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Topological defects control collective dynamics in neural progenitor cell cultures


Cultured stem cells have become a standard platform not only for regenerative medicine and developmental biology but also for biophysical studies. Yet, the characterization of cultured stem cells at the level of morphology and of the macroscopic patterns resulting from cell-to-cell interactions remains largely qualitative. Here we report on the collective dynamics of cultured murine neural progenitor cells (NPCs), which are multipotent stem cells that give rise to cells in the central nervous system1. At low densities, NPCs moved randomly in an amoeba-like fashion. However, NPCs at high density elongated and aligned their shapes with one another, gliding at relatively high velocities. Although the direction of motion of individual cells reversed stochastically along the axes of alignment, the cells were capable of forming an aligned pattern up to length scales similar to that of the migratory stream observed in the adult brain2. The two-dimensional order of alignment within the culture showed a liquid-crystalline pattern containing interspersed topological defects with winding numbers of +1/2 and −1/2 (half-integer due to the nematic feature that arises from the head–tail symmetry of cell-to-cell interaction). We identified rapid cell accumulation at +1/2 defects and the formation of three-dimensional mounds. Imaging at the single-cell level around the defects allowed us to quantify the velocity field and the evolving cell density; cells not only concentrate at +1/2 defects, but also escape from −1/2 defects. We propose a generic mechanism for the instability in cell density around the defects that arises from the interplay between the anisotropic friction and the active force field.

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Figure 1: Two-dimensional patterning and collective motion of NPCs.
Figure 2: Single-cell tracking reveals the transition from random to bipolar motion at high density.
Figure 3: Long-range nematic order induced by artificial boundaries.
Figure 4: Active topological defects.


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We thank H. Chaté, H. Kori, K. Nagai, A. Isomura, K. Takeuchi, D. Nishiguchi, T. Yamamoto, and members of the Kageyama and Sano laboratories for discussions. We acknowledge WPI-iCeMS, Kyoto University, for technical help with flow cytometry. We thank A. M. Klein for supplying equipment and reagents for additional experiments. This work was supported by Core Research for Evolutional Science and Technology (JPMJCR12W2, K.K. and R.K.) and by KAKENHI (numbers 25103004 “Fluctuation & Structure” and 16H06480) from MEXT, Japan (K.K., R.K. and M.S.), and the Platform for Dynamic Approaches to Living Systems from MEXT, Japan (R.K.). K.K. acknowledges two Grants-in-Aid for JSPS Fellows (numbers 24-8031and 28-908).

Author information

Authors and Affiliations



K.K., R.K. and M.S. designed the project and wrote the manuscript. K.K. performed the experiments and developed the image analysis methods. K.K. and M.S. developed the theory.

Corresponding authors

Correspondence to Kyogo Kawaguchi or Masaki Sano.

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The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks A. Bausch, D. Discher, L. Hirst and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Growing nematic order in NPC culture.

a, Nematic order (see equation (S18) in Supplementary Information) calculated for a fixed system size L = 185 μm (chosen as an intermediate size that is larger than a single cell and smaller than the typical distance between defects) for each time frame in the two separate experiments. b, Cell density versus nematic order.

Extended Data Figure 2 Velocity and angle of cell motion.

a, Time-dependence of average cell velocity calculated from the displacement of cells between frames from experiment 2 (high cell density, time frames C and D shown in Fig. 2a). b, Distribution of the direction of motion of cells with respect to the longitudinal direction calculated for each cell trajectory. See Supplementary Information for details. c, Spatial correlation of velocity in the direction of alignment calculated from the displacements in ordered regions (size about 0.2 mm2, cropped from images in time frames C and D in Fig. 2a). Longitudinal: correlation of velocity in the direction of alignment between two cells that are apart in the direction of the alignment ( in Supplementary Information). Transversal: correlation of velocity in the direction of alignment between two cells that are apart in the direction perpendicular to the alignment ( in Supplementary Information). Exponential: the line is a guide to the eye with values proportional to with length scale r0 = 35 μm.

Extended Data Figure 3 Pattern disruption by low laminin concentration, nocodazole treatment, and NCAM knockdown.

a, Lowering laminin concentration in the laminin-coated culture changes the behaviour of the NPCs. Cells tend to aggregate when laminin is low. b, Nocodazole (a microtubule polymerization inhibitor)-treated NPCs (24 h), showing disrupted pattern, consistent with the bipolar shape of the NPCs being supported by microtubules. c, Immunocytochemistry of NPCs. Left, NCAM. Right, PSA-NCAM. NPCs express NCAM but not its polysialylated form. d, Pattern of NPCs under stable NCAM knockdown by shRNA lentivirus (the control is shRNA with a non-specific scrambled sequence). See also Supplementary Video 4. Scale bars, 100 μm.

Extended Data Figure 4 Reversal of the direction of motion during the same cell cycle phase.

ac, Autocorrelations (a), nematic autocorrelations (b) (where angle brackets indicate the ensemble average), and distribution of velocity angle (c) relative to the longitudinal angle calculated for cells in different cell cycle phases (G1 and G2) from the same experiment of Fucci-labelled NPCs at high cell density (>3,000 cells mm−2). The inset in a is the flipping time quantified from the fitting of autocorrelation by an exponential function (solid lines in a). Error bars correspond to the standard error of fitting. See also Supplementary Video 6.

Extended Data Figure 5 Giant number fluctuation and global order parameter in regions without defect.

a, Giant cell number N fluctuation in the dense culture (size about 0.2 mm2, cropped from images in time frames C and D in Fig. 2a). The fluctuation rescaled by the square root of the mean cell number in the different defined system sizes was calculated from counting of the cell nuclei. Cell density has grown from 3,000 mm−2 to 4,500 mm−2 during the 15-h period. We find ΔN Nα (where ΔN is the fluctuation and 〈N〉 is the average cell number within the fixed size window) with an exponent α larger than 0.7 in the straight region where the system size is larger than the cell and smaller than the maximum window size. b, Global nematic order as a function of system size (see equation (S18) in Supplementary Information) in the same time frames as a. Nematic order was calculated from the velocity field obtained by the global tracking algorithm. The solid lines are guides to the eye.

