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Reaction–diffusion processes at the nano- and microscales

Abstract

The bottom-up fabrication of nano- and microscale structures from primary building blocks (molecules, colloidal particles) has made remarkable progress over the past two decades, but most research has focused on structural aspects, leaving our understanding of the dynamic and spatiotemporal aspects at a relatively primitive stage. In this Review, we draw inspiration from living cells to argue that it is now time to move beyond the generation of structures and explore dynamic processes at the nanoscale. We first introduce nanoscale self-assembly, self-organization and reaction–diffusion processes as essential features of cells. Then, we highlight recent progress towards designing and controlling these fundamental features of life in abiological systems. Specifically, we discuss examples of reaction–diffusion processes that lead to such outcomes as self-assembly, self-organization, unique nanostructures, chemical waves and dynamic order to illustrate their ubiquity within a unifying context of dynamic oscillations and energy dissipation. Finally, we suggest future directions for research on reaction–diffusion processes at the nano- and microscales that we find hold particular promise for a new understanding of science at the nanoscale and the development of new kinds of nanotechnologies for chemical transport, chemical communication and integration with living systems.

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Figure 1: Three-dimensional Turing patterns generated by reaction–diffusion in an emulsion of nanodroplets containing the oscillatory Belousov–Zhabotinsky (BZ) reaction.
Figure 2: Self-assembly integrated with chemical reactions.
Figure 3: Self-organization of abiological systems.
Figure 4: Reaction–diffusion processes at the nanoscale.
Figure 5: Pattern formation, communication and energy conversion produced by chemical oscillations.

References

  1. 1

    Epstein, I. R. The consequences of imperfect mixing in autocatalytic chemical and biological systems. Nature 374, 321–327 (1995). This paper shows that autocatalysis and heterogeneity in chemical reactions can generate complex behaviours in both biological and abiological systems.

    CAS  Google Scholar 

  2. 2

    Bánsagi, T. Jr, Vanag, V. K. & Epstein, I. R. Tomography of reaction–diffusion microemulsions reveals three-dimensional Turing patterns. Science 331, 1309–1312 (2011). This paper demonstrates that reaction–diffusion in nanoemulsions can generate 3D Turing patterns.

    Google Scholar 

  3. 3

    Vanag, V. K. & Epstein, I. R. Segmented spiral waves in a reaction–diffusion system. Proc. Natl Acad. Sci. USA 100, 14635–14638 (2003).

    CAS  Google Scholar 

  4. 4

    Mattia, E. & Otto, S. Supramolecular systems chemistry. Nature Nanotech. 10, 111–119 (2015).

    CAS  Google Scholar 

  5. 5

    Mann, S. Self-assembly and transformation of hybrid nano-objects and nanostructures under equilibrium and non-equilibrium conditions. Nature Mater. 8, 781–792 (2009).

    CAS  Google Scholar 

  6. 6

    Epstein, I. R. et al. Chemical oscillators in structured media. Acc. Chem. Res. 45, 2160–2168 (2012).

    CAS  Google Scholar 

  7. 7

    Noble, D. The Music of Life: Biology Beyond Genes (Oxford Univ. Press, 2008).

    Google Scholar 

  8. 8

    Whitesides, G. M. & Grzybowski, B. Self-assembly at all scales. Science 295, 2418–2421 (2002).

    CAS  Google Scholar 

  9. 9

    Sawin, K. E., Leguellec, K., Philippe, M. & Mitchison, T. J. Mitotic spindle organization by a plus-end-directed microtubule motor. Nature 359, 540–543 (1992). This paper reports a sophisticated natural example of self-organization.

    CAS  Google Scholar 

  10. 10

    Rodenbaugh, D. W., Collins, H. L. & Dicarlo, S. E. Submitting illuminations for review. Adv. Physiol. Educ. 26, 222–223 (2002).

    Google Scholar 

  11. 11

    Muller, P. et al. Differential diffusivity of Nodal and Lefty underlies a reaction–diffusion patterning system. Science 336, 721–724 (2012).

    Google Scholar 

  12. 12

    Boekhoven, J., Hendriksen, W. E., Koper, G. J., Eelkema, R. & van Esch, J. H. Transient assembly of active materials fueled by a chemical reaction. Science 349, 1075–1079 (2015).

