7th Annual Symposium Physics of Cancer Leipzig, Germany October 46, 2016 
PoC  Physics of Cancer  Annual Symposium 

Contributed Talk
Change matters: a timevarying parameter model for cell migration
FriedrichAlexander University ErlangenNürnberg, Department of Physics, Biophysics group, Henkestraße 91, Erlangen, Germany
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Depending on cell type and the local environment, tumor cells show a variety of different migration modes, including mesenchymal and amoeboid motion. As the cell interacts with a spatially changing extracellular matrix, cell movements are highly heterogeneous in space and time and thus do not comply with conventional statistical models. Common measures of cell motility which regard cell migration as a homogeneous random walk (like the step width distribution or the mean squared displacement) may therefore fail to distinguish between cell migration in different environments as well as the migration patterns of different cell types. To provide a more sensible measure of cell motility, we build stochastic models for cell migration that explicitly allow for temporal changes of its parameters. As the parameters of such models may change at each time step, the number of parameter values to infer from measured data is proportional to the number of recorded cell movements. The two existing approaches to fit such highdimensional models (Hamiltonian Monte Carlo and Variational Bayes) either do not scale well for long time series, or do not provide an objective measure of goodnessoffit or require expert knowledge to adapt them to different models. To overcome these issues, we use a sequential inference approach, effectively breaking down one highdimensional inference problem into many lowdimensional ones. We subsequently solve these lowdimensional inference problems by approximating the probability distributions of the parameters on a discrete, regular grid. This gridbased approach allows for an efficient calculation of the model evidence, i.e. the probability that the data is produced by the model. The model evidence as an objective measure of goodnessoffit is essential to test the existence and infer the magnitude of temporal parameter changes. Our method can be applied to a large class of timevarying parameter models and is available as opensource Python code. Here, we reconstruct the timevarying directional persistence and migratory activity from measured migration paths of tumor cells in 1, 2 and 3dimensional environments. First, we show that our estimates of cell persistence and activity highly correlate with the local microenvironment of the cell, using a microstructured array of narrow channels and wide chambers. We demonstrate that the temporal changes in persistence and activity, rather than their mean values, provide a distinct fingerprint of the strategies that cells employ to cope with different environments. For example, persistence is positively correlated with activity in a 3dimensional collagen matrix over much longer time periods compared to migration on 2dimensional substrates, supporting the hypothesis that cells are able to pull themselves along collagen fibers and hence use the surrounding matrix to their advantage. To test this hypothesis, we measure cell pulling forces in a collagen gel with 3D traction force microscopy. We find that directional persistence of invading MDAMB231 breast carcinoma cells is highly correlated with contractility and cell elongation. Finally, we analyze the migration of four different cell types (A125, MDAMB231, HT1080, IFDUC) on a 2dimensional substrate. We show that the crosscorrelation between persistence and activity allows to accurately classify the cell type based only on its dynamics. Furthermore, the prevalence of phases with simultaneously high/low persistence and activity shows an intriguing connection to the respective invasivity of these four cell types in 3dimensional collagen gels.
