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Geometry of disordered porous environments regulates cell migration
Phys. Rev. E 113, 014407 – Published 27 January, 2026
DOI: https://doi.org/10.1103/hvtd-qwp1
Abstract
Cell migration is a dynamic process that is of critical importance to various aspects of living organisms, including organogenesis, wound healing, and immune responses. Several external factors are known to influence and direct active cell movement, such as chemokine gradients and the composition and mechanical properties of the extracellular matrix (ECM). While progress has been made in elucidating some of the biochemical pathways that control cell migration, little is known about the impact of the porous structure of the ECM on active cell motion. Here, by combining computational modeling and theory, we reveal how porous environments, as represented by the ECM, determine cell migration dynamics. Simulating cell movement in a 3D cellular Potts model accounting for amoeboid-like cell shape dynamics, we show that cell migration within disordered porous environments is characterized by distinct transient motility regimes that deviate from persistent motion and are best described by the ‘hopping’ of cells between ‘traps.’ Using theory, we can show how these motility regimes and large-scale transport properties are linked to geometrical properties of the microstructure. Importantly, our analyses reveal that spatial heterogeneities in the porosity lead to nonhomogeneous cell distributions and effectively guide cell movement toward regions of low porosity, an effect which we term as porotaxis. Overall, our work reveals the porosity of the ECM as an important control parameter that shapes cell migration and cellular distribution, and provides a conceptual framework to relate experimentally observed cell motility modes to tissue structures and vice versa. This connection between geometry and cell motility could enhance our understanding of how structural elements shape cell migration and tissue organization in various conditions, such as chronic inflammation, immunity, and cancer.
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References (90)
- U. H. von Andrian and T. R. Mempel, Homing and cellular traffic in lymph nodes, Nat. Rev. Immunol. 3, 867 (2003).
- M. Zhao, B. Song, J. Pu, T. Wada, B. Reid, G. Tai, F. Wang, A. Guo, P. Walczysko, Y. Gu, T. Sasaki, A. Suzuki, J. V. Forrester, H. R. Bourne, P. N. Devreotes, C. D. McCaig, and J. M. Penninger, Electrical signals control wound healing through phosphatidylinositol-3-OH kinase- and PTEN, Nature (London) 442, 457 (2006).
- D. Masopust and J. M. Schenkel, The integration of T cell migration, differentiation and function, Nat. Rev. Immunol. 13, 309 (2013).
- R. Ananthakrishnan and A. Ehrlicher, The forces behind cell movement, Int. J. Biol. Sci. 3, 303 (2007).
- M. Murrell, P. W. Oakes, M. Lenz, and M. L. Gardel, Forcing cells into shape: The mechanics of actomyosin contractility, Nat. Rev. Mol. Cell Biol. 16, 486 (2015).
- W.-J. Rappel and L. Edelstein-Keshet, Mechanisms of cell polarization, Curr. Opin. Syst. Biol. 3, 43 (2017).
- K. M. Yamada and M. Sixt, Mechanisms of 3D cell migration, Nat. Rev. Mol. Cell Biol. 20, 738 (2019).
- F. Merino-Casallo, M. J. Gomez-Benito, S. Hervas-Raluy, and J. M. Garcia-Aznar, Unravelling cell migration: Defining movement from the cell surface, Cell Adhes. Migr. 16, 25 (2022).
- M. R. Chastney, J. Kaivola, V.-M. Leppänen, and J. Ivaska, The role and regulation of integrins in cell migration and invasion, Nat. Rev. Mol. Cell Biol. 26, 147 (2025).
- X. Trepat, Z. Chen, and K. Jacobson, Cell migration, Compr. Physiol. 2, 2369 (2012).
- S. SenGupta, C. A. Parent, and J. E. Bear, The principles of directed cell migration, Nat. Rev. Mol. Cell Biol. 22, 529 (2021).
- J. d'Alessandro, A. Barbier–Chebbah, V. Cellerin, O. Benichou, R. M. Mège, R. Voituriez, and B. Ladoux, Cell migration guided by long-lived spatial memory, Nat. Commun. 12, 4118 (2021).
