Math Biology Seminar: Tommi Muller

The dynamics of the T immune cell membrane and the motion of its surface-bound receptors can be analyzed using a sophisticated microscopy technique called Total Internal Reflection Fluorescence Microscopy (TIRF), where receptors can be tagged with light-emitting particles that are illuminated by a laser. Methods in probability and numerical analysis, such as the Finite-State Hidden Markov Model and the Metropolis-Hastings algorithm, were applied to the trajectories of the receptors from the microscopy images using single-particle tracking to estimate parameters such the diffusivity and Markov state transition probabilities of the receptors. This, however, is very computationally expensive, taking days on a supercomputer for the data analysis to complete. There is also another issue involving the Finite-State Hidden Markov Model: Before applying the model, the user must first choose and fix the number of states to model in the system. This is a significant limitation as it disables the model from adjusting to new data and it increases the possibility of over/under-fitting data and cherry-picking data. In this presentation, we will explore TIRF, the Metropolis-Hastings Algorithm, and an approach to reduce computation time: an Embarrassingly Parallel Monte Carlo Markov Chain (MCMC) heuristic. We will also discuss the potential of using the newly developed Infinite Hidden Markov Model, which aims to overcome the limitation of fixing a finite number of states by allowing an arbitrary number of states to dynamically model data, chosen from an infinite-sized state space.