Spontaneous motion in hierarchically assembled active matter

Abstract

With remarkable precision and reproducibility, cells orchestrate the cooperative action of thousands of nanometre-sized molecular motors to carry out mechanical tasks at much larger length scales, such as cell motility, division and replication1. Besides their biological importance, such inherently non-equilibrium processes suggest approaches for developing biomimetic active materials from microscopic components that consume energy to generate continuous motion2,3,4. Being actively driven, these materials are not constrained by the laws of equilibrium statistical mechanics and can thus exhibit sought-after properties such as autonomous motility, internally generated flows and self-organized beating5,6,7. Here, starting from extensile microtubule bundles, we hierarchically assemble far-from-equilibrium analogues of conventional polymer gels, liquid crystals and emulsions. At high enough concentration, the microtubules form a percolating active network characterized by internally driven chaotic flows, hydrodynamic instabilities, enhanced transport and fluid mixing. When confined to emulsion droplets, three-dimensional networks spontaneously adsorb onto the droplet surfaces to produce highly active two-dimensional nematic liquid crystals whose streaming flows are controlled by internally generated fractures and self-healing, as well as unbinding and annihilation of oppositely charged disclination defects. The resulting active emulsions exhibit unexpected properties, such as autonomous motility, which are not observed in their passive analogues. Taken together, these observations exemplify how assemblages of animate microscopic objects exhibit collective biomimetic properties that are very different from those found in materials assembled from inanimate building blocks, challenging us to develop a theoretical framework that would allow for a systematic engineering of their far-from-equilibrium material properties.

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Figure 1: Active microtubule networks exhibit internally generated flows.
Figure 2: ATP concentration controls dynamics of active microtubule networks.
Figure 3: Dynamics of 2D streaming nematics confined to fluid interfaces.
Figure 4: Motile water-in-oil emulsion droplets.

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Acknowledgements

We acknowledge discussions with R. Meyer, R. Bruinsma and E. Frey about the nature of liquid crystalline defects. Biotin-labelled kinesin 401 (K401) was a gift from J. Gelles. This work was supported by the W. M. Keck Foundation, the National Institute of Health (5K25GM85613), the National Science Foundation (NSF-MRSEC-0820492, NSF-MRI 0923057) and the Pioneer Research Center Program through the National Research Foundation of Korea (2012-0001255). We acknowledge use of the MRSEC Optical Microscopy and Microfluidics facilities.

Author information

T.S., D.T.N.C., S.J.D. and Z.D. conceived the experiments and interpreted the results. T.S., D.T.N.C. and S.J.D. performed the experiments. T.S. and D.T.N.C. conducted data analysis. T.S., D.T.N.C. and Z.D. wrote the manuscript. M.H. synthesized surfactant and contributed to the assembly of active emulsions.

Correspondence to Zvonimir Dogic.

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Competing interests

The authors declare no competing financial interests.

Supplementary information

41586_2012_BFnature11591_MOESM63_ESM.mov

Kinesin motor clusters cause a pair of bundles to slide off each other when they merge with an initial orientation. However, when these same two bundles rotate by 180° and remerge no sliding is observed. Markers indicate relative bundle polarity. Scale bar is 5µm. (MOV 6762 kb)

Dynamics of dilute extensile microtubule bundles confined to a quasi-2D chamber

Kinesin motor clusters cause a pair of bundles to slide off each other when they merge with an initial orientation. However, when these same two bundles rotate by 180° and remerge no sliding is observed. Markers indicate relative bundle polarity. Scale bar is 5µm. (MOV 6762 kb)

41586_2012_BFnature11591_MOESM64_ESM.mov

At high concentration, active extensile MT bundles form a percolating network, leading to the emergence of robust, internally-generated chaotic flows. Part 1: The onset of chaotic flows as the sample is introduced into the microscopy chamber. The initial uniform flow from right to left is due to the sample being loaded into the flow cell. Scale bar, 50 µm. Part 2: The steady-state mixing and chaotic flows are robust phenomena that span millimeter sized samples and persist for many hours. Scale bar, 150 µm. (MOV 27263 kb)