- J. Renkawitz, A. Kopf, J. Stopp, I. De Vries, M. K. Driscoll, J. Merrin, R. Hauschild, E. S. Welf, G. Danuser, R. Fiolka, and M. Sixt, Nuclear positioning facilitates amoeboid migration along the path of least resistance, Nature (London) 568, 546 (2019).
- Z. Sadjadi, R. Zhao, M. Hoth, B. Qu, and H. Rieger, Migration of cytotoxic T lymphocytes in 3D collagen matrices, Biophys. J. 119, 2141 (2020).
- T. H. Harris, E. J. Banigan, D. A. Christian, C. Konradt, E. D. Tait Wojno, K. Norose, E. H. Wilson, B. John, W. Weninger, A. D. Luster, A. J. Liu, and C. A. Hunter, Generalized Lévy walks and the role of chemokines in migration of effector cells, Nature (London) 486, 545 (2012).
- T. R. Mempel, T. Junt, and U. H. Von Andrian, Rulers over randomness: Stroma cells guide lymphocyte migration in lymph nodes, Immunity 25, 867 (2006).
- G. M. Fricke, K. A. Letendre, M. E. Moses, and J. L. Cannon, Persistence and adaptation in immunity: T cells balance the extent and thoroughness of search, PLoS Comput. Biol. 12, e1004818 (2016).
- P.-H. Wu, A. Giri, S. X. Sun, and D. Wirtz, Three-dimensional cell migration does not follow a random walk, Proc. Natl. Acad. Sci. USA 111, 3949 (2014).
- J. W. Griffith, C. L. Sokol, and A. D. Luster, Chemokines and chemokine receptors: Positioning cells for host defense and immunity, Annu. Rev. Immunol. 32, 659 (2014).
- O. Schulz, S. I. Hammerschmidt, G. L. Moschovakis, and R. Förster, Chemokines and chemokine receptors in lymphoid tissue dynamics, Annu. Rev. Immunol. 34, 203 (2016).
- K. J. Cheung and S. Horne-Badovinac, Collective migration modes in development, tissue repair and cancer, Nat. Rev. Mol. Cell Biol. 26, 741 (2025).
- M. Miron-Mendoza, J. Seemann, and F. Grinnell, The differential regulation of cell motile activity through matrix stiffness and porosity in three dimensional collagen matrices, Biomaterials 31, 6425 (2010).
- S. R. Peyton, Z. I. Kalcioglu, J. C. Cohen, A. P. Runkle, K. J. Van Vliet, D. A. Lauffenburger, and L. G. Griffith, Marrow-Derived stem cell motility in 3D synthetic scaffold is governed by geometry along with adhesivity and stiffness, Biotechnol. Bioeng. 108, 1181 (2011).
- A. Pathak and S. Kumar, Independent regulation of tumor cell migration by matrix stiffness and confinement, Proc. Natl. Acad. Sci. USA 109, 10334 (2012).
- K. Wolf, M. Te Lindert, M. Krause, S. Alexander, J. Te Riet, A. L. Willis, R. M. Hoffman, C. G. Figdor, S. J. Weiss, and P. Friedl, Physical limits of cell migration: Control by ECM space and nuclear deformation and tuning by proteolysis and traction force, J. Cell Biol. 201, 1069 (2013).
- J.-P. Bouchaud and A. Georges, Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications, Phys. Rep. 195, 127 (1990).
- V. Zaburdaev, S. Denisov, and J. Klafter, Lévy walks, Rev. Mod. Phys. 87, 483 (2015).
- J. Bickmann and R. Wittkowski, Collective dynamics of active Brownian particles in three spatial dimensions: A predictive field theory, Phys. Rev. Res. 2, 033241 (2020).
- A. Datta, C. Beta, and R. Großmann, Random walks of intermittently self-propelled particles, Phys. Rev. Res. 6, 043281 (2024).
- G. S. Giardini, G. L. Thomas, C. R. Da Cunha, and R. M. De Almeida, Membrane fluctuations in migrating mesenchymal cells preclude instantaneous velocity definitions, Physica A 647, 129915 (2024).
- J. B. Beltman, A. F. Marée, J. N. Lynch, M. J. Miller, and R. J. De Boer, Lymph node topology dictates T cell migration behavior, J. Exp. Med. 204, 771 (2007).