    CAS  Google Scholar 

  13. 13

    Wang, W., Duan, W. T., Ahmed, S., Mallouk, T. E. & Sen, A. Small power: autonomous nano- and micromotors propelled by self-generated gradients. Nano Today 8, 531–554 (2013). This paper summarizes important abiological, primitive systems of self-organization.

    CAS  Google Scholar 

  14. 14

    Kundu, P. K. et al. Light-controlled self-assembly of non-photoresponsive nanoparticles. Nature Chem. 7, 646–652 (2015).

    CAS  Google Scholar 

  15. 15

    Duan, W., Liu, R. & Sen, A. Transition between collective behaviors of micromotors in response to different stimuli. J. Am. Chem. Soc. 135, 1280–1283 (2013).

    CAS  Google Scholar 

  16. 16

    Sun, Y. G. & Xia, Y. N. Shape-controlled synthesis of gold and silver nanoparticles. Science 298, 2176–2179 (2002).

    CAS  Google Scholar 

  17. 17

    Sun, Y. G., Mayers, B. T. & Xia, Y. N. Template-engaged replacement reaction: a one-step approach to the large-scale synthesis of metal nanostructures with hollow interiors. Nano Lett. 2, 481–485 (2002).

    CAS  Google Scholar 

  18. 18

    Yin, Y. D. et al. Formation of hollow nanocrystals through the nanoscale Kirkendall effect. Science 304, 711–714 (2004). This paper illustrates that nano- and microscale reaction–diffusion processes result in very different outcomes.

    CAS  Google Scholar 

  19. 19

    Kawamura, R., Kakugo, A., Shikinaka, K., Osada, Y. & Gong, J. P. Ring-shaped assembly of microtubules shows preferential counterclockwise motion. Biomacromolecules 9, 2277–2282 (2008).

    CAS  Google Scholar 

  20. 20

    Lehn, J. M. Supramolecular chemistry — scope and perspectives. Molecules, supermolecules, and molecular devices. Angew. Chem. Int. Ed. Engl. 27, 89–112 (1988).

    Google Scholar 

  21. 21

    Macdonald, J. C. & Whitesides, G. M. Solid-state structures of hydrogen-bonded tapes based on cyclic secondary diamides. Chem. Rev. 94, 2383–2420 (1994).

    CAS  Google Scholar 

  22. 22

    Lehn, J. M. Perspectives in chemistry — aspects of adaptive chemistry and materials. Angew. Chem. Int. Ed. 54, 3276–3289 (2015).

    CAS  Google Scholar 

  23. 23

    Sreenivasachary, N. & Lehn, J. M. Gelation-driven component selection in the generation of constitutional dynamic hydrogels based on guanine-quartet formation. Proc. Natl Acad. Sci. USA 102, 5938–5943 (2005).

    CAS  Google Scholar 

  24. 24

    Yang, Z. M. et al. Enzymatic formation of supramolecular hydrogels. Adv. Mater. 16, 1440–1444 (2004). This paper illustrates the feasibility of integrating enzymatic reaction and molecular self-assembly.

    CAS  Google Scholar 

  25. 25

    Williams, R. J. et al. Enzyme-assisted self-assembly under thermodynamic control. Nature Nanotech. 4, 19–24 (2009).

    CAS  Google Scholar 

  26. 26

    Otto, S. Dynamic molecular networks: from synthetic receptors to self-replicators. Acc. Chem. Res. 45, 2200–2210 (2012).

    CAS  Google Scholar 

  27. 27

    Nitschke, J. R. & Lehn, J. M. Self-organization by selection: generation of a metallosupramolecular grid architecture by selection of components in a dynamic library of ligands. Proc. Natl Acad. Sci. USA 100, 11970–11974 (2003).

    CAS  Google Scholar 

  28. 28

    Carnall, J. M. A. et al. Mechanosensitive self-replication driven by self-organization. Science 327, 1502–1506 (2010).

    CAS  Google Scholar 

  29. 29

    Poolman, J. M. et al. Variable gelation time and stiffness of low-molecular-weight hydrogels through catalytic control over self-assembly. Nature Protoc. 9, 977–988 (2014).

    CAS  Google Scholar 

  30. 30

    Toledano, S., Williams, R. J., Jayawarna, V. & Ulijn, R. V. Enzyme-triggered self-assembly of peptide hydrogels via reversed hydrolysis. J. Am. Chem. Soc. 128, 1070–1071 (2006).

