From dynamic self-assembly to networked chemical systems

Bartosz A. Grzybowski *ab, Krzysztof Fitzner *c, Jan Paczesny ab and Steve Granick ab
aIBS Center for Soft and Living Matter, UNIST, UNIST-gil 50, Eonyang-eup, Ulju-gun, Ulsan, 689-798, Republic of Korea. E-mail:
bDepartment of Chemistry, UNIST, UNIST-gil 50, Eonyang-eup, Ulju-gun, Ulsan, 689-798, Republic of Korea
cFaculty of Non-Ferrous Metals, AGH University of Science and Technology, Mickiewicza Ave. 30, 30-059 Krakow, Poland. E-mail:

Received 3rd February 2017

First published on 13th July 2017

Although dynamic self-assembly, DySA, is a relatively new area of research, the past decade has brought numerous demonstrations of how various types of components – on scales from (macro)molecular to macroscopic – can be arranged into ordered structures thriving in non-equilibrium, steady states. At the same time, none of these dynamic assemblies has so far proven practically relevant, prompting questions about the field's prospects and ultimate objectives. The main thesis of this Review is that formation of dynamic assemblies cannot be an end in itself – instead, we should think more ambitiously of using such assemblies as control elements (reconfigurable catalysts, nanomachines, etc.) of larger, networked systems directing sequences of chemical reactions or assembly tasks. Such networked systems would be inspired by biology but intended to operate in environments and conditions incompatible with living matter (e.g., in organic solvents, elevated temperatures, etc.). To realize this vision, we need to start considering not only the interactions mediating dynamic self-assembly of individual components, but also how components of different types could coexist and communicate within larger, multicomponent ensembles. Along these lines, the review starts with the discussion of the conceptual foundations of self-assembly in equilibrium and non-equilibrium regimes. It discusses key examples of interactions and phenomena that can provide the basis for various DySA modalities (e.g., those driven by light, magnetic fields, flows, etc.). It then focuses on the recent examples where organization of components in steady states is coupled to other processes taking place in the system (catalysis, formation of dynamic supramolecular materials, control of chirality, etc.). With these examples of functional DySA, we then look forward and consider conditions that must be fulfilled to allow components of multiple types to coexist, function, and communicate with one another within the networked DySA systems of the future. As the closing examples show, such systems are already appearing heralding new opportunities – and, to be sure, new challenges – for DySA research.

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Bartosz A. Grzybowski

Bartosz A. Grzybowski received his PhD from Harvard in 2000 and is now a Distinguished Professor of Chemistry at the Ulsan Institute of Science and Technology, UNIST, and a Group Leader in Korea's Institute for Basic Science. He is also a Professor at the Institute of Organic Chemistry of the Polish Academy of Sciences in Warsaw. Bartosz published one book and some 220 peer reviewed articles. He received numerous awards including the 2013 Nanoscience Prize and the 2016 Feynman Prize in Nanotechnology. His scientific interests include chemical networks and systems, theory of organic synthesis, nanoscience, self-assembly, non-equilibrium chemistries, and reaction-diffusion systems.

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Krzysztof Fitzner

Krzysztof Fitzner obtained his PhD from the Institute for Metals Research at the Polish Academy of Sciences in Krakow in 1973, where he worked until 1995. He then moved to the Faculty of Non-Ferrous Metals at AGH, where he was the Head of the laboratory of Physical Chemistry and Electrochemistry until 2012, and Chairman of the Department from 2005 to 2012. Krzysztof is an author of some 180 scientific papers. His scientific interests include thermodynamics and phase equilibria, solubility of gases in alloys, experimental determination of thermodynamic properties of high temperature systems, nanoscale electrochemistry, and reactions in microreactor systems.

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Jan Paczesny

Jan Paczesny graduated maxima cum laude in chemistry from the Adam Mickiewicz University in Poznan, Poland, in 2009 and received his PhD in physical chemistry from the Institute of Physical Chemistry of the Polish Academy of Sciences in Warsaw, Poland, in 2012 (with honors). Afterwards, he was appointed as assistant professor in the same institution. For the following three years he was leading a team working on bio-inspired functional nanomaterials. In 2016 he joined the group of Professor Bartosz A. Grzybowski at the Institute for Basic Science in Ulsan, South Korea.

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Steve Granick

Steve Granick is the Director of the IBS Center for Soft and Living Matter in Korea's Institute for Basic Science. Previously he spent 30 years at the University of Illinois (USA), most recently as Racheff Chair of Materials Science and Engineering, Professor of Chemistry, Professor of Chemical and Biomolecular Engineering, and Professor of Physics and Biophysics. Among his major awards are APS national Polymer Physics Prize (2009) and ACS national Colloid and Surface Chemistry Prize (2013). He is a member of the US National Academy of Sciences.

1. Introduction

Self-assembly, SA, is a process in which individual parts come together spontaneously – without any external “supervision” or manipulation – to form ordered and/or functional structures.1–3 There are at least two aspects of SA that are quite inspiring: first, all forms of life are self-assembling and so, understanding self-assembly processes could give us a better understanding of life itself. Second, the apparent ease with which self-assembly can construct complex structures from simple components spurs imagination for the futuristic modes of “autonomous” fabrication or manufacturing. Yet, the simplicity of SA is somewhat misleading – the real difficulty is, of course, in that the “parts” need to be appropriately “programmed” to come together in correct orientations. Putting together black and white squares into a box and shaking vigorously will not produce a chessboard unless there are some rules stipulating that black squares should favor contacts with white squares, etc. In systems at thermodynamic equilibrium, the knowledge of interparticle interactions and of the thermodynamic parameters of the system (e.g., temperature, defining how vigorously the parts are agitated) suffices to define the conditions for and the outcomes of self-assembly. Such equilibrium self-assembly, ESA (Fig. 1a), has been studied for decades and can be understood in quantitative detail using the seasoned concepts of classical thermodynamics. The limitation of ESA is, however, that for a given set of thermodynamic parameters, the system will evolve to the equilibrium state at which it will then persist – that is, ESA evolves components into stable, ordered structures, of which crystals (be it molecular,4,5 nanoparticle,6,7 colloidal,8–10 or macroscopic11) are perhaps most representative. On the other hand, conditions of thermodynamic equilibrium preclude self-assembly at steady-states, at which order is maintained at the cost of externally delivered energy (which is, in part, dissipated to produce entropy). While the vocabulary of “non-equilibrium,” “dissipation,” and “entropy production” might not be as familiar to chemists as Gibbs free energy, these terms are key to describing living systems – in fact, all organisms consume and dissipate externally delivered energy (in the form of food or radiation) to power their internal operation and to maintain order. Moreover, depending on the incoming flux of energy, these organisms can reconfigure to perform different functions, amplify signals, self-replicate, etc. These properties illustrate well the promise of self-assembly outside of equilibrium – the so-called dynamic self-assembly, DySA (Fig. 1b) – as a means to create life-like, reconfigurable, and “intelligent” materials and systems.
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Fig. 1 Self-assembly and self-assembling systems. (a) Scheme illustrating equilibrium self-assembly, ESA, of interacting components (here, two types of spherical particles) into a stable, crystalline structure. The graph on the right illustrates that at equilibrium, the entropy S of the entire system (beads plus the environment) is maximized whereas the Gibbs free energy G (of beads) is minimized. The arrows next to the S and G curves illustrate the “directions” of all spontaneous processes (increasing S/decreasing G), thus ultimately driving the system towards Smax/Gmin (maximum/minimum at the dashed line). (b) Dynamic self-assembly, DySA, in which an ordered, steady-state structure persists only as long energy is delivered. Some of this energy is dissipated as heat. Note that for DySA, there is no general principle predicting which function would be maximized or minimized at the non-equilibrium state. (c) A scheme of a hypothetical system in which non-equilibrium DySA processes are arranged into a sequence. Here, the particles from (b) first assemble into an array that “catalyzes” the assembly of pyramids into cubes. These pyramids then use the energy of ATP to assemble into larger structures. “Networked” systems of this type are the subject and the vision of the review.

The study of DySA is a relatively new area of research with the name itself proposed only in the 2000 Nature paper by Grzybowski, Stone and Whitesides.12 Starting with macroscopic systems (e.g., of magnetic spinners interacting by vortex–vortex forces13 or contact-electrifying granular materials14,15), we have gradually learned how to control dynamic self-assembly at micro,16,17 nanoscopic18,19 and macromolecular20,21 scales. On the other hand, these demonstrations have not provided a deeper and more unifying understanding of DySA, which needs to be considered on a case-by-case basis, with different dynamic/kinetic models describing different systems. Save some qualitative considerations, there are not yet any generally applicable principles of DySA – and in fact, it is not even clear whether such principles exist. Moreover, while it is quite evident why DySA is of interest to physicists (trying to generalize thermodynamics to non-equilibrium systems) and biologists (trying to understand the organization and operations of cells), it remains somewhat unclear why chemists should care. In chemistry, there are many materials that self-assemble (molecular crystals,4,5 MOFs,22,23 micelles,24etc.) but these are typically sought to be robust rather than steady-state. There are also many “dynamic” molecules (molecular switches,25 rotaxanes26) but these are generally studied as individual entities in solution rather than ordered assemblies. Why should we then care about dynamic/switchable molecules, nanoparticles or colloids that form transient, dynamic aggregates?

Given increasing interest in DySA, these are timely questions to which different answers can certainly be given. Our own and perhaps subjective view is that DySA itself is only a prerequisite for a larger enterprise of creating self-assembling chemical networks and systems which will redefine the future of chemistry. Historically, the main focus of the chemical sciences has been to develop new methodologies for the synthesis of useful and/or complex molecules. This effort has met with quite a remarkable success and nowadays even the most intricate natural products – taxol, strychnine, maitotoxin, vincristine, etc. – can be made, given adequate time and resources. Yet, there remains a fundamental difference how chemistry and biology synthesize molecules: Whereas our synthetic schemes comprise individual steps interspersed with purification procedures, biology operates simultaneously entire networks of reactions coupled by molecular transport, synchronized in space and in time, and overall functioning as molecular “assembly lines”. Our grand vision for DySA is that its dynamic entities would become the control elements of similar but abiological functional, networked systems (Fig. 1c). For instance, catalysts that assemble/disassemble to become active/inactive upon applying an external stimulus18,27 could catalyze desired reactions in multistep sequences. Oligomeric molecules could be stitched together by molecular assemblers based on rotaxane chemistries.28 Dynamically assembling/disintegrating vesicles29–31 would provide transient reactors in which some reactions incompatible with the rest of the system's chemistries would be carried out. These and other processes would all be coupled by the transfer of mass between system's subregions mediated either by diffusion32 or by actively propelling assemblies33–35 carrying molecular cargo. Ideally, we see such systems interfaced with various outside sources of energy and with time optimizing – either autonomously or perhaps, for the time being, via a feedback to outside controllers, as in systems developed by the Cronin's group36–39 – the energy usage to find most efficient synthetic paths and/or the ways of trafficking the system's components. Although such ideas might appear far-fetched, we point out that all individual dynamic components are already known, as evidenced by the references cited. The main challenge is then, in our opinion, to learn how to integrate DySA components into spatially distributed systems and “wire them up”21,40–50 to communicate both with the outside environment and with each other. This effort in integrating non-equilibrium self-assembly processes at various length scales seems to us well justified given future possibilities one might envision. As already hinted, one exciting opportunity would be to design chemical reactors in which multiple substrates are simultaneously present but only desired reactions and reaction sequences are carried out “on demand” depending on which dynamic catalysts/“controls” are activated. Dynamic systems with in-build nonlinearities – especially positive feedback loops – could also give rise to new, ultrasensitive detection modalities amplifying molecular-level events into larger scale self-assembly “readouts” (cf. early examples in ref. 51). A combination of DySA and reaction-diffusion could be harnessed for chemical through-space signaling and communication which we see operative in all living cells but are only beginning to understand in man-made systems.32,52 Finally, self-assembly of templated, non-equilibrium structures is essential for self-replication which, if extended beyond nucleic acids,53–56 could completely transform chemical production. Engaging a broad audience into these challenges is our main motivation for writing this review.