- M. Chiang and D. Marenduzzo, Glass transitions in the cellular Potts model, Europhys. Lett. 116, 28009 (2016).
- A. Goychuk, D. B. Brückner, A. W. Holle, J. P. Spatz, C. P. Broedersz, and E. Frey, Morphology and motility of cells on soft substrates, arXiv:1808.00314.
- B. Loewe, M. Chiang, D. Marenduzzo, and M. C. Marchetti, Solid-Liquid transition of deformable and overlapping active particles, Phys. Rev. Lett. 125, 038003 (2020).
- L. van Steijn, J. A. Wondergem, K. Schakenraad, D. Heinrich, and R. M. Merks, Deformability and collision-induced reorientation enhance cell topotaxis in dense microenvironments, Biophys. J. 122, 2791 (2023).
- A. Hopkins, B. Loewe, M. Chiang, D. Marenduzzo, and M. C. Marchetti, Motility induced phase separation of deformable cells, Soft Matter 19, 8172 (2023).
- D. B. Brückner, A. Fink, C. Schreiber, P. J. F. Röttgermann, J. O. Rädler, and C. P. Broedersz, Stochastic nonlinear dynamics of confined cell migration in two-state systems, Nat. Phys. 15, 595 (2019).
- D. B. Brückner and C. P. Broedersz, Learning dynamical models of single and collective cell migration: A review, Rep. Prog. Phys. 87, 056601 (2024).
- T. Brandstätter, E. Brieger, D. B. Brückner, G. Ladurner, J. O. Rädler, and C. P. Broedersz, Data-Driven theory reveals protrusion and polarity interactions governing collision behavior of distinct motile cells, PRX Life 3, 033015 (2025).
- K. Goswami, A. G. Cherstvy, A. Godec, and R. Metzler, Anomalous diffusion of active Brownian particles in responsive elastic gels: Nonergodicity, non-Gaussianity, and distributions of trapping times, Phys. Rev. E 110, 044609 (2024).
- K. Schakenraad, L. Ravazzano, N. Sarkar, J. A. J. Wondergem, R. M. H. Merks, and L. Giomi, Topotaxis of active Brownian particles, Phys. Rev. E 101, 032602 (2020).
- F. Moore, J. Russo, T. B. Liverpool, and C. P. Royall, Active Brownian particles in random and porous environments, J. Chem. Phys. 158, 104907 (2023).
- M. S. Alber, M. A. Kiskowski, J. A. Glazier, and Y. Jiang, On cellular automaton approaches to modeling biological cells, in Mathematical Systems Theory in Biology, Communications, Computation, and Finance, edited by D. N. Arnold, F. Santosa, J. Rosenthal, and D. S. Gilliam (Springer, New York, 2003), Vol. 134, pp. 1–39.
- T. Hirashima, E. G. Rens, and R. M. H. Merks, Cellular Potts modeling of complex multicellular behaviors in tissue morphogenesis, Dev. Growth Differ. 59, 329 (2017).
- F. Ziebert and I. S. Aranson, Computational approaches to substrate-based cell motility, npj Comput. Mater. 2, 16019 (2016).
- A. Moure and H. Gomez, Phase-field model of cellular migration: Three-dimensional simulations in fibrous networks, Comput. Methods Appl. Mech. Eng. 320, 162 (2017).
- A. Moure and H. Gomez, Phase-Field modeling of individual and collective cell migration, Arch. Comput. Methods Eng. 28, 311 (2021).
- M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
- D. Bi, X. Yang, M. C. Marchetti, and M. L. Manning, Motility-driven glass and jamming transitions in biological tissues, Phys. Rev. X 6, 021011 (2016).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/hvtd-qwp1, Supplemental Video 1: (Movie-1.mp4) CPM simulation of a single cell performing a persistent random walk in free space; Supplemental Video 2: (Movie-2.mp4) Simulation of amoeboid cell migration in disordered fibrous porous media. Supplemental Video 3: (Movie-3.mp4) Cells migrate through disordered porous media via hopping and trapping; Supplemental Video 4:(Movie-4.mp4) Spatial inhomogeneities in porosity result in directed motion toward regions with higher confinement (porotaxis).