    CAS  Google Scholar 

  31. 31

    Huc, I. & Lehn, J. M. Virtual combinatorial libraries: dynamic generation of molecular and supramolecular diversity by self-assembly. Proc. Natl Acad. Sci. USA 94, 2106–2110 (1997).

    CAS  Google Scholar 

  32. 32

    Yang, Z. M., Liang, G. L., Wang, L. & Xu, B. Using a kinase/phosphatase switch to regulate a supramolecular hydrogel and forming the supramolecular hydrogel in vivo. J. Am. Chem. Soc. 128, 3038–3043 (2006).

    CAS  Google Scholar 

  33. 33

    Hirst, A. R. et al. Biocatalytic induction of supramolecular order. Nature Chem. 2, 1089–1094 (2010).

    CAS  Google Scholar 

  34. 34

    Boekhoven, J. et al. Dissipative self-assembly of a molecular gelator by using a chemical fuel. Angew. Chem. 122, 4935–4938 (2010).

    Google Scholar 

  35. 35

    Zhao, F., Gao, Y., Shi, J., Browdy, H. M. & Xu, B. Novel anisotropic supramolecular hydrogel with high stability over a wide pH range. Langmuir 27, 1510–1512 (2010).

    Google Scholar 

  36. 36

    Yang, Z., Liang, G. & Xu, B. Enzymatic hydrogelation of small molecules. Acc. Chem. Res. 41, 315–326 (2008).

    CAS  Google Scholar 

  37. 37

    Raghupathi, K. R., Guo, J., Munkhbat, O., Rangadurai, P. & Thayumanavan, S. Supramolecular disassembly of facially amphiphilic dendrimer assemblies in response to physical, chemical, and biological stimuli. Acc. Chem. Res. 47, 2200–2211 (2014).

    CAS  Google Scholar 

  38. 38

    Lagzi, I., Kowalczyk, B., Wang, D. & Grzybowski, B. A. Nanoparticle oscillations and fronts. Angew. Chem. Int. Ed. 49, 8616–8619 (2010).

    CAS  Google Scholar 

  39. 39

    Grzybowski, B. A., Stone, H. A. & Whitesides, G. M. Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid–air interface. Nature 405, 1033–1036 (2000).

    CAS  Google Scholar 

  40. 40

    Paxton, W. F. et al. Catalytic nanomotors: autonomous movement of striped nanorods. J. Am. Chem. Soc. 126, 13424–13431 (2004).

    CAS  Google Scholar 

  41. 41

    Bala Saidulu, N. & Sebastian, K. L. Interfacial tension model for catalytically driven nanorods. J. Chem. Phys. 128, 074708 (2008).

    CAS  Google Scholar 

  42. 42

    Wang, Y. et al. Dynamic interactions between fast microscale rotors. J. Am. Chem. Soc. 131, 9926–9927 (2009).

    CAS  Google Scholar 

  43. 43

    Kline, T. R. et al. Catalytic micropumps: microscopic convective fluid flow and pattern formation. J. Am. Chem. Soc. 127, 17150–17151 (2005).

    CAS  Google Scholar 

  44. 44

    Ikezoe, Y. et al. Peptide assembly-driven metal–organic framework (MOF) motors for micro electric generators. Adv. Mater. 27, 288–291 (2015).

    CAS  Google Scholar 

  45. 45

    Ikezoe, Y., Washino, G., Uemura, T., Kitagawa, S. & Matsui, H. Autonomous motors of a metal–organic framework powered by reorganization of self-assembled peptides at interfaces. Nature Mater. 11, 1081–1085 (2012).

    CAS  Google Scholar 

  46. 46

    Kirschner, M. & Mitchison, T. Beyond self-assembly — from microtubules to morphogenesis. Cell 45, 329–342 (1986).

    CAS  Google Scholar 

  47. 47

    Chirieleison, S. M., Allen, P. B., Simpson, Z. B., Ellington, A. D. & Chen, X. Pattern transformation with DNA circuits. Nature Chem. 5, 1000–1005 (2013).

    CAS  Google Scholar 

  48. 48

    Zhang, Y. et al. Unfolding a molecular trefoil derived from a zwitterionic metallopeptide to form self-assembled nanostructures. Nature Commun. 6, 6165 (2015).