With this vision in place – but mindful that much of the ESA/DySA background was covered extensively in our previous reviews on this topic57–60 – we will start with a brief discussion of thermodynamic potentials and how they determine the fates of systems at equilibrium. We will survey various types of interactions that can mediate equilibrium self-assembly, ESA, and will provide some illustrative examples of ESA structures. Then, we will turn our attention to systems in which the equilibrium concepts no longer apply, and will strive to identify the key features distinguishing DySA from ESA, focusing on the concepts of energy dissipation and concomitant entropy production. We will then consider the practical design heuristics of DySA and how they were realized in experiment. With these foundations, we will be in a position to discuss the first, promising examples of DySA acting as control elements of other processes. The last part will focus on how these non-equilibrium parts could be connected into larger, networked systems we ultimately envision.

2. Self-assembly at thermodynamic equilibrium

2.1. Thermodynamic potentials and equilibrium

One of the most fundamental laws of nature is the Second Law of thermodynamics stating that the total entropy of an isolated system always increases over time. The change in entropy can be related to the heat exchanged with the environment by image file: c7cs00089h-t1.tif where T is the temperature and dSi is the (always positive) amount of entropy produced due to spontaneous/irreversible processes. For an isolated system, dS = dSi ≥ 0 defines the system's direction of change – that is, all spontaneous changes increase the entropy. It follows that at equilibrium – which by definition is stable against any spontaneous changes – entropy is maximized, Seq = Smax (cf.Fig. 1a).

The principle of entropy maximization dictates the behavior of the so-called thermodynamic potentials at equilibrium. To show this, one uses the First Law of thermodynamics relating internal energy to the heat absorbed by the system and the work performed by the system, dU = dQ − dW. Substituting from the Second Law, dS ≥ dQ/T, one then has dU + dWTdS ≤ 0. Now, taking as an example a system at constant temperature and pressure and assuming the only work is volumetric, pdV, we have d(U + pVTS) ≤ 0 which, by introducing enthalpy, H = U + pV, can be rewritten as d(HTS) ≤ 0. The function in the parenthesis, HTS, is defining the famous Gibbs free energy,61 and so dG ≤ 0. This is a very profound inequality – note that in deriving it, we used the Second Law (which leads to entropy maximization at equilibrium) but imposed additional constraints of p and T being constant. Under these constraints, any spontaneous change has to decrease G and so the equilibrium state – again, being stable to spontaneous changes – has to correspond to the minimum of Gibbs free energy, Geq = Gmin (cf.Fig. 1a). Put yet differently, minimization of G at equilibrium is a special case of maximization of entropy at equilibrium, save the fact that two additional constraints (p, T) are imposed on the system. There are several important reasons why dG ≤ 0 rather than the dS ≥ 0 criterion is so widely used in the chemical sciences and in the self-assembly research: (i) the change in standard Gibbs free energy can be related to the equilibrium constant, ΔG0 = −RT[thin space (1/6-em)]ln[thin space (1/6-em)]K, and thus to the concentration of molecules of interest; (ii) it is much easier to calculate dG's than dS's; and (iii) Gibbs free energies can be conveniently “partitioned” into the familiar enthalpic and entropic contributions. It is then the balance of these contributions that determines the overall sign of dG and the outcome of a chemical reaction or of a self-assembly process.

2.2. Equilibrium self-assembly, ESA

We first consider ESA dominated by enthalpic factors. Since self-assembly processes typically occur under constant pressure and the volumetric changes are small, the changes in system's enthalpy are almost identical to those of internal energy. Thus, the outcome of self-assembly is determined by the energies of interactions between the system's components. We have narrated the nature and the scaling properties of available types of interactions in detail in two previous reviews58,59 – here, we just summarize them in Table 1, along with some illustrative examples (focusing on recent works).
Table 1 Types and scaling of interactions commonly used in self-assembly
Interaction Range Scaling Examples and references
Electrostatic (attractive/repulsive) Without screening: no scale image file: c7cs00089h-t7.tif (Coulomb energy) Ionic crystals62
With screening: 1 nm–1 μm image file: c7cs00089h-t8.tif, where image file: c7cs00089h-t9.tif is screening length (kBT – thermal energy, ε0ε – dielectric permittivity of solvent, e – fundamental charge, cs – concentration of salt). Colloidal crystals9,63 and polyelectrolyte multilayers64
Dipole–dipole (attractive/repulsive) 0.1 to 1 nm image file: c7cs00089h-t10.tif for fixed and image file: c7cs00089h-t11.tif for rotating dipoles (Keesom energy). The energy of interaction of two dipoles of strength 1D separated by 0.2 nm is around 10 kJ mol−1. Colloidal superparticles,65,66 binary colloidal structures,67 liquid crystals,68 and supramolecular materials69
π – interactions (attractive) 0.1 to 1 nm Magnitude scales with the number of π electrons in overlapping p orbitals, but depends also on the geometry and the chemical nature of interacting species. The binding energy of two organic molecules is usually below 10 kJ mol−1,70 but might reach ∼160 kJ mol−1 for arenes and cations interacting in the gas phase.71 Typical length scale is ≈3.4 Å. Controlled assembly–disassembly of vesicles,72 molecular switches26 and motors25
Hydrogen bonding (attractive) 0.1–1 nm Approximately image file: c7cs00089h-t12.tif. The strength of most hydrogen bonds is in the range from 10 to 40 kJ mol−1. Folding DNA to create nanoscale shapes and patterns,73,74 and DNA based self-assembly of nanostructures7,75–78
van der Waals (typically attractive) 1–10 nm image file: c7cs00089h-t13.tif (London dispersion energy). The strength is around 10 kJ mol−1 for two alkane molecules in water. 2D self-assembly,79–81 self-assembly and crystallization of nanoparticles82–85
Steric (repulsive) 1–100 nm image file: c7cs00089h-t14.tif for two surfaces with grafted polymers of the radius of gyration Rg. Formation of superlattices from tetrahedral nanocrystals86
Hydrophobic (attractive) 1–100 nm image file: c7cs00089h-t15.tif for two hydrophobic surfaces in water, where λ ≈ 1–2 nm (characteristic length scale). Bolaamphiphile assembly into spherical particles or 2D anisotropic platelets,87 peptide self-assembly,88 and self-assembly assisted by soft templates89
Capillary/menisci (attractive/repulsive) 0.1–10 mm image file: c7cs00089h-t16.tif for two floating spheres near contact. Lc is the capillary length. Self-assembly of mesoscale plates at interfaces,90–92 hierarchical structures,93,94 topographical control over nanoparticles' assembly,95 and nanostructuring of 2D materials96
Depletion (attractive/repulsive97) 1 nm–5 cm98 For hard spheres of radius rL separated by distance r and for moderately low densities of depletants (smaller spheres of radius rS) image file: c7cs00089h-t17.tif Granular materials,98 colloidal crystallization,99,100 nonamphiphilic colloidal membranes,101 and Janus colloidal assembly102

We note that many of these interactions might be considered somewhat “disjoint” in the sense that they appear hard to combine into individual “molecular parts” of self-assembling systems. For instance, it was and remains difficult to prepare molecules that would interact simultaneously via magnetic dipole–dipole, electrostatic, and perhaps hydrogen-bonding interactions. Such limitations, however, have been largely abolished with the recent progress in nanoscience whereby many different properties can be combined within one nanoparticle. For the specific example given, one can easily imagine nanoparticles with Fe3O4 cores mediating magnetic dipole–dipole interactions and decorated with a mixed self-assembled monolayer103,104 of organic ligands terminated in charged groups and well as groups capable of hydrogen bonding. Moreover, the relative strength of these interactions can be regulated by the particle's size and the composition of the ligand shell. This flexibility of design at the nanoscale might as well explain why many of the modern examples of ESA are based on appropriately crafted “nanoparts” rather than small molecules (as in the classic works on the so-called crystal engineering from the 1990s4,5,105–109).

To illustrate, the groups of Seeman73 and Rothemund74 pioneered the self-assembly of appropriately designed DNA strands into a range of complex “origami” structures. Mirkin's group has developed a family of nanoparticles covered with complementary DNA strands75,76,78 – when assembling, these particles combine the specificity of base pairing with the strength reflecting the polyvalency of interactions between multiple strands. By skillfully using these effects they were able to “program” the assembly of such nanoparticles into crystals with various internal orderings (Fig. 2a).7,110–114 Liedl and co-workers115 demonstrated DNA-nanoparticle self-assembly whereby multiple, appropriately designed DNA helix bundles of oligonucleotides were first arranged into a DNA-origami scaffold onto which the nanoparticles (covered with DNA ligands) were then tethered at specific locations to ultimately form optically active, helical structures (Fig. 2b). Akcora and co-workers116 combined repulsive entropic interactions between macromolecules uniformly tethered onto spherical nanoparticles with the attractive van der Waals interactions between the particle's cores. What is interesting about this work is that the balance between repulsive and attractive interactions caused spontaneous symmetry breaking and the particles – despite being spherical – assembled into anisotropic superstructures (Fig. 2c). In another clever demonstration, Bishop's group assembled “adaptive” nanoparticles covered with mixed monolayers comprising both hydrophobic and hydrophilic ligands (Fig. 2d).117 Depending on the properties of the surrounding solvent, these ligands could rearrange on particles' surfaces forming hydrophobic “patches” through which the particles then “bonded” into either chain-like or micellar structures. Our own group studied extensively nanoparticle assembly mediated by electrostatic forces6,18,57–60,63,65,66,118,119 often in conjunction with other types of interactions. Of note, in several types of assemblies, interactions such as van der Waals forces between particles' cores84 or hydrogen-bonding between particle-stabilizing ligands120 offset the electrostatic repulsions, and the particles self-assembled into large, crystalline structures – despite all these particles presenting charges of the same polarity.

image file: c7cs00089h-f2.tif
Fig. 2 Equilibrium self-assembly, ESA, based on nanoparticles. (a) By controlling particle sizes and the nature of capping DNA ligands, nanoparticles can be crystallized into various types of superlattices. The DNA strands that drive the assembly comprise (i) an alkylthiol moiety and a nonbinding region, (ii) a recognition sequence that binds to a DNA linker, (iii) a spacer sequence of programmable length to control interparticle distance, and (iv) a “sticky end” sequence that drives self-assembly via DNA hybridization. The SEM image in the top-left is of a bcc microcrystal made of 20 nm gold nanoparticles (scale bar = 1 μm). Other schemes and TEM images illustrate ordering in nanoparticle superlattices isostructural with bcc, CsCl, Cr3Si (left column, top to bottom), fcc, hcp, AlB2 and Cs6C60 (right column, top to bottom). Scale bars in TEM images = 50 nm. Reproduced from ref. 7 (with permission from AAAS) and ref. 111 (with permission from Macmillan Publishers Ltd: Nature, copyright 2014). (b) Left- and right-handed nanohelices formed by nine gold nanoparticles attached to the surface of DNA origami 24-helix bundles. Each attachment site consists of three 15-nucleotide-long single-stranded extensions of staple oligonucleotides. Nanoparticles are capped with thiol-modified DNA strands complementary to staple extensions. The scale bar in the TEM image = 100 nm. Adapted with permission from Macmillan Publishers Ltd: Nature, from ref. 115, copyright 2012. (c) Spherical silica nanoparticles grafted with polystyrene brushes and mixed with a polystyrene matrix form a range of anisotropic structures depending on the grafting density, molecular mass of the polymers, and annealing time. Scale bar = 0.5 μm. Adapted with permission from Macmillan Publishers Ltd: Nat. Mater., from ref. 116, copyright 2009. (d) Gold nanoparticles functionalized with mixed monolayers of DTT (hydrophobic) and MUA (hydrophilic) ligands form chain-like structures via hydrophobic “patches”. Adapted with permission from ref. 117. Copyright 2014 American Chemical Society. (e) Positively-charged nanotriangular prisms (see inset, scale bar = 100 nm) assemble into close-packed, mono- and multilayer arrays when electrostatic repulsions are offset by van der Waals attractions. Scale bars in SEM images = 1 μm. Adapted with permission from ref. 84. Copyright 2010 Wiley-VCH. (f) Scheme of nanoparticles decorated with mixed SAMs comprising ligands with terminal carboxylic (MUA) or quaternary amine (TMA) groups. Although the particles have net positive charges, their crystallization is driven by hydrogen bonding between MUAs. SEM images of 3D crystals resulting from the self-assembly of 4.2 nm, AuNPs at pH ∼ 4. Adapted from ref. 120 with permission from the Royal Society of Chemistry.

