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The basic unit of life, the cell, is a complex system that performs a myriad of functions at the nano- and microscales through chemical reactions1 and molecular interactions. This sophis-ticated nanoscale machinery, which arose through evolution, has been an unlimited source of inspiration for physical scientists. Over the past two decades, much interest has been focused on the bottom-up construction of nanoscale building blocks, the forma-tion of structural and sometimes functional nanostructures, and the application of these nanostructures to mimic nanoscale phenomena in cells. Despite this success, integrating the fundamental dynamic features of cells1 into a synthetic nanosystem remains an elusive tar-get. In this Review, inspired by recent progress in reactiondiffusion (RD) to generate 3D Turing patterns2 using chemical oscillation in nanodroplets3, we argue as also recently suggested46 that it is time to move from the generation of structural building blocks to the exploration of dynamic processes (RD, oscillation, transport and communication) at the nano- and microscales7.

Despite their daunting complexity, all cells share several common features, among them self-assembly8, self-organization9 and far-from-equilibrium RD processes. In fact, RD represents the unifying theme among these three processes because it consumes energy and leads to ordered structures or patterns. For example, it is estimated that the energy consumed by the cells in an average person (50 to 75kg) requires the recycling of 0.2mol of adenosine triphosphate (ATP) 500750 times per day10. Without such energy consumption, the cells would not be able to sustain their dynamic and ordered nanostructures and would die. In a cell-like, far-from-equilibrium system, chemical reactions must give rise to dynamic order, and when the reactions stop that order must vanish. The system shown in Fig.1 captures these essential elements: as a far-from-equilibrium system, the Turing pattern a type of dynamic order exhibited by BelousovZhabotinsky (BZ) reaction droplets would not exist if the reaction, and thus the dissipation of energy by the system, stopped.

In this Review, we highlight recent progress in the physical sci-ences towards a unified view of self-assembly8, self-organization9

Reactiondiffusion processes at the nano- and microscalesIrving R. Epstein* and Bing Xu

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 reactiondiffusion 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 reactiondiffusion 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 reactiondiffusion 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.

and RD process2,11 in a single synthetic system, besides the study of BZ-type reactions1215. The development of bona fide, nanoscale, self-organizing systems requires that we advance our understanding of RD processes, a subject that has made great progress in the context of chemical kinetics and chemical oscillation, but has been largely overlooked by scientists working on nanoscience and nanotechnol-ogy, with only a few notable exceptions in which RD processes have been applied to generate nanostructures or active materials1619. We start by highlighting the use of RD processes for self-assembly and self-organization, and for synthesizing nanostructures. We then introduce chemical oscillation as a consequence of RD, discuss the associated pattern formation, describe the use of chemical oscilla-tion for chemical communication and illustrate a few examples of the application of chemical oscillation in designing chemomechani-cal systems. Finally, we outline modelling efforts of RD processes and share some thoughts for future investigations.

Self-assembly and self-organizationEarlier studies of self-assembly largely dealt with non-covalent interactions between molecules in a single crystal20,21 at thermody-namic equilibrium. Obviously, diffusion is an integral part of the self-assembly processes, and these initial studies have led to an appreciation of the interplay between these two processes. Notable examples are dynamic covalent self-assembly22,23 and enzymatic self-assembly processes24,25.

In the case of dynamic covalent self-assembly systems, vari-ous groups have developed several strategies to reach equilib-rium more rapidly26. In one example, selecting components from a dynamic library of ligands generated supramolecular grids27. In another example, self-replication, of either hexameric or hepta-meric self-assembled units (Fig. 2a), was dependent on how the reactant solution had been shaken28; either multimer further self-assembles to form nanofibrils (Fig. 2b), disfavouring the forma-tion of lower-molecular-weight trimers, tetramers or pentamers. In a further example, a catalyst altered the rate of formation of a

Department of Chemistry, Brandeis University, Waltham, Massachusetts 02454-9110, USA. *e-mail: epstein@brandeis.edu

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hydrazone-based gelator from two water-soluble compounds29; the inherent kinetic nature of the gelation process promotes a cor-relation between the mechanical stiffness of the final gel and the concentration of the catalyst. This example illustrates the use of a catalyst to accelerate the approach to equilibrium in dynamic cova-lent self-assembly systems in order to achieve a desired function.

