Scale-Free Networks in Molecular Biology: Algorithms and Random Walks Analyses

In this research, I focus on I) the mean field analysis of algorithms for scale-free networks in molecular biology and II) the analysis of biological networks using random walks and related algorithms. I: Many systems in nature and society are described by means of complex networks. Research indicates that these complex networks exhibit scale-free properties. Studying the organizing principles of scale-free networks has significant implications in different fields including developing better drugs, defending the internet from hackers, halting the spread of deadly epidemics, developing marketing strategies, etc. The sampling of scale-free networks in molecular biology is usually achieved by growing networks from a seed using recursive algorithms with elementary moves which include the addition and deletion of nodes and bonds. These algorithms include the Barabasi-Albert algorithm. Later algorithms, such as the Duplication-Divergence algorithm, the Sole algorithm and the iSite algorithm, were inspired by biological processes underlying the evolution of protein networks, and the networks they produce differ essentially from networks grown by the Barabasi-Albert algorithm. The mean field analysis of these algorithms is reconsidered, and extended to variant and modified implementations of the algorithms. II: The second part of this research focuses on improving biological networks using random walks and related algorithms. I use different algorithms with the goal of finding highly connected hubs and clusters of proteins which are closely related to one another. This is done by building up protein-protein interaction networks and miRNA-gene interaction networks which are then subjected to the action of two algorithms. The first algorithm used is the random walk with resistance algorithm. As an alternative, I am proposing solving the lattice laplacian on a network as a method to discover clusters of biologically related genes. These approaches seek to find ways of solving complex pathway membership problems in protein interaction databases. The clusters obtained provide more biological insight as opposed to a process of local pairwise comparison between interacting proteins. They may also predict new members in functional pathways or clusters. Underlying these algorithms are simulated biased random walks on the network for determining membership of proteins in given clusters