In addition to the tuning of interparticle forces, ESA can be effected by entropy alone. This, at the first sight, might sound suspicious since the popular view of entropy is that it “increases disorder” rather than drives the formation of ordered structures. In reality, however, entropy is a measure of states available to the entire system and the reason some components organize (decreasing their entropy) is that other parts of the system actually gain more entropy. A classic example here is that of a mixture of large and small hard-spheres in which the large ones clump together (or crystallize) to let the smaller spheres explore more configurations/states.121–123 When particles are not spherical, the number of possible configurations increases dramatically and the packing within the final structure is often not obvious. The entropic ordering into smectic and nematic phases is well known in liquid crystals (often, rod-like shaped molecules) at high volume fractions: When the molecular rods are randomly oriented, their freedom of motion is significantly reduced; when, however, the rods align, the loss of some residual rotational freedom is compensated by their ability to translate more freely (Fig. 3a). The problem of this entropic ordering was treated analytically (sic!) almost seventy years ago by Lars Onsager.124 Later, these concepts were used to assemble, for instance, smectic phases of viruses (Fig. 3b),125 or structures in which layers of ordered viruses were interspersed with layers of colloidal particles.126 In an interesting recent computational study, Glotzer and co-workers introduced the concept of directional entropic forces (DEFs) and showed that these forces tend to align neighboring anisotropic particles.127 van Blaaderen, Dijkstra and co-workers128 studied entropic interactions under spherical confinement and showed that under such circumstances spherical particles can form icosahedral clusters comprising up to 100[thin space (1/6-em)]000 particles. Their simulations demonstrated that the specific nature of interactions between the particles is not important for icosahedral order suggesting that entropy confinement may provide a general route to small crystals of unusual symmetries. For further discussion of entropic forces, the Reader is directed to an excellent recent article by Frenkel.129

image file: c7cs00089h-f3.tif
Fig. 3 (a) Random vs. aligned ordering of rod-like objects. Despite appearing more ordered, the aligned structure on the right has higher entropy (see the main text for discussion). (b) Smectic phases formed by mutants of the fd virus of different length (0.64 μm, left; 1.2 μm, right) at high volume fractions. Scale bar = 2 μm. Experimental images reproduced from ref. 125 with permission from Elsevier.

Naturally, the most general scenario of ESA is when enthalpic and entropic effects are both operative, often resulting in truly complex behaviors even for simple, spherical building blocks. In one classic example, a combination of electrostatic, steric, dipolar and entropic forces allowed for the preparation of more than 15 different types of nanoparticle lattices including ten structures that had not been reported previously (Fig. 4a).82,130 In a recent work by Feng et al.,131 colloidal particles interacted via the polymer chains dispersed in surrounding solution – the polymers could bridge the particles (enthalpic interaction) or be excluded from between the particles (entropic, so-called depletion interaction), in both cases amounting to an attractive interaction. What is unexpected and interesting about this system is that these interactions were found to depend on temperature such that the colloids were dispersed at intermediate temperatures but self-assembled at either low or high temperatures.

image file: c7cs00089h-f4.tif
Fig. 4 Equilibrium self-assembly based on multiple interactions and/or non-spherical building blocks. (a) TEM images of select (out of more than 15 actually demonstrated) binary nanoparticle superlattices whose self-assembly is driven by the interplay between electrostatic, steric, dipolar and entropic forces. Insets show modelled unit cells. The superlattices comprise (1) 13.4 nm γ-Fe2O3 and 5.0 nm Au; (2) 7.6 nm PbSe and 5.0 nm Au; (3) 6.2 nm PbSe and 3.0 nm Pd; (4) 6.7 nm PbS and 3.0 nm Pd; (5) 6.2 nm PbSe and 3.0 nm Pd; (6) 5.8 nm PbSe and 3.0 nm Pd; (7) 7.2 nm PbSe and 4.2 nm Ag; (8) 6.2 nm PbSe and 3.0 nm Pd nanoparticles. Reproduced with permission from Macmillan Publishers Ltd: Nature, from ref. 82, copyright 2006. (b) Triblock Janus spheres hydrophobic on the poles (black, with an opening angle of 65°) and charged in the equator section (white) interact via hydrophobic attractions and screened electrostatic repulsions to form a colloidal kagome lattice (inset – fast Fourier transform). Scale = 4 μm. The scheme illustrates particle orientations within the lattice. Adapted with permission from Macmillan Publishers Ltd: Nature, from ref. 133, copyright 2011. (c) Self-assembly of nanoclusters made from composite Fe3O4/Au nanoparticles comprising smaller Au (radius R1) and larger Fe3O4 domains (R2). The morphologies of the clusters depend on the “bond strength” which, in turn, depends on the concentration of dithiol linkers bridging the Au domains and the “steric hindrance” due to the Fe3O4 parts (and quantified by the ratio of radii R2/R1). All scale bars are 50 nm. Reproduced with permission form ref. 134. Copyright 2009 Wiley-VCH.

When one adds to the above list the design flexibility offered by using “patchy” (Fig. 4b) or Janus (Fig. 4c) particles132–134 – that is, particles comprising domains of different properties – one begins to imagine the diversity of ordered structures that can, in principle, be achieved by self-assembly. On the other hand, within ESA, these structures are static crystals incapable of on-demand change and, as such, do not offer functional diversity. For functional, dynamic assemblies, one needs to venture outside of the equilibrium regime.

3. Self-assembly outside of equilibrium

3.1. Non-equilibrium, dissipation, and entropy production

In thermodynamics, the equilibrium state is defined as a stable state at which no matter is exchanged with the environment and there is also no net flux of energy through the system. The non-equilibrium is then defined by one of these requirements not being fulfilled. In the case of self-assembly, we can restrict our interest to systems in which there is no transfer of mass to/from outside, as the “parts” of the system can organize but cannot “disappear” or “appear” during the process. The more subtle question is that of the systematic flux of energy – “systematic” here means continuous and “flux” implies some directionality. This is a judicious definition since it excludes some phenomena that could be well described by the change in system's thermodynamic parameters and by the theory of phase transitions based on the equilibrium formalism. For example, when water is exposed to a temperature decrease from T > 0 °C to T < 0 °C, it will freeze. Yet, even intuitively we feel that we should not talk here of some non-equilibrium self-assembly of water molecules into ice crystals – instead, the phenomenon is just the first-order phase transition due to the change of system's thermodynamic parameter T. In contrast, when a laser beam irradiates particles covered with photoswitchable ligands16,65 and these particles assemble, there is net flux of photons and a non-equilibrium situation is established. We observe that in this case, some energy is irreversibly lost (“dissipated”) into thermal degrees of freedom (e.g., during the photoswitching of the ligands or during the motion of particles into the assembled state). By the Second Law, such irreversible losses correspond to entropy being produced, dSi > 0. In fact, energy dissipation and concomitant entropy production are the hallmarks of all non-equilibrium processes, including dynamic self-assembly, DySA, under non-equilibrium conditions.

Entropy production has been studied for decades and in various contexts but what concerns us here is whether this measure can somehow be used to predict the outcomes of DySA, akin to the maximization of entropy (or minimization of G) determining the outcomes of ESA (see Section 2.1). In the 1970s, the answer seemed to be in the affirmative when Prigogine formulated his celebrated Minimal Entropy Production (MEP) theorem stating that at steady states outside of equilibrium, the rate at which entropy is produced, σ = dSi/dt, is minimized. In the context of our Review, MEP implies that dynamically self-assembling systems should evolve into structures that are dissipating the least amount of energy possible and thus minimize the rate of entropy production. Notwithstanding its appeal – due to simplicity and apparent generality – this theorem received serious criticism and it is probably fair to say that today it is largely discounted,135,136 as are some other “extremum principles” proposed for dissipative systems (e.g., ref. 137 and 138). Part of the problem with MEP is that it is applicable only within the linear regime, close to equilibrium – unfortunately, there are no reliable measures that would quantify how close to equilibrium the system actually is, and whether it is “close enough” to apply MEP. For us, the value of MEP was mostly to stimulate our early research on DySA and find model systems in which the rates of entropy production could be calculated exactly.

In the archetypical DySA system we designed – in fact, one for which the DySA name was originally coined12 – millimeter-sized polymeric discs doped with magnetite are floating at an interface between the water/diethylene glycol mixture and air (Fig. 5). A permanent magnet is placed below this interface – when it starts rotating (with angular velocity ω ∼ 10 Hz), the individual disks start rotating, in the process creating vortices in the surrounding fluid (Fig. 5b and c). These vortices give rise to repulsive interactions between the disks (FD in Fig. 5a). At the same time, the rotating magnet creates a confining magnetic potential and all particles experience a centrosymmetric force FC that attracts them toward the magnet's axis of rotation. Importantly, the competition between FC and FD evolves particles into open-lattice, dynamic “crystals”12,13,139–148 which persist only as long as the particles harness energy from the external rotating magnetic field, and then dissipate this “captured” energy into fluid flows.

image file: c7cs00089h-f5.tif
Fig. 5 DySA based on magnetic and hydrodynamic interactions. (a) Scheme of the experimental arrangement, in which an external magnet drives the rotations of small, magnetic particles immersed in a viscous liquid at a liquid/air interface. Repulsive vortex–vortex forces are indicated by red arrows; the confining magnetic forces are indicated by blue arrows. The vortex flows can be visualized by the addition of dyes (here, Crystal Violet). (b) Shows the top view of the flows around two rotating particles (each, 2 mm in diameter) while (c) shows the corresponding side view along the plane of the interface. Figure reproduced with permission from ref. 148. Copyright 2013 Wiley-VCH.

From a theoretical perspective, this system is interesting for two reasons: (1) for some numbers of disks (e.g., n = 10 and n = 12, Fig. 6a and b) the disks evolve into two distinct, stable, “polymorphic” structures; and (2) the dissipation rates (and entropy production) for each of these structures can be calculated exactly by solving the Navier–Stokes equations describing fluid flows. In other words, it is possible to study quantitatively whether and how dissipation dictates the selection of a particular dynamic structure, and whether MEP applies in this selection.

image file: c7cs00089h-f6.tif
Fig. 6 Polymorphic structures observed for (a) n = 10 and (b) n = 12 rotating particles in experiments (black-and-white images) and in the simulations (color images). The particular experimental structures here were obtained at ω = 500 rpm in a 3[thin space (1/6-em)]:[thin space (1/6-em)]1 w/w mixture of diethylene glycol and water (Re ∼ 0.52). Scale bar = 1 cm and is the same for all experimental images. (c) Probabilities of occurrence of various polymorphs plotted as a function of the calculated values of the difference in their dissipation rates, Δε. Markers are based on experiment, lines are based on eqn (3) and (4) in the main text. Figure adapted with permission from ref. 148. Copyright 2013 Wiley-VCH.

