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Licensed Unlicensed Requires Authentication Published by De Gruyter February 5, 2021

Defects in Active Nematics – Algorithms for Identification and Tracking

  • Dennis Wenzel , Michael Nestler , Sebastian Reuther , Maximilian Simon and Axel Voigt ORCID logo EMAIL logo

Abstract

The growing interest in active nematics and the emerging evidence of the relevance of topological defects in biology asks for reliable data analysis tools to identify, classify and track such defects in simulation and microscopy data. We here provide such tools and demonstrate on two examples, on an active turbulent state in an active nematodynamic model and on emerging nematic order in a multi-phase field model, the possibility to compare statistical data on defect velocities with experimental results. The considered tools, which are physics based and data driven, are compared with each other.

MSC 2010: 74L15; 76T30; 70K25

Funding statement: Axel Voigt acknowledges financial support from DFG through FOR3013. The work was also supported by the Sino-German Science Center on the occasion of the Chinese–German Workshop on Computational and Applied Mathematics in Kiel 2019. We further acknowledge computing resources provided by JSC under grant HDR06 and ZIH/TU Dresden.

References

[1] H. Abels, G. Dolzmann and Y. Liu, Well-posedness of a fully coupled Navier–Stokes/Q-tensor system with inhomogeneous boundary data, SIAM J. Math. Anal. 46 (2014), no. 4, 3050–3077. 10.1137/130945405Search in Google Scholar

[2] J. M. Ball and A. Majumdar, Nematic liquid crystals: From Maier-Saupe to a continuum theory, Molec. Crys. Liq. Cryst. 525 (2010), 1–11. 10.1080/15421401003795555Search in Google Scholar

[3] A. M. Bazan and S. H. Gerez, Systematic methods for the computation of the directional fields and singular points of fingerprints, IEEE Trans. Patt. Anal. Mach. Intell. 24 (2002), 905–919. 10.1109/TPAMI.2002.1017618Search in Google Scholar

[4] A. N. Beris and B. J. Edwards, Thermodynamics of Flowing Systems with Internal Microstructure, Oxford Eng. Sci. Ser. 36, The Clarendon Press, New York, 1994. 10.1093/oso/9780195076943.001.0001Search in Google Scholar

[5] C. Blanch-Mercader, V. Yashunsky, S. Garcia, G. Duclos, L. Giomi and P. Silberzan, Turbulent dynamics of epithelial cell cultures, Phys. Rev. Lett. 120 (2018), Article ID 208101. 10.1103/PhysRevLett.120.208101Search in Google Scholar PubMed

[6] B. A. Camley and W.-J. Rappel, Physical models of collective cell motility: From cell to tissue, J. Phys. D 50 (2017), Article ID 113002. 10.1088/1361-6463/aa56feSearch in Google Scholar PubMed PubMed Central

[7] B. A. Camley, Y. Zhang, B. Zhao, Y. and Li, E. Ben-Jacob, H. Levine and W.-J. Rappel, Polarity mechanisms such as contact inhibition of locomotion regulate persistent rotational motion of mammalian cells on micropatterns, Proc. Natl. Acad. Sci. (USA) 111 (2014), 14770–14775. 10.1073/pnas.1414498111Search in Google Scholar PubMed PubMed Central

[8] N. Chenouard and et al., Objective comparison of particle tracking methods, Nature Meth. 11 (2014), 281–290. 10.1038/nmeth.2808Search in Google Scholar PubMed PubMed Central

[9] S. J. DeCamp, G. S. Redner, A. Baskaran, M. F. Hagan and Z. Dogic, Orientational order of motile defects in active nematics, Nature Mat. 14 (2015), no. 11, 1110–1115. 10.1038/nmat4387Search in Google Scholar PubMed PubMed Central

[10] T. Delmarcelle and L. Hesselink, The topology of symmetric, second-order tensor fields, Proceedings Visualization ’94, IEEE Press, Piscataway (1994), 140–147. 10.1109/VISUAL.1994.346326Search in Google Scholar