In enzymatic self-assembly processes, where enzymes trigger the self-assembly, two main strategies for making30 or breaking24 bonds have been developed (Fig.2c). Both routes allow an enzyme to convert a precursor to a hydrogelator to form supramolecular assemblies in an aqueous environment, resulting in gelation. In general, the process of bond breaking occurs much faster than that of bond making, which can be reversible in a dynamic library31. Gelation also serves as a simple assay for studying molecular self-assembly in water. Intriguingly, an enzyme is able to regulate its substrate to form defect-free supramolecular nanofibres (Fig.2d), resulting in superior fibres to those obtained from a simple change of pH32. In this context, it would be worth applying RD analysis to determine, or estimate, the rate of each step and use these rates in a mechanistic simulation to evaluate how the combination of enzymatic reaction and molecular self-assembly can provide quick access to higher-ordered structures33.

Perhaps the most exciting recent result of self-assembly involv-ing RD is the transient assembly of active materials fuelled by a chemical reaction12. In this system, the lifetime, stiffness and self-regeneration capability of the self-assembly of synthetic molecules is determined by the interconversion rate between inactive and active monomers and the amount of reactant34 (Fig.2e). Strikingly, the nanofibres formed by the monomers exhibit growth and shrink-age during the reaction, similar to microtubules or actin filaments (Fig. 2f). One common characteristic of these RD-assisted self-assembly processes is that a reaction is not required to maintain the nanostructures once they are formed, even though in some cases the chemical reaction is the only path to generate ordered struc-tures35. In other words, when the reaction stops, the order remains.

In living organisms, besides regulating the formation36 or disso-ciation37 of molecular assemblies according to a specific biological condition or environment, enzymes frequently act as building blocks to form ordered molecular assemblies, such as microtubules. In the case of microtubules, however, when the reaction stops, the order dis-appears a genuine sign of self-organization taking place far from equilibrium. Inspired by these biological examples, several abiologi-cal systems of far-from-equilibrium self-organization at the nano- and microscale have been reported5,13,38,39. A primitive example may be found in the chemical nanomotors literature13, in which platinumgold nanorods catalyse the formation of oxygen from H2O2 solutions (Fig.3a) at the Pt end. The oxygen powers these nanorods to move along their axes (Fig.3b)40, and their motion can be modelled and described analytically41. Rotors42 and pumps43 (Fig.3c) that operate on a similar principle have also been reported. Recently, it was shown that self-organization of Ag3PO4 microparticles in aqueous media occurred on addition of NH3, resulting in the exclusion of micro-particles on a negatively charged glass slide (Fig. 3d); subsequent removal of NH3 by evaporation causes the microparticle system to school together. As the Ag3PO4 microparticles are ultraviolet-sensi-tive, one can use ultraviolet light to maintain the microparticles in the exclusion state15. A similar concept has been used to control the self-assembly of non-photoresponsive nanoparticles by light14. Following this principle, more complex swimmers comprising dipeptideMOF motifs (where MOF is a metalorganic framework) were used to fabricate a microrotor and to demonstrate that the microrotor can generate electric power44, albeit with low efficiency. Despite their sim-plicity, these systems represent a fascinating emergent behaviour at the nanoscale arising from chemical or photochemical reactions.

Moving from nanorod-based to MOF-based motors, the sophis-tication of the systems increases considerably, and their functional-ity becomes more elaborate. These systems, however, are still fairly primitive. None of them13,39,44,45 is able to achieve the spatiotempo-rally regulated molecular self-organization (that is, the formation of actin filaments or microtubules19,46) seen in biological systems under

a b c d

e f g h

FieldKrsNoyes mechanism

Products

BrO2

HBrO2

Br2

Br

BrMA

CO2 and products

Malonic acid (MA)