In our recent work,148 we performed a series of experiments in which we observed how many times each of the structures shown in Fig. 6a and b was observed under different experimental conditions – by repeating the experiments hundreds of times for each condition, we were able to estimate the probability of occurrence of the polymorphs. For n = 10, the structure with two disks in the center, {10,2}, was more probable than that with three disks, {10,3} (i.e., P{10,2} > P{10,3}). For n = 12, the {12,3} state was realized more often than {12,4} (i.e., P{12,3} > P{12,4}). Then, for each of the conditions we calculated the dissipation rates, ε, to ultimately relate them to probabilities, P(ε), akin to energies being related to probabilities via the Boltzmann criterion in equilibrium systems. The calculation of the dissipation rates required solving the Navier–Stokes equations with moving boundary conditions.149 These calculations provided the distribution of velocities in the fluid. Using the Cartesian components ux, uy, and uz of the velocities, the so-called viscous dissipation function150 was then calculated,

image file: c7cs00089h-t2.tif(1)
Integration of this function over the entire volume of the fluid gives the dissipation rate and entropy production:
image file: c7cs00089h-t3.tif(2)

Remarkably, we found that within each of the n = 10 and n = 12 pairs, the polymorphs occurring more frequently (i.e., {10,2} and {12,3}) have lower dissipation rates and the probabilities of occurrence decrease (exponentially) with increasing dissipation rates (Fig. 6c):

image file: c7cs00089h-t4.tif(3)
image file: c7cs00089h-t5.tif(4)
In these expressions, superscripts “high” and “low” denote, respectively, the states observed with higher and lower probabilities, Cn is a constant, and Δε is the difference in the polymorph's dissipation rates. Moreover, additional calculations revealed that energies of the polymorphs (potential, U, kinetic, K, total, E) are essentially equal meaning that energies are irrelevant in the system “choosing” a particular structure.

In the context of our discussion of DySA, these results provide a counterexample to MEP – and thus disprove it as a “general rule”. Specifically, this particular system does not always evolve into the least dissipative structure minimizing entropy production, and the more dissipative alternatives are also observed, albeit with probability exponentially decreasing with increasing dissipation rate. Interestingly, eqn (3) and (4) show an interesting asymptotic behavior, whereby as the dissipation difference Δε between competing structures becomes infinite, the probability of the more frequently realized, low-dissipation structure tends to unity and that of the less frequently observed, high-dissipation structure tends to zero – that is, when Δε → ∞, Phigh = 1 and Plow = 0. In other words, the system will choose the minimally dissipative structure (as prescribed by MEP) only if other alternatives have unrealistically high dissipation rates. Also, regarding the functional form of eqn (3) and (4), the presence of Δε in the exponential's denominator hints that dissipation in non-equilibrium systems might play a role analogous to temperature in equilibrium systems (for which P ∼ exp(−E/kT)). This would, in turn, imply that non-equilibrium trajectories visiting a steady-state are not determined by random collisions between the system and the thermal bath, but rather by the ability to dissipate energy to the surroundings in order to reach the ordered state. This line of reasoning also suggests that the probabilities of observed structures reflect the system's phase space dynamics57,151–155 and the statistics of non-equilibrium paths leading to specific assemblies.

The ideas of phase-space dynamics and paths traced by the assembling particles have provided the basis for the recent study by Szleifer and co-workers156 who sought a relationship between the so-called Kolomogorov-Sinai, KS, dynamical entropy and energy dissipation during non-equilibrium self-assembly. KS entropies are not synonymous with traditional thermodynamic entropies measuring the availability of microstates – instead, they measure the degree of temporal order in system's dynamics such that more disordered dynamics have a larger KS entropy and the evolution of nearby trajectories is predictable over a shorter timescale. The interesting aspect of Szleifer's study is that KS entropy appears to be linearly proportional to the energy dissipated from the system to the thermal bath acting as an energy sink. The constant of proportionality in this relation is the characteristic timescale over which dissipation occurs.

Around the same time as Szleifer, England157 took a different and quite promising approach to trajectories between non-equilibrium states, effectively linking the concept of dissipation with that of irreversibility. In brief, he showed that the more irreversible a spontaneous process, the greater the minimum entropy this process produces158 – that is, more irreversible processes are more dissipative and energetically wasteful. England pointed out that this concept can be relevant to DySA in predicting that structures built with the most expenditure of dissipated energy should be the most stable/robust (since they were built in the most irreversible fashion) and hardest for the thermal fluctuations to disassemble into isolated components. Continuing this line of thought, it might also be possible to estimate the lifetime of the assembly based on how much dissipation it “costs” to be built. For more discussion of these fascinating concepts, the Reader is directed to Prof. England's own review in this Special Issue.

As evidenced from the above examples, recent years have brought some fresh ideas about theory of non-equilibrium self-assembly. It seems to us that we are finally collectively “self-assembling” around the right set of concepts – e.g., the rules for structure evolution (England) and selection (Grzybowski) based on dissipation rates, or measures of characteristic times inherent to dynamic systems (Szleifer). It appears, however, that future prospects are largely dependent on the accessibility of experimental systems on which these ideas could be tested. Fortunately, even without the grand theory in place, DySA systems can be synthesized in the laboratory based on a set of heuristic design rules to which we now turn.

3.2. The heuristics of DySA design and illustrative examples

3.2.1. Design considerations. In our own practice of designing DySA systems, we have generally followed three heuristic rules: (1) the interactions acting in the system cannot be either all repulsive or all attractive. If there are only repulsions, the particles will never aggregate; if there are only attractions, the particles will simply clump together and will not be dynamic and capable of transitioning to other steady-state structures. (2) At least one type of interactions operative in the system must be responsive to the flux of externally delivered energy – otherwise, the system would be completely closed to the environment and the assembly process would be an equilibrium one. (3) The repulsive and attractive interactions should be of similar magnitudes to “balance” one another in the steady-state. This requirement implies that one needs to consider how the interactions scale with the sizes of the assembling objects and with the distance between them. For example, consider large, millimeter-sized superparamagnetic particles of which some are covered with self-assembled monolayers, SAMs, of positively charged ligands, and some with monolayers of negatively charged ligands (Fig. 7). When magnetic dipoles are induced in the particles by an external magnet (say, changing direction with time so that a dynamic situation is established), the magnitude of these interactions will be orders of magnitude larger than that of electrostatic forces (be it “+ +” or “− −” repulsions or “+ −” attractions) given that each particle presents only femtomoles of charged ligands (typical ligand density in SAMs is ∼1014 cm−2; see ref. 103 and 104). Under these circumstances, the particles will likely form chains typical of assemblies held up by dipolar forces alone.58 However, if the particles are made much smaller, the relative strengths of electrostatic forces due to surface ligands (scaling with particle's surface area) will increase compared to the strength of dipolar interactions (scaling with particle's volume). When these forces are commensurate, electrostatics will strive to assemble the particles into ionic-like crystals whereas the magnetic forces will still strive to form chain like structures – without actually performing this experiment, the exact outcomes are hard to predict but one might reasonably hypothesize that the assemblies would be anisotropic, tubular crystals.
image file: c7cs00089h-f7.tif
Fig. 7 A hypothetical modality of DySA in which interaction between induced dipoles (here, changing direction over time) competes with electrostatic interactions. (top scheme) When supraparamagnetic particles are large, magnetics alone dominates DySA. (bottom scheme) When the particles are small, the magnetic and electrostatic forces are of comparable magnitudes.

With these heuristics in place, one might consider many types of interactions that can be altered by external stimuli and thus provide the basis for DySA – since we described these interactions in detail our previous reviews57–59 we will focus our discussion here on those that have been used most often and also most recently.

3.2.2. DySA driven by light. At molecular scales, suitable dynamic interactions can originate from the so-called molecular switches – that is, molecules that change their conformations and/or properties reversibly upon light irradiation, electric current, pH, etc. Of much practical value to DySA are switches responsive to light, which is an impulse that can be delivered rapidly and, if desired, only to select locations within the system. Molecules containing azobenzene units159 are particularly attractive because one of the isomers, trans, has no dipole moment, whereas the other, cis, isomer – obtained under UV irradiation – has a large dipole moment of ∼3.0 Debye160 (Fig. 8a). In this way, irradiation with UV can induce dipole–dipole interactions between the azobenzenes or larger objects decorated with azobenzenes. These interactions persist as long as UV irradiation continues – when it ceases, the azobenzenes spontaneously return to the trans isomer and the dipole moment vanishes. This strategy has been used originally by us to drive DySA of nanoparticles into metastable crystals65 (Fig. 8b). When DySA was performed in a gel matrix,161 the aggregation of the nanoparticles over irradiated regions caused color change therein (by red-shifting of the surface plasmon resonance) effectively allowing for writing information/images into the material (Fig. 8c). When the irradiation ceased, the nanoparticles disassembled and the images self-erased at timescales regulated by the concentration of light-switchable units on the particles' surfaces. This modality of DySA was later creatively extended by the Klajn group who prepared gold nanoparticles covered with substituted azobenzenes switchable at two different wavelengths, thus allowing for selective particle assembly.162,163 Ai et al. used nanocrystals of copper covered with azobenzenes as switchable building blocks from which either nanoribbons or spheres could be dynamically assembled and interconverted (Fig. 8d).164 Huskens and co-workers165 used host–guest complexation between cucurbit[8]uril, a redox active methyl viologen polymer, and molecules functionalized with azobenzene units to drive the assembly and disassembly of the so-called supramolecular nanoparticles. In this case, the assembly was observed only when the azobenzenes were in the trans form and the methyl viologens were oxidized, effectively making the assembly process a mimic of a supramolecular AND logic gate. For many years, azobenzenes have also been used as switches controlling the self-assembly of micellar and vesicular assemblies.166 For instance, Liu and Jiang demonstrated167 the light-driven self-assembly of micelles from copolymers decorated with azobenzenes. Once assembled, the polymers could be crosslinked making these assemblies permanent. More recently, Yan and Huang synthesized168 an intricate system in which azobenzene-decorated surfactants complex with β-cyclodextrins to form vesicles which, upon UV irradiation develop thin cilia akin to those observed in bacteria (Fig. 8e). The remarkable feature of this system is that when the vesicles were loaded with a doxorubicin anticancer drug, it could be controllably released from the “leaky” cilia regions. This process was completely under optical control in the sense that when irradiated with visible light, the cilia withdrew.
image file: c7cs00089h-f8.tif
Fig. 8 Light-controlled DySA based on azobenzene switches. (a) Scheme of an azobenzene switch in trans (top) and cis (bottom) conformations. The cis form has a dipole moment of ∼3 D. (b) Schemes of nanoparticles covered with azobenzene-terminated ligands and interacting via light-induced dipoles (when the azobenzenes are in the cis form). The electron-microscopy images are of crystals formed by the particles. (c) When light-induced DySA takes place in the gel, the aggregating particles change color (due to surface-plasmon-resonance). This allows for writing and erasing various images into the nanoparticle-based “paper”. (d) Electron-microscopy images illustrating the time evolution of Cu nanoclusters decorated with photoresponsive azobenzene-based ligands. Upon UV irradiation, the morphology of the assemblies changes from nanoribbons to nanospheres. (e) Scheme and experimental images of light-triggered drug release from vesicles (made of C4AG@2β-cyclodextrins (CD)) which upon UV-irradiation develop bacteria-like cilia. Figures adapted from (a) ref. 169, copyright 2010 IUPAC, (b) from ref. 170 with permission from the Royal Society of Chemistry (scheme) and ref. 65 (electron microscopy pictures), copyright 2007 National Academy of Sciences, (c) ref. 161, copyright 2009 Wiley-VCH, (d) ref. 164, copyright 2016 American Chemical Society, and (e) ref. 168, copyright 2014 American Chemical Society.

