<p>Many cells are remarkably proficient at tracking even shallow chemical gradients, despite tiny differences in receptor occupancy across the cell. Stochastic receptor-ligand interactions introduce considerable noise in instantaneous receptor occupancy, so it is thought that spatial information must be integrated over time to allow noise filtering. The mechanism of temporal integration is unknown. We used the mating response of the budding yeast, <italic>Saccharomyces cerevisiae</italic>, as a model to study eukaryotic gradient tracking. </p><p>During mating, yeast cells polarize and grow up a gradient of pheromone to find and fuse with opposite-sex partners. Exposure to pheromone causes polarity regulators to cluster into a tight "patch" at the cortex, directing growth toward that site. Timelapse microscopy of fluorescently-labeled polarity proteins revealed that the patch wandered around the cortex during gradient tracking. Mathematical modeling and genetic analysis suggested that fusion of vesicles near the polarization site could perturb the polarity patch and promote wandering. Wandering is decreased due to global effects from pheromone signaling as well as interactions between receptor-activated G&beta; and the exchange factor for the polarity regulator Cdc42. We found that artificially stabilizing patch wandering impaired accurate gradient tracking.</p><p>We suggest that ongoing polarized vesicle traffic causes patch wandering, which is locally reduced by pheromone-bound receptors. Thus, over time, spatial information from the pheromone gradient biases the random wandering of the polarity patch so that growth occurs predominantly up-gradient. Such temporal integration may enable sorting the low signal from stochastic noise when tracking shallow gradients.</p> / Dissertation

Biological signal processing can help us gain knowledge about biological complexity, as well as using this knowledge to engineer better systems. Three areas are identified as critical to understanding biology: 1) understanding DNA, 2) examining the overall biological function and 3) evaluating these systems in environmental (ie: turbulent) conditions. DNA is investigated for coding structure and redundancy, and a new tandem repeat region, an indicator of a neurodegenerative disease, is discovered. The linear algebraic framework can be used for further analysis and techniques. The work illustrates how signal processing is a tool to reverse engineer biological systems, and how our better understanding of biology can improve engineering designs. Then, the way a single-cell mobilizes in response to a chemical gradient, known as chemotaxis, is examined. Inspiration from receptor clustering in chemotaxis combined with a Hebbian learning method is shown to improve a gradient-source (chemical/thermal) localization algorithm. The algorithm is implemented, and its performance is evaluated in diffusive and turbulent environments. We then show that sensor cross-correlation can be used in solving chemical localization in difficult turbulent scenarios. This leads into future techniques which can be designed for gradient source tracking. These techniques pave the way for use of biologically-inspired sensor networks in chemical localization.