Math Biology Seminar: Rebeca Cardim Falcao

Single particle tracking is a powerful tool to study the mobility of molecules in the cell membrane. The most common approaches in analyzing these kinds of data are mean squared displacement and analyses with one or more hidden Markov states. However, in most experiments, positional measurements contain systematic and random errors, and to achieve proper fits, we must take these errors into account. In this work, we develop a hidden Markov model with multiple diffusive states. Our goal is to estimate the diffusion coefficients and transition probabilities between different states incorporating uncertainty due to measurement error in a rational way. Moreover, we also develop a Bayesian nonparametrics framework to estimate the number of states in the hidden Markov model, and then using information from the data we find the optimal Markov Model that describes that data. We test our methods using simulated data and present results using particle tracks obtained from surface receptor molecules on B cells.