Extended Data Figure 6 Spatial correlation of the fluctuation of density and alignment.

Spatial (two-dimensional displacement r) correlations of density fluctuation and alignment fluctuation (Cρn, Cρρ and Cnn) calculated in the ordered region without defect (size about 0.2 mm2, cropped from images in time frames C and D in Fig. 2a). The colours indicate the values of the correlations (red is positive and blue is negative), where the values are normalized using the standard deviations of the density and alignment fluctuations (see equations (S13)–(S15) in Supplementary Information for definitions). The horizontal axis corresponds to the alignment direction defined in the analysed regions. The correlation is the average value calculated from densities and alignments at four separate regions.

Extended Data Figure 7 Comparing the tensor method and the tracking method to extract alignment from image.

a, Phase contrast image of NPC culture in the high-density regime. Scale bar, 200 μm. b, Direction of alignment obtained by applying the tensor method on the phase contrast image data. c, Fluorescent image of the cell nucleus (white) in the same position as a, overlaid with the displacements (green arrows) in a single time frame (5-min interval). Only about 20% of the calculated displacements (elongated 15-fold) are shown, for the sake of visualization. d, Alignment field obtained from the nematic order calculated within the boxes (60 pixels × 60 pixels = 54.7 × 54.7 μm2) using the displacement vectors. e, Merge of the alignment fields obtained by two independent methods. Bars indicating the direction of alignment (same as d) were coloured according to the same rule as b to see a match between the two fields. f, Correlation of the angle of alignment calculated using displacement vectors (d) versus the tensor method (b). Each dot corresponds to an angle calculated within a box at the same time frame. Eight time frames with interval 2 h from four different positions were used. The colour shows the nematic order parameter in each box.

Extended Data Figure 8 Patterning and correlations in myoblast cell culture C2C12.

a, Large-field image of C2C12 culture. Colour (right) indicates the angle of the local alignment calculated using the tensor method (see Supplementary Information) from the phase contrast image (left). Scale bar, 1 mm. b, Spatial correlation of the fluctuation of density and alignment in C2C12 calculated in the ordered region without defect. See equations (S13)–(S15) in Supplementary Information for definitions.

Extended Data Figure 9 Cell density evolution and nematic order around defects.

a, Raw cell density evolution quantified without normalization. The decrease of cell density around the −1/2 defects is unclear compared with the case of normalized cell density (see Fig. 4h), owing to the competition of the outflow and the growth of cells. b, Fit of the nematic order near the defect calculated from the data points obtained by the tracking method (corresponding to Fig. 4c). A radially symmetric form of the nematic order is assumed (see Supplementary Information), and R0 is the fitted length scale of the defect. Although the nematic order should converge to 1 at large R, the value calculated here is small owing to finite binning (23 μm) and the small fluctuations in the alignment angle over time and independent defects. c, Phase contrast (left) and immunofluorescent images (right) of fixed NPCs around topological defects. Nestin (a neural stem cell marker) is universally expressed, meaning that there is no noticeable cell differentiation occurring around the defects. Scale bars, 100 μm.

Extended Data Figure 10 Absence of cell accumulation and escape around defects in C2C12.

a, Phase contrast image of C2C12 cells, highlighting the existence of +1/2 and −1/2 topological defects in the ordered pattern. b, Cell density dynamics around the defects. Average of four defects each from the same dish over the same time course.

Supplementary information

Supplementary Information

This file contains Supplementary text, including details of the image analysis and theory. (PDF 116 kb)

Live images of neural progenitor cell migration at low density

Live phase contrast (left) and fluorescent (right) images taken over 27 hours. Fluorescent signals from H2B-mCherry (nucleus marker) is shown by pseudo-color. (MOV 1498 kb)

Live images of neural progenitor cell migration at high density in a wide field of view

Live phase contrast (left) and fluorescent (right) images taken over 24 hours. Fluorescent signals from H2B-mCherry (nucleus marker) is shown by pseudo-color. (MOV 20901 kb)

Tracking of single cells using nucleus marker

White: Fluorescent live image of H2B-mcherry in the high-density culture of neural progenitors (24 hours). Green boxes are the results of the half-manual tracking of single cells. (MOV 2866 kb)

Live images of NCAM knockdown NPCs

Live phase contrast (left) and fluorescent (right) images of stable NCAM knockdown NPCs established using lentivirus. Taken over 24 hours. (MOV 18344 kb)

Live images of NPCs cultured under the boundary condition of a thin lane

18 hour fluorescent live image of H2B-mcherry (top) and phase contrast image (bottom) under a boundary condition of thin lane made by scaping the subsrate surface. (MOV 3581 kb)

Tracking of single cells using Fucci.

Cells at G1 phase (red) and G2 phase (green) observed by the Fucci marker through fluorescent microscopy (24 hours). The boxes represent the results of the half-manual tracking method. (MOV 2760 kb)

Live image around a +1/2 topological defect

Live phase contrast (left) and fluorescent (right) images around a +1/2 topological defect over 24 hours. (MOV 4790 kb)

Live image around a -1/2 topological defect

Live phase contrast (left) and fluorescent (right) images around a -1/2 topological defect over 24 hours. (MOV 4229 kb)

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Kawaguchi, K., Kageyama, R. & Sano, M. Topological defects control collective dynamics in neural progenitor cell cultures. Nature 545, 327–331 (2017).

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