Another class of useful switches, recently reviewed by Klajn, are spiropyrans171 in which ring opening creates “+” and “−” charges in the so-called merocyanine form (Fig. 9a). In one of the early demonstrations,172 this light-induced creation of charge was used to control adsorption and release of amino-acids onto gold nanoparticles covered with spiropyran ligands (Fig. 9b). In another delivery system, block copolymers incorporating spiropyrans formed light-switchable micelles which, under irradiation with UV released the doxorubicin drug.173 When tethered onto gold particles,174 spiropyran switches were able to guide particles' DySa into dynamic structures akin to those formed using azobenzenes (cf. above). Subsequently, amphiphilic particles covered with mixed monolayers of poly(ethylene glycols) and spiropyrans were shown175 to dynamically self-assemble into oligomers that exhibited switchable plasmonic coupling and tunable surface-enhanced Raman scattering (SERS) (Fig. 9c). Spiropyrans have also been used to drive the assembly of Janus particles.176 These particles featured a Pt domain that catalyzed the decomposition of hydrogen peroxide causing the particles to move. The role of the spiropyrans was – under UV irradiation – to drive the assembly of individual motors. These motor aggregates exhibited different motility patterns but could be reverted to “mono-motors” when exposed to green light (Fig. 9d).

image file: c7cs00089h-f9.tif
Fig. 9 Light-controlled DySA based on spiropyran switches. (a) Scheme illustrating reversible transformations between the four states of a spiropyran switch: spiropyran (SP) 1, merocyanine (MC) 2, protonated merocyanine (MCH+) 3, and protonated spiropyran (SPH+) 4 (it is also possible that the additional proton resides on the nitro group or on the spiro O atom177). Reproduced from ref. 171 with permission from The Royal Society of Chemistry. (b) Scheme of a delivery system in which the adsorption/release of the cargo (here, amino acids) is controlled by the charge state of spiropyran ligands tethered onto a gold nanoparticle. Figure inspired by ref. 172. Copyright 2003 American Chemical Society. (c) Scheme of light-induced self-assembly/disassembly processes of nanoparticles coated with a mixture of hydrophilic poly(ethylene glycol) and hydrophobic, photoresponsive polymethacrylate containing spiropyran units. Reversible AuNP aggregates exhibit switchable plasmonic properties useful in tuning surface-enhanced Raman scattering. Electron-microscopy images show the transitions upon UV (1 to 2) and then visible light irradiation (2 to 3). Adapted with permission from ref. 175. Copyright 2015 American Chemical Society. (d) SiO2–Pt Janus-particle catalytic micromotors functionalized with spiropyran moieties on the SiO2 parts exhibit autonomous self-propulsion and can dynamically assemble into motor clusters. This assembly is driven by UV-induced electrostatic attractions and π–π stacking between merocyanine units. Reproduced with permission from ref. 175. Copyright 2015 American Chemical Society. (e) Electron-microscopy image (1) of a polymeric colloid housing a hematite cube (darker upper portion). Such composite particles self-propel in the presence of hydrogen peroxide fuel and upon blue-light illumination. Under such conditions, dynamic, “living” crystals (2) are formed. After blue light is turned off for 10 s (3) the structures melt by thermal diffusion. Time evolution of clusters is shown in (4). Scale bars correspond to 11 μm in (1) and 10 μm in (2) to (4). Adapted from ref. 16 with permission from AAAS.

An interesting form of light-switching – one based on an inorganic material – has been demonstrated by Palacci et al.16 They used polymeric colloids loaded with hematite. Under blue light irradiation, these particles assembled into “living crystals” which could spontaneously break, explode, and reform in different locations (Fig. 9e). This system was powered by light, causing the decomposition of the H2O2 “fuel” at the surface of hematite grains, creating chemical gradients and osmotic flows.

3.2.3. DySA driven by magnetic fields. In Section 3.1, we discussed a prototypical system in which the DySa was powered by magnetic field, causing the rotation of magnetic spinners and establishing dynamic, repulsive interactions. In its various configurations, this system exhibited a multitude of DySa modalities, including chiral recognition (when the spinning particles were chiral13), formation of “atom-like” structures,139 assembly in 3D via both in-plane and out-of-plane hydrodynamic forces,143 and more (Fig. 10).12,13,140–142,144,178
image file: c7cs00089h-f10.tif
Fig. 10 Magnetohydrodynamic DySA of millimeter-sized magnetic particles rotating at a fluid–air interface. (a) As the particles begin to rotate, the vortex–vortex repulsions push them apart. When these repulsions are balanced by a confining magnetic potential, dynamic, open-lattice structures emerge. For most particle numbers, the assemblies are stable in time; for some (e.g., n = 19), the structures interconvert with time. Images are reproduced from ref. 12, with permission from Macmillan Publishers Ltd: Nature, copyright 2000, ref. 140, copyright 2001 American Chemical Society and ref. 147 with permission from The Royal Society of Chemistry. (b) When the particles are chiral (in 2D plane of the interface), their interactions are chirality-specific. As a result, particles of one chirality (here, R) form dimers, while the others (S) repel one another. Images reproduced from ref. 13 with permission from AAAS. (c) Scheme of dynamic vortex–vortex interactions between particles rotating at two proximal, parallel interfaces. Since these interactions are repulsive, the structures at each plane are rotated with respect to one another. The pairs of numbers above experimental images give the number of particles at each interface. Reproduced with permission from ref. 143. Copyright 2002 American Chemical Society. (d) Fusion of two macroscopic “artificial atoms” of rotating disks into an “artificial molecule”. The smaller “atom” is composed of one disk 2.08 mm in diameter, and seven disks 1.27 mm in diameter; the larger atom has one 2.42 mm disk and ten 1.27 mm disks. The “atoms” are initially prepared in two separate energy minima created by field concentrators above the plane of the interface, and are “reacted” by moving the concentrators towards each other. Reproduced with permission from ref. 140. Copyright 2001 American Chemical Society. (e) Examples of self-assembling fluidic machines in which the magnetic gears (black) are powered by an external rotating magnet and run around nonmagnetic tracks (red) or power other nonmagnetic gears (purple). All components are held together by capillary forces. Reproduced with permission from ref. 178. Copyright 2003 American Chemical Society.

Snezhko and Aranson179 used much smaller ferromagnetic colloids and also introduced time-varying magnetic fields acting perpendicular to a liquid–liquid interface at which the particles were placed. These alternating fields “rocked” the chains of magnetic particles (thus causing the deformation of the interface), and simultaneously excited hydrodynamic streaming flows. The combination of these effects led to the formation of various dynamic structures, including individual asters, arrays of such asters, or crescent-shaped assemblies (Fig. 11a). Interestingly, when an additional field in the plane of the interface was applied, the asters could be made to open up and to engulf larger, non-magnetic particles (Fig. 11b). In later work,180 the same group investigated periodic forcing by an in-plane magnetic field. Under these circumstances, and depending on the forcing frequency, the particles formed either pulsating clusters, or one-particle-thick chains, or dynamic arrays of spinners (self-assembled short chains) rotating in either direction.

image file: c7cs00089h-f11.tif
Fig. 11 (a) “Aster” structures formed at a liquid/liquid interface by ferromagnetic colloids subject to an alternating magnetic field applied perpendicular to the interface between the liquids. (b) At certain field arrangements, the asters can open up into a crescent-shaped structures. (c) When non-magnetic particles are also present, asters can open up and then close to engulf these particles. (d) Examples of open-lattice, dynamic structures formed in a microfluidic channel by the balance between lift and viscous-disturbance forces. Panels (a–c) reprinted with permission from Macmillan Publishers Ltd: Nat. Mater., from ref. 179, copyright 2011, and panel (d) from ref. 184, copyright 2010 National Academy of Sciences.

These examples illustrate, on one hand, the flexibility with which magnetic fields can be arranged to power various modalities of DySA and, on the other hand, the limitation of magnetics to particles (nano- to macroscopic) rather than molecules. Unlike strong light-induced dipole moments in molecular switches (cf. Section 3.2.2), magnetic moments of individual molecules at ambient temperatures are too small to overcome thermal noise and thus be useful in self-assembly schemes.

3.2.4. DySA controlled by flow fields. In the examples of magnetic spinners or Aranson's asters, the individual particles set up local flows around themselves, which then mediate dynamic interparticle interactions. In some cases, the global flows – that is, flows at the level of the entire system – can couple to the dynamics of individual parts (for example bubbles181 or droplets182,183) to arrange these parts in steady-state structures. In one example, Stone, Di Carlo and co-workers184 passed microscopic polymeric particles through a microfluidic channel and observed that these particles formed ordered, steady-state arrangements (Fig. 11c) whose dimensions could be controlled by the flow parameters. They explained this dynamic organization by an interplay between inertial lift forces (due to gradients of shear in a channel flow) that tend to keep particles at finite separations and repulsive interparticle forces due to viscous disturbance flows induced by particles' rotations. Another type of flow used to control DySA has been the well-known Benard–Marangoni convection185 in which a thin layer of heated or evaporating fluid spontaneously develops convection rolls of alternating flow chirality. Wang et al. used such convective flows to drive the assembly of zeolite nanoparticles into cellular surface micropatterns.186
3.2.5. Chemically powered DySA. In living systems, DySA is not effected by external fields but rather by chemical “signals” between the interacting parts. At microscopic and larger scales, such “communication” can be directional due to spatial gradients of signaling chemicals (e.g., of biosurfactants in bacterial swarming). Swarm-like behaviors have been recreated in assemblies of segmented Pt–Au nanorods powered by the catalytic decomposition of H2O2 and communicating through the gradients of protons and counterions in the surrounding solution.187 Another swarming DySA system used gel particles loaded with camphor (a.k.a. camphor boats188) and placed at a water/air interface. When camphor diffused out of the particles, it acted as a surfactant creating surface tension gradients and convective rolls in the fluid. These flows effectively translated into dynamic interactions between the particles that not only kept the particles at steady-state positions but also caused them to move collectively, including situations when smaller particles flocked and followed a larger-particle “leader” (Fig. 12a).189 In yet another gradient-based DySA system, the group of Huskens190 prepared an array of surface bound β-cyclodextrin receptors that could bind either a rhodamine derivative or an electroactive, ferrocene carboxylic acid competitor (Fig. 12b). When the array was flanked by two electrodes, electrochemical generation and annihilation of the electroactive competitor established its concentration gradient between the electrodes. This gradient was dissipative in the sense that it persisted only as long as the electrochemical energy was consumed. The gradient also affected the assembly of rhodamine ligands and cyclodextrin receptors and translated into their supramolecular surface gradient.
image file: c7cs00089h-f12.tif
Fig. 12 (a) A collection of swarming gel pieces loaded with camphor (a.k.a. camphor boats). The large, v-shaped particle moves spiked-end forward; the smaller particles flock behind the large leader. Reproduced with permission from ref. 189. Copyright 2011 American Chemical Society. (b) Husken's supramolecular system in which electrochemical generation and annihilation of an electroactive competitor (denoted by FcCA) translates into the dynamic surface gradient of binding events. This competition manifests itself by inhomogeneous fluorescence over the spaces between the electrodes. Adapted with permission from ref. 190. Copyright 2015 Wiley-VCH.

4. Intermezzo

As the above examples illustrate, skillful use of optical, magnetic, or flow fields and of concentration gradients allows driving objects of (macro)molecular to macroscopic sizes into various ordered assemblies thriving in steady, non-equilibrium states. This variety certainly attests the progress made by DySA in little over a decade of research. On the other hand, one would be hard pressed to identify any of the above realizations as practically useful, either by themselves or as parts of larger systems. Interestingly, the Web of Science query reveals that the number of papers on DySA is decreasing in recent years which, we think, reflects precisely the lack of any practically relevant function from which applications might (one day) emerge. In the next part of this review, we therefore focus on the recent (and very recent) examples of DySA that finally started to appear, and in which dynamic ordering is accompanied by at least rudimentary functionality.

