Migrating cells are active soft matter systems. What determines their individual shape, speed and orientational decision making? Who do collectives of cells interact and form spatio-temporal patterns? In this context, artificial micro-pattern are convenient platforms to study cell motion as they provide defined geometric boundaries and surface chemistry. Using scanning time-lapse microscopy we monitor large ensembles of single cells navigating in parallel arrays of short stripes, ring-shaped micro-lanes and dumbbell pattern. Cell motion is tracked and the statistics of single cell behavior is analyzed using data driven models.

Cell-mechanical parameter estimation from 1D cell trajectories using simulation-based inference

Johannes C. J. Heyn, Miguel Atienza Juanatey, Martin Falcke, Joachim O. Rädler bioRxiv (2024)

This study presents a novel application of simulation-based inference (SBI) to elucidate cell-specific parameters governing migratory behavior in human epithelial cell lines, MCF-10A and MDA-MB-231. Utilizing high-throughput 1D trajectory data from automated imaging of cell migration on micro-patterned fibronectin lanes, we employed a trained neural density estimator to infer model parameters linked to cell dynamics. Results highlighted significant distinctions in parameter distributions related to actin polymerization and resting protrusion length between the two cell lines. The inference process demonstrated efficacy in capturing the effects of inhibitors like Latrunculin A and Y-27632, indicating potential pathways for further investigation into cytoskeletal mechanics and their influence on cell motility. This research paves the way for enhanced mechanistic modeling of cellular behavior and elucidates the role of specific parameters in fine-tuning motility characteristics, vital for understanding metastasis in cancer biology.

Nuclear deformation and dynamics of migrating cells in 3D confinement reveal adaptation of pulling and pushing forces

Stefan Stöberl, Johannes Flommersfeld, Maximilian M. Kreft, Martin Benoit, Chase P. Broedersz, Joachim O. Rädler Science Advances (2024)

Eukaryotic cells show an astounding ability to remodel their shape and cytoskeleton, to migrate through pores and constrictions smaller than their nuclear diameter. However, the relation of nuclear deformation and migration dynamics in confinement remains unclear. Here, we study the mechanics and dynamics of mesenchymal cancer cell nuclei transitioning through 3D compliant hydrogel channels. We find a biphasic dependence of migration speed and transition frequency on channel width, peaking at widths comparable to the nuclear diameter. Employing confocal imaging and hydrogel bead displacement, we determine nuclear deformations and corresponding forces during confined migration. The nucleus deforms reversibly with a reduction in volume during confinement. With decreasing channel width, the nuclear shape during transmigration changes biphasically concomitant with the transitioning dynamics. Our proposed physical model explains the observed nuclear shapes and transitioning dynamics in terms of the cytoskeletal force-generation adapting from purely pulling-based to a combined pulling- and pushing-based mechanism with increasing nuclear confinement.

Mesenchymal cell migration on one-dimensional micropatterns

Quantitative studies of mesenchymal cell motion are important to elucidate cytoskeleton function and mechanisms of cell migration. To this end, confinement of cell motion to one dimension (1D) significantly simplifies the problem of cell shape in experimental and theoretical investigations. Here we review 1D migration assays employing micro-fabricated lanes and reflect on the advantages of such platforms. Data are analyzed using biophysical models of cell migration that reproduce the rich scenario of morphodynamic behavior found in 1D. We describe basic model assumptions and model behavior. It appears that mechanical models explain the occurrence of universal relations conserved across different cell lines such as the adhesion-velocity relation and the universal correlation between speed and persistence (UCSP). We highlight the unique opportunity of reproducible and standardized 1D assays to validate theory based on statistical measures from large data of trajectories and discuss the potential of experimental settings embedding controlled perturbations to probe response in migratory behavior.

Single cell migration on a 1D micropattern. 1D micropatterns facilitate the study of mesenchymal cell migration by enabling the acquisition of large statistics.

(A) Schematic sketch of a cell on a lane that has been functionalized with an extracellular matrix (ECM) protein. The migration of the cell is defined by the position of its front xf, its nucleus xn and its back xb over time. (B) A human breast cancer cell (MDA-MB-231) on a fibronectin (FN) lane. The phase contrast image visualizes the contour of the cell. The nucleus has been stained violet and the ECM protein green. Scale bar 10 µm. (C) Kymograph of a migrating cell whose trajectory displays changes in velocity and direction as well as in cell length. Time runs from left to right. The vertical axis represents the position along the center of a micropatterned lane. Horizontal scale bar 1h, vertical scale bar 100 µm.

