Light-induced assembly and repeatable actuation in Ca2+-driven chemomechanical protein networks

1. Gompper, G. et al. The 2025 motile active matter roadmap. J. Phys.: Condens. Matter 37, 143501 (2025).

2. Yashin, V. V. & Balazs, A. C. Pattern formation and shape changes in self-oscillating polymer gels. Science 314, 798 (2006).

   Google Scholar 

3. Yoshida, R. Self-oscillating gels driven by the Belousov–Zhabotinsky reaction as novel smart materials. Adv. Mater. 22, 3463 (2010).

   Google Scholar 

4. Grinthal, A. & Aizenberg, J. Adaptive all the way down: building responsive materials from hierarchies of chemomechanical feedback. Chem. Soc. Rev. 42, 7072 (2013).

   Google Scholar 

5. Blanc, B. et al. Active pulsatile gels: From a chemical microreactor to a polymeric actuator. Langmuir 40, 6862 (2024).

   Google Scholar 

6. Blanc, B. et al. Collective chemomechanical oscillations in active hydrogels. Proc. Natl Acad. Sci. USA. 121, e2313258121 (2024).

   Google Scholar 

7. Xue, L. et al. Light-regulated growth from dynamic swollen substrates for making rough surfaces. Nat. Commun. 11, 963 (2020).

   Google Scholar 

8. Chen, M., Zhong, M. & Johnson, J. A. Light-controlled radical polymerization: mechanisms, methods, and applications. Chem. Rev. 116, 10167 (2016).

   Google Scholar 

9. Whitesides, G. M. & Grzybowski, B. Self-assembly at all scales. Science 295, 2418 (2002).

   Google Scholar 

10. Freeman, R. et al. Reversible self-assembly of superstructured networks. Science 362, 808 (2018).

    Google Scholar 

11. Kim, Y.-K., Wang, X., Mondkar, P., Bukusoglu, E. & Abbott, N. L. Self-reporting and self-regulating liquid crystals. Nature 557, 539 (2018).

    Google Scholar 

12. Li, S. et al. Liquid-induced topological transformations of cellular microstructures. Nature 592, 386 (2021).

    Google Scholar 

13. Liu, S., Shankar, S., Marchetti, M. C. & Wu, Y. Viscoelastic control of spatiotemporal order in bacterial active matter. Nature 590, 80 (2021).

    Google Scholar 

14. Sokolov, A., Apodaca, M. M., Grzybowski, B. A. & Aranson, I. S. Swimming bacteria power microscopic gears. Proc. Natl Acad. Sci. USA. 107, 969 (2010).

    Google Scholar 

15. Gu, H. et al. Magnetic cilia carpets with programmable metachronal waves. Nat. Commun. 11, 2637 (2020).

    Google Scholar 

16. Wang, W. et al. Cilia metasurfaces for electronically programmable microfluidic manipulation. Nature 605, 681 (2022).

    Google Scholar 

17. Sanchez, T., Chen, D. T. N., DeCamp, S. J., Heymann, M. & Dogic, Z. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431 (2012).

    Google Scholar 

18. Schaller, V., Weber, C., Semmrich, C., Frey, E. & Bausch, A. R. Polar patterns of driven filaments. Nature 467, 73 (2010).

    Google Scholar 

19. Muresan, C. G. et al. F-actin architecture determines constraints on myosin thick filament motion. Nat. Commun. 13, 7008 (2022).

    Google Scholar 

20. Yadav, V. et al. Filament nucleation tunes mechanical memory in active polymer networks. Adv. Funct. Mater. 29, (2019).

21. Linsmeier, I. et al. Disordered actomyosin networks are sufficient to produce cooperative and telescopic contractility. Nat. Commun. 7, 12615 (2016).

    Google Scholar 

22. Redford, S. A. et al. Motor crosslinking augments elasticity in active nematics. Soft Matter 20, 2480 (2024).

    Google Scholar 

23. Lemma, L. M. et al. Spatio-temporal patterning of extensile active stresses in microtubule-based active fluids. PNAS Nexus 2, pgad130 (2023).