    CAS  Google Scholar 

  49. 49

    Zhang, Y. et al. A redox responsive, fluorescent supramolecular metallohydrogel consists of nanofibers with single-molecule width. J. Am. Chem. Soc. 135, 5008–5011 (2013).

    CAS  Google Scholar 

  50. 50

    Pappas, C. G., Sasselli, I. R. & Ulijn, R. V. Biocatalytic pathway selection in transient tripeptide nanostructures. Angew. Chem. Int. Ed. 54, 8119–8123 (2015).

    CAS  Google Scholar 

  51. 51

    Murray, C. B., Norris, D. J. & Bawendi, M. G. Synthesis and characterization of nearly monodisperse CdE (E = S, Se, Te) semiconductor nanocrystallites. J. Am. Chem. Soc. 115, 8706–8715 (1993).

    CAS  Google Scholar 

  52. 52

    Strobel, M., Reiss, S., Heinig, K. H. & Moller, W. Computer simulation of precipitate coarsening: a unified treatment of diffusion and reaction controlled Ostwald ripening. Radiat. Effects Defects Solids 141, 99–111 (1997).

    CAS  Google Scholar 

  53. 53

    Smigelskas, A. D. & Kirkendall, E. O. Zinc diffusion in alpha brass. Trans. AIME 171, 130–142 (1947).

    Google Scholar 

  54. 54

    Aldinger, F. Controlled porosity by an extreme Kirkendall effect. Acta Metall. 22, 923–928 (1974).

    CAS  Google Scholar 

  55. 55

    Xia, Y. et al. Gold nanocages: from synthesis to theranostic applications. Acc. Chem. Res. 44, 914–924 (2011).

    CAS  Google Scholar 

  56. 56

    Liang, F., Zhang, C. & Yang, Z. Rational design and synthesis of Janus composites. Adv. Mater. 26, 6944–6949 (2014).

    CAS  Google Scholar 

  57. 57

    Wei, Y., Han, S., Walker, D. A., Fuller, P. E. & Grzybowski, B. A. Nanoparticle core/shell architectures within MOF crystals synthesized by reaction diffusion. Angew. Chem. Int. Ed. 51, 7435–7439 (2012).

    CAS  Google Scholar 

  58. 58

    Wei, Z. Y. & Matsui, H. Rational strategy for shaped nanomaterial synthesis in reverse micelle reactors. Nature Commun. 5, 8 (2014).

    Google Scholar 

  59. 59

    Gao, J. H. et al. FePt@CoS2 yolk–shell nanocrystals as a potent agent to kill HeLa cells. J. Am. Chem. Soc. 129, 1428–1433 (2007).

    CAS  Google Scholar 

  60. 60

    Han, S., Hermans, T. M., Fuller, P. E., Wei, Y. & Grzybowski, B. A. Transport into metal–organic frameworks from solution is not purely diffusive. Angew. Chem. Int. Ed. 51, 2662–2666 (2012).

    CAS  Google Scholar 

  61. 61

    Gu, H. W., Yang, Z. M., Gao, J. H., Chang, C. K. & Xu, B. Heterodimers of nanoparticles: formation at a liquid–liquid interface and particle-specific surface modification by functional molecules. J. Am. Chem. Soc. 127, 34–35 (2005).

    CAS  Google Scholar 

  62. 62

    Gu, H. W., Zheng, R. K., Zhang, X. X. & Xu, B. Facile one-pot synthesis of bifunctional heterodimers of nanoparticles: a conjugate of quantum dot and magnetic nanoparticles. J. Am. Chem. Soc. 126, 5664–5665 (2004).

    CAS  Google Scholar 

  63. 63

    Gorodetskii, V., Lauterbach, J., Rotermund, H. H., Block, J. H. & Ertl, G. Coupling between adjacent crystal planes in heterogeneous catalysis by propagating reaction–diffusion waves. Nature 370, 276–279 (1994). This paper demonstrates nanoscale reaction–diffusion processes for generating a chemical wave.

    CAS  Google Scholar 

  64. 64

    Hildebrand, M., Kuperman, M., Wio, H., Mikhailov, A. S. & Ertl, G. Self-organized chemical nanoscale microreactors. Phys. Rev. Lett. 83, 1475–1478 (1999).