On multistability and constitutive relations of cell motion on fibronectin lanes

Behnam Amiri, Johannes C.J. Heyn, Christoph Schreiber, Joachim O. Rädler, Martin Falcke Biophysical Journal (2023)

Biophysical comprehension of cell motion and morphodynamics means to characterize them experimentally and explain them based on the internal cell dynamics. We characterize motion of MDA-MB-231 cells by analyzing 29,500 trajectories on one-dimensional fibronectin lanes. We suggest the intrinsic dynamics to derive from three constituents, namely the protrusion edge force balance, the noisy clutch mechanism of retrograde flow, and integrin signaling. Corresponding theory reproduces the measured morphodynamics. It also captures the measured motion characteristics given as the constitutive adhesion-velocity relation and persistence-speed relation and its response to drugs. We predict the constitutive force-velocity relation. Hence, the constituents of the mechanism, which apply to many cell types, explain the complex morphodynamics and constitutive motion relations.

Learning the dynamics of cell–cell interactions in confined cell migration

David B. Brückner, Nicolas Arlt, Alexandra Fink, Pierre Ronceray, Joachim O. Rädler and Chase P. Broedersz PNAS (2021)

When cells migrate collectively, such as to heal wounds or invade tissue, they coordinate through cell–cell interactions. While much is known about the molecular basis of these interactions, the system-level stochastic dynamics of interacting cell behavior remain poorly understood. Here, we design an experimental “cell collider,” providing a large ensemble of interacting cell trajectories. Based on these trajectories, we infer an interacting equation of motion, which accurately predicts characteristic pairwise collision behaviors of different cell lines, including reversal, following, or sliding events. This data-driven approach can be used to quantitatively study how molecular perturbations control cell–cell interactions and may be extended to larger cell collectives, where the inferred interactions could provide key insights into multicellular dynamics.

On the adhesion–velocity relation and length adaptation of motile cells on stepped fibronectin lanes

C. Schreiber, B. Amiri, J. C. J. Heyn, J. O. Rädler and M. Falcke PNAS (2021)

Cells exert forces on their environment by contracting actin networks, friction of intracellular F-actin flow, and polymerization when they move, e.g., during tumor metastasis or development. In this context, the relation between adhesion and cell velocity is a general cell-type-independent observation, the investigation of which bears the chance of understanding basic mechanisms. Restricting cell motion to one-dimensional lanes simplifies the problem and allows for comparison to mathematical models. Polymerization at the cell’s leading edge drives F-actin network flow and pushes the membrane. The drag of detaching the cell, the membrane, and the cell body resist motion. Since only velocity-controlled forces shape motion, cells can move even across highly adhesive areas without getting stuck.

Area and Geometry Dependence of Cell Migration in Asymmetric Two-State Micropatterns

A. Fink, D. B. Brückner, C. Schreiber, P. J. F. Röttgermann, C. P. Broedersz, J. O. Rädler Biophysical Journal (2020)

Microstructured surfaces provide a unique framework to probe cell migration and cytoskeletal dynamics in a standardized manner. Here, we report on the steady-state occupancy probability of cells in asymmetric two-state microstructures that consist of two fibronectin-coated adhesion sites connected by a thin guidance cue. We study the dynamics of human breast carcinoma cells (MDA-MB-231) in microstructures as a function of area, shape, and orientation of the adhesion sites. On square adhesive sites with different areas, we find that the occupancy probability ratio is directly proportional to the ratio of corresponding adhesion site areas. Sites of equal area but different shape lead to equal occupancy if shapes are isotropic (e.g., squared or circular). In contrast, an asymmetry in the occupancy is induced by anisotropic shapes like rhombi, triangles, or rectangles that enable motion in the direction perpendicular to the transition axis.

Stochastic Nonlinear Dynamics of Confined Cell Migration in Two-State Systems

D.B. Brückner, A. Fink, C. Schreiber, P. J. F. Röttgermann, J. O. Rädler and C. P. Broedersz Nature Physics (2019)

Migrating cells in physiological processes, including development, homeostasis and cancer, encounter structured environments and are forced to overcome physical obstacles. Yet, the dynamics of confined cell migration remains poorly understood, and thus there is a need to study the complex motility of cells in controlled confining microenvironments. Here, we develop two-state micropatterns, consisting of two adhesive sites connected by a thin constriction, in which migrating cells perform repeated stochastic transitions. This minimal system enables us to obtain a large ensemble of single-cell trajectories. From these trajectories, we infer an equation of cell motion, which decomposes the dynamics into deterministic and stochastic contributions in position–velocity phase space. Our results reveal that cells in two-state micropatterns exhibit intricate nonlinear migratory dynamics, with qualitatively similar features for a cancerous (MDA-MB-231) and a non-cancerous (MCF10A) cell line. In both cases, the cells drive themselves deterministically into the thin constriction; a process that is sped up by noise. Interestingly, however, these two cell lines have distinct deterministic dynamics: MDA-MB-231 cells exhibit a limit cycle, while MCF10A cells show excitable bistable dynamics. Our approach yields a conceptual framework that may be extended to understand cell migra-tion in more complex confining environments.