- M. R. Shaebani, A. Wysocki, R. G. Winkler, G. Gompper, and H. Rieger, Computational models for active matter, Nat. Rev. Phys. 2, 181 (2020).
- A. Ziepke, I. Maryshev, I. S. Aranson, and E. Frey, Multi-scale organization in communicating active matter, Nat. Commun. 13, 6727 (2022).
- A. Hayn, T. Fischer, and C. T. Mierke, Inhomogeneities in 3D collagen matrices impact matrix mechanics and cancer cell migration, Front. Cell Dev. Biol. 8, 593879 (2020).
- C. Kurzthaler, S. Mandal, T. Bhattacharjee, H. Löwen, S. S. Datta, and H. A. Stone, A geometric criterion for the optimal spreading of active polymers in porous media, Nat. Commun. 12, 7088 (2021).
- S. Torquato and B. Lu, Chord-length distribution function for two-phase random media, Phys. Rev. E 47, 2950 (1993).
- T. Bhattacharjee and S. S. Datta, Bacterial hopping and trapping in porous media, Nat. Commun. 10, 2075 (2019).
- V. N. Burganos and S. V. Sotirchos, Simulation of Knudsen diffusion in random networks of parallel pores, Chem. Eng. Sci. 43, 1685 (1988).
- M. M. Tomadakis and S. V. Sotirchos, Effective Knudsen diffusivities in structures of randomly overlapping fibers, AIChE J. 37, 74 (1991).
- P. L. Krapivsky, S. Redner, and E. Ben-Naim, A Kinetic View of Statistical Physics (Cambridge University Press, Cambridge, 2010).
- J. Han, S. W. Turner, and H. G. Craighead, Entropic trapping and escape of long DNA molecules at submicron size constriction, Phys. Rev. Lett. 83, 1688 (1999).
- R. Zwanzig, Diffusion past an entropy barrier, J. Phys. Chem. 96, 3926 (1992).
- A.-L. Barabási and M. Pósfai, Network Science (Cambridge University Press, Cambridge, 2016).
- H. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions, Physica 7, 284 (1940).
- S. N. Mueller, M. Matloubian, D. M. Clemens, A. H. Sharpe, G. J. Freeman, S. Gangappa, C. P. Larsen, and R. Ahmed, Viral targeting of fibroblastic reticular cells contributes to immunosuppression and persistence during chronic infection, Proc. Natl. Acad. Sci. USA 104, 15430 (2007).
- J. L. Chitty and T. R. Cox, The extracellular matrix in cancer: From understanding to targeting, Trends Cancer 11, P839 (2025).
- R. Belousov, A. Hassanali, and É. Roldán, Statistical physics of inhomogeneous transport: Unification of diffusion laws and inference from first-passage statistics, Phys. Rev. E 106, 014103 (2022).
- A. Pacheco-Pozo, M. Balcerek, A. Wyłomanska, K. Burnecki, I. M. Sokolov, and D. Krapf, Langevin equation in heterogeneous landscapes: How to choose the interpretation, Phys. Rev. Lett. 133, 067102 (2024).
- T. Bhattacharjee and S. S. Datta, Confinement and activity regulate bacterial motion in porous media, Soft Matter 15, 9920 (2019).
- A. Datta, S. Beier, V. Pfeifer, R. Großmann, and C. Beta, Bacterial swimming in porous gels exhibits intermittent run motility with active turns and mechanical trapping, Sci. Rep. 15, 20320 (2025).
- C. Bousige, P. Levitz, and B. Coasne, Bridging scales in disordered porous media by mapping molecular dynamics onto intermittent Brownian motion, Nat. Commun. 12, 1043 (2021).
- T. Bhattacharjee, D. B. Amchin, J. A. Ott, F. Kratz, and S. S. Datta, Chemotactic migration of bacteria in porous media, Biophys. J. 120, 3483 (2021).
- R. Sunyer and X. Trepat, Durotaxis, Curr. Biol. 30, R383 (2020).
- J. Park, D.-H. Kim, H.-N. Kim, C. J. Wang, M. K. Kwak, E. Hur, K.-Y. Suh, S. S. An, and A. Levchenko, Directed migration of cancer cells guided by the graded texture of the underlying matrix, Nat. Mater. 15, 792 (2016).
