Modeling three-dimensional T-cell motility using clustering and hidden Markov models

Recent advances in imaging technologies now allow for real-time tracking of fast-moving immune cells as they search for targets such as pathogens and tumor cells through complex three-dimensional tissues. Cytotoxic T cells are specialized immune cells that continually scan tissues for such targets to engage and kill, and have emerged as the principle mediators of breakthrough immunotherapies against cancers. Modeling the way these T cells move is of great value in furthering our understanding of their collective search efficiency. T-cell motility is characterized by heterogeneity at two levels: (a) Individual cells display different distributions of translational speeds and turning angles, and (b) each cell can during a given track, its motility, switch between local search and directional motion. Despite a likely considerable influence on a motile population's search performance, statistical models that accurately capture both such heterogeneities in a distinguishing manner are lacking. Here, we model three-dimensional T-cell trajectories through a spherical representation of their incremental steps and compare model outputs to real-world motility data from primary T cells navigating physiological environments. T cells in a population are clustered based on their directional persistence and characteristic "step lengths" therein capturing between-cell heterogeneity. The motility dynamics of cells within each cluster are individually modeled through hidden Markov model to capture within-cell transitions between local and more extensive search patterns. We explore the importance of explicitly capturing altered motility patterns when cells lie in close proximity to one another, through a non-homogenous hidden Markov model.