B3

B2

B1

A3

A2A1

C1

C2

Overall reaction: BrO3 + malonic acid (MA) G 0

CO2 + products

i

RuL33+

RuL32+

BrO3

Figure 1 | Three-dimensional Turing patterns generated by reactiondiffusion in an emulsion of nanodroplets containing the oscillatory BelousovZhabotinsky (BZ) reaction. ah, Tomographically reconstructed concentration fields for 3D Turing patterns. a, Spots. b, Hexagonal close-packing. c,Horizontal snapshots of pattern in b. d, Labyrinthine pattern. e, Tube. f, Half-pipe. g, Lamellar pattern. h, Concentric hemispherical lamellae. i, The reaction network of the BZ system. Although the overall reaction is the oxidation of malonic acid by bromate, the concentrations of intermediates, especially the catalytic species (for example RuL32+/RuL33+, L=bipyridine), oscillate. A1A3, B1B3 and C1C2 are the key steps of the three essential component processes of the BZ reaction. Figure adapted with permission from: ah, ref. 2, AAAS.

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a flux of energy. Several recent studies, however, have made nota-ble progress in this direction. In an elegant example, non-enzymatic self-assembled DNA circuits were able to reveal the edges of simple patterns47. Evolution has selected enzymes as the elementary build-ing blocks to accomplish molecular self-organization in cells (as an example, tubulins, the building blocks of microtubules, catalyse the hydrolysis of guanosine-5-triphosphate)46. This fundamental fact implies that abiotic molecular catalysts may be attractive candidates for the development of complex self-organization systems. In fact, not only are some catalysts able to self-assemble48, but their state of assembly responds to redox reactions49. Studying the kinetics of these or related types of catalysts33,50 may yield further progress towards self-organization resulting from nanoscale RD processes.

Syntheses, chemical waves and networksReactiondiffusion processes can be used to generate nearly mono-disperse, often sophisticated nanostructures. For example, using the pyrolysis of organometallic reagents in a hot coordinating solvent, nearly monodisperse, high-quality CdS nanocrystals have been synthesized in large scale51. The key to the success of this semi-nal finding is a temporally discrete nucleation at the nanoscale by

Ostwald ripening, an RD process52. Hollow nanocrystals18 based on the Kirkendall effect53 at the nanoscale have also been reported. The Kirkendall effect is a mechanism for the formation of poros-ity during an alloying or oxidation reaction and involves atomic diffusion occurring through vacancy exchange rather than by the direct interchange of atoms; that is, a flow of vacancies balances the net directional flow of matter, even though the diffusion rates of matter and vacancies are different. As shown in Fig.4a, react-ing cobalt nanocrystals with sulfur at high temperature produces relatively uniform hollow nanostructures. Moreover, the evolu-tion of the cobalt nanocrystals during their reaction with sele-nium confirms a nanoscale Kirkendall effect (Fig.4b). Because the Kirkendall effect on microparticles results in a large volume frac-tion of pores, but with non-uniform geometry and size distribu-tion54, these results imply that RD phenomena at the nanoscale may differ from those observed macroscopically, highlighting the potential of RD at the nanoscale as an approach for creating sophisticated nanostructures5562.

The difference between RD phenomena at the nano- and macro-scopic scales is observed in other systems and seems to be a general phenomenon. For example, catalytic oxidation on Pt nanoparticles

a

= 1 200 nm

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Break bond

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Enzyme+

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O

HN

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NH

OO

O

O

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OO S S

NH

OOCH3

O

(CH3)2SO4 CH3SO4

OHCH3OH

t = 6.9 h

t = 7.1 h

t = 7.3 h

fc

Figure 2 | Self-assembly integrated with chemical reactions. a,b, A building block mechanically forms a hexamer or heptamer (a), which self-assembles to form nanofibrils (b). c, Two modes of enzymatic self-assembly of molecules in water (hydrogelators). Examples include use of a phosphatase to convert a precursor to a hydrogelator that forms supramolecular nanofibres in water24, and use of thermolysin to catalyse bond formation for producing an amphiphilic peptide hydrogelator that self-assembles in water to form nanofibres30. d, An example of enzymatic formation of nanofibres in water via alkaline phosphatase-catalysed bond breaking. e, The interconversion of inactive and active monomers and the assembly of monomers into one-dimensional fibres and the breakdown of fibres into monomers. f, Confocal micrographs over time, showing distinct fibre growth, shrinkage and overlapping periods during a reaction cycle. Growing fibres are ringed in blue, shrinking fibres in red. Figure adapted with permission from: a,b, ref. 28, AAAS; d, ref. 32, American Chemical Society; e, ref. 117, AAAS; f, ref. 12, AAAS.

