Cell migration is a complex process involving many intracellular and extracellular factors, with different cell types adopting sometimes strikingly different morphologies. Modeling realistically behaving cells in tissues is computationally challenging because it implies dealing with multiple levels of complexity. We extend the Cellular Potts Model with an actin-inspired feedback mechanism that allows small stochastic cell rufflings to expand to cell protrusions. This simple phenomenological model produces realistically crawling and deforming amoeboid cells, and gliding half-moon shaped keratocyte-like cells. Both cell types can migrate randomly or follow directional cues. They can squeeze in between other cells in densely populated environments or migrate collectively. The model is computationally light, which allows the study of large, dense and heterogeneous tissues containing cells with realistic shapes and migratory properties.

8 9T cells are key effector cells in the immune system that are well-known for their ability to adapt their shape and 10 behavior to environmental cues. It has been suggested that these highly diverse, context-dependent migration 11 patterns reflect an optimization process -where T cells adjust motility parameters such as speed and persistence 12 to aid their search for antigen. Whereas models investigating such "search strategies" typically treat speed and 13 persistence as independent variables, one aspect of cell motility was recently found to be conserved across 14 a large variety of cell types: fast-moving cells turn less frequently. This raises the question whether T cells 15 can tune speed and persistence independently of each other. We therefore investigated to what extent this 16 universal coupling between cell speed and persistence (UCSP) shapes the behavior of migrating T cells. We 17 first show that the UCSP emerges spontaneously in an in silico Cellular Potts Model (CPM) of T cell migration. 18 Our model shows a link between the UCSP and cell shape dynamics, which put an upper bound on both the 19 speed and the persistence a cell can reach. We then use the CPM to examine how environmental constraints 20 affect motility patterns of T cells migrating in the crowded environments they also face in vivo, and show that T 21 cells completely lose their speed-persistence coupling when confined in a densely packed environment such 22 as the epidermis. Thus, although our model further highlights the validity of the UCSP in migrating cells, it 23 also demonstrates that environmental factors may overrule this coupling. Our data show that T cell motility 24 parameters are subject to both cell-intrinsic and extrinsic constraints, suggesting that "optimal" T cell search 25 strategies may not always be attainable in vivo. 26 1 28 T cells have the rare ability to migrate in nearly all tissues within the human body. Especially in tissues with a 29 high risk of infection -like the lung, the gut, and the skin -T cells are continuously on the move in search of 30 foreign invaders. Furthermore, migration in lymphoid organs such as the thymus and lymph nodes is crucial 31 for T cell function. 32Although T cells preserve their motility in these different contexts, they do adapt their morphology and 33 migratory behavior to environmental cues. It has been suggested that this remarkably flexible behavior reflects 34 different "search strategies" that allow T cells to maximize the chance of encountering antigen (Krummel et al., 35 2016). For example, naive T cells rapidly crawl along a network of stromal cells in the lymph node, alternating 36 between short intervals of persistent movement and random changes in direction (Miller et al., 2002(Miller et al., , 2003 37 Bajnoff et al., 2006; Beauchemin et al., 2007). This "stop and go" behavior allows them to cover large areas of the 38 lymph node in a short amount of time, and appears to be a good strategy for finding rare antigens without prior 39 information o...

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Excessive migration and proliferation of smooth muscle cells (SMCs) has been observed as a major factor contributing to the development of in-stent restenosis after coronary stenting. Building upon the results from in vivo experiments, we formulated a hypothesis that the speed of the initial tissue re-growth response is determined by the early migration of SMCs from the injured intima. To test this hypothesis, a cellular Potts model of the stented artery is developed where stent struts were deployed at different depths into the tissue. An extreme scenario with a ruptured internal elastic lamina was also considered to study the role of severe injury in tissue re-growth. Based on the outcomes, we hypothesize that a deeper stent deployment results in on average larger fenestrae in the elastic lamina, allowing easier migration of SMCs into the lumen. The data also suggest that growth of the neointimal lesions owing to SMC proliferation is strongly dependent on the initial number of migrated cells, which form an initial condition for the later phase of the vascular repair. This mechanism could explain the in vivo observation that the initial rate of neointima formation and injury score are strongly correlated.