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 (β) 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 β 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

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

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