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displays sustained temporal oscillations as well as chemical waves63. A sequence of field ion microscopy images from a Pt nanoparticle in hydrogen oxidation conditions shows that the formation of water molecules at the nanoscale exhibits temporal oscillation (Fig.4c), unlike the behaviour of water on macroscopic single crystals. The product of the diffusion coefficient and the effective rate constant roughly determines the speed of chemical waves on the Pt nano-particles. This result indicates that RD at the nanoscale, coupled with catalytic conversion, can result in chemical oscillations and travelling nanoscale structures6466. A related phenomenon is the formation of Liesegang rings, a precipitation pattern by nanopar-ticles67, which constitutes a type of periodic switching. In addition, RD at the nanoscale is technologically important in nanoelectron-ics, because the resolution of photolithography based on chemically

amplified photoresists is determined by the spatial evolution of the relevant RD phenomena in the photoresists68.

At the microscale, microfluidic devices have been used to create functional chemical reaction networks69,70. Microfluidic networks can implement a distance-to-time transformation if mixing occurs sufficiently rapidly. In a simple approach, solution mixing in micro-fluidic channels71 was used to build a synthetic chemical reaction network that employs autocatalysis to perform one- and two-stage chemical amplification69. This network relies on autocatalytic reduc-tion of Co3+ and can perform 5,000-fold chemical amplification with a threshold response. This type of network may be particularly useful for investigating RD processes far from equilibrium, such as autocatalytic reactions. Because of its versatility in handling RD in picolitre volumes, this microfluidic chemical network is attractive for developing practical applications in bioanalysis72. In an innova-tive approach, enzymes, inhibitors and substrates confined in dif-ferent layers of a hydrogel made up a biochemical reaction network capable of recognizing the spatial distribution of an enzyme73.

Pattern formation, communication and energy conversionThe most distinctive RD process is chemical oscillation, which has been thoroughly investigated using the apparently simple, but quite complex, BZ reaction74,75 (Fig.1i). One of the most remark-able RD phenomena related to chemical oscillation is the formation of Turing structures. These spatially periodic, temporally station-ary patterns, which emerge from the instability of a homogeneous steady state, were proposed by Alan Turing in 1952as a mechanism for morphogenesis in living systems76. Like the Kirkendall effect, the Turing mechanism requires a difference in the diffusion rates of two or more species. The first experimental evidence of Turing struc-tures was obtained in the chloriteiodidemalonic acid oscillating reaction in a strip of starch-impregnated gel77 and in a closed, homo-geneous reaction mixture78,79. A two-variable model can be used to analyse the spatiotemporal behaviour of this reaction, suggesting that complex formation between I3 and starch bound to the gel results in the difference between the diffusion rates of the activator (iodide) and inhibitor (chlorite) necessary for Turing structures80.

A related mechanism might be responsible for pattern forma-tion in biological systems, where membrane-bound species and substrate inhibition provide a common means of dynamic regula-tion80. Chemical oscillators, such as the BZ reaction (Fig.1b), can also be studied in microemulsions. A mixture of water, oil and an ionic surfactant generates a thermodynamically stable reverse microemulsion of water nanodroplets in oil. The polar BZ reactants and catalyst are confined within the droplets, but nonpolar inter-mediates (Br2 and BrO2) generated during the reaction can enter and leave the continuous oil phase, providing a means of interdro-plet communication. The highly polar species (Br) are confined to the water droplets and exchanged when the droplets collide dur-ing fission and fusion, whereas the less-polar (HBrO2) or nonpolar (Br2) species diffuse through the oil as single molecules. The result-ing difference in diffusion rates of the polar and nonpolar species leads to the Turing patterns. By varying the droplet fraction, the droplet radius and the BZ reactant concentrations, it is possible to generate a large gallery of patterns (Fig.5a). Most of these pat-terns are unique to the microemulsion system. These distinctive morphologies include Turing structures81, which are temporally stationary, spatially periodic patterns76; antispirals82, which propa-gate in towards their centre, in contrast to normal spirals, which propagate out from their centre; packet waves83; segmented waves3; and jumping waves84. Localized patterns, such as memory85 and localized waves86, might be a potential route to efficient chemi-cal information storage87. Numerical simulations with models that contain species with different diffusion rates give excellent quali-tative agreement with the experiments81,88,89. A striking feature of this system is that the collection of nanodroplets produces complex

