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Dynamic traction force measurements of migrating immune cells in 3D biopolymer matrices

Nature Physics (2024)Cite this article

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Abstract

Immune cells, such as natural killer cells, migrate with high speeds of several micrometres per minute through dense tissue. However, the magnitude of the traction forces during this migration is unknown. Here we present a method to measure dynamic traction forces of fast migrating cells in biopolymer matrices from the observed matrix deformations. Our method accounts for the mechanical nonlinearity of the three-dimensional tissue matrix and can be applied to time series of confocal or bright-field image stacks. It allows for precise force reconstruction over a wide range of force magnitudes and object sizes—even when the imaged volume captures only a small part of the matrix deformation field. We demonstrate the broad applicability of our method by measuring forces from around 1 nN for axon growth cones up to around 10 μN for mouse intestinal organoids. We find that natural killer cells show bursts of large traction forces around 50 nN that increase with matrix stiffness. These force bursts are driven by myosin II contractility, mediated by integrin β1 adhesions, focal adhesion kinase and Rho-kinase activity, and occur predominantly when the cells migrate through narrow matrix pores.

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Fig. 1: Material model for a nonlinear fibre matrix.
Fig. 2: Contractile phases during NK cell migration.
Fig. 3: Mechanosensing of migrating NK cells in 3D collagen networks.
Fig. 4: Force reconstruction benchmark tests.
Fig. 5: Accuracy and broad applicability of Saenopy.

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Data availability

Source data from this study are are provided with this paper and as part of the Saenopy GitHub repository50. Image raw data are available upon request from the corresponding author.

Code availability

The software (Saenopy) and all dependent packages are available on GitHub as an open-source Python package with a graphical user interface50. Figures are created using the Python packages Pylustrator66 and PyVista67 using a colourblind-friendly colour palette from ref. 68.

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Acknowledgements

This work was funded by the German Research Foundation (DFG; project 326998133 – TRR-SFB 225 – subprojects A01, B09 and C02; project 460333672 – CRC 1540 – subprojects A01, A05, B02 and C05; project 375876048 – TRR-SFB 241 – subprojects A07 and C04; project 461063481 – LO 2465/6-1; project 414058251 – SPP-1782, LO 2465/2-1), the National Institutes of Health (HL120839), the Emerging Fields Initiative of the University of Erlangen-Nuremberg and the Alexander von Humboldt Foundation (Humboldt Professorship, K.F.). We thank the ENB Biological Physics programme of the University Bayreuth for support, R. Henriques for the LaTeX layout, I. Thievessen for help with differential interference contrast imaging and R. Reimann for designing the Saenopy logo.

Author information

Authors and Affiliations

  1. Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

    David Böhringer, Lars Bischof, Tina Czerwinski, Andreas Bauer, Christoph Mark, Ben Fabry & Richard Gerum

  2. Life Sciences Technology Department, Interuniversity Micro-Electronics Centre, Leuven, Belgium

    Mar Cóndor

  3. Biomechanics Section, Department of Mechanical Engineering, KU Leuven, Leuven, Belgium

    Mar Cóndor

  4. Institute of Medical Physics and Microtissue Engineering, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

    Niklas Gampl & Kristian Franze

  5. Max-Planck-Zentrum für Physik und Medizin, Erlangen, Germany

    Niklas Gampl & Kristian Franze

  6. Department of Medicine 1, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

    Phuong Anh Ngo & Rocío López-Posadas

  7. Deutsches Zentrum Immuntherapie (DZI), Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

    Phuong Anh Ngo, Caroline Voskens & Rocío López-Posadas

  8. Department of Dermatology, University Hospital Erlangen, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

    Caroline Voskens

  9. Department of Physiology, Development and Neuroscience, University of Cambridge, Cambridge, UK

    Kristian Franze

  10. Institute of Continuum Mechanics and Biomechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

    Silvia Budday

  11. Department of Physics and Astronomy, York University, Toronto, Ontario, Canada

    Richard Gerum

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  1. David Böhringer
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Contributions

Methodology: R.G., D.B., M.C., B.F. and C.M. Software: R.G., D.B., M.C. and A.B. Rheology: D.B., M.C., L.B., S.B. and N.G. Immune cell experiments: L.B., T.C., D.B. and C.V. Organoid experiments: P.A.N., D.B. and R.L.-P. Neuronal cell experiments: K.F. and N.G. Data analysis: D.B., L.B., C.M. and R.G. Writing: D.B., B.F., M.C., C.M. and R.G.