    Google Scholar 

24. Murrell, M., Oakes, P. W., Lenz, M. & Gardel, M. L. Forcing cells into shape: the mechanics of actomyosin contractility. Nat. Rev. Mol. Cell Biol. 16, 486 (2015).

    Google Scholar 

25. Sakamoto, R. et al. Tug-of-war between actomyosin-driven antagonistic forces determines the positioning symmetry in cell-sized confinement. Nat. Commun. 11, 3063 (2020).

    Google Scholar 

26. Sakamoto, R., Izri, Z., Shimamoto, Y., Miyazaki, M. & Maeda, Y. T. Geometric trade-off between contractile force and viscous drag determines the actomyosin-based motility of a cell-sized droplet. Proc. Natl Acad. Sci. USA. 119, e2121147119 (2022).

    Google Scholar 

27. Adkins, R. et al. Dynamics of active liquid interfaces. Science 377, 768 (2022).

    Google Scholar 

28. Ruijgrok, P. V. et al. Optical control of fast and processive engineered myosins in vitro and in living cells. Nat. Chem. Biol. 17, 540 (2021).

    Google Scholar 

29. Ross, T. D. et al. Controlling organization and forces in active matter through optically defined boundaries. Nature 572, 224 (2019).

    Google Scholar 

30. Malik-Garbi, M. et al. Scaling behaviour in steady-state contracting actomyosin networks. Nat. Phys. 15, 509 (2019).

    Google Scholar 

31. Oakes, P. W. et al. Optogenetic control of RhoA reveals zyxin-mediated elasticity of stress fibres. Nat. Commun. 8, 15817 (2017).

    Google Scholar 

32. Schuppler, M., Keber, F. C., Kröger, M. & Bausch, A. R. Boundaries steer the contraction of active gels. Nat. Commun. 7, 13120 (2016).

    Google Scholar 

33. Cavanaugh, K. E., Oakes, P. W. & Gardel, M. L. Optogenetic control of RhoA to probe subcellular mechanochemical circuitry. Curr. Protoc. Cell Biol. 86, e102 (2020).

    Google Scholar 

34. Chandrasekar, S., Beach, J. R. & Oakes, P. W. Shining a light on RhoA: optical control of cell contractility. Int. J. Biochem. Cell Biol. 161, 106442 (2023).

    Google Scholar 

35. Qu, Z. et al. Persistent fluid flows defined by active matter boundaries. Commun. Phys. 4, 1 (2021).

    Google Scholar 

36. Mathijssen, A. J. T. M., Culver, J., Bhamla, M. S. & Prakash, M. Collective intercellular communication through ultra-fast hydrodynamic trigger waves. Nature 571, 560 (2019).

    Google Scholar 

37. Ruiz, F., Garreau de Loubresse, N., Klotz, C., Beisson, J. & Koll, F. Centrin deficiency in Paramecium affects the geometry of basal-body duplication. Curr. Biol. 15, 2097 (2005).

    Google Scholar 

38. Mahadevan, L. & Matsudaira, P. Motility powered by supramolecular springs and ratchets. Science 288, 95 (2000).

    Google Scholar 

39. Hawkes, R. B. & Holberton, D. V. Myonemal contraction of Spirostomum. I. Kinetics of contraction and relaxation. J. Cell. Physiol. 84, 225 (1974).

    Google Scholar 

40. Misra, G., Dickinson, R. B. & Ladd, A. J. C. Mechanics of Vorticella contraction. Biophys. J. 98, 2923 (2010).

    Google Scholar 

41. Kilpatrick, A. M., Honts, J. E., Sleister, H. M. & Fowler, C. A. Solution NMR structures of the C-domain of Tetrahymena cytoskeletal protein Tcb2 reveal distinct calcium-induced structural rearrangements. Proteins 84, 1748 (2016).

    Google Scholar 

42. Floyd, C. et al. A unified model for the dynamics of ATP-independent ultrafast contraction. Proc. Natl. Acad. Sci. USA. 120, e2217737120 (2023).

