Former Graduate Fellows

• Viviane Callier
  Metabolism, Trachea, and Mitochondria
  Mathematical modeling of insulin signaling: connecting molecular mechanisms to physiological function

  Insulin signaling and associated pathways form a network that integrates information from diverse signals such as nutrition, growth hormones, and oxidative stress, and regulates cell growth, division, and death. Defects in this signaling network result in diseases such as diabetes, obesity, and cancer; nevertheless, little is known about how a cell integrates multiple inputs to choose between alternative outputs.

  I am expanding a model of insulin signaling by Sedaghat et al. (2002) to include the known mechanisms by which excess lipids and amino acids downregulate the sensitivity of glucose transporters to insulin and regulate growth. Studying the dynamics of this network will help us understand the etiology of lipid- and amino-acid-induced insulin resistance.

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• Rick Dilling
  Building a Better Model of Fruit Fly Wing Development
  Construction of a PDE model of Drosophila wing development incorporating explicit genetic controls and anisotropic domain growth

  The goal of this project is to construct an explicit PDE reaction-diffusion model of Drosophila wing growth in two spatial dimensions that incorporates how the gene networks (anterior/posterior and dorsal/ventral) involved in wing development influence the orientation of cell division and how the anisotropic growth of the wing domain depends on this. This model will be validated against existing data to see if perturbations to the model recapitulate the results of comparable experimental perturbations and will also be used to make new experimental predictions.

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• Emily Moran
  Seed Dispersal and Gene Flow in Red Oak

  The future of biodiversity will depend on species’ capacity to migrate or adapt in response to climate change. Gene flow via seed and pollen is important to both processes, yet has been challenging to estimate in forest trees. I developed a hierarchical Bayesian model that combines ecological and genetic data in order to estimate the scale of seed and pollen movement, applied it to two populations of red oaks in North Carolina and tested whether the scale of dispersal varies between sites.

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• Anand Pai
  Quorum Sensing and Bacterial Cooperation
  Modeling bacterial cooperation mediated by quorum sensing

  Bacteria, despite being supposedly simple unicellular organisms, demonstrate cooperative behavior. One example is their secretion of ‘public good’ proteins that are beneficial to all nearby bacteria. Such cooperative actions are often controlled by a phenomena known as ‘quorum sensing’ wherein bacteria initiate actions (such as secretion of proteins) depending on their population density. To better understand this cooperation and its evolution, I will develop mathematical models for quorum sensing controlled bacterial cooperation that will represent the various biological and physical mechanisms involved.

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• Adam Sokolow
  Measuring the Forces of Wound Healing
  Cell shape oscillations and cell delamination in tissue

  We study cell shape changes in tissue in the model system Drosophila during a stage in development known as dorsal closure. Using in vivo, time-lapsed confocal microscopy coupled with segmentation software, we are able to image living embryos and quantify the areas of almost all cells in the tissue throughout most of closure. By characterizing the kinematics of cell shape changes using area we gain insight into two relevant time scales of dynamics. We find these cells oscillate in a highly viscous, low Reynolds environment, as well as delaminate from the tissue at a slower time scale. Using mathematical analysis and biophysical modeling we gain insight into the active contractile force producing mechanisms that give rise to these two processes.

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• Gavin Taylor
  Feature Selection for Value Function Approximation

  Value function approximation is a useful step in creating or analyzing policies for Markov Decision Processes. Because it is often impractical to store an explicit value for every state, it is often advantageous to approximate the value function with a linear combination of a small number of features or basis functions. Using
  mathematical and statistical techniques, we seek ways of identifying or computing helpful features for linear value function representation.

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• Xiacheng Zeng
  Equilibrium Sampling for Biomolecules under Mechanical Tension

  In the studies of force-induced conformational transitions of biomolecules, the large time-scale difference from experiments presents the challenge of obtaining convergent sampling for molecular dynamics simulations. To circumvent this fundamental problem, an approach combining the replica-exchange method1 and umbrella sampling (REM-US) is developed to simulate mechanical stretching of polysaccharides under equilibrium conditions. Equilibrium properties of conformational transitions can be obtained directly from simulations without further assumptions.

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