Cell migration

Cell migration is a dynamic process that results from a complex interplay of different molecular components (e.g. actin and myosin or ion channels and transporters). In addition, external stimuli such as chemotactic signals or cell-cell interactions can influence the direction and persistence of movements.

The aim of the work in this field is the quantification and classification of movement on the basis of experimentally obtained cell paths (see figure) and the detection of changes, e.g. due to modifications of cell components (such as ion channels or transporters) or due to external influences.

Single cell dynamics

We were able to detect such effects in the migration of tumor cells or immune cells, for example.  From a theoretical point of view, the movement paths of migrating cells appear at first glance to have strong similarities with diffusive dynamics. However, our work has shown that long-range temporal correlations dominate the dynamics, which deviate strongly from normal diffusive behavior. The differentiation between normal and correlated anomalous behavior is often done in the literature by analyzing the mean squared displacement. However, there are limitations that can be circumvented by considering the spatial covariances of different anomalous processes (such as fractional / scaled Brownian motion or fractional Langevin equation) and by using Bayesian data analysis. 

Most recently, for example, we were able to show how the modification of a calcium channel (TRPC6) and the deactivation of a chemotactic receptor (CXCR2) on neutrophil granulocytes leads to a loss (tempering) of the temporal correlations. In addition, the results from in-vitro analyses were successfully used to make predictions for in-vitro studies of the immune response of a mouse to an inflammatory reaction with the aid of simulations.

The existing experience and techniques can be applied to other biological problems of single cell migration. Furthermore, there are additional perspectives in the modeling of relationships between the (macroscopic) parameters of the stochastic models and the microscopic processes of the cell migration machinery on the basis of an interplay of theory and experimental data.

Konfluente Zelldynamik

In recent years, PhD students supervised by us have generated and analyzed extensive data sets of the dynamics of confluent endothelial cells (especially HUVEC cells). The high number of several 10000 'tracked' cells per experiment showed a high heterogeneity of movements, but also various manifestations of collective dynamics, which manifest themselves in the local formation of vortices or streets. Excitingly, the confluent cell cultures show not only a short-range repulsion but also very long-range spatial correlations that extend over about 100 cell diameters.  We are currently investigating how external influences modify the dynamics of wound healing (at the level of the single cell or the macroscopic wound).

On the theoretical side, the observed dynamics of confluent cells provide the exciting realization of an active, interacting multi-particle system that develops far from equilibrium. Cross-connections to the application of stochastic thermodynamics and fluctuation relations are also possible here.

• Dieterich P, Lindemann O, Moskopp ML, Tauzin S, Huttenlocher A, Klages R, Chechkin A, Schwab A. Asymmetric anomalous diffusion in neutrophil chemotaxis. PLoS Computational Biology 18(5), e1010089/1-26 (2022).
• Dieterich P, Klages R, Chechkin AV. Fluctuation relations for anomalous dynamics generated by time-fractional Fokker–Planck equations. New J. Phys. 17 075004 (2015).
• Schneider L, Stock CM, Dieterich P, Jensen BH, Pedersen LB, Satir P, Schwab A, Christensen ST, Pedersen SF. The Na+/H+ exchanger NHE1 is required for directional migration stimulated via PDGFR-alpha in the primary cilium. J Cell Biol. V185(1):163-76 (2009).
• *Nechyporuk-Zloy V, *Dieterich P, Oberleithner H, Stock C, Schwab A. Dynamics of single potassium channel proteins in the plasma membrane of migrating cells. Am J Physiol Cell Physiol. V294(4):C1096-102 (2008). [*equal contribution]
• Dieterich P, Klages R, Preuss R, Schwab A. Anomalous dynamics of cell migration. Proc Natl Acad Sci USA V105(2):459-63 (2008).
• Stock C, Gassner B, Hauck CR, Arnold H, Mally S, Eble JA, Dieterich P, Schwab A. Migration of human melanoma cells depends on extracellular pH and Na+/H+ exchange. J Physiol. V567(1):225-38 (2005).
• Dieterich P, Odenthal-Schnittler M, Mrowietz C, Kramer M, Sasse L, Oberleithner H, Schnittler HJ. Quantitative morphodynamics of endothelial cells within confluent cultures in response to fluid shear stress. Biophys J. 2000 V79(3):1285-97 (2000).