A Stochastic Model for Hydrodynamic Dispersion

In this chapter we develop one dimensional model without resorting to Fickian assumptions and discuss the methods of estimating the parameters. As of many contracted description of a natural phenomena the model presented in this chapter has its weaknesses. But we model the fluctuation of the solute velocity due to porous structure and incorporate the fluctuation in the mass conservation of solute. Then we need to characterise the fluctuations so that we can relate them to the porous structure

Integrated signaling pathway and gene expression regulatory model to dissect dynamics of <em>Escherichia coli </em>challenged mammary epithelial cells

AbstractCells transform external stimuli, through the activation of signaling pathways, which in turn activate gene regulatory networks, in gene expression. As more omics data are generated from experiments, eliciting the integrated relationship between the external stimuli, the signaling process in the cell and the subsequent gene expression is a major challenge in systems biology. The complex system of non-linear dynamic protein interactions in signaling pathways and gene networks regulates gene expression.The complexity and non-linear aspects have resulted in the study of the signaling pathway or the gene network regulation in isolation. However, this limits the analysis of the interaction between the two components and the identification of the source of the mechanism differentiating the gene expression profiles. Here, we present a study of a model of the combined signaling pathway and gene network to highlight the importance of integrated modeling.Based on the experimental findings we developed a compartmental model and conducted several simulation experiments. The model simulates the mRNA expression of three different cytokines (RANTES, IL8 and TNFα) regulated by the transcription factor NFκB in mammary epithelial cells challenged with E. coli. The analysis of the gene network regulation identifies a lack of robustness and therefore sensitivity for the transcription factor regulation. However, analysis of the integrated signaling and gene network regulation model reveals distinctly different underlying mechanisms in the signaling pathway responsible for the variation between the three cytokine's mRNA expression levels. Our key findings reveal the importance of integrating the signaling pathway and gene expression dynamics in modeling. Modeling infers valid research questions which need to be verified experimentally and can assist in the design of future biological experiments

Using emergent clustering methods to analyse short time series gene expression data from childhood leukemia treated with glucocorticoids

Acute lymphoblastic leukemia (ALL) causes the highest number of deaths from cancer in children aged between one and fourteen. The most common treatment for children with ALL is chemotherapy, a cancer treatment that uses drugs to kill cancer cells or stop cell division. The drug and dosage combinations may vary for each child. Unfortunately, chemotherapy treatments may cause serious side effects. Glucocorticoids (GCs) have been used as therapeutic agents for children with ALL for more than 50 years. Common and widely drugs in this class include prednisolone and dexamethasone. Childhood leukemia now has a survival rate of 80% (Pui, Robison, & Look, 2008). The key clinical question is identifying those children who will not respond well to established therapy strategies.GCs regulate diverse biological processes, for example, metabolism, development, differentiation, cell survival and immunity. GCs induce apoptosis and G1 cell cycle arrest in lymphoid cells. In fact, not much is known about the molecular mechanism of GCs sensitivity and resistance, and GCs-induced apoptotic signal transduction pathways and there are many controversial hypotheses about both genes regulated by GCs and potential molecular mechanism of GCs-induced apoptosis. Therefore, understanding the mechanism of this drug should lead to better prognostic factors (treatment response), more targeted therapies and prevention of side effects. GCs induced apoptosis have been studied by using microarray technology in vivo and in vitro on samples consisting of GCs treated ALL cell lines, mouse thymocytes and/or ALL patients. However, time series GCs treated childhood ALL datasets are currently extremely limited. DNA microarrays are essential tools for analysis of expression of many genes simultaneously. Gene expression data show the level of activity of several genes under experimental conditions. Genes with similar expression patterns could belong to the same pathway or have similar function. DNA microarray data analysis has been carried out using statistical analysis as well as machine learning and data mining approaches. There are many microarray analysis tools; this study aims to combine emergent clustering methods to get meaningful biological insights into mechanisms underlying GCs induced apoptosis. In this study, microarray data originated from prednisolone (glucocorticoids) treated childhood ALL samples (Schmidt et al., 2006) (B-linage and T-linage) and collected at 6 and 24 hours after treatment are analysed using four methods: Selforganizing maps (SOMs), Emergent self-organizing maps (ESOM) (Ultsch & Morchen, 2005), the Short Time series Expression Miner (STEM) (Ernst & Bar-Joseph, 2006) and Fuzzy clustering by Local Approximation of MEmbership (FLAME) (Fu & Medico, 2007). The results revealed intrinsic biological patterns underlying the GCs time series data: there are at least five different gene activities happening during the three time points; GCs-induced apoptotic genes were identified; and genes active at both time points or only at 6 hours or 24 hours were determined. Also, interesting gene clusters with membership in already known pathways were found thereby providing promising candidate gens for further inferring GCs induced apoptotic gene regulatory networks