5. Emerging examples of functional DySA

For DySA to be functional, self-assembly must be coupled to some other process one wishes to control or direct. The first examples of such coupling started to appear around 2010 when our group demonstrated two systems based on gold nanoparticles, AuNPs, coupled to, respectively, a chemical oscillator40 and a catalytic reaction.18 In the first of these systems, AuNPs were covered with 2-fluoro para-mercatophenol ligands and were coupled to a chemical oscillator which rhythmically changed the solution pH between ∼6.8 and ∼9.3. At low pH, the ligands were protonated and aggregated; at high pH, they deprotonated and the electrostatic repulsions caused particle disaggregation. In effect, the particles were oscillating between aggregated and dispersed states with a frequency equal to that of the entraining oscillator (Fig. 13a).
image file: c7cs00089h-f13.tif
Fig. 13 (a) As the methylene glycol–sulfite–gluconolactone chemical oscillator periodically changes pH between 6.8 and 9.3, the 2-fluoro para-mercatophenol ligands on gold nanoparticles become, respectively, protonated and deprotonated. These changes in the particles' surface charge translate into their rhythmic assembly and disassembly. Figure based on ref. 40. Copyright 2011 Wiley-VCH. (b) Gold nanoparticles covered with photoactive ligands catalyze hydrosilylation reaction when dispersed but lose catalytic activity when aggregated upon UV exposure. Reprinted with permission from ref. 18. Copyright 2010 American Chemical Society. (c) When gold nanoparticles covered with azobenzene ligands assemble under UV light, they form crystals in whose voids (“dynamic flasks”) polar molecules are trapped and can undergo chemical reactions. The molecules are liberated when the crystals disassemble upon irradiation with visible light. Reproduced with permission from Macmillan Publishers Ltd: Nat. Nanotechnol., from ref. 27, copyright 2016.

In the second system,18 AuNPs were covered with a mixed monolayer comprising alkane thiols terminated in photoswitchable azobenzene units and “background” alkyl amine ligands. The role of the azobenzene units was to mediate the light-induced assembly of the nanoparticles (cf. Section 3.2.2) whereas the amine ligands stabilized the nanoparticles but, by virtue of their weaker binding, did not eliminate gold's catalytic activity. In the dispersed state, the NPs presented large surface area and were able to catalyze reactions such as hydrosilylation of 4-methoxybenzaldehyde. Under UV irradiation, however, the particles assembled into supraspherical aggregates of much lower surface area and the catalysis effectively ceased. The catalytic activity was switched “on” and “off” by, respectively, UV and Vis irradiation (Fig. 13b).

In a creative modification of light-driven DySA of AuNPs, Klajn's group made use of the voids between the assembled particles to selectively trap organic molecules and to enhance the rates of reactions in which these molecules partake.27 The authors noticed that when the azobenzene moieties of alkane thiolates stabilizing the particles and driving the DySA process (cf. Section 3.2.2) isomerize to the dipolar cis form, they make the particle surfaces in the assembling aggregates hydrophobic and capable of adsorbing small, polar molecules from the surrounding non-polar solvent (Fig. 13c). Based on this observation, they were able to concentrate such polar solutes (predominantly those acting as hydrogen bond donors or those capable of π–π stacking interactions) into the interparticle voids – which they termed “dynamic nanoflasks” – and then release them when the particles were dispersed under irradiation with visible light. Remarkably, when the on-particle monolayers contained chiral ligands, the trapping could be made enantioselective. Also, simultaneous incorporation of pairs of substrate molecules into the “dynamic nanoflasks” increased their local concentrations and resulted in reaction rates increasing by up to two orders of magnitude. Last but not least, the “nanoflasks” appeared to preorganize certain ligands altering the solution-observed ratios of thermodynamic-to-kinetic products. These examples are, to our knowledge, the first successful demonstration of DySA controlling chemical reactivity.

However, as pointed out by Eelkema, van Esch and co-workers,21 DySA based on nanoparticles is often limited to a narrow range of working conditions (e.g., solvents in which the NPs are stable) and can require external signals that may be harmful to living systems. The pioneering example of how DySA can be extended to all-macromolecular structures comes from the Otto group.191,192 The building blocks of their system were short peptides with aromatic dithiol groups capable of forming disulphide linkages and assembling first into trimeric or tetrameric cyclic aggregates and then into stacked-up “nanopillars” made of larger macrocycles such as hexamers and heptamers (Fig. 14a). Importantly, both the macrocycles and the “nanopillars” form at appreciable rates only when the sample is mechanically agitated. The role of agitation is to create new nucleation sites at which trimers and tetramers can be templated to continue pillar's growth. One of the intriguing aspects of these experiments is that depending on the agitation conditions, certain macrocycles can be favored over others (e.g., hexamer formation dominates upon shaking and heptamer formation upon stirring) and, even if both are initially present in solution, can out-compete the rivalling “species” to replicate only select structures (e.g., heptameric fibers generally out-compete hexameric ones).

image file: c7cs00089h-f14.tif
Fig. 14 DySA and reaction cycles. (a) Scheme illustrating the key steps in the formation of dynamic fibers from thiol-functionalized peptide building blocks. Assembly is driven by components' stacking; disassembly is driven by mechanical agitation. (b) Actin filaments and microtubules are examples of biological fibers kept at non-equilibrium states by the competition between fiber elongation and disassembly. (c) A general scheme of a futile cycle in which “opposing” assembly/disassembly processes are powered by chemical reactions. (d) A specific implementation of such a futile cycle as described by Eelkema, van Esch and co-workers in ref. 21. Assembly occurs when the molecular building blocks lose their negative charges; when charge is regenerated by ester hydrolysis, the fibrous assemblies disintegrate. (e) Another example of a futile cycle in which naphthalene diimide derivative (NDPA) assemblies adopt opposite helical conformations (P and M helices) depending on the enzymes and the chemical fuels used. Scheme adapted with permission from ref. 49. Copyright 2017 Wiley-VCH.

While analogies to biological replicators are obvious (and exciting), the “biomimicry” of Otto's system is limited by its reliance of external mechanical agitation – in contrast, in living cells, the assembly of dynamic, supramolecular structures such as actin filaments or microtubules193 is powered not by external fields but by other, high-energy molecules (e.g., GTP or ATP). Such supramolecular structures are maintained in the non-equilibrium states by a balance between reaction(s) driving assembly and reaction(s) driving disassembly (Fig. 14b). Conceptually, this situation corresponds to a reaction cycle shown in Fig. 14c. We point out that although many similar wirings of (bio)chemical reactions are known (the so-called futile cycles194), the distinguishing feature of cycles relevant to DySA is that “powering” reactions (side red arrows) couple to and control the process of structure assembly/disassembly (blue arrows). Achieving such coupling has proven difficult and it has only been in the last two years that first examples emerged.

Specifically, Eelkema, van Esch and co-workers21,195 demonstrated DySA of dynamically gelating supramolecular fibers akin to microtubules (Fig. 14d). The building blocks of these fibers were gelator molecules containing two or three carboxylic acid groups. Above the acid's pKa ∼ 4.5, these groups were negatively charged and the “gelators” remained unaggregated on account of mutual electrostatic repulsions. However, when a chemical “fuel” – in the form of dimethyl sulfate, DMS – was added, it converted the carboxylic groups into methyl esters. This “activating” reaction removed the repulsive negative charges and the gelators started forming fibers, ca. 10 nm in diameter and over one micron in length. Under the basic conditions of the experiment (pH above ca. 9), this assembly process was countered by a “deactivating” reaction, which hydrolyzed the methyl esters back to charged carboxylic acids, causing fibers' disassembly. The net result of these processes was that the reaction mixture first gelated (in a matter of minutes) but then slowly reverted to the liquid state, with the time constant of the disassembly process being controlled by various experimental parameters. The authors pointed out that the key prerequisite for the formation of the transient, fibrillar structures is that the activating and deactivating reactions within the cycle must run along different paths – if the paths were identical, adding that a reactant would merely shift the chemical equilibrium, as is typically observed in triggered (as opposed to dynamic) self-assembly processes.196,197

An important extension of these concepts has been very recently demonstrated by George and co-workers49 who synthesized transient assemblies with helicity switchable by ATP and ADP fuels. At the heart of this work lies an observation that certain naphthalene diimide derivatives functionalized with zinc(II) dipicolylethylenediamine phosphate receptors (abbreviated as NDPA in Fig. 14e) can assemble into fibers whose helicity is adenosine-phosphate-selective – specifically, a P-helix forms upon binding of ATP and an M-helix upon binding with ADP. These conformations are highly dynamic and can adapt to the ATP/ADP fuels. In their system, the authors sought to design a reaction cycle that would “switch” between the fuels and thus dynamically interconvert the P and M helices. This was cleverly accomplished by using two complementary phosphoryl transferase enzymes, hexokinase and creatine phosphokinase. The former transfers a phosphate group from ATP to glucose to yield glucose-6-phosphate and ADP. The latter transfers phosphate from a sacrificial reagent phosphocreatine to ADP, producing ATP and creatine as a side product. When implemented, this system of reactions was indeed capable of dynamic stereomutation on timescales of few hundred seconds which could further be adjusted by changing the enzyme concentrations.

The discussion of recent advances in functional dynamic systems would not be complete without mentioning molecular machines. While the details on their design will be more eloquently covered by Prof. Stoddard in his contribution to this issue, we would like to focus on one example from Leigh's group, where the machines achieved a remarkable feat of acting as a molecular assembly line.28 In their design, a molecular strand had three peptides (in protected forms) attached to it via weak phenolic ester linkages. Upon a click reaction, a macrocyclic ring was threaded onto the peptide-bearing strand and a terminal stopper/blocking group as schematically shown in Fig. 15a. The ring was subsequently decorated with a reactive “side arm” containing a protected cysteine derivative (Fig. 15b). At this stage, the assembly was stable as the ring could not move past or react with the bulky groups flanking it. The machine was put in action when the cysteine moiety and the amino acids on the template were deprotected. The free thiolate residue of the cysteine underwent a transacylation reaction with the first amino acid phenolic ester to form a thioester (Fig. 15c) – importantly, this thioester reacted further, via native chemical ligation, to transfer the amino acid onto the reactive arm of the machine, simultaneously regenerating the catalytic thiolate group, ready for the cleavage and transfer of further building blocks (Fig. 15d). This sequence of steps was then repeated with the second and third amino acids, until the macrocycle detached from the strand with the newly formed, full-length peptide attached (Fig. 15e and f).

image file: c7cs00089h-f15.tif
Fig. 15 An artificial machine for sequence-specific peptide synthesis. (a) The rotaxane machine is assembled by click chemistry between terminal azide and ethyne groups, (b) is decorated with reactive “side arm,” and is activated by acidic cleavage of tert-butyloxycarbonyl (Boc) and trityl (Trt) protecting groups. Successive reactions (c and d) transfer the amino acid building blocks to the peptide-elongation site. The order of amino acids is dictated by the design of the thread. (e) Once the last amino acid present at the thread is transferred to the newly synthetized oligopeptide, the macrocycle dethreads from the strand. (f) The final product is released from the macrocycle by hydrolysis. Figure inspired by ref. 28.

Although its function certainly appears “dynamic”, there is a major conceptual difference between this machine and the DySA cycles discussed earlier in this section. Whereas in the cycles the activating and deactivating reactions were operative simultaneously, the “inputs” and “outputs” of chemical energy in the rotaxane system are separated in time. First, energy is expended to assemble the machine which is then stable/trapped in the high-energy state. Then, the removal of the protecting groups removes the kinetic barrier and the reactions that ensue are all energetically downhill. In this sense, the system is not, per se, a demonstration of DySA but of a driven assembly followed by spontaneous relaxation. To make it a DySA, some other reactions would have to be coupled in to recover the used building blocks, reassemble the machine, and make it operate more than one cycle. We are sure that given the current interest in molecular machines, such demonstrations are forthcoming – though with systems of this level of chemical complexity, ensuring that all of the processes within the assembly–operation–disassembly–reassembly cycle would work without cross-reactivity conflicts will certainly be a hurdle to overcome.