Fluid flow

H+

ePt Au

2H2O

H2O2 2H+ + 2e + H2O2

2H+ + 2e + O2

a

b

Ag

Au

Pump

AuRu

Rotor

AuPt

Motorc

5 m

Electrical field

Electro-osmosisElectrophoresis

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Electro-osmosisElectrophoresis

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OH HPO42 Ag(NH3)2+

d

Ag3PO4

Figure 3 | Self-organization of abiological systems. a, AuPt nanorods (370nm in diameter, consisting of 1-m Pt and Au segments) as bimetallic nanomotors operating in H2O2 solution by catalysing the formation of oxygen at the Pt end. b, Trajectories of three 2-m-long platinumgold rods illustrated in a over 5s in 2.5% aqueous hydrogen peroxide. c, Catalytic micromotors, rotors (in 15% H2O2 solution) and pumps (in 0.1% H2O2 solution) based on electrocatalytic reactions of fuels in bi- and trimetallic structures. In the trimetallic structure (rotor), the intermediate layer (white) consists of Au and Cr/SiO2/Cr. Arrows represent the direction of movement, rotation, and convective flow for the motor, rotor, and pump, respectively. d, Transition between exclusion (left) and schooling (right) behaviour based on silver phosphate particles. Figure adapted with permission from: a,c, ref. 13, Elsevier; b, ref. 40, American Chemical Society; d, ref. 15, Americal Chemical Society.

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patterns comprising millions of droplets, but a single nanodroplet is too small to act even as a simple oscillator. Such emergent behav-iour highlights the importance of studying RD processes at both the nano- and microscales.

To assess how dimensionality affects Turing pattern formation, the BZ reaction was studied in a microemulsion contained in a cylindrical quartz capillary. Optical tomography was used to visu-alize the 3D Turing structures, showing patterns that exist only in three dimensions, including curved surfaces, hexagonally packed cylinders, spots, and labyrinthine and lamellar patterns (Fig.1a)2. These results suggest that both dimensionality and initial conditions are important features for pattern formation in nature.

Besides the formation of Turing patterns, chemical oscillation also gives rise to behaviour that is similar to quorum sensing (for example, in cells, gene expression in response to fluctuations in cell population density)90. By immobilizing the catalyst of the BZ reac-tion in porous microparticles, chemical oscillators can be made to mimic the coordinated activity of unicellular organisms such as yeast90, which is regulated by population density and transport of signalling species through the surrounding medium. Varying the density of the microparticles and/or the interparticle exchange rate of the inhibitor and activator by simply changing the stirring rate results in two types of synchronization: gradual and sudden switch-ing on of oscillatory activity. This collective behaviour is believed to arise through communication by chemical signalling through the solution. This study shows that controlling RD processes offers an effective way to modulate the collective behaviour of a large, hetero-geneous collection of chemical oscillators.

In another example, the communication between small numbers of chemical oscillators was monitored in the BZ reaction in indi-vidual microdroplets91 generated by microfluidic techniques. In a one-dimensional arrangement, communication between droplets, mediated by the inhibitory Br, results in antiphase oscillation, in which neighbouring droplets oscillate 180 out of phase, as the most stable pattern70. In two dimensions, the droplets self-assemble into a hexagonal lattice, leading to a variety of stable patterns92. In one case, in each triangle of droplets one is stationary and the other two oscillate antiphase (Fig.5b). Another stable pattern consists of droplets oscillating 120 out of phase with their neighbours92. By controlling the mix of inhibitory and excitatory coupling of RD processes in the droplets, it should be possible to generate complex patterns of computational activity.

