Defining the quantitative limits of intravital two-photon lymphocyte tracking.

Two-photon microscopy has substantially advanced our understanding of cellular dynamics in the immune system. Cell migration can now be imaged in real time in the living animal. Strikingly, the migration of naive lymphocytes in secondary lymphoid tissue appears predominantly random. It is unclear, however, whether directed migration may escape detection in this random background. Using a combination of mathematical modeling and experimental data, we investigate the extent to which modern two-photon imaging can rule out biologically relevant directed migration. For naive T cells migrating in uninfected lymph nodes (LNs) at average 3D speeds of around 18 µm/min, we rule out uniform directed migration of more than 1.7 µm/min at the 95% confidence level, confirming that T cell migration is indeed mostly random on a timescale of minutes. To investigate whether this finding still holds for longer timescales, we use a 3D simulation of the naive T cell LN transit. A pure random walk predicts a transit time of around 16 h, which is in good agreement with experimental results. A directional bias of only 0.5 µm/min-less than 3% of the cell speed-would already accelerate the transit twofold. These results jointly strengthen the random walk analogy for naive T cell migration in LNs, but they also emphasize that very small deviations from random migration can still be important. Our methods are applicable to cells of any type and can be used to reanalyze existing datasets.

Analytical results on the Beauchemin model of lymphocyte migration.

The Beauchemin model is a simple particle-based description of stochastic lymphocyte migration in tissue, which has been successfully applied to studying immunological questions. In addition to being easy to implement, the model is also to a large extent mathematically tractable. This article provides a comprehensive overview of both existing and new analytical results on the Beauchemin model within a common mathematical framework. Specifically, we derive the motility coefficient, the mean square displacement, and the confinement ratio, and discuss four different methods for simulating biased migration of pre-defined speed. The results provide new insight into published studies and a reference point for future research based on this simple and popular lymphocyte migration model.