    CAS  Google Scholar 

  65. 65

    Hildebrand, M., Mikhailov, A. S. & Ertl, G. Traveling nanoscale structures in reactive adsorbates with attractive lateral interactions. Phys. Rev. Lett. 81, 2602–2605 (1998).

    CAS  Google Scholar 

  66. 66

    Hildebrand, M., Ipsen, M., Mikhailov, A. S. & Ertl, G. Localized nonequilibrium nanostructures in surface chemical reactions. New J. Phys. 5, 61 (2003).

    Google Scholar 

  67. 67

    Lagzi, I., Kowalczyk, B. & Grzybowski, B. A. Liesegang rings engineered from charged nanoparticles. J. Am. Chem. Soc. 132, 58–60 (2010).

    CAS  Google Scholar 

  68. 68

    Lin, E. K. et al. Direct measurement of the reaction front in chemically amplified photoresists. Science 297, 372–375 (2002).

    CAS  Google Scholar 

  69. 69

    Gerdts, C. J., Sharoyan, D. E. & Ismagilov, R. F. A synthetic reaction network: chemical amplification using nonequilibrium autocatalytic reactions coupled in time. J. Am. Chem. Soc. 126, 6327–6331 (2004).

    CAS  Google Scholar 

  70. 70

    Toiya, M., Vanag, V. K. & Epstein, I. R. Diffusively coupled chemical oscillators in a microfluidic assembly. Angew. Chem. Int. Ed. 47, 7753–7755 (2008).

    CAS  Google Scholar 

  71. 71

    Song, H., Tice, J. D. & Ismagilov, R. F. A microfluidic system for controlling reaction networks in time. Angew. Chem. Int. Ed. 42, 768–772 (2003).

    CAS  Google Scholar 

  72. 72

    Kelley, S. O. et al. Advancing the speed, sensitivity and accuracy of biomolecular detection using multi-length-scale engineering. Nature Nanotech. 9, 969–980 (2014).

    CAS  Google Scholar 

  73. 73

    Semenov, S. N., Markvoort, A. J., de Greef, T. F. & Huck, W. T. Threshold sensing through a synthetic enzymatic reaction–diffusion network. Angew. Chem. Int. Ed. 53, 8066–8069 (2014).

    CAS  Google Scholar 

  74. 74

    Vavilin, V. A., Zhabotin, A. & Zaikin, A. N. Auto-oscillations of concentration of iodide ions in iodate-catalysed decomposition of hydrogen peroxide. Russ. J. Phys. Chem. USSR 44, 755–756 (1970).

    Google Scholar 

  75. 75

    Zhabotinsky, A. M., Buchholtz, F., Kiyatkin, A. B. & Epstein, I. R. Oscillations and waves in metal-ion-catalyzed bromate oscillating reactions in highly oxidized states. J. Phys. Chem. 97, 7578–7584 (1993).

    CAS  Google Scholar 

  76. 76

    Turing, A. M. The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B 237, 37–72 (1952). This paper proposes to generate static patterns from reaction–diffusion processes.

    Google Scholar 

  77. 77

    Castets, V., Dulos, E., Boissonade, J. & De Kepper, P. Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern. Phys. Rev. Lett. 64, 2953–2956 (1990).

    CAS  Google Scholar 

  78. 78

    Lengyel, I., Rábai, G. & Epstein, I. R. Systematic design of chemical oscillators. 67. Experimental and modeling study of oscillations in the chlorine dioxide-iodine-malonic acid reaction. J. Am. Chem. Soc. 112, 9104–9110 (1990).

    CAS  Google Scholar 

  79. 79

    Lengyel, I., Rabai, G. & Epstein, I. R. Systematic design of chemical oscillators. 64. Batch oscillation in the reaction of chlorine dioxide with iodine and malonic acid. J. Am. Chem. Soc. 112, 4606–4607 (1990).

    CAS  Google Scholar 

  80. 80

    Lengyel, I. & Epstein, I. R. Modeling of Turing structures in the chlorite iodide-malonic acid-starch reaction system. Science 251, 650–652 (1991).

    CAS  Google Scholar 

  81. 81

    Vanag, V. K. & Epstein, I. R. Pattern formation in a tunable medium: the Belousov–Zhabotinsky reaction in an aerosol OT microemulsion. Phys. Rev. Lett. 87, 228301 (2001).

