The first three chapters of this dissertation describe a novel Bayesian methodology which uses random walk sampling for rapid inference of the statistical properties of undirected networks with weighted or unweighted edges. The statistics of interest include, but are not limited to, the node degree distribution, the average degree of nearest-neighbor nodes, and the node clustering coefficient. Our formalism yields high-accuracy estimates of the probability distribution of any network node-based property, and of the network size, after only a small fraction of network nodes has been explored. The Bayesian nature of our approach provides rigorous estimates of all parameter uncertainties. We demonstrate our framework on several standard examples, including random, scale-free, and small-world networks, and apply it to study epidemic spreading on a scale-free network. We also infer properties of the large-scale network formed by hyperlinks between Wikipedia pages.
During our analysis of complex networks, the connection between the frequencies of codons and the first-passage dynamics on the underlying single-point mutational network, which describes the evolution of gene sequences, was investigated. Viewing codon evolution as a random walk with deleterious sequences representing absorbing states inevitably led to the development of a detailed biophysical model for the investigation of codon usage bias. Frequencies of synonymous codons are typically non-uniform, despite the fact that such codons correspond to the same amino acid in the genetic code. This phenomenon, known as codon usage bias, is believed to be due to a combination of factors including genetic drift, mutational effects, and selection for speed and accuracy of codon translation; however, its quantitative modeling has been elusive. Here we develop a biophysical population genetics model capable of explaining genome-wide codon frequencies. Our model implements codon-level treatment of mutations with transition/transversion biases, and includes two contributions to codon fitness which describe codon translation speed and accuracy. Furthermore, it allows wobble pairing—codon-anticodon base pairing mismatches at the 3’ nucleotide position of the codon. We find that the observed patterns of genome-wide codon usage are consistent with a strong selective penalty for mistranslated amino acids. In contrast, the dependence of codon fitness on translation speed is weaker on average compared to the strength of selection against mistranslation. Although no constraints on codon-anticodon pairing are imposed a priori, a reasonable hierarchy of pairing rates, which conforms to the wobble hypothesis and is consistent with available structural evidence, is predicted by the model. Finally, we estimate mutation rates per nucleotide directly from the coding sequences by treating the translation process explicitly in the context of a finite ribosomal pool, and predict that mutation rates are inversely proportional to the number of genes. Overall, our approach offers a unified biophysical and population genetics framework for studying codon bias.
|Advisor:||Morozov, Alexandre V.|
|School:||Rutgers The State University of New Jersey, School of Graduate Studies|
|Department:||Physics and Astronomy|
|School Location:||United States -- New Jersey|
|Source:||DAI-B 81/7(E), Dissertation Abstracts International|
|Keywords:||Biophysical modeling, Codon usage bias, Complex networks, First-passage, Population genetics, Random walks|
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