    Google Scholar 

43. Upadhyaya, A. et al. Power-limited contraction dynamics of Vorticella convallaria: an ultrafast biological spring. Biophys. J. 94, 265 (2008).

    Google Scholar 

44. Chung, E. G. & Ryu, S. Stalk-length-dependence of the contractility of Vorticella convallaria. Phys. Biol. 14, 066002 (2017).

    Google Scholar 

45. Ryu, S., Lang, M. J. & Matsudaira, P. Maximal force characteristics of the Ca²⁺-powered actuator of Vorticella convallaria. Biophys. J. 103, 860 (2012).

    Google Scholar 

46. Chang, R. & Prakash, M. Topological damping in an ultrafast giant cell. Proc. Natl. Acad. Sci. USA. 120, e2303940120 (2023).

    Google Scholar 

47. Chang, R. & Prakash, M. Cellular Olympics: Ultrafast Cellular Motility Across the Tree of Life. Annu. Rev. Microbiol. 79, 405–426 (2025).

48. Lannan, J. et al. Fishnet mesh of centrin-Sfi1 drives ultrafast calcium-activated contraction of the giant cell Spirostomum ambiguum. bioRxiv 2024 (2024).

49. Norton, M. M., Grover, P., Hagan, M. F. & Fraden, S. Optimal control of active nematics. Phys. Rev. Lett. 125, 178005 (2020).

    Google Scholar 

50. Ghosh, S., Joshi, C., Baskaran, A. & Hagan, M.F. Spatiotemporal control of structure and dynamics in a polar active fluid. Soft Matter 20, 7059–7071 (2024).

51. Ghosh, S., Baskaran, A. & Hagan, M.F. Achieving designed texture and flows in bulk active nematics using optimal control theory. J. Chem. Phys. 162, 134902 (2025).

52. Wagner, C. G., Norton, M. M., Park, J. S. & Grover, P. Exact coherent structures and phase space geometry of preturbulent 2D active nematic channel flow. Phys. Rev. Lett. 128, 028003 (2022).

    Google Scholar 

53. Nishiyama, K. et al. Closed-loop control of active nematic flows. Phys. Rev. X. 15, 041053 (2025)

54. Shankar, S., Scharrer, L. V., Bowick, M. J. & Marchetti, M. C. Design rules for controlling active topological defects. Proc. Natl Acad. Sci. USA. 121, e2400933121 (2024).

    Google Scholar 

55. Floyd, C., Dinner, A.R. & Vaikuntanathan, S. Learning to control non-equilibrium dynamics using local imperfect gradients. arXiv:2404.03798 (2024).

56. Floyd, C., Dinner, A.R. & Vaikuntanathan, S. Tailoring interactions between active nematic defects with reinforcement learning. Soft Matter. 21, 4488–4497 (2025).

57. Takemasa, T. et al. Cloning and sequencing of the gene for Tetrahymena calcium-binding 25-kDa protein. J. Biol. Chem. 264, 19293 (1989).

    Google Scholar 

58. Kilpatrick, A. M. et al. Backbone and side-chain chemical shift assignments for the C-terminal domain of Tcb2, a cytoskeletal calcium-binding protein from Tetrahymena thermophila. Biomol. NMR Assign. 10, 281 (2016).

    Google Scholar 

59. Hanyu, K., Takemasa, T., Numata, O., Takahashi, M. & Watanabe, Y. Immunofluorescence localization of a 25-kDa Tetrahymena EF-hand Ca²⁺-binding protein, TCBP-25, in the cell cortex and possible involvement in conjugation. Exp. Cell Res. 219, 487 (1995).

    Google Scholar 

60. Nakagawa, T., Fujiu, K., Cole, E. S. & Numata, O. Involvement of a 25 kDa Tetrahymena Ca²⁺-binding protein in pronuclear exchange. Cell Struct. Funct. 33, 151 (2008).