6. Reaction compatibility and compartmentalization of functional DySA

As the molecular DySA systems become more complex, it will be increasingly more difficult to find suitable reactions that not only “fuel” the desired assembly processes but, at the same time, are chemically compatible with one another, avoiding cross-reactivity conflicts. For instance, DySA in which the assembly process is fueled by a reaction requiring water-free conditions while the disassembly step must proceed in an aqueous environment is clearly impossible in one phase. There are two strategies to avoid such problems: (1) by choosing compatible reactions, and (2) by performing different steps in different compartments. The first of these options benefits from decades of research on sequences of organic reactions that can be performed “one pot”, in the same reaction medium.198–201 Historically, the design of “one pot” sequences has relied on the experience (and intuition!) of chemists but it has recently been facilitated by computational analysis in which all participating chemicals are screened for the mutual compatibility of the functional groups they contain, the compatibility of reaction conditions and solvents used at different steps, and other factors (in total, several tens of thousands of cross-reactivity rules). As described in ref. 41 this approach was verified experimentally by “wiring up” individual steps into one-pot sequences (Fig. 16) ultimately leading to inhibitors of phosphoinositide 3-kinase delta (PI3Kδ), a key enzyme in the signaling pathway involved in airway inflammation.
image file: c7cs00089h-f16.tif
Fig. 16 Rewiring networks of individual reactions involving PI3Kδ inhibitors and closely related compounds. Literature-reported, individual reactions correspond to black arrows; 2-step one-pot sequences are represented by red arrows, 3-step sequences by blue arrows, and a 4-step sequence is denoted by a purple arrow. Numbers next to the arrows correspond to the yields achieved when the predicted one-pot reaction sequences were tested experimentally. Figure adapted with permission from ref. 41. Copyright 2012 Wiley-VCH.

The alternative to choosing compatible reactions is to conduct the incompatible ones in separate compartments – such a compartmentalization strategy is used widely in biological systems. Recent years have witnessed increased interest in constructing liquid compartments (micelles, vesicles, macroscopic droplets) supporting various non-equilibrium processes, often in the context of constructing cell-mimics (a.k.a. artificial cells202–204). Since such “non-equilibrium droplets” have been recently reviewed,31 we only narrate their key aspects relevant to DySA.

With the aim of mimicking the basic form of in-droplet “metabolism,” Leroux demonstrated205 non-equilibrium vesicles and liposomes encapsulating enzymes in their active forms and establishing concentration gradients to actively “pump” and “metabolize” molecules from their surroundings – in particular, toxic substances that could then be remedied. Another approach capitalized on the fact that if a vesicle supports a pH gradient, unionized compounds can diffuse into the vesicle but are ionized therein and trapped206 – this principle allowed, for example, for selective capture and degradation (by an encapsulated enzyme) of cyanide207 or organophosphorus agents.208 Selective membrane permeability and maintenance of concentration differences were also used to modulate reactivity of trapped molecules (e.g., peptides209).

An exciting form of compartmentalized DySA was realized in a system where a droplet was able – via its artificial “metabolism” combining catalysis and positive feedback – to completely autonomously synthesize its own components. In this system,210 a synthetic catalyst was embedded in a phospholipid membrane and was capable of making its own copies via copper-catalyzed click reaction (Fig. 17a and c). In addition, the same catalyst was able to generate the membrane's phospholipids from lysolipid building blocks (Fig. 17b and c). This sophisticated autocatalytic mechanism (Fig. 17c) transformed simpler, high-energy building blocks into new components of the membrane, such that its surface area grew and the volume of the enclosed vesicle increased (Fig. 17d).

image file: c7cs00089h-f17.tif
Fig. 17 (a) The copper complex catalyst makes its own copy via a click reaction involving three 1-azidododecane (“azide”) substrates and tripropargylamine (“alkyne scaffold”). This newly formed molecule is activated into a catalyst upon Cu(I) metalation. (b) The catalyst also makes new triazole phospholipid from 1-azidododecane (azide) and an alkyne modified lysolipid. (c) Scheme of the entire system whose ultimate role is to continuously generate a new phospholipid membrane from the available precursors. (d) Experimental realization of the system illustrating the growth of a vesicle driven by the synthesis of the membrane. Scale bar = 3 μm. Figure reproduced with permission from ref. 210. Copyright 2015 National Academy of Sciences.

Another example of a highly non-equilibrium compartment was recently demonstrated by Prins and co-workers.211 These authors studied vesicles formed by surfactants comprising a C16 chain and a 1,4,7-triazacyclononane·Zn2+ head group. This surfactant was chosen because the vesicles it formed could be stabilized by multivalent counterions such as ATP. The system was displaced away from equilibrium upon addition of potato apyrase enzyme rapidly hydrolyzing ATP into adenosine 5-monophosphate (AMP) and two molecules of orthophosphate Pi – when this occurred, the vesicles fell apart but could be reconstituted when fresh ATP was added. The function of the dynamic vesicles thus constructed was then coupled with a nucleophilic aromatic substitution reaction between two non-polar molecules (4-chloro-7-nitrobenzofurazan and 1-octanethiol). When the vesicles were in the assembled state, the reaction took place in the vesicle's non-polar bilayer; when the vesicles disintegrated, the reaction came to an almost complete halt. In effect, the authors were able to couple chemical reactivity to the transient state of a chemically powered DySA system.

Another class of dynamic processes involving liquid compartments is observed when an interfacial reaction generates additional surfactant species, such that the interfacial area initially increases until the droplet or vesicle breaks into smaller progenies. This self-division process has been powered by a range of reactions191,212,213 and used, for instance, to partition molecular cargos present in the original container.214 Recently, the process of self-division has been coupled to DNA amplification reaction within vesicles (Fig. 18a)215,216 allowing these vesicles to first divide and then grow, mimicking real self-replication. Moreover, Adamala and Szostak217 showed that vesicles supporting chemical reactions can both replicate and undergo basic Darwinian evolution in which they compete with each other for resources to ultimately ensure the “survival” of the fittest “species” (Fig. 18b).

image file: c7cs00089h-f18.tif
Fig. 18 (a) Scheme of a system in which a PCR reaction replicates DNA inside of a cationic vesicle, and then incorporates some of this DNA into the bilayer. The bilayer-entrapped DNA recruits additional building blocks V* which are, with the help of catalyst C, converted into new membrane components. Membrane growth results in budding off a new vesicle. Adapted with permission from Macmillan Publishers Ltd: Nat. Chem., from ref. 215, copyright 2011. (b) Scheme illustrating adaptive changes and competition between protocell vesicles driven by an encapsulated catalyst (dipeptide Ser-His). Catalytic reaction between substrates LeuNH2 and AcPheOEt generates dipeptide AcPheLeuNH2, which localizes to the bilayer membrane (1). In the presence of additional micelles, vesicles with AcPheLeuNH2 in the membrane (red) grow faster than vesicles without dipeptide (grey) (3). Without additional building blocks “red” vesicles grow at the expense of “grey” ones (2). Adapted with permission from Macmillan Publishers Ltd: Nat. Chem., from ref. 217, copyright 2013. (c and d) Maze solving by chemotactic droplets (here, 1 μL, 20% v/v HDA in DCM). In (c), the HDA/DCM droplet solves the maze without any detours. In (d), the droplet goes astray at two locations but ultimately corrects itself to find the shortest path leading to the maze's exit. Figure adapted with permission from ref. 218. Copyright 2010 American Chemical Society.

Last but not least, droplets have been constructed that exhibit various forms of taxis in response to outside signals altering droplet's interfacial properties. When the “signals” are chemical reactions, the droplets are chemotactic and even simple acid–base reactions can give rise to quite complex behaviors such as maze solving (Fig. 18c).218 When the surfactants covering the droplet are photoactive (e.g., surfactants based on azobenzenes,219 rotaxanes,220 or spiropyrans221), they can migrate along gradients of light intensity. Such tactic droplets are potentially interesting as active transporters within multicompartment, networked DySA systems.

7. System-wide communication modalities

As evidenced by the examples in the last two sections, we are finally gaining proficiency in both constructing various functional DySA systems and in localizing them into self-assembling and sometimes already dynamic compartments. The next step in the development of this field will be the ability to “wire” up many such processes/compartments together such that, as we envisioned in the Introduction, they could start serving as true non-equilibrium “assembly lines” channeling and processing matter (or information) in programmed ways. While we are not yet able to construct such networked systems we know they are, in principle, possible (vide living cells). In this light, we think that the time is ripe to consider the key challenge that lies upfront – namely, how will the components of these systems communicate with one another? How will they pass matter and/or information?

7.1. Active transport

The appealing feature of actively powered transport is that it can be directional and deliver the molecular “cargo” straight to the desired locations within the system. In biology, microtubules serve as directional rails along which kinesin and dynein motors shuttle vesicles and/or organelles from the cell periphery to the nucleus. Although this transport modality is directional and rapid (∼3 μm s−1), its main disadvantage is that it costs energy supplied by molecules such as ATP. In ref. 32 we estimated that if a cell wished to move all its components by such active means, it would have to spend more than half of its energetic resources on transportation alone. Additionally, systems such as microtubules/kinesins rely on precisely crafted ratcheting222–224/asymmetric energy landscapes which are hard to mimic with non-biological, (macro)molecular components. It has only been recently that first macromolecular systems capable of active transport of molecular or nanoparticle cargos over appreciable distances (few hundred nm) were demonstrated based on rigid DNA origami pseudo-rotaxanes.225 Motors based on concerted rotations of molecular switches have been shown to rotate macroscopic objects25 – it is worth emphasizing that in these and other similar systems individual molecules must act in synchrony since separately they are too weak to beat the effects of thermal noise.226 There are many more examples of self-propelled constructs at larger scales, although few have been shown to act as delivery vehicles that could be useful in the context of larger, “networked” systems. For a recent review of these motors – based on asymmetric particles,176,227,228 MOFs,229,230 red blood cells,231 and more – the reader is directed to a recent review.232 In addition, various types of tactic droplets have been reviewed by us in ref. 31.

7.2. Diffusive transport

Diffusive motions might appear chaotic and ineffective, but at small dimensions they can actually be faster than active transport. In addition, diffusion does not consume chemical energy and, instead, is powered by the omnipresent thermal noise. Diffusion gives rise to a flux, j, which is linearly proportional to the local concentration gradient, [J with combining right harpoon above (vector)]([r with combining right harpoon above (vector)],t) = −Dc([r with combining right harpoon above (vector)],t) where D is the diffusion coefficient, c is the concentration, ∇ is the gradient operator, and [r with combining right harpoon above (vector)] is the position vector. Since diffusion conserves the number of molecules, the net diffusive flux into any small element of space is balanced by the concentration change within this element, image file: c7cs00089h-t6.tif. By substituting the expression for the flux, we then obtain the diffusion equation, ∂c([r with combining right harpoon above (vector)],t)/∂t = D2c([r with combining right harpoon above (vector)],t). Introducing characteristic diffusion time, τ, and characteristic dimension, L, dimensional analysis233 allows us to approximate the terms of the diffusion equation as ∂c/∂tc/τ and D2c/∂x2Dc/L from which we obtain τL2/D. This result is important as it tells us that the typical time for diffusion to move an object over a given distance scales quadratically with this distance. For example, a typical protein moving inside of a bacterium or a mammalian cell (D ∼ 10−6–10−7 cm2 s−1[thin space (1/6-em)]234,235) will need only 0.01–0.1 s to diffuse over 1 μm, already 1–10 s to move over 10 μm, and as much as 104–105 s to move over 1 mm. Clearly, diffusion is not a way to transmit molecular signals over large/macroscopic distances. On the other hand, it has been shown236 that at very small distances (i.e., for very small L's), diffusion can actually be faster than other modes of molecular transportation, even those that are powered by molecular motors. For example, Fig. 19 plots the characteristic transport times of differently sized nanoobjects (say, proteins) moving through a medium whose properties are mimicking those of a cell interior. The colored curves correspond to the diffusive transport while the black curve corresponds to the active transport with constant speed (e.g., ∼3 μm s−1 as for vesicles being transported along microtubules237). As seen, for typical small objects/proteins, r < ∼4 nm, diffusion beats active transport (i.e., τdiff < τactive), provided that the characteristic travel distance is smaller than Lcrit ∼ 8 μm which, quite remarkably, corresponds to a typical radius of an eukaryotic cell. Indeed, detailed analysis in ref. 236 indicates that the sizes of living cells (both prokaryotic and eukaryotic) are such that diffusive transport is faster than the energetically costly active transport. From the viewpoint of systems’ design, diffusion can be a useful transport modality over small distances and for large diffusion coefficients (i.e., for small objects and for low-viscosity media236).
image file: c7cs00089h-f19.tif
Fig. 19 Calculated times, τ, needed to transport a “cargo” of a given radius, r = 3–10 nm, either by diffusion (green, red, blue, and yellow curves) or by active transport (black line) over a distance L and through a medium having diffusion coefficient similar to that of the cell interior. Provided that L < ∼8 μm, diffusion transports small molecules and typical macromolecules (of size up to 3–4 nm) faster than active transport. Figure reproduced with permission from ref. 236. Copyright 2013 American Chemical Society.