- R. K. Sadhu, M. Luciano, W. Xi, C. Martinez-Torres, M. Schröder, C. Blum, M. Tarantola, S. Villa, S. Penič, A. Iglič, C. Beta, O. Steinbock, E. Bodenschatz, B. Ladoux, S. Gabriele, and N. S. Gov, A minimal physical model for curvotaxis driven by curved protein complexes at the cell's leading edge, Proc. Natl. Acad. Sci. USA 121, e2306818121 (2024).
- D. Fuller, W. Chen, M. Adler, A. Groisman, H. Levine, W.-J. Rappel, and W. F. Loomis, External and internal constraints on eukaryotic chemotaxis, Proc. Natl. Acad. Sci. USA 107, 9656 (2010).
- G. Micali and R. G. Endres, Bacterial chemotaxis: Information processing, thermodynamics, and behavior, Curr. Opin. Microbiol. 30, 8 (2016).
- I. Andreu, B. Falcones, S. Hurst, N. Chahare, X. Quiroga, A.-L. Le Roux, Z. Kechagia, A. E. M. Beedle, A. Elosegui-Artola, X. Trepat, R. Farré, T. Betz, I. Almendros, and P. Roca-Cusachs, The force loading rate drives cell mechanosensing through both reinforcement and cytoskeletal softening, Nat. Commun. 12, 4229 (2021).
- A. Pathni, K. Wagh, I. Rey-Suarez, and A. Upadhyaya, Mechanical regulation of lymphocyte activation and function, J. Cell Sci. 137, jcs219030 (2024).
- S. S. Deville and N. Cordes, The extracellular, cellular, and nuclear stiffness, a trinity in the cancer resistome—a review, Front. Oncol. 9, 1376 (2019).
- R. Borst, L. Meyaard, and M. I. Pascoal Ramos, Understanding the matrix: Collagen modifications in tumors and their implications for immunotherapy, J. Transl. Med. 22, 382 (2024).
- M. F. Krummel, F. Bartumeus, and A. Gérard, T cell migration, search strategies and mechanisms, Nat. Rev. Immunol. 16, 193 (2016).
- H. Du, J. M. Bartleson, S. Butenko, V. Alonso, W. F. Liu, D. A. Winer, and M. J. Butte, Tuning immunity through tissue mechanotransduction, Nat. Rev. Immunol. 23, 174 (2023).
- B. D. Hale, Y. Severin, F. Graebnitz, D. Stark, D. Guignard, J. Mena, Y. Festl, S. Lee, J. Hanimann, N. S. Zangger, M. Meier, D. Goslings, O. Lamprecht, B. M. Frey, A. Oxenius, and B. Snijder, Cellular architecture shapes the naïve T cell response, Science 384, eadh8697 (2024).
- Simulation code and geometries used to generate data presented here are available, https://github.com/GrawLab/CellMigration_Porosity; https://identifiers.org/morpheus/M9342.
- J. Starruß, W. De Back, L. Brusch, and A. Deutsch, Morpheus: A user-friendly modeling environment for multiscale and multicellular systems biology, Bioinformatics 30, 1331 (2014).
- R. Belousov, S. Savino, P. Moghe, T. Hiiragi, L. Rondoni, and A. Erzberger, Poissonian cellular Potts models reveal nonequilibrium kinetics of cell sorting, Phys. Rev. Lett. 132, 248401 (2024).
- M. J. Miller, S. H. Wei, I. Parker, and M. D. Cahalan, Two-Photon imaging of lymphocyte motility and antigen response in intact lymph node, Science 296, 1869 (2002).
- M. J. Miller, S. H. Wei, M. D. Cahalan, and I. Parker, Autonomous T cell trafficking examined in vivo with intravital two-photon microscopy, Proc. Natl. Acad. Sci. USA 100, 2604 (2003).
- C. W. Gardiner, Handbook of Stochastic Methods: For Physics, Chemistry, and the Natural Sciences, Springer Series in Synergetics, Vol. 13 (Springer-Verlag, 1983).
- J. Gostick, Z. Khan, T. Tranter, M. Kok, M. Agnaou, M. Sadeghi, and R. Jervis, PoreSpy: A Python toolkit for quantitative analysis of porous media images, J. Open Source Software 4, 1296 (2019).