    Google Scholar 

61. Ohnishi, K. & Watanabe, Y. Purification and some properties of a new Ca²⁺-binding protein (TCBP-10) present in Tetrahymena cilium. J. Biol. Chem. 258, 13978 (1983).

    Google Scholar 

62. Abramson, J. et al. Accurate structure prediction of biomolecular interactions with AlphaFold 3. Nature 630, 493 (2024).

    Google Scholar 

63. Honts, J. E. & Williams, N. E. Novel cytoskeletal proteins in the cortex of Tetrahymena. J. Eukaryot. Microbiol. 50, 9 (2003).

    Google Scholar 

64. Yang, C.-F. & Tsai, W.-C. Calmodulin: The switch button of calcium signaling. Tzu Chi Med. J. 34, 15 (2022).

    Google Scholar 

65. DMNP-EDTA, tetrapotassium salt (caged calcium). Biotium https://biotium.com/product/dmnp-edta-tetrapotassium-salt-caged-calcium (2016).

66. Bers, D. M., Patton, C. W. & Nuccitelli, R. A practical guide to the preparation of Ca²⁺ buffers. Methods Cell Biol. 40, 3 (1994).

    Google Scholar 

67. Barreto-Chang, O.L. & Dolmetsch, R.E. Calcium imaging of cortical neurons using Fura-2 AM. J. Vis. Exp. (2009).

68. Tsien, R. & Pozzan, T. Measurement of cytosolic free Ca²⁺ with Quin2. Methods Enzymol. 172, 230–262 (1989).

    Google Scholar 

69. Bechhoefer, J.Control Theory for Physicists (Cambridge Univ. Press, 2021).

70. Polygon: Cellular-resolution optogenetics & photostimulation. Mightex https://www.mightexbio.com/polygon (2017).

71. Yang, F., Liu, S., Lee, H. J., Phillips, R. & Thomson, M. Dynamic flow control through active matter programming language. Nat. Mater. 24, 615 (2025).

    Google Scholar 

72. Chandrasekharan, N.P., Lei, X., Honts, J., Bhamla, S. & Coyle, S.M. Decoding ultrasensitive self-assembly of the calcium-regulated Tetrahymena cytoskeletal protein Tcb2 using optical actuation. J. Biol. Chem. 301, 10824 (2025).

73. Phan-Thien, N. & Mai-Duy, N.Understanding Viscoelasticity: An Introduction to Rheology (Springer, 2013).

74. Ashby, M. F. & Cebon, D. Materials selection in mechanical design. J. Phys. IV 3, C7 (1993).

    Google Scholar 

75. Li, X. et al. Tensile force-induced cytoskeletal remodeling: Mechanics before chemistry. PLoS Comput. Biol. 16, e1007693 (2020).

    Google Scholar 

76. Sutton, R.S. & Barto, A.G.Reinforcement Learning: An Introduction (MIT Press, 2018).

77. Falk, M. J., Alizadehyazdi, V., Jaeger, H. & Murugan, A. Learning to control active matter. Phys. Rev. Res. 3, 033291 (2021).

    Google Scholar 

78. Chennakesavalu, S. & Rotskoff, G.M. Probing the theoretical and computational limits of dissipative design. J. Chem. Phys. 155, (2021).

79. Silver, D. et al. Deterministic policy gradient algorithms. in Proc. International Conference on Machine Learning 387–395 (PMLR, 2014).

80. Lillicrap, T.P. et al. Continuous control with deep reinforcement learning. arXiv:1509.02971 (2015).

81. Floyd, C., Levine, H., Jarzynski, C. & Papoian, G. A. Understanding cytoskeletal avalanches using mechanical stability analysis. Proc. Natl Acad. Sci. USA. 118, e2110239118 (2021).

    Google Scholar 

82. Vicente-Manzanares, M., Ma, X., Adelstein, R. S. & Horwitz, A. R. Non-muscle myosin II takes centre stage in cell adhesion and migration. Nat. Rev. Mol. Cell Biol. 10, 778 (2009).