    CAS  Google Scholar 

  82. 82

    Vanag, V. K. & Epstein, I. R. Inwardly rotating spiral waves in a reaction–diffusion system. Science 294, 835–837 (2001).

    CAS  Google Scholar 

  83. 83

    Vanag, V. K. & Epstein, I. R. Packet waves in a reaction–diffusion system. Phys. Rev. Lett. 88, 088303 (2002).

    Google Scholar 

  84. 84

    Cherkashin, A. A., Vanag, V. K. & Epstein, I. R. Discontinuously propagating waves in the bathoferroin-catalyzed Belousov–Zhabotinsky reaction incorporated into a microemulsion. J. Chem. Phys. 128, 204508 (2008).

    Google Scholar 

  85. 85

    Kaminaga, A., Vanag, V. K. & Epstein, I. R. A reaction–diffusion memory device. Angew. Chem. Int. Ed. 45, 3087–3089 (2006).

    CAS  Google Scholar 

  86. 86

    Vanag, V. K. & Epstein, I. R. Localized patterns in reaction–diffusion systems. Chaos 17, 037110 (2007).

    Google Scholar 

  87. 87

    Coullet, P., Riera, C. & Tresser, C. A new approach to data storage using localized structures. Chaos 14, 193–198 (2004).

    CAS  Google Scholar 

  88. 88

    Vanag, V. K. & Epstein, I. R. A model for jumping and bubble waves in the Belousov–Zhabotinsky-aerosol OT system. J. Chem. Phys. 131, 7 (2009).

    Google Scholar 

  89. 89

    Vanag, V. K. & Epstein, I. R. Design and control of patterns in reaction–diffusion systems. Chaos 18, 11 (2008).

    Google Scholar 

  90. 90

    Taylor, A. F., Tinsley, M. R., Wang, F., Huang, Z. Y. & Showalter, K. Dynamical quorum sensing and synchronization in large populations of chemical oscillators. Science 323, 614–617 (2009).

    CAS  Google Scholar 

  91. 91

    Tompkins, N. et al. Testing Turing's theory of morphogenesis in chemical cells. Proc. Natl Acad. Sci. USA 111, 4397–4402 (2014).

    CAS  Google Scholar 

  92. 92

    Toiya, M., Gonzalez-Ochoa, H. O., Vanag, V. K., Fraden, S. & Epstein, I. R. Synchronization of chemical micro-oscillators. J. Phys. Chem. Lett. 1, 1241–1246 (2010).

    CAS  Google Scholar 

  93. 93

    Lodish, H. et al. Molecular Cell Biology 7th edn (Freeman, 2012).

    Google Scholar 

  94. 94

    Yoshida, R., Takahashi, T., Yamaguchi, T. & Ichijo, H. Self-oscillating gel. J. Am. Chem. Soc. 118, 5134–5135 (1996). This paper shows that the Belousov–Zhabotinsky reaction can be used to convert chemical energy to mechanical energy.

    CAS  Google Scholar 

  95. 95

    Suzuki, D., Sakai, T. & Yoshida, R. Self-flocculating/self-dispersing oscillation of microgels. Angew. Chem. Int. Ed. 47, 917–920 (2008).

    CAS  Google Scholar 

  96. 96

    Zhang, Y. et al. Giant volume change of active gels under continuous flow. J. Am. Chem. Soc. 136, 7341–7347 (2014).

    CAS  Google Scholar 

  97. 97

    Chen, I. C. et al. Shape- and size-dependent patterns in self-oscillating polymer gels. Soft Matter 7, 3141–3146 (2011).

    CAS  Google Scholar 

  98. 98

    Qian, H., Saffarian, S. & Elson, E. L. Concentration fluctuations in a mesoscopic oscillating chemical reaction system. Proc. Natl Acad. Sci. USA 99, 10376–10381 (2002).

    CAS  Google Scholar 

  99. 99

    Lizana, L., Bauer, B. & Orwar, O. Controlling the rates of biochemical reactions and signaling networks by shape and volume changes. Proc. Natl Acad. Sci. USA 105, 4099–4104 (2008).

    CAS  Google Scholar 

  100. 100

    Lizana, L., Konkoli, Z. & Orwar, O. Tunable filtering of chemical signals in a simple nanoscale reaction–diffusion network. J. Phys. Chem. B 111, 6214–6219 (2007).

