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Über dieses Buch

This brief introduces people with a basic background in probability theory to various problems in cancer biology that are amenable to analysis using methods of probability theory and statistics. The title mentions “cancer biology” and the specific illustrative applications reference cancer data but the methods themselves are more broadly applicable to all aspects of computational biology.

Aside from providing a self-contained introduction to basic biology and to cancer, the brief describes four specific problems in cancer biology that are amenable to the application of probability-based methods. The application of these methods is illustrated by applying each of them to actual data from the biology literature.

After reading the brief, engineers and mathematicians should be able to collaborate fruitfully with their biologist colleagues on a wide variety of problems.



Chapter 1. The Role of System Theory in Biology

In this chapter we introduce the reader to current methods for generating biological data, including such topics as micro-array (or gene expression) studies, ChIP-seq studies, siRNAs, and micro-RNAs. Special features of biological data that necessitate the development of new algorithms are highlighted, such as the lack of standardization in experimental procedures that lead in turn to broad variability of the data sets.
Mathukumalli Vidyasagar

Chapter 2. Analyzing Statistical Significance

In this chapter we review some popular methods for estimating the statistical significance of various conclusions that can be drawn from experimental data. These include the \(\chi ^2\)-text, the Kolmogorov–Smirnov (K–S) test for goodness of fit, the ‘student’ \(t\)-test for testing the null hypothesis that two sets of data have the same mean, Significance Analysis for Microarrays (SAM), Pattern Analysis for Microarrays (PAM) and Gene Set Enhancement Analysis (GSEA).
Mathukumalli Vidyasagar

Chapter 3. Inferring Gene Interaction Networks

This chapter contains the original research results on the monograph. We study the problem of reverse-engineering context-specific, genome-wide interaction networks from expression data. Two existing classes of methods, namely those based on mutual information and those based on Bayesian networks, are described first. Then a new algorithm, based on the so-called phi-mixing coefficient between random variables, is introduced. Unlike mutual information, the phi-mixing coefficient provides a directionally sensitive measure of the dependence between two random variables. The algorithm based on this new approach produces a gene interaction network in the form of a directed, strongly connected graph. The approach is validated on ChIP-seq data around the transcription factor ASCL1 in a lung cancer network.
Mathukumalli Vidyasagar

Chapter 4. Some Research Directions

In this final chapter, three different directions for future research are sketched. The first problem is that of harmonizing prior knowledge about gene interaction networks that is scattered throughout the literature with the output of the phixer algorithm. This is formulated as a problem in graph theory, and possible approaches are indicated. The second problem is to identify ‘genomic machines’, that is, sets of genes that are connected by edges that are all over-expressed, or all under-expressed, in a common context. This problem is formulated as one of computing (or at least approximating) the stationary distribution of a large Markov chain, where the states correspond to individual genes. The last problem is to separate causal mutations (drivers of cancer) from coincidental mutations (passengers in cancer). It is surmised that a seven-dimensional vector known as the developmental gene expression profile plays a role in discriminating between drivers and passengers. Preliminary evidence from colorectal cancer is examined, and it is suggested that further studies should be carried out using recently published comprehensive analysis of colorectal cancer.
Mathukumalli Vidyasagar
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