[11] A. Doostmohammadi, J. Ignes-Mullol, J. M. Yeomans and F. Sagues, Active nematics, Nature Comm. 9 (2018), Article ID 3246. 10.1038/s41467-018-05666-8Search in Google Scholar PubMed PubMed Central

[12] G. Duclos, C. Erlenkamper, J.-F. Joanny and P. Silberzan, Topological defects in confined populations of spindle-shaped cells, Nature Phys. 13 (2017), 58–62. 10.1038/nphys3876Search in Google Scholar

[13] L. Giomi, Geometry and topology of turbulence in active nematics, Phys. Rev. X 5 (2015), Article ID 031003. 10.1103/PhysRevX.5.031003Search in Google Scholar

[14] L. Giomi, M. J. Bowick, P. Mishra, R. Sknepnek and M. C. Marchetti, Defect dynamics in active nematics, Phil. Trans. Roy. Soc. A 372 (2014), Article ID 20130365. 10.1098/rsta.2013.0365Search in Google Scholar PubMed PubMed Central

[15] J.-F. Joanny and S. Ramaswamy, A drop of active matter, J. Fluid Mech. 705 (2012), 46–57. 10.1017/jfm.2012.131Search in Google Scholar

[16] F. Jülicher, S. W. Grill and G. Salbreux, Hydrodynamic theory of active matter, Rep. Progr. Phys. 81 (2018), no. 7, Article ID 076601. 10.1088/1361-6633/aab6bbSearch in Google Scholar PubMed

[17] K. Kawaguchi, R. Kageyama and M. Sano, Topological defects control collective dynamics in neural progenitor cell cultures, Nature 545 (2017), 327–331. 10.1038/nature22321Search in Google Scholar PubMed

[18] K. Kruse, J. F. Joanny, F. Jülicher, J. Prost and K. Sekimoto, Asters, vortices, and rotating spirals in active gels of polar filaments, Phys. Rev. Lett. 92 (2004), Article ID 078101. 10.1103/PhysRevLett.92.078101Search in Google Scholar PubMed

[19] S. Ling, W. Marth, S. Praetorius and A. Voigt, An adaptive finite element multi-mesh approach for interacting deformable objects in flow, Comput. Methods Appl. Math. 16 (2016), no. 3, 475–484. 10.1515/cmam-2016-0003Search in Google Scholar

[20] J. Loeber, F. Ziebert and I. S. Aranson, Collisions of deformable cells lead to collective migration, Sci. Rep. 5 (2015), Article ID 9172. 10.1038/srep09172Search in Google Scholar PubMed PubMed Central

[21] W. Marth, S. Aland and A. Voigt, Margination of white blood cells: A computational approach by a hydrodynamic phase field model, J. Fluid Mech. 790 (2016), 389–406. 10.1017/jfm.2016.15Search in Google Scholar

[22] W. Marth, S. Praetorius and A. Voigt, A mechanism for cell motility by active polar gels, J. Roy. Soc. Interf. 12 (2015), Article ID 20150161. 10.1098/rsif.2015.0161Search in Google Scholar PubMed PubMed Central

[23] W. Marth and A. Voigt, Collective migration under hydrodynamic interactions: A computational approach, Interf. Focus 6 (2016), no. 5, Article ID 20160037. 10.1098/rsfs.2016.0037Search in Google Scholar PubMed PubMed Central

[24] E. Meijering, O. Dzyubachyk and I. Smal, Methods for cell and particle tracking, Methods Enzymol. 504 (2012), 183–200. 10.1016/B978-0-12-391857-4.00009-4Search in Google Scholar PubMed

[25] A. M. Menzel, Tuned, driven, and active soft matter, Phys. Rep. 554 (2015), 1–45. 10.1016/j.physrep.2014.10.001Search in Google Scholar

[26] R. Mueller, J. M. Yeomans and A. Doostmohammadi, Emergence of active nematic behavior in monolayers of isotropic cells, Phys. Rev. Lett. 122 (2019), Article ID 048004. 10.1103/PhysRevLett.122.048004Search in Google Scholar PubMed

[27] M. Nonomura, Study on multicellular systems using a phase field model, PLoS ONE 7 (2012), Article ID e33501. 10.1371/journal.pone.0033501Search in Google Scholar PubMed PubMed Central

