Bayesian Inference of Complex Networks & A Network-Inspired Approach to the Codon Bias
Complex networks are numerous in the life sciences with examples from clusters of cells to the scale of full ecosystems. To make predictions about the dynamics of these complex systems, properties of the underlying networks often must be known. Random walk sampling is one method for acquiring information about these complex systems when it is impractical or impossible to query the entire network. Using the results of non-equilibrium statistical mechanics and Bayes' theorem, we have developed a theoretical formalism for generating estimators of global network properties within the framework of random walk sampling. After introducing this formalism, I will present the results of applying this sampling process to several examples of complex networks in the fields of Computer Science and Epidemiology, and show that the estimators converge to the true network values even after only a small portion of the full network has been sampled.
A further application of networks in the life sciences arises in my investigation of the codon bias. The central dogma of biology has triplets of nucleotides called codons translated into amino acids for the production of all proteins. As there are far more codons than amino acids, this translation code is necessarily degenerate with as many as six codons translated into a single amino acid. With the functionality of proteins determined by their amino acid sequences, the choice of synonymous codon should be determined solely by mutation. The unexpected enrichment in the usage of certain synonymous codons observed in genomic data is known as the codon bias. A proposed explanation for this bias is that certain codons are more efficiently translated, where efficiency can be characterized as a balance between translation speed and accuracy. Additionally, the bias is further determined by the topology of the mutational network formed by single-point nucleotide changes between codons. For this portion of the talk, I will present a population genetics and biophysical model in which the fitness of each organism is determined by codon translation efficiency and demonstrate that with reasonable biophysical parameters the codon bias is well characterized as a balance between mutation and selection across many organisms when the Wobble Hypothesis is included in sufficient detail.