    Google Scholar 

83. Sakamoto, R. & Murrell, M. P. Mechanical power is maximized during contractile ring-like formation in a biomimetic dividing cell model. Nat. Commun. 15, 9731 (2024).

    Google Scholar 

84. Soares e Silva, M. et al. Active multistage coarsening of actin networks driven by myosin motors. Proc. Natl Acad. Sci. USA. 108, 9408 (2011).

    Google Scholar 

85. Wagoner, J. A. & Dill, K. A. Evolution of mechanical cooperativity among myosin II motors. Proc. Natl Acad. Sci. USA. 118, e2101871118 (2021).

    Google Scholar 

86. Krishna, A., Savinov, M., Ierushalmi, N., Mogilner, A. & Keren, K. Size-dependent transition from steady contraction to waves in actomyosin networks with turnover. Nat. Phys. 20, 123–134 (2024).

87. Mattila, P. K. & Lappalainen, P. Filopodia: molecular architecture and cellular functions. Nat. Rev. Mol. Cell Biol. 9, 446 (2008).

    Google Scholar 

88. Murrell, M. P. & Gardel, M. L. F-actin buckling coordinates contractility and severing in a biomimetic actomyosin cortex. Proc. Natl Acad. Sci. USA. 109, 20820 (2012).

    Google Scholar 

89. Lenz, M. Reversal of contractility as a signature of self-organization in cytoskeletal bundles. eLife 9, e51751 (2020).

    Google Scholar 

90. Bement, W. M. et al. Activator–inhibitor coupling between Rho signalling and actin assembly makes the cell cortex an excitable medium. Nat. Cell Biol. 17, 1471 (2015).

    Google Scholar 

91. Maxian, O., Dinner, A.R. & Munro, E. Actin network heterogeneity tunes activator-inhibitor dynamics at the cell cortex. Proc. Natl. Acad. Sci. U.S.A. 122, e2520485122 (2025).

92. Ishihara, A., Gee, K., Schwartz, S., Jacobson, K. & Lee, J. Photoactivation of caged compounds in single living cells: an application to the study of cell locomotion. Biotechniques 23, 268 (1997).

    Google Scholar 

93. Blosser, M. C., Horst, B. G. & Keller, S. L. cDICE method produces giant lipid vesicles under physiological conditions of charged lipids and ionic solutions. Soft Matter 12, 7364 (2016).

    Google Scholar 

94. Abkarian, M., Loiseau, E. & Massiera, G. Continuous droplet interface crossing encapsulation (cDICE) for high throughput monodisperse vesicle design. Soft Matter 7, 4610 (2011).

    Google Scholar 

95. Moga, A., Yandrapalli, N., Dimova, R. & Robinson, T. Optimization of the inverted emulsion method for high-yield production of biomimetic giant unilamellar vesicles. ChemBioChem 20, 2674 (2019).

    Google Scholar 

96. Kirillov, A. et al. Segment anything. Proc. IEEE/CVF Int. Conf. Comput. Vis. 4015–4026 (2023).

97. Nar, K. segment-anything-video: MetaSeg: Packaged version of the Segment Anything repository. GitHub.

98. Thielicke, W. & Sonntag, R. Particle image velocimetry for MATLAB: Accuracy and enhanced algorithms in PIVlab. J. Open Res. Softw. 9, 12 (2021).

    Google Scholar 

99. Karaev, N. et al. CoTracker: It is better to track together. in Proc. ECCV (2024).

100. Tian, J. & other contributors. ReinforcementLearning.jl: A reinforcement learning package for the Julia programming language. GitHub https://github.com/JuliaReinforcementLearning/ReinforcementLearning.jl (2020).

101. Lei, X. et al. Light-induced assembly and repeatable actuation in Ca²⁺-driven chemomechanical protein networks_Nat_Comm_2026. Zenodo https://doi.org/10.5281/zenodo.18318970 (2026).

102. Lei, X. et al. TCB2 network: Tcb2 NatComm 2026Jan. Zenodo https://doi.org/10.5281/zenodo.18394283 (2026).

Download references