Leukocyte Motility Models Assessed through Simulation and Multi-objective Optimization-Based Model Selection

The advent of two-photon microscopy now reveals unprecedented, detailed spatio-temporal data on cellular motility and interactions in vivo. Understanding cellular motility patterns is key to gaining insight into the development and possible manipulation of the immune response. Computational simulation has become an established technique for understanding immune processes and evaluating hypotheses in the context of experimental data, and there is clear scope to integrate microscopy-informed motility dynamics. However, determining which motility model best reflects in vivo motility is non-trivial: 3D motility is an intricate process requiring several metrics to characterize. This complicates model selection and parameterization, which must be performed against several metrics simultaneously. Here we evaluate Brownian motion, Lévy walk and several correlated random walks (CRWs) against the motility dynamics of neutrophils and lymph node T cells under inflammatory conditions by simultaneously considering cellular translational and turn speeds, and meandering indices. Heterogeneous cells exhibiting a continuum of inherent translational speeds and directionalities comprise both datasets, a feature significantly improving capture of in vivo motility when simulated as a CRW. Furthermore, translational and turn speeds are inversely correlated, and the corresponding CRW simulation again improves capture of our in vivo data, albeit to a lesser extent. In contrast, Brownian motion poorly reflects our data. Lévy walk is competitive in capturing some aspects of neutrophil motility, but T cell directional persistence only, therein highlighting the importance of evaluating models against several motility metrics simultaneously. This we achieve through novel application of multi-objective optimization, wherein each model is independently implemented and then parameterized to identify optimal trade-offs in performance against each metric. The resultant Pareto fronts of optimal solutions are directly contrasted to identify models best capturing in vivo dynamics, a technique that can aid model selection more generally. Our technique robustly determines our cell populations’ motility strategies, and paves the way for simulations that incorporate accurate immune cell motility dynamics.Author Summary: Advances in imaging technology allow investigators to monitor the movements and interactions of immune cells in a live animal, processes essential to understanding and manipulating how an immune response is generated. T cells in the brains of Toxoplasma gondii-infected mice have previously been described as performing a Lévy walk, an optimal strategy for locating sparsely, randomly distributed targets. Determining which motility model best characterizes a population of cells is problematic; multiple metrics are required to specify as intricate and nuanced a process as 3D motility, and the tools to evaluate model-parameter combinations have been lacking. We have developed a novel framework to perform this model evaluation through simulation, a popular tool for exploring complex immune system phenomena. We find that Lévy walk offers an inferior capture of our data to another class of motility model, the correlated random walk, and this determination was possible because we are able to explicitly evaluate several motility metrics simultaneously. Further, we find evidence that leukocytes differ in their inherent translational and rotational speeds. These findings facilitate more accurate immune system simulations aimed at unravelling the processes underpinning this critical biological function.