Until very recently, I was a mathematician working at the interface of biology, physics and mathematics. I worked as a Postdoctoral Associate in the lab of Jonathon Howard at Yale University (Molecular Biophysics and Biochemistry Department). My interests included the fractal-like distribution networks that occur on many scales in physiological system, such as the vascular system, bronchial tree and both neural and mitochondrial networks. My research focus was on those at the cellular scale and key questions were:
1. What type of branching, growth and transport principles allow a sensory neuron, for example, to perform its function? How efficient and how precise are these processes? What energetic constraints are they under? To answer this my collaborators and I have begun to characterize the morphology of the Class IV sensory neurons in Drosophila larvae (above is a confocal image of such a neuron taken by my collaborator Xin Liang).
2. How does a growing cell supply its energetic needs? The amount of ATP synthesized by oxidative phosphorylation is limited by the surface area $$a$$ of the inner mitochondrial membrane. Yet, as a cell grows, its energetic needs scale with cytoplasmic volume $$V$$, implying that $$a$$, a surface, necessarily scales like $$V$$, a volume. The cell seems to circumvent this geometric paradox by having both a reticulated inner mitochondrial membrane with cristae and a mitochondrial network that is fractal-like (between the scales of an individual mitochondrion and total network size). I am interested in how such a network scales with cellular volume and am particularly fascinated by how this works during development, where cells run a whole gamut of sizes over a very short period of time. In particular, I am thinking about zebrafish embryogensis and am collaborating with experimentalists in the Neugabauer Lab.
3. I was collaborating with Fernando Carrillo Oesterreich (also a postdoc. in the Howard lab) on what we refer to broadly as the mechanisms of alternative splicing. We were interested in quantitatively distinguishing between functionally-important splicing events and those arising from mis-splicing events (for example, those resulting from the intrinsic noisiness of the cellular environment). We looked at a variety of model systems, from S. pombe to Danio rerio.
4. I previously worked in the Howard Lab at the Max Planck Institute for Cell Biology and Genetics, where my primary work was on microtubule dynamics. My research here involved the following: predictive mathematical modeling of microtubule dynamics; analyzed in vitro data to construct a model that accounted for the multistep nature of catastrophe and the relative insensitivity of lifetime with respect to tubulin concentration; techniques employed include analytic solutions to master equations developed from our models, parameter estimation (e.g. maximum likelihood estimation), implementation of Monte Carlo simulations and statstical tests. You can find our paper Microtubule dynamic instability: a new model with coupled GTP hydrolysis and multistep catastrophe here.