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Correspondence to Ben Fabry.

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Extended data

Extended Data Fig. 1 Nonlinear material model.

The nonlinear material model divides the mechanical response of individual fibers into a region where fiber stiffness (ω″) decreases exponentially with decreasing strain under compression (buckling), a region of constant fiber stiffness for small strains (straightening), and a region of exponentially increasing fiber stiffness for larger strains (stretching)12. Non-linear materials are modelled according to Eq. (1) using four material parameters: The linear stiffness k0, the buckling coefficient d0, the characteristic strain λs, and the stiffening coefficient ds. For small extensional strain in the linear range (0 < λ < λs), fibers exhibit a constant stiffness k. For compressive strain (− 1 < λ < 0), fibers buckle and show an exponential decay of the stiffness with a characteristic buckling coefficient d0. For larger extensional strain beyond the linear range (λs < λ), the fibers show strain stiffening with an exponential increase of stiffness with a characteristic stiffening coefficient ds. Dashed lines indicate the different regimes. Figure adapted with permission from ref. 12, Springer America Inc.

Extended Data Fig. 2 Rheology and material model for collagen Batch A, B, C.

Collagen hydrogels from three different batches (a, b, c) at different concentrations of 0.6 mg/ml (purple), 1.2 mg/ml (blue), and 2.4 mg/ml (orange) are characterized using cone-plate shear-rheological measurements (top; inset shows schematic of experimental setup) and uniaxial stretch-experiments (bottom; inset shows schematic of experimental setup) as described in the Methods section of the main text. The solid lines represent the mean value and the shaded areas represent the standard error for N individual samples. Dashed lines show the fit of the finite element model to the averaged data per condition. The red axis label in c indicates different scaling compared to a, b. d, Material model parameters (Extended Data Fig. 1) for non-linear elastic biopolymers (linear stiffness k0, the buckling coefficient d0, the characteristic strain λs, and the stiffening coefficient ds.) for each condition. Previously measured parameters from Steinwachs et al.12 are given for comparison. For each batch, we performed both individual fits to the data for each concentration separately, or global fits where the parameters λs, ds, and d0 were the same for all or some of the concentrations. Global fit parameters were preferred if the fit quality was comparable to individual fits, in order to reduce the number of free fit parameters. The increased stiffness of collagen batch C compared to batch A and B is consistent with the observation of decreased cell-generated deformations (Extended Data Fig. 5). These stiffness differences can be attributed to batch-to-batch variation. Model parameters for 1.2 mg/ml collagen gels of Batch A were previously published in ref. 58.

Source data.

Extended Data Fig. 3 Small amplitude rheology.

a, Storage modulus derived from frequency sweeps with a cone-plate shear-rheometer at 1% strain amplitude for different collagen concentrations (Batch A, see Extended Data Fig. 2). Dashed lines indicate mean values, and shaded area indicate } one standard deviation. N indicates the number of collagen gels, where each gel was measured in an independent experiment. b, Storage modulus (mean value at 0.02 Hz) scales with collagen concentration according to a power-law with exponent of 1.91 in agreement to previously predicted and measured values69,70. Bars indicate mean }se and dashed line indicates powerlaw fit curve. Individual collagen gels are shown as dots. The sample size is the same as in a. c, Loss tangent δ (loss modulus G″ divided by storage modulus \({G}^{{\prime} }\), averaged between 0.02-2 Hz from the data presented in a) remains below 0.2 for all collagen concentrations,indicating predominantly elastic behavior. d, The FE model parameter k0 (indicating the linear stiffness of the collagen fibers) for different collagen concentrations (see Extended Data Fig. 2) increases approximately linearly with the storage modulus \({G}^{{\prime} }\) of the collagen gels (measured at 0.02 Hz at a strain amplitude of 1% as shown in a). The gray dashed line indicates the predication from continuum mechanics, where k0 =6E, with Young’s modulus E = 2G(1 + v) and Poisson ratio ν = 0.25 for linear elastic, isotropic fiber networks12. Hence, k0 = 15G.