Living systems have evolved highly efficient nanoscale RD processes to transduce chemical energy to produce motion at the nanoscale. For example, the energy released by ATP hydrolysis powers the directed movement of a kinesin on a microtubule93, which, in turn, is able to generate movement over longer length scales13. Thus, it should be possible to develop synthetic systems that mimic RD processes in nature for generating mechanical forces from chemical reactions with high efficiency. Indeed, self-oscillating gels that convert chemical energy into mechanical energy have been reported. These systems, which combine the softness of gels and the oscillatory feature of the BZ reaction, show emergent properties, such as flocculation of oscillating microgel particles94,95. BelousovZhabotinsky gels in microfluidic channels can mimic the action of capillary channels for biochemical trans-port96 and exhibit an extremely large volume change (>500%) dur-ing each oscillation under optimal, continuous flow. This effect is significantly larger than that observed in oscillating gels without flow (~25%97; Fig. 5c)96. Considering the inherent heterogeneity of the gels, these results imply that control of RD processes at the nanoscale is critical for chemomechanical conversion.

Modelling of reactiondiffusion processesChemical oscillations are an ideal experimental starting point for studying RD processes under a variety of conditions and an

excellent vehicle for modelling such processes. Numerical simu-lations that consider species with different diffusion rates often achieve substantial agreement with experiments81,88,89. It is currently possible to follow the concentration fluctuations in an oscillating chemical reaction system98, as well as model the rate of product for-mation in an enzymatic reaction. In enzymatic RD systems, the spa-tiotemporal properties are extremely sensitive to sudden changes in network topology; selected reactions can be initiated or boosted at certain nodes as a function of connectivity99. Numerical studies have also shown that processing of a chemical signal by a nanoscale network can exhibit threshold behaviour. In particular, two micro-metre-sized containers, one of which hosts an enzymatic chemical reaction, joined by a nanotube can function as a filtering element in a primitive chemical computational device100. Moreover, models that combine the kinetics of the BZ reaction with the mechanical forces generated when a BZ gel shrinks and swells have also been developed101. These modelling studies provide useful mechanistic insights and helpful guidelines for the design and implementation of new experimental systems that would take advantage of RD pro-cesses at the nano- and microscales.

Co

Co9S8

a+ S8

0 s 10 s 20 s

1 min 2 min 30 min

b

50 nm

20 nm

0.0 s 1.52 s 1.68 s 1.84 s

2.0 s 6.0 s 10.0 s 14.0 s

18.0 s 22.0 s 26.0 s 30.0 s

c

Figure 4 | Reactiondiffusion processes at the nanoscale. a, The Kirkendall effect in cobalt nanocrystals (blue) that react with sulfur (Co:S ratio=9:8), forming Co9S8 at the surface (yellow). Cobalt ions diffuse outward faster than sulfur diffuses inward, resulting in a shell of cobalt sulfide. As the cobalt nanocrystals shrink, bridging occurs between the cobalt core and the resulting shell. After consumption of all the cobalt, an empty pore remains inside the cobalt sulfide shell. b, Evolution of CoSe hollow nanocrystals following injection of a suspension of selenium in o-dichlorobenzene into a cobalt nanocrystal solution at 455K. The Co/Se molar ratio was 1:1. c,Sequence of field ion microscopy images from a Pt tip with 180-nm radius under constant conditions of catalytic oxidation of hydrogen. In the centre region, the oscillation cycle starts with an oxygen-covered surface and elimination of the hexagonal lattice on the Pt(100) face. Then, H2O+ (bright) nucleates near the centre and spreads, which restores the hexagonal Pt(100). The adjacent Pt(311) plane provides a source for waves of oxygen propagating towards and reacting with the hydrogen adsorbed on the central region (dark), which becomes smaller as oxygen covers the surface to restore the initial state. Figure adapted with permission from: a, ref. 118, AAAS; b, ref. 18, AAAS; c,ref.63, Nature Publishing Group.

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Future perspectiveWhereas evolution has integrated self-assembly, self-organization and periodic RD processes at the nanoscale to produce beautiful nanomachinery, there is clearly a lot to do to combine these three processes in nanoscale abiological systems. We believe that the advances outlined in this Review have laid the foundation for inves-tigating self-assembly, self-organization and RD at the nano- and microscales in a holistic manner.

Recent studies of the prototypical BZ oscillating chemical reac-tion in nano- and microdroplets have provided considerable insight into how emergent properties arise from RD processes. Moreover, self-assembly systems have reached a high level of sophistication. Using DNA origami, for example, it is now possible to design a sequence of DNA that will give almost any desired shape102. A

future challenging task would be to render such DNA objects with desired functionalities as well47. From an instrumentation point of view, the rapid progress of tools such as cryo-electron microscopy103 and X-ray crystallography104 has greatly enhanced our capability to study self-assembly, self-organization and RD processes.

