7th Annual Symposium
Physics of Cancer
Leipzig, Germany
October 4-6, 2016
Contributed Talk
Change matters: a time-varying parameter model for cell migration
Christoph Mark, Claus Metzner, Julian Steinwachs, Lena Lautscham, Ben Fabry
Friedrich-Alexander University Erlangen-Nürnberg, 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 high-dimensional models (Hamiltonian Monte Carlo and Variational Bayes) either do not scale well for long time series, or do not provide an objective measure of goodness-of-fit or require expert knowledge to adapt them to different models. To overcome these issues, we use a sequential inference approach, effectively breaking down one high-dimensional inference problem into many low-dimensional ones. We subsequently solve these low-dimensional inference problems by approximating the probability distributions of the parameters on a discrete, regular grid. This grid-based 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 goodness-of-fit is essential to test the existence and infer the magnitude of temporal parameter changes. Our method can be applied to a large class of time-varying parameter models and is available as open-source Python code. Here, we reconstruct the time-varying directional persistence and migratory activity from measured migration paths of tumor cells in 1-, 2- and 3-dimensional environments. First, we show that our estimates of cell persistence and activity highly correlate with the local micro-environment of the cell, using a micro-structured 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 3-dimensional collagen matrix over much longer time periods compared to migration on 2-dimensional 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 MDA-MB-231 breast carcinoma cells is highly correlated with contractility and cell elongation. Finally, we analyze the migration of four different cell types (A125, MDA-MB-231, HT1080, IFDUC) on a 2-dimensional substrate. We show that the cross-correlation 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 3-dimensional collagen gels.
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