on the rates of cell quiescence and necrosis.

Zinc chelatase in human lymphocytes: detection of the enzymatic defect in erythropoietic protoporphyria

We describe a fluorometric assay for heme synthetase, the enzyme that is genetically deficient in erythropoietic protoporphyria. The method, which can readily detect activity in 1 microliter of packed human lymphocytes, is based on the formation of zinc protoheme from protoporphyrin IX. That zinc chelatase and ferrochelatase activities reside in the same enzyme was shown by the competitive action of ferrous ions and the inhibitory effects of N-methyl protoporphyrin (a specific inhibitor of heme synthetase) on zinc chelatase. The Km for zinc was 11 micrograms and that for protoporphyrin IX was 6 microM. The Ki fro ferrous ions was 14 microM. Zinc chelatase was reduced to 15.3% of the mean control activity in lymphocytes obtained from patients with protoporphyria, thus confirming the defect of heme biosynthesis in this disorder. The assay should prove to be useful for determining heme synthetase in tissues with low specific activity and to investigate further the enzymatic defect in protoporphyria.

The global effect of follicle-stimulating hormone and tumour necrosis factor α on gene expression in cultured bovine ovarian granulosa cells

Background Oocytes mature in ovarian follicles surrounded by granulosa cells. During follicle growth, granulosa cells replicate and secrete hormones, particularly steroids close to ovulation. However, most follicles cease growing and undergo atresia or regression instead of ovulating. To investigate the effects of stimulatory (follicle-stimulating hormone; FSH) and inhibitory (tumour necrosis factor alpha; TNFα) factors on the granulosa cell transcriptome, bovine ovaries were obtained from a local abattoir and pools of granulosa cells were cultured in vitro for six days under defined serum-free conditions with treatments present on days 3–6. Initially dose–response experiments (n = 4) were performed to determine the optimal concentrations of FSH (0.33 ng/ml) and TNFα (10 ng/ml) to be used for the microarray experiments. For array experiments cells were cultured under control conditions, with FSH, with TNFα, or with FSH plus TNFα (n = 4 per group) and RNA was harvested for microarray analyses. Results Statistical analysis showed primary clustering of the arrays into two groups, control/FSH and TNFα/TNFα plus FSH. The effect of TNFα on gene expression dominated that of FSH, with substantially more genes differentially regulated, and the pathways and genes regulated by TNFα being similar to those of FSH plus TNFα treatment. TNFα treatment reduced the endocrine activity of granulosa cells with reductions in expression of FST, INHA, INBA and AMH. The top-ranked canonical pathways and GO biological terms for the TNFα treatments included antigen presentation, inflammatory response and other pathways indicative of innate immune function and fibrosis. The two most significant networks also reflect this, containing molecules which are present in the canonical pathways of hepatic fibrosis/hepatic stellate cell activation and transforming growth factor β signalling, and these were up regulated. Upstream regulator analyses also predicted TNF, interferons γ and β1 and interleukin 1β. Conclusions In vitro, the transcriptome of granulosa cells responded minimally to FSH compared with the response to TNFα. The response to TNFα indicated an active process akin to tissue remodelling as would occur upon atresia. Additionally there was reduction in endocrine function and induction of an inflammatory response to TNFα that displays features similar to immune cells.

A moving mesh approach for modelling avascular tumour growth

A key step in many numerical schemes for time-dependent partial differential equations with moving boundaries is to rescale the problem to a fixed numerical mesh. An alternative approach is to use a moving mesh that can be adapted to focus on specific features of the model. In this paper we present and discuss two different velocity-based moving mesh methods applied to a two-phase model of avascular tumour growth formulated by Breward et al. (2002) J. Math. Biol. 45(2), 125-152. Each method has one moving node which tracks the moving boundary. The first moving mesh method uses a mesh velocity proportional to the boundary velocity. The second moving mesh method uses local conservation of volume fraction of cells (masses). Our results demonstrate that these moving mesh methods produce accurate results, offering higher resolution where desired whilst preserving the balance of fluxes and sources in the governing equations.