The availably of completely-sequenced genomes and various kinds of system-wide datasets have motivated a great deal of interests in the quantitative studies of biology. Owing to the large amount of data, statistical analysis is usually employed. In particular, tools or methods used in statistical physics can be useful in this kind of analysis. In this dissertation, I summarize my work on genome-wide or system-wide studies of biological evolution and biological networks.

Regarding biological evolution, we present a study on the genome-wide distributions of sequence identities of paralogous protein pairs in various model organisms. We introduced a simple birth-and-death model based on gene duplication, gene deletion and point mutations to explain the common features in these distributions. Our mathematical framework revealed many important details including the relative rates of the evolutionary processes, previously unknown universality of intra-protein substitution rates and the consequences of whole genome duplications.

In the past decade, the idea of biological networks has emerged as a backbone to understand the complex interactions in biological systems. The studies presented in this dissertation cover three different aspects of biological networks: evolution, dynamics and algorithm. On the subject of network evolution, we quantified the topological divergence between paralogs in various protein networks and demonstrated that they provide certain functional redundancy. We also found that, at least in yeast, duplicated proteins lose their common regulators at a faster rate than common physical interaction partners. This can help explain how species with very similar gene contents can evolve novel properties in a relatively short timescale.

While the topology of biological networks serves as a starting point, it is important to study the underlying dynamical processes on networks. We present a study on the association and dissociation of proteins in a genome-wide protein interaction network. Like many biochemical reactions in a cell, physical interactions between proteins are stochastic in nature. We studied how fluctuations in protein abundance lead to those in free protein concentrations and dimers concentrations. In addition to induced fluctuations, we studied the thermal noise of the system and found that it is affected by both the network topology and the heterogeneity in protein abundance. Our results suggest that undesirable cross-talk mediated by reversible protein interactions can be significantly suppressed. From a practical point of view, very large networks appear in biology as a way to represent data from high-throughput experiments.

In the final part of this dissertation, we present a network-based algorithm to predict and verify indirect regulatory interactions in a large-scale genetic regulatory network. This algorithm is tailored for large and heavily interconnected networks, which are of growing importance due to the rapid accrual of regulatory interactions. We applied the algorithm to the regulatory networks of several model organisms curated from literature, resulting in novel predictions along with calibrated reliability of existing ones.