Molecular motors are proteins or groups of proteins which convert chemical energy to mechanical energy within living cells. My work has specifically focused on processive linear molecular motors which carry cargos along microtubules. Since these motors are at the nanoscale and their progression requires chemical kinetics, the models to describe their motion are typically stochastic. Recently, my research has focused on creating more biologically relevant models which incorporate the interaction between chemical events and physical diffusion. I have been working with Will Hancock of the Bioengineering Department and members of his lab to build these models and to link them with biological experiments. Through these efforts to connect models to experiments, we have also create statistical methods for the images that result from fluorescence microscopy experiments. John Hughes, a graduate student in the Statistics Department, has been a major contributor to this project, both on statistical methods and numerical techniques. This work is supported by the NSF/NIH joint initiative in mathematical biology (DMS 0714939).
Below is a movie (taken in the Hancock lab) of fluorescently tagged kinesin motors (green) "walking" on microtubules (red).
Biological fluids are complex with an assortment of proteins and other particles suspended within. Understanding microscopic diffusion through this material is important to understand biological function and create clinical strategies to treat disease. My research has focused on finding techniques to efficiently simulate stochastic models for diffusion in complex fluids (such as the generalized Langevin equation) and methods for statistical inference for these models when observing the path of a single microscopic particle.
In addition to diffusion in complex fluids, I have been creating statistical methods using hidden Markov models for particles which alternate between diffusing and binding to the surface of membranes. This is ongoing work with Tim Elston's lab, Greg Forest (UNC Math), and others at the medical school at UNC.
I am also involved in two projects in conjunction with the Center for Infectious Disease Dynamics at Penn State.
With Matthew Ferrari (PSU Biology), we are developing dynamic models for country wide dynamics of measles to facilitate immunization programs at the WHO. We are also developing associated statistical methods to fit these dynamic models in order to predict and confirm case numbers for particular countries. Chen Shi, a graduate student in Entomology, is also working on this project.
With Mary Poss (PSU Biology) and several other collaborators, we are working to model an in vitro system of epitheleal cells which are infected with Respiratory Syncytial Virus (RSV). I am working with Francesca Chiaromonte and Ivan Simeonov of the Statistics Department to develop spatial point process models to explore the dynamics of this system.