Source data.

Extended Data Fig. 4 Microstructure of collagen networks.

The collagen fiber structure of two different collagen batches (a-c: Batch A; e-g: Batch C) is imaged using confocal reflection microscopy for three different collagen concentrations (imaged volume of 160x160x200 μm with voxel-sizes of 0.314x0.314x0.642 μm). Grayscale images show a single slice of the imaged volume.3D pore diameters are computed from the covering radius transform as described in71,72. The mean pore diameters for each collagen concentration (d, h) are calculated from 8 different regions within an stack (80x80x100 μm with 0.314x0.314x0.642 μm voxel-size). The error bars represent the standard deviation of the mean pore diameter between different regions (shown as individual points) of the imaged stack. Mean value and standard deviation of the pore diameters are listed in the table. See SI Video 1 for 3D representations of the collagen fiber networks.

Source data.

Extended Data Fig. 5 Dependence of immune cell migration and force generation on matrix stiffness and pore size.

Cell contractility (a, e), matrix deformations (b, f), cell speed (c, g), and cell travelled distance (d, h) are measured in collagen gels (0.6 mg/ml, 1.2 mg/ml, and 2.4 mg/ml from different collagen batches) with different stiffnesses (a-d) and pore sizes (e-h). The storage modulus of different collagen gels is measured with a cone-plate shear-rheometer at 0.02 Hz (1% strain amplitude, see Extended Data Fig. 3), and the pore size is derived from confocal reflection images(see Extended Data Fig. 4). Colored bars and error bars indicate mean }se for n individual cells (black points) from three (pink and orange bars) or four (green and blue bars) independent experiments. * indicates p<0.05 and ** indicates p<0.01 for two-sided t-test with Bonferroni correction51. For clarity, the legend, data points, statistical tests, and cell numbers are only shown in the top row. (a, e), Maximum contractility of each cell during a 23 min measurement period. (b, f), Maximum of the absolute matrix deformation vector (99% percentile) of each cell during a 23 min measurement period. (c, g), Mean cell speed during a 23 min measurement period. (d, h), Migration distance of cells after 23 min in 1.2 mg/ml collagen gels. Distance is calculated as the diagonal of the smallest rectangle containing the cell trajectory. Here, only trajectories containing at least 20 data points (corresponding to trajectories of at least 19 min duration) are included in the analysis. Cell contractility monotonically increases, and matrix deformation monotonically decreases with matrix stiffness. Migration speed and travelled distance show a maximum response at intermediate pore sizes.

Source data.

Extended Data Fig. 6 Force reconstitution for different cell types.

For different cell types, cell-generated matrix deformations are measured and then interpolated onto a finite-element mesh (left). The reconstructed matrix deformations (center) and forces (right) are obtained using Saenopy. The force epicenter is shown in pink, and the size of the image stack is indicated in the lower right. a, Human natural killer cell (NK92) embedded in a 1.2 mg/ml collagen gel (Batch A) during a contractile phase (Fig. 2, SI Videos 6–8). b, Hepatic stellate cell (human liver fibroblast) in a 1.2 mg/ml collagen gel (Batch C) after 2 days of culture (SI Video 11). c, Axon growth cones of a frog retinal ganglion cell embedded in a 1.0 mg/ml collagen gel (Batch D) during a contractile phase (SI Video 10). d, Mouse intestinal organoid in a 1.2mg/ml collagen gel (Batch C) after 24 hours. Time-lapse images of organoid contraction and drug-induced relaxation are shown in SI Video 12.

Extended Data Fig. 7 Saenopy resolves 3D force fields from bright-field image stacks.

Matrix deformations and forces around a NK92 cell embedded in a 1.2 mg/ml collagen gel (Batch C). Bright-field images are acquired with an ASI RAMM microscope (Applied Scientific Instrumentation, Eugene), CMOS-camera (acA4096-30um, Basler, Ahrensburg),and 20x objective (0.7NA, air, Olympus, Tokyo). The cells are kept at 37∘C and 5% CO2 in a stage incubator (Tokai HIT, Fujinomiya). Matrix deformations (left) are calculated from bright-field image stacks (120 × 120 × 120 μm, with a voxel-size of 0.15 × 0.15 × 2 μm, dt = 30 s) during a contractile phase (SI Video 13, at t = 2 min). Cell forces (right) and corresponding matrix deformations (middle) are reconstructed using a regularization parameter of 1011. Maximum intensity projected image stacks are shown below the 3D cubes.