At high concentrations extensile MT bundles form a percolating network, leading to the emergence of robust internally-generated chaotic flows

At high concentration, active extensile MT bundles form a percolating network, leading to the emergence of robust, internally-generated chaotic flows. Part 1: The onset of chaotic flows as the sample is introduced into the microscopy chamber. The initial uniform flow from right to left is due to the sample being loaded into the flow cell. Scale bar, 50 µm. Part 2: The steady-state mixing and chaotic flows are robust phenomena that span millimeter sized samples and persist for many hours. Scale bar, 150 µm. (MOV 27263 kb)

41586_2012_BFnature11591_MOESM65_ESM.mov

Individual bundles merge with random polarity (red arrows), extend, and buckle (green dashed lines) since their ends are coupled to the viscoelastic network. Subsequently, bundles fracture into smaller fragments which quickly merge with other bundles, resulting in another cycle of extension, buckling, fracturing and self-healing. Scale bar is 10µm. (MOV 5455 kb)

High magnification video of MT bundles reveal the microscopic processes underlying the collective large-scale chaotic dynamics of active networks

Individual bundles merge with random polarity (red arrows), extend, and buckle (green dashed lines) since their ends are coupled to the viscoelastic network. Subsequently, bundles fracture into smaller fragments which quickly merge with other bundles, resulting in another cycle of extension, buckling, fracturing and self-healing. Scale bar is 10µm. (MOV 5455 kb)

41586_2012_BFnature11591_MOESM66_ESM.mov

Fluorescent videos of active MT networks taken at ATP concentrations of 0 µM, 57 µM, and 1.4 mM ATP. Irrespective of ATP concentration, all active samples exhibit the same emergent length scale on the order of 100µm. Scale bar is 70µm. (MOV 6188 kb)

ATP concentration controls the dynamics of active MT networks

Fluorescent videos of active MT networks taken at ATP concentrations of 0 µM, 57 µM, and 1.4 mM ATP. Irrespective of ATP concentration, all active samples exhibit the same emergent length scale on the order of 100µm. Scale bar is 70µm. (MOV 6188 kb)

41586_2012_BFnature11591_MOESM67_ESM.mov

Dynamics of 3 µm tracer particles embedded in active MT networks at ATP concentrations of 0 µM, 52 µM, and 1 mM. In absence of ATP, the non-sticky particles move sub-diffusively in a cross-linked MT network. As the ATP concentration is increased, transport of the particles is enhanced and MSDs become super-diffusive. For highest ATP concentrations, the MSDs are essentially ballistic. Scale bar is 70 µm. (MOV 3029 kb)

Dynamics of 3 µm tracer particles embedded in active MT networks at varying ATP concentrations

Dynamics of 3 µm tracer particles embedded in active MT networks at ATP concentrations of 0 µM, 52 µM, and 1 mM. In absence of ATP, the non-sticky particles move sub-diffusively in a cross-linked MT network. As the ATP concentration is increased, transport of the particles is enhanced and MSDs become super-diffusive. For highest ATP concentrations, the MSDs are essentially ballistic. Scale bar is 70 µm. (MOV 3029 kb)

41586_2012_BFnature11591_MOESM68_ESM.mov

Compression of a very large droplet between cover glass and microscope slip creates robust, flat interfaces, elucidating the microscopic dynamics of active nematic liquid crystals. Part 1: Dynamics of internally generated flows of 2D active nematic is characterized by extension, buckling and internal fracture of nematic domains. The fracture line is accompanied by creation of a pair of disclination defects of charge ½ and -½ defects (red and blue arrows). When the fracture line self-heals, the pair of defects remains unbound and streams around until annihilating with oppositely charged defects. Scale bar is 15μm. Part 2: Same dynamics in nematics assembled at a perfectly planar interface, and viewed with lower magnification. Scale bar is 45 μm. (MOV 12511 kb)

Microscopic dynamics of active nematic liquid crystals is characterized by internal fractures and self-healing as well as unbinding and annihilation of disclinations defects