Ring-Shaped Microlanes and Chemical Barriers as a Platform for Probing Single-Cell Migration

C. Schreiber, F. J. Segerer, E. Wagner, A. Roidl & J. O. Rädler Scientific Reports (2016)

Quantification and discrimination of pharmaceutical and disease-related effects on cell migration requires detailed characterization of single-cell motility. In this context, micropatterned substrates that constrain cells within defined geometries facilitate quantitative readout of locomotion. Here, we study quasi-one-dimensional cell migration in ring-shaped microlanes. We observe bimodal behavior in form of alternating states of directional migration (run state) and reorientation (rest state). Both states show exponential lifetime distributions with characteristic persistence times, which, together with the cell velocity in the run state, provide a set of parameters that succinctly describe cell motion. By introducing PEGylated barriers of different widths into the lane, we extend this description by quantifying the effects of abrupt changes in substrate chemistry on migrating cells. The transit probability decreases exponentially as a function of barrier width, thus specifying a characteristic penetration depth of the leading lamellipodia. Applying this fingerprint-like characterization of cell motion, we compare different cell lines, and demonstrate that the cancer drug candidate salinomycin affects transit probability and resting time, but not run time or run velocity. Hence, the presented assay allows to assess multiple migration-related parameters, permits detailed characterization of cell motility, and has potential applications in cell biology and advanced drug screening.

Emergence and Persistence of Collective Cell Migration on Small Circular Micropatterns

F. J. Segerer, F. Thüroff, A. Piera Alberola, E. Frey, J.O. Rädler Physical Review Letters (2015)

The spontaneous formation of vortices is a hallmark of collective cellular activity. Here, we study the onset and persistence of coherent angular motion as a function of the number of cells N confined in circular micropatterns. We find that the persistence of coherent angular motion increases with N but exhibits a pronounced discontinuity accompanied by a geometric rearrangement of cells to a configuration containing a central cell. Computer simulations based on a generalized Potts model reproduce the emergence of vortex states and show in agreement with experiment that their stability depends on the interplay of the spatial arrangement and internal polarization of neighboring cells. Hence, the distinct migrational states in finite size ensembles reveal significant insight into the local interaction rules guiding collective migration.

Flow and diffusion in channel-guided cell migration

Marel, A.-K., Zorn, M., Klingner, C., Wedlich-Söldner, R., Frey, E., and Rädler, J. O. Biophysical Journal (2014)

In confluent epithelial sheets, the dynamics have been found to be highly heterogeneous, exhibiting spontaneous formation of swirls, long-range correlations, and glass-like dynamic arrest as a function of cell density. In contrast, the flow-like properties of one-sided cell-sheet expansion in confining geometries are not well understood. Here, we studied the short- and long-term flow of Madin-Darby canine kidney (MDCK) cells as they moved through microchannels. Using single-cell tracking and particle image velocimetry (PIV), we found that a defined averaged stationary cell current emerged that exhibited a velocity gradient in the direction of migration and a plug-flow-like profile across the advancing sheet. The observed flow velocity can be decomposed into a constant term of directed cell migration and a diffusion-like contribution that increases with density gradient. The diffusive component is consistent with the cell-density profile and front propagation speed predicted by the Fisher-Kolmogorov equation. Our work thus suggests that active cell migration manifests itself in an underlying, spatially uniform drift as well as in randomized bursts of short-range correlated motion that lead to a diffusion-mediated transport.

Further publications

J. Flommersfeld, S. Stöberl, O. Shah, J. O. Rädler, and C. P. Broedersz Geometry-Sensitive Protrusion Growth Directs Confined Cell Migration Phys. Rev. Lett. 132, 098401, (2024)

S. Stöberl, M. Balles, T. Kellerer and J. O. Rädler Photolithographic microfabrication of hydrogel clefts for cell invasion studies Lab on a chip, Issue 7, (2023)

D. B. Brückner, M. Schmitt, A. Fink, G. Ladurner, J. Flommersfeld, N. Arlt, E. Hannezo, J. O. Rädler, and C. P. Broedersz Geometry Adaptation of Protrusion and Polarity Dynamics in Confined Cell Migration Physical Review X 12, 031041, (2022)

D. B. Brückner, A. Fink, J. O. Rädler, and C. P. Broedersz Disentangling the behavioural variability of confined cell migration J R Soc Interface, vol. 17, no. 163, p. 20190689, (2020)

M. Dietrich, H. Le Roy, D. B. Brückner, H. Engelke, R. Zantl, J. O. Rädler, and C. P. Broedersz Guiding 3D Cell Migration in Deformed Synthetic Hydrogel Microstructures, Soft Matter (2018), 15

Zorn, M. L., Marel, A.-K., Segerer, F. J., Rädler, J. O. Phenomenological approaches to collective behavior in epithelial cell migration Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, (2015)

A.-K. Marel, A. Piera Alberola, J. O. Rädler Proliferation and Collective Migration of Small Cell Groups Released from Circular Patches Biophysical Reviews and Letters Vol. 7, Nos. 1 & 2, 15–28, (2012)