Supplementary information

Supplementary Information

Supplementary Figs. 1–14.

Reporting Summary

Supplementary Video 1

Video showing collagen fibre networks of different concentrations (3D representation): 3D representation of collagen fibre networks (batch C) of different concentrations (0.6, 1.2 and 2.4 mg ml−1). Collagen fibres were imaged using confocal reflection microscopy. Images are Sato-filtered for ridge detection, highlighting the fibre structure73. The recorded stack size is 160 × 160 × 50 μm with a voxel size of 0.314 × 0.314 × 0.642 μm.

Supplementary Video 2

Video of an NK92 cell migrating through collagen (bright-field and confocal reflection): intensity projected image stacks of an NK92 cell migrating through a 1.2 mg ml−1 collagen gel (stack size of 123 × 123 × 123 μm with a voxel size of 0.24 × 0.24 × 1 μm) recorded every minute. The cell shows a phase of high contractility at around t = 4 min. Left: bright-field image. Right: confocal reflection image. Projected matrix deformations are indicated by coloured arrows. Scale bar, 20 μm. For better visualization of matrix deformations, the video is followed by a forward–backward sequence of consecutive images during a phase with high contractility.

Supplementary Video 3

Video of an NK92 cell migrating through collagen (differential interference contrast): differential contrast images of an NK92 cell migrating through a 1.2 mg ml−1 collagen gel. The time between consecutive frames is 2 seconds. The focus has been adjusted manually during the recording. For better visualization of matrix deformations, the video is followed by a forward–backward sequence of consecutive images during a phase with high contractility.

Supplementary Video 4

Video of an NK92 cell migrating through collagen (3D representation): 3D representation of an NK92 cell (green) migrating through dense constrictions in a 1.2 mg ml−1 collagen gel (brown). The cell was imaged using calcein staining (2 μM calcein AM, Thermo Fisher Scientific) and segmented using Yen thresholding74. Collagen fibres were imaged using confocal reflection microscopy. Images are Sato-filtered for ridge detection, highlighting the fibre structure73. The transparency of the cell and collagen image stacks were determined by the intensity values according to a sigmoidal transfer function. The recorded stack size is 123 × 123 × 40 μm with a voxel size of 0.24 × 0.24 × 1.5 μm. The time between consecutive image stacks is 1 min. Matrix deformations are indicated by coloured arrows. For better visualization of matrix deformations, the video is followed by a forward–backward sequence of consecutive images during a phase with high contractility.

Supplementary Video 5

Video of an NK92 cell migrating through collagen (3D representation): 3D representation of an NK92 cell (green) migrating through dense constrictions in a 1.2 mg ml−1 collagen gel (brown). The cell was imaged using calcein staining (2 μM calcein AM, Thermo Fisher Scientific) and segmented using Yen thresholding74. Collagen fibres were imaged using confocal reflection microscopy. Images are Sato-filtered for ridge detection, highlighting the fibre structure73. The transparency of the cell and collagen image stacks were determined by the intensity values according to a sigmoidal transfer function. The recorded stack size is 123 × 123 × 40 μm with a voxel size of 0.24 × 0.24 × 1.5 μm. The time between consecutive image stacks is 1 min. Matrix deformations are indicated by coloured arrows.

Supplementary Video 6

Video of matrix deformations around an NK92 cell migrating through collagen: deformation field around an NK92 cell during migration in a 1.2 mg ml−1 collagen gel (stack size of 123 × 123 × 123 μm with a voxel size of 0.24 × 0.24 × 1 μm, dt = 1 min). The cell shows a phase of high contractility at around t = 5 min. Intensity projected bright-field image stacks are shown below the 3D fields. Note that the contractile phase occurs when the cell moves through a narrow constriction.

Supplementary Video 7

Video of matrix deformations calculated from confocal reflection images of collagen fibres around an NK92 cell: the deformation field around the NK92 cell shown in Supplementary Video 6 at t = 5 min (peak of the contractile phase). The deformation field is calculated from confocal reflection images using PIV27. Individual images are recorded using a resonance scanner operated at 8,000 Hz in combination with a galvo stage to move the sample in z direction. The entire image stack is recorded within 10 seconds (no line or frame averaging). Despite substantial image noise, the deformation field can be reliably calculated.