    CAS  Google Scholar 

  101. 101

    Yashin, V. V. & Balazs, A. C. Modeling polymer gels exhibiting self oscillations due to the Belousov–Zhabotinsky reaction dissolved BZ reagents. Macromolecules 39, 2024–2026 (2006).

    CAS  Google Scholar 

  102. 102

    Andersen, E. S. et al. Self-assembly of a nanoscale DNA box with a controllable lid. Nature 459, 73–75 (2009).

    CAS  Google Scholar 

  103. 103

    Kühlbrandt, W. Cryo-EM enters a new era. eLife 3, e03665 (2014).

    Google Scholar 

  104. 104

    Petsko, G. A. 100 years of X-ray crystallography. Chem. Eng. News 92, 42–43 (2014).

    Google Scholar 

  105. 105

    Goldbeter, A. Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour (Cambridge Univ. Press, 1997).

    Google Scholar 

  106. 106

    Rábai, G., Orbán, M. & Epstein, I. R. Systematic design of chemical oscillators. 77. A model for the pH-regulated oscillatory reaction between hydrogen-peroxide and sulfide ion. J. Phys. Chem. 96, 5414–5419 (1992).

    Google Scholar 

  107. 107

    Kurin-Csörgei, K., Orbán, M., Rábai, G. & Epstein, I. R. Model for the oscillatory reaction between hydrogen peroxide and thiosulfate catalysed by copper(ii) ions. J. Chem. Soc. Farad. Trans. 92, 2851–2855 (1996).

    Google Scholar 

  108. 108

    Feynman, R. P. Feynman Lectures on Computation (Addison-Wesley, 1998).

    Google Scholar 

  109. 109

    Zhou, J. & Xu, B. Enzyme-instructed self-assembly: a multistep process for potential cancer therapy. Bioconjugate Chem. 26, 987–999 (2015).

    CAS  Google Scholar 

  110. 110

    Du, X. W., Zhou, J., Wu, L. H., Sun, S. H. & Xu, B. Enzymatic transformation of phosphate decorated magnetic nanoparticles for selectively sorting and inhibiting cancer cells. Bioconjugate Chem. 25, 2129–2133 (2014).

    CAS  Google Scholar 

  111. 111

    Kuang, Y. et al. Pericellular hydrogel/nanonets inhibit cancer cells. Angew. Chem. Int. Ed. 53, 8104–8107 (2014). This paper shows that localized reaction–diffusion processes on the cell surface can be used to control the fate of cells.

    CAS  Google Scholar 

  112. 112

    Ball, R. & Brindley, J. The life story of hydrogen peroxide II: a periodic pH and thermochemical drive for the RNA world. J. R. Soc. Interf. 12, 20150366 (2015).

    Google Scholar 

  113. 113

    Ludlow, R. F. & Otto, S. Systems chemistry. Chem. Soc. Rev. 7, 101–108 (2008).

    Google Scholar 

  114. 114

    Balazs, A. C. & Epstein, I. R. Emergent or just complex? Science 325, 1632–1634 (2009).

    CAS  Google Scholar 

  115. 115

    Branscomb, E. & Russell, M. J. Turnstiles and bifurcators: the disequilibrium converting engines that put metabolism on the road. Biochim. Biophys. Acta Bioenerg. 1827, 62–78 (2013).

    CAS  Google Scholar 

  116. 116

    Martin, W., Baross, J., Kelley, D. & Russell, M. J. Hydrothermal vents and the origin of life. Nature Rev. Microbiol. 6, 805–814 (2008).

    CAS  Google Scholar 

  117. 117

    van der Zwaag, D. & Meijer, E. W. Self-organization. Fueling connections between chemistry and biology. Science 349, 1056–1057 (2015).

    CAS  Google Scholar 

  118. 118

    Buriak, J. M. Chemistry with nanoscale perfection. Science 304, 692–693 (2004).

    CAS  Google Scholar 

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Acknowledgements

This work was supported by the W. M. Keck Foundation.

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Correspondence to Irving R. Epstein.

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Epstein, I., Xu, B. Reaction–diffusion processes at the nano- and microscales. Nature Nanotech 11, 312–319 (2016). https://doi.org/10.1038/nnano.2016.41

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