[28] A. U. Oza and J. Dunkel, Antipolar ordering of topological defects in active liquid crystals, New J. Phys. 18 (2016), no. 9, Article ID 093006. 10.1088/1367-2630/18/9/093006Search in Google Scholar

[29] D. J. G. Pearce, P. W. Ellis, A. Fernandez-Nieves and L. Giomi, Geometrical control of active turbulence in curved topographies, Phys. Rev. Lett. 122 (2019), Article ID 168002. 10.1103/PhysRevLett.122.168002Search in Google Scholar PubMed

[30] G. Peyret, R. Mueller, J. d’Alessandro, S. Begnaud, P. Marcq, R.-M. Mege, J. M. Yeomans, A. Doostmohammadi and B. Ladoux, Sustained oscillations of epithelial cell sheets, Biophys. J. 117 (2019), 464–478. 10.1016/j.bpj.2019.06.013Search in Google Scholar PubMed PubMed Central

[31] S. Praetorius and A. Voigt, Collective cell behavior – A cell-based parallelization approach for a phase field active polar gel model, Proceedings of the 9th NIC Symposium, John von Neumann Institute for Computing, Jülich (2018), 369–376. Search in Google Scholar

[32] J. Prost, F. Jülicher and J.-F. Joanny, Active gel physics, Nature Phys. 11 (2015), 111–117. 10.1038/nphys3224Search in Google Scholar

[33] T. Sanchez, D. T. N. Chen, S. J. DeCamp, N. Heymann and Z. Dogic, Spontaneous motion in hierarchically assembled active matter, Nature 491 (2012), 431–434. 10.1038/nature11591Search in Google Scholar PubMed PubMed Central

[34] T. B. Saw, A. Doostmohammadi, V. Nier, L. Kocgozlu, S. Thampi, Y. Toyama, P. Marcq, C. T. Lim, J. M. Yeomans and B. Ladoux, Topological defects in epithelia govern cell death and extrusion, Nature 544 (2017), 212–216. 10.1038/nature21718Search in Google Scholar PubMed PubMed Central

[35] I. F. Sbalzarini and P. Koumoutsakos, Feature point tracking and trajectory analysis for video imaging in cell biology, J. Struc. Bio. 151 (2005), 182–195. 10.1016/j.jsb.2005.06.002Search in Google Scholar PubMed

[36] J. Schindelin and et al., Fiji: An open-source platform for biological-image analysis, Nature Meth. 9 (2012), 676–682. 10.1038/nmeth.2019Search in Google Scholar PubMed PubMed Central

[37] S. Vey and A. Voigt, AMDiS: Adaptive multidimensional simulations, Comput. Vis. Sci. 10 (2007), no. 1, 57–67. 10.1007/s00791-006-0048-3Search in Google Scholar

[38] M. Waltters, Q. Wi and J. Y. Chen, Machine learning topological defects of confined liquid crystals in two dimensions, Phys. Rev. E 99 (2019), Article ID 062701. 10.1103/PhysRevE.99.062701Search in Google Scholar PubMed

[39] D. Wenzel, S. Praetorius and A. Voigt, Topological and geometrical quantities in active cellular structures, J. Chem. Phys. 150 (2019), Article ID 164108. 10.1063/1.5085766Search in Google Scholar PubMed

[40] T. Witkowski, S. Ling, S. Praetorius and A. Voigt, Software concepts and numerical algorithms for a scalable adaptive parallel finite element method, Adv. Comput. Math. 41 (2015), no. 6, 1145–1177. 10.1007/s10444-015-9405-4Search in Google Scholar

[41] F. Ziebert, S. Swaminathan and I. S. Aranson, Model for self-polarization and motility of keratocyte fragments, J. R. Soc. Interface 9 (2012), 1084–1092. 10.1098/rsif.2011.0433Search in Google Scholar PubMed PubMed Central

Received: 2020-02-23
Revised: 2020-12-18
Accepted: 2021-01-31
Published Online: 2021-02-05
Published in Print: 2021-07-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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