Compression of a very large droplet between cover glass and microscope slip creates robust, flat interfaces, elucidating the microscopic dynamics of active nematic liquid crystals. Part 1: Dynamics of internally generated flows of 2D active nematic is characterized by extension, buckling and internal fracture of nematic domains. The fracture line is accompanied by creation of a pair of disclination defects of charge ½ and -½ defects (red and blue arrows). When the fracture line self-heals, the pair of defects remains unbound and streams around until annihilating with oppositely charged defects. Scale bar is 15μm. Part 2: Same dynamics in nematics assembled at a perfectly planar interface, and viewed with lower magnification. Scale bar is 45 μm. (MOV 12511 kb)

41586_2012_BFnature11591_MOESM69_ESM.mov

Dynamics of motile aqueous droplets which are encapsulating active MT networks. Videos are taken with brightfield microscopy. Left: In presence of ATP, confined active networks exert internal stresses that result in autonomous droplet motility. Right: In absence of ATP no effective motion is observed except for minor drift due to uniform internal flows. Part 1: Video taken at high magnifications reveals that droplets preferentially move in periodic pattern. Scale bar is 100 μm. Part 2: Video taken at much lower magnification demonstrate that droplet motility is highly robust with dozens of droplets simultaneously exhibiting motile behavior. Scale bar is 500 μm. (MOV 6177 kb)

Encapsulating active MT networks in water-in-oil emulsions leads to motile droplets

Dynamics of motile aqueous droplets which are encapsulating active MT networks. Videos are taken with brightfield microscopy. Left: In presence of ATP, confined active networks exert internal stresses that result in autonomous droplet motility. Right: In absence of ATP no effective motion is observed except for minor drift due to uniform internal flows. Part 1: Video taken at high magnifications reveals that droplets preferentially move in periodic pattern. Scale bar is 100 μm. Part 2: Video taken at much lower magnification demonstrate that droplet motility is highly robust with dozens of droplets simultaneously exhibiting motile behavior. Scale bar is 500 μm. (MOV 6177 kb)

41586_2012_BFnature11591_MOESM70_ESM.mov

For larger droplets, bundles spontaneously adsorb onto the oil-water interface where they form an active 2D nematic liquid crystal characterized by fast internally generated streaming flows. Initially, the video focuses on the droplet surface. Subsequently, the focus is shifted to the droplet center, demonstrating that the majority of MTs are expelled to the interface. Scale bar is 10 μm. Part 2: For smaller droplets (less than 40μm diameter), high interface curvature frustrates the MT bundles from adsorbing onto the surface. Consequently, bundles remain dispersed throughout the entire droplet. Scale bar is 5 μm. (MOV 12538 kb)

Dynamics of fluorescently labeled MT bundles confined within aqueous droplets

For larger droplets, bundles spontaneously adsorb onto the oil-water interface where they form an active 2D nematic liquid crystal characterized by fast internally generated streaming flows. Initially, the video focuses on the droplet surface. Subsequently, the focus is shifted to the droplet center, demonstrating that the majority of MTs are expelled to the interface. Scale bar is 10 μm. Part 2: For smaller droplets (less than 40μm diameter), high interface curvature frustrates the MT bundles from adsorbing onto the surface. Consequently, bundles remain dispersed throughout the entire droplet. Scale bar is 5 μm. (MOV 12538 kb)

41586_2012_BFnature11591_MOESM71_ESM.mov

Part 1: The droplet moves in the direction that is opposite to the internal liquid crystalline flows. Part 2: A pair of interacting motile droplets. Scale bars are 50µm. (MOV 6087 kb)

Streaming flow of active nematics confined to the oil-water interface drive droplet motility

Part 1: The droplet moves in the direction that is opposite to the internal liquid crystalline flows. Part 2: A pair of interacting motile droplets. Scale bars are 50µm. (MOV 6087 kb)

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Sanchez, T., Chen, D., DeCamp, S. et al. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012). https://doi.org/10.1038/nature11591

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