Supplementary Video 8

Video showing the force reconstruction of a migrating NK92 cell: measured matrix deformations (left), reconstructed matrix deformations (centre) and reconstructed force field (right) around the NK92 cell shown in Supplementary Video 6 at t = 5 min (peak of the contractile phase). The measured matrix deformations agree well with the reconstructed deformations. Intensity projected bright-field image stacks are shown below the 3D fields. The pink dot denotes the force epicentre of the force field.

Supplementary Video 9

Video showing elastic matrix deformations around NK92 cells: NK92 cells embedded in 1.2 mg ml−1 collagen gels during contractile phases imaged by confocal reflection microscopy. To visualize changes in collagen structure, the initial state of the matrix is shown in red and the current timestep is shown in green. The video is followed by a sequence of images showing the state of the matrix before, during and after a contractile burst. The collagen fibres relax back to their initial position, indicating predominantly elastic matrix deformations without notable plastic deformations.

Supplementary Video 10

Video of axon growth cones: maximum projected confocal reflection image stacks of Xenopus retinal ganglion cell axon growth cones in a 1.0 mg ml−1 collagen gel (batch D). The recorded stack size is 145 × 145 × 50 μm with a voxel size of 0.14 × 0.14 × 1 μm. The time between consecutive image stacks is t = 5 min. Similar to contractile phases of immune cells, we observe contractile phases during axon growth cone development. For better visualization, we show a projected volume of 124 × 124 × 10 μm around the axon growth cones and show a forward–backward sequence of the contractile phases at the end of the video.

Supplementary Video 11

Videos showing force reconstruction of a hepatic stellate cell: confocal reflection and fluorescence image stacks around a human hepatic stellate cell in a 1.2 mg ml−1 collagen gels are acquired after a culture time of 2 days (stack size of (370 μm)3 with a voxel size of 0.72 × 0.72 × 0.99 μm). Matrix deformations were calculated from the confocal reflection image stacks before and after relaxation of cellular forces using 10 μM cytochalsin D. The measured matrix deformation field (left) agrees well with the reconstructed deformation field (centre). Intensity projected image stacks of the calcein-stained cell are shown below the 3D fields. The purple outline indicates the 3D reconstruction of the calcein-stained cell and the pink dot represents the force epicentre (right).

Supplementary Video 12

Video of an intestinal organoid in collagen: image stacks of an intestinal organoid in collagen (1.2 mg ml−1) were recorded using confocal reflection microscopy (stack size 738 × 738 × 100 μm with a voxel size of 0.74 × 0.74 × 2 μm, dt = 20 min). Organoids were relaxed after 24 hours using 10 μM cytochalsin D and 0.1% Triton x-100. Images are Sato-ridge filtered to highlight the fibre structure73. The full time-lapse sequence is followed by a forward–backward sequence of an image pair taken before and after relaxation of cellular forces to visualize the total contraction.

Supplementary Video 13

Video showing a contractile phase of a migrating NK92 cell measured from bright-field image stacks: bright-field image stacks of a NK92 cell during migration in 1.2 mg ml−1 collagen gel (batch C) were acquired with an ASI RAMM microscope (Applied Scientific Instrumentation), a CMOS camera (acA4096-30um, Basler) and a ×20 objective (0.7 numerical aperture, air, Olympus). Cells were kept at 37 °C and 5% CO2 in a stage incubator (Tokai HIT). Matrix deformations were calculated from bright-field image stacks (dt = 30 s, volume 120 × 120 × 120 μm, with a voxel size of 0.15 × 0.15 × 2 μm). Contractions are visualized by a forward–backward sequence of an image pair taken 30 s apart. The left panel shows the maximum intensity projected bright-field image stack (40 μm height around the centred cell) with differential matrix deformations (arrows). The matrix deformations are clearly visible even though the individual collagen fibres cannot be resolved (right, single image plane).

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Böhringer, D., Cóndor, M., Bischof, L. et al. Dynamic traction force measurements of migrating immune cells in 3D biopolymer matrices. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02632-8

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