Stochastic Modeling of Telomere Biology: Probabilistic Analysis of Telomere Shortening and Network-Based Approach to Gene Expression Analysis
Lee, Kyung Hyun
Doctor of Philosophy
We consider stochastic models of telomere shortening and lengthening in normal and malignant cells. Telomeres are repetitive nucleotide caps located at the ends of each eukaryotic chromosome. Normally, they are subject to shortening during each DNA replication, and their length is a tool that cells use to sense the number of divisions. Short telomeres initiate a proliferative arrest of cells, which is termed `replicative senescence.’ It has been shown to occur at approximately 50 cell divisions, the so-called Hayflick’s limit. However, in cancer cells, telomere lengths are stabilized by two known mechanisms, activation of telomerase and Alternative Lengthening of Telomeres (ALT), thereby allowing continual cell replication. The connections between the two mechanisms are complicated and still poorly understood. This Ph.D. dissertation proposes a stochastic analysis of two specific questions in telomere biology: time-dependent correlation among genes associated with telomere maintenance mechanisms and dynamics of telomere lengths. In the first part, we suggest that two stochastic models motivated by queueing theory, G-Networks and Stochastic Automata Networks (SANs), are useful to analyze gene regulatory networks. Our study using G-Networks detects statistically significant genes (CEBPA, FOXM1, E2F1, c-MYC, hTERT) in cells with telomere maintenance. A new algorithm based on SANs is then introduced to show how the time-dependent correlation between two genes of interest varies according to telomere maintenance mechanism and each cell condition (normal or malignant). This study expands our existing knowledge of genes associated with telomere maintenance and provides a platform to understand similarities and differences between telomerase and ALT. In the second part, we propose a stochastic model for the shortest telomere lengths in cells with telomere maintenance mechanisms. Based on a necessary condition for the existence of stationarity, an explicit stationary probability distribution is derived when elongated telomere lengths follow geometric and uniform distributions. Moreover, we identify the distributional properties of attrition and elongation rates using maximum likelihood estimation and Bayes estimation. This study investigates the mathematical relationship between the telomere attrition and elongation rates in cells with telomere maintenance which can be a useful biomarker of disease diagnosis and prognosis.