Finally, observing that a key feature of life is its rhythmic nature105, we take chemical oscillation as an example to direct the reader towards a set of specific problems that merit attention from researchers. First, new chemical oscillators: the BZ reaction has revealed many important insights about oscillating reactions and may still serve as a good toy model; how can we use these princi-ples to develop new types of chemical oscillator for controlling RD processes106,107 or regulating RD processes in living systems? Second, communication, computation and memory: we know that BZ oscilla-tors can communicate and exhibit certain features of computation108 and memory systems, so how can we develop synthetic systems, with intermediate complexity between chemical oscillators and the brain, but not based on silicon electronics, that can perform such tasks? Third, motion: nature has evolved ATP motors by integrating self-assembly, self-organization and RD processes, so what do we need to construct an analogous efficient chemomechanical engine? Fourth, periodicity: how can nanoscale oscillations that result in micro- and macroscale phenomena help us to develop RD processes for control-ling the fate of cells and treating diseases? (Although some progress has been made towards this latter goal, we are still at a very early stage before we can treat diseases109111.) Fifth, multiscale aspects: although there is an observable, phenomenological link between a variety of nanoscale processes and microscale phenomena, how can we rationalize how large-scale behaviour emerges from an under-standing of nanoscale processes and interactions?

We hope that this short Review will stimulate scientists to develop new, nanoscale, synthetic systems for a wide range of functions and inspire them to shift from studying single molecules (or objects) to multiple entities, from homotypic to heterotypic molecular interac-tions, from single to multiple events, from static to dynamic patterns, and from structure to function. Of course, it is unlikely that the inte-gration of self-assembly, self-organization and RD processes at the nanoscale will produce systems that capture all the features of living systems. But exploration along these lines will undoubtedly not only lead to a new paradigm of doing nanoscience and to the develop-ment of new nanotechnologies, but may also help address fundamen-tal questions, such as how life evolves from the coupling of chemical reactions1,112114 and other types of nonlinear behaviour115,116.

Received 1 September 2015; accepted 18 February 2016; published online 5 April 2016

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aJumping waves

Tim

e

Space

Spiral inchaotic waves

Bubble waves

Turing patterns Segmented spirals Memory

Oscillon

Standing waves Packet waves AntispiralsLocalized

waves

1 2 3

64 5 7

8 9 10 11 12

13 14 15 16

17 18 19

bBZ

BZ

Reduced[Ru(ii)]

Oxidized [Ru(iii)]

~500% volumechange

c

Figure 5 | Pattern formation, communication and energy conversion produced by chemical oscillations. a, Pattern formation in BZ reactions occurring in a microemulsion of the surfactant sodium bis(2-ethylhexyl)sulfosuccinate. Jumping waves are presented as snapshots (left) and as a spacetime plot (right, obtained across the white line shown in the left snapshot). Three types of Turing pattern are shown: left, black dots (honeycomb); centre, frozen waves; and right, white dots (distorted hexagons). Standing waves are shown as two antiphase snapshots. Memory shows persistence of image briefly projected onto a photosensitive medium that exhibits localized subcritical Turing structures. Localized waves are obtained in the same manner using a striped mask. Other patterns are spiral in chaotic waves, bubble waves, oscillion, segmented sprials, packet waves, and antispirals. b, Pattern generation in macroemulsions produced by microfluidics. Schematic of two-dimensional S pattern in which each triangle of drops is composed of two drops that are radians out of phase with one another, and the third is stationary: grey circles represent stationary (non-oscillatory) droplets; blue and red circles show oscillatory droplets 180 out of phase with each other. c,Chemomechanical oscillation of active gels with flow of aqueous BZ solution that achieve ~500% volume change. Figure adapted with permission from: a, ref. 6, American Chemical Society; b,ref.92, American Chemical Society; c, ref. 96, American Chemical Society.

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

Additional informationReprints and permissions information is available online at www.nature.com/reprints. Correspondence should be addressed to I.R.E.

Competing financial interestsThe authors declare no competing financial interests.

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