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

CDK2 and CKI targeting can significantly lower the cellular senescence bar - reveals a mathematical model of G1/S checkpoint pathway

Cellular senescence, a mechanism employed by cells for thwarting proliferation, has shown to play an important role in protecting cells against cancer development in recent experimental observations, indicating that a deeper understanding of the cellular senescence pathway can help exploit its capacity for more effective cancer treatment. Furthermore, some experimental evidence points out that inhibition of CDK2 or Skp2 can be the critical trigger for cellular senescence. However, no mathematical model has been developed to highlight cellular senescence until now. In this study, we first implement a mathematical model of G1/S transition involving the DNA-damage pathway to highlight cellular senescence by lowering the critical trigger- CDK2. For this, we focus on the behaviour of two important proteins (E2F and CycE) for several reduced CDK2 levels under two DNA-damage conditions by calculating the probability (&#x3b2;) of DNA-damaged cells passing the G1/S. Our recently published results from the same model indicated that a large percentage of damaged cells pass G1/S under normal CDK2 levels, reaching &#x3b2; values of up to 65% under high level of DNA damage. The current study reveals that reduced CDK2 levels can significantly lower the percentage of damaged cells passing the G1/S; in particular, 50% reduction in CDK2 achieves 65% reduction in the passage of damaged cells. Furthermore, the model analyses the relationship between CDK2 and its CKIs in search of other effective ways to bring forward cellular senescence. Results show that the degradation rate of p21 and initial concentration of p27 can be effectively used to lower the senescence threshold. Specifically, p27 is the most effective, followed by CDK2 and p21. However, the combined effect of CDK2 and CKIs is dramatic with CDK2/p27 combination almost totally arresting the passage of damaged cells. Biologists may wish to validate the efficacy of these targets for treating cancer