An accelerated pace of discovery in biological sciences is made possible by a new generation of computational biology and bioinformatics tools. In this dissertation we develop novel computational, analytical, and high performance simulation techniques for biological problems, with applications to the yeast cell division cycle, and to the RNA-Sequencing of the yellow fever mosquito.

Cell cycle system evolves stochastic effects when there are a small number of molecules react each other. Consequently, the stochastic effects of the cell cycle are important, and the evolution of cells is best described statistically. Stochastic simulation algorithm (SSA), the standard stochastic method for chemical kinetics, is often slow because it accounts for every individual reaction event. This work develops a stochastic version of a deterministic cell cycle model, in order to capture the stochastic aspects of the evolution of the budding yeast wild-type and mutant strain cells. In order to efficiently run large ensembles to compute statistics of cell evolution, the dissertation investigates parallel simulation strategies, and presents a new probabilistic framework to analyze the performance of dynamic load balancing algorithms. This work also proposes new accelerated stochastic simulation algorithms based on a fully implicit approach and on stochastic Taylor expansions.

Next Generation RNA-Sequencing, a high-throughput technology to sequence cDNA in order to get information about a sample's RNA content, is becoming an efficient genomic approach to uncover new genes and to study gene expression and alternative splicing. This dissertation develops efficient algorithms and strategies to find new genes in Aedes aegypti, which is the most important vector of dengue fever and yellow fever. We report the discovery of a large number of new gene transcripts, and the identification and characterization of genes that showed male-biased expression profiles. This basic information may open important avenues to control mosquito borne infectious diseases.