7.3. Coupling of diffusion with chemical reactions

In addition to considering distances over which molecules travel (as in the previous section), it is important to control the fashion and the quantity in which they arrive at their targets. Such control can be achieved by coupling diffusion with reaction(s), into what is called reaction-diffusion, RD, systems.32,52 In addition to the changes in local concentration due to diffusive motions, RD equations account for the creation or consumption of molecules taking the general form of ∂c([r with combining right harpoon above (vector)],t)/∂t = D2c([r with combining right harpoon above (vector)],t) + Ri({cj},t), where i denotes molecules of a specific type, {cj} is a set of concentrations on which reaction term Ri depends, and dependencies of cj on time and on position are omitted to simplify notation. Importantly, when the kinetic terms are nonlinear (e.g., autocatalytic as in Rici2), RD systems can exhibit a range of fascinating behaviors such as stationary Turing patterns238–241 of propagating chemical waves.242,243

Connecting with our discussion of DySA systems based on futile cycles (cf. Section 5 and Fig. 14 and 15), it is interesting to examine how biology uses the same architectures – arranged in series – to operate RD systems whose role is to amplify chemical signals propagating from the cell membrane to the nucleus. In these so-called signaling cascades (Fig. 20), signal transduction starts with the binding of a certain ligand molecule to its cognate membrane receptor. The receptor activated in this way in turn activates cytoplasmic signaling proteins that ultimately transmit the signal to the nucleus where they trigger cellular response (e.g., gene expression). This process relies on two forms of proteins that are interconverted by two types of enzymes of “opposing” activities, for instance, protein kinases phosphorylating other proteins (into phosphoproteins) and protein phosphatases responsible for dephosphorylation244 – the architecture of one such phosphorylation/dephosphorylation cycle is illustrated in the left portion of Fig. 20. Importantly, the kinases are localized almost exclusively in the cell membrane, whereas the phosphatases are typically distributed uniformly throughout the cytoplasm. As a result, the signal of phosphoproteins is attenuated as they diffuse toward the nucleus. At steady-state,245,246 the pertinent reaction-diffusion equation247 for such a process can be written as, D2P(x) − kP(x)P(x) = 0 where P(x) is the concentration of the phosphoprotein at rescaled location x (x = 0 corresponds to the membrane and x = 1 corresponds to the surface of the nucleus) and kP is the rate constant of dephosphorylation (usually well approximated as the first-order248). Solving this equation indicates that the phosphorylation signal (i) decays exponentially with the distance from the membrane and is only ∼10% of the original “strength” by the time it reaches the nucleus.248

image file: c7cs00089h-f20.tif
Fig. 20 Chemical signaling/communication via reaction “cascades”. (a) A cycle motif common in signaling pathways. Two enzymes of “opposing” activities cycle a signaling protein between active/phosphorylated and inactive/dephosphorylated forms. An orange ellipse denotes the phosphate group”. (b) Scheme of mitogen-activated protein (MAP) kinase cascade involving three phosphorylation/dephosphorylation cycles and collectively establishing the phosphoprotein gradient directed from the cell membrane towards cell nucleus. (c and d) Steady-state concentration profiles of the phosphorylated kinases. (c) The concentration profiles of a simplified model discussed in the main text. Near the nucleus, at x = 1, the concentration of MAPK-P is ca. three times that of MAPKKK-P. (d) A more sophisticated theoretical treatment (see ref. 247) predicts the concentration of MAPK-P at the nucleus surface ca. 20 times higher than that of MAPKKK-P. Figure reproduced with permission from ref. 32. Copyright 2010 Wiley-VCH.

Nature remedies this attenuation problem with a skillful use of the cascades of phosphorylation/dephosphorylation cycles along which the signal is “propagated”. A classic249 example is the so-called mitogen-activated protein kinase (MAPK) signaling cascade illustrated in the right portion of Fig. 20. Here, MAPKKK protein (a kinase of kinase MAPKK) becomes phosphorylated/activated by upstream receptor kinase in the cell membrane. This phosphorylated MAPKKK (MAPKKK-P) subsequently phosphorylates MAPKK (a kinase of MAPK) in the cytoplasm. In turn, the phosphorylated MAPKK (MAPKK-P) activates MAPK (MAP kinase) into MAPK-P which, finally, triggers a specific biological response (i.e., expression of specific genes). A system of steady-state reaction-diffusion equations describing this multistep process can be written as:247

D2PMAPKKK-P(x) − k1(x)PMAPKKK-P(x) = 0

D2PMAPKK-P(x) + k2(x)PMAPKKK-P(x) − k3(x)PMAPKK-P(x) = 0

D2PMAPK-P(x) + k4(x)PMAPKK-P(x) − k5(x)PMAPK-P(x) = 0
where, P's are the concentration of the specific proteins, the terms involving rate constants k1, k3 and k5 describe the dephosphorylation of the respective species MAPKKK-P, MAPKK-P, and MAPK-P in the cytoplasm, while the terms involving k2 and k4 refer to the generation of MAPKK-P and MAPK-P by their upstream kinases MAPKKK-P and MAPKK-P, respectively.

Numerical integration of the RD equations gives concentration profiles of the phosphorylated proteins shown in Fig. 20c. The comparison to make here is between the concentration of MAPK-P reaching the nucleus (x = 1) and the concentration of MAPKKK-P (which, in the one-protein model described earlier, would be the only signaling phosphoprotein) at the same location. As seen, the ratio of these concentrations is close to three indicating that the presence of the “cascade” effectively amplifies the signal reaching the nucleus (the amplification effect is even more pronounced, close to 20 if the kinetics of phosphorylation/dephosphorylation is treated more accurately, see Fig. 20d and ref. 247).

This example highlights that although individual reaction cycles might appear just energetically wasteful (hence, “futile cycles”), their coupling gives rise to a system, which transmits molecular information in a domino-like fashion and effectively amplifies it. The fact that this system “does more than its parts” is mathematically reflected by the coupling between individual RD equations – we will see the importance of such coupling in systems we will discuss later. (ii) The operation of the system depends crucially on the ability of the participating molecules to switch between two states and also act to activate other proteins. (iii) The transmittal of the signal depends on the existence of the micron-scale concentration gradients – we note that without such gradients there would be no nonlinearities in the system and no signal amplification.

7.4. Illustrative examples

With the above conceptual basis of different transport modalities, we are in a position to survey the examples of coupled dynamic – and also DySA – systems that have been emerging in recent years. In the category of systems coupled by diffusion, there are droplet-based chemical oscillators, mainly from the Epstein's group.250 Chemical oscillators are complex networks of non-biological reactions involving non-linear kinetics and feedback loops and exhibiting rhythmic concentration changes.251 Epstein and co-workers studied ensembles of such oscillators (based on the so-called Belousov–Zhabotisky chemistry, Fig. 21a) confined to nanometer-sized water droplets stabilized with anionic surfactants and suspended in oil. These droplets could synchronize their oscillations into system-wide waves, Turing patterns, oscillons, etc. via diffusion of the less polar intermediates the reactions generate, in particular the Br2 inhibitor and the BrO2 activator.
image file: c7cs00089h-f21.tif
Fig. 21 (a) The key reactions involved in a modified251 version of the famous Belousov–Zhabotinsky (BZ) oscillator involving A ≡ BrO3, B ≡ Br2, H ≡ H+, M ≡ CH2(COOH)2, M′ ≡ BrCH(COOH)2, O ≡ oxidation products (i.e., CH2O, COOH, CO2), P ≡ HOBr, T ≡ triggering reagent (e.g., CH2O or CH3OH), X ≡ HBrO2, Y ≡ Br, Z ≡ Fe(phen)33+ (oxidized ferroin indicator colored blue), and Z′ ≡ Fe(phen)32+ (reduced ferroin, pale red). This system of reactions gives rise to rhythmic color oscillations and, in spatially distributed media, to propagating chemical waves. (b) Wiring scheme of the oscillator illustrates the coupling and feedbacks between the reactions. Red circles represent chemical species (for simplicity, H+ is omitted), and blue diamonds represent chemical reactions. The species on the left “feed” the dynamic system of “metabolic” reactions in the outlined region; “waste products” are emitted to the right. The highlighted green arrow corresponds to the autocatalytic production of X by reaction R5′. Such autocatalysis is necessary (but not sufficient) for oscillatory behavior. (c) Morphogenesis in 2D arrays of droplets supporting BZ oscillations: (i) initial, uniform state; (ii) droplets differentiated in terms of their oxidation states; (iii) droplets differentiated in terms of both oxidation states and sizes. Figures (a) and (b) used with permission from B. A. Grzybowski, Chemistry in Motion: Reaction-Diffusion Systems for Micro- and Nanotechnology, John Wiley & Sons, 2009 (ref. 233). Figure (c) reproduced from ref. 250 with permission from The Royal Society of Chemistry.

The same team was also able to prepare arrays of larger but individually addressable (with 450 nm light pulses) oscillating droplets.252 Because the coupling between the adjacent droplets was negative – due to the diffusion of the Br2 inhibitor through the oil phase – these droplets exhibited mostly antiphase oscillations. In addition, the coupling between reaction kinetics within the droplets and the diffusive transport between these droplets gave rise to instabilities that ultimately lead to physical morphogenesis,253 verifying a hypothesis proposed by Turing decades ago. This exciting result is illustrated in Fig. 21b, whereby droplets initially nearly homogeneous in both size and chemical composition first evolve into a Turing pattern made of oscillators in reduced and oxidized steady-states, and ultimately into a pattern in which the reduced droplets grow at the expense of the oxidized ones (i.e., into an ensemble comprising two physically distinct sub-populations).

We note that very recently, Whitesides and co-workers254 demonstrated sustained oscillations and also bistability in a CSTR system housing only organic molecules and based on reactions that might have been operative in early living or prebiotic systems (amide formation, thiolate–thioester exchange, thiolate–disulfide interchange and conjugate addition). In a similar genre of creating primitive mimics of metabolic cycles, Huck's group demonstrated255in vitro, out-of-equilibrium enzymatic reaction networks built around autoactivation and delayed negative feedback of the trypsin enzyme.

At scales larger than molecular, Rurack and co-workers43 demonstrated an interesting “communicating” system that combined diffusive transport of “messenger” molecules with their triggered release from the channels of mesoporous silica nanoparticles, NPs. The channels were first filled with the desired “messengers” and then capped with stabilizing ligands. Importantly, these ligands could be cleaved and the “messengers” released in the presence of an external chemical signal (to initiate the “cascade”) or signals relayed from other NPs. Fig. 22 illustrates the specific chemistries used. The first class of NPs in the cascade are loaded with the reducing agent tris(2-carboxyethyl)phosphine (TCEP, red balls in Fig. 22a) and are stabilized with a saccharide derivative (Glucidex). The initiation “signal” is in the form of a specific enzyme (pancreatin) hydrolyzing the grafted polysaccharide such that TCEP can diffuse out. The TCEP then acts on the second type of NPs capped with polyethylene glycol (PEG) chains attached through disulfide linkages to the silica surface. When TCEP ruptures the redox-labile disulfide bonds, these NPs now release their cargo, dodecyltrimethylammonium bromide (DTAB, green cylinders in Fig. 22). Finally, the released DTAB disrupts a lipid bilayer (prepared from 1,2-dioleoyl-sn-glycero-3-phosphocholine, DOPC) capping particles of the third type. These particles then release safranin O (yellow balls in Fig. 22) which is the terminal “signal” from the three-NP “cascade”. Through a series of control experiments, the authors confirmed that there is no unintended cross-talk between the particles such that (i) a strong safranin signal is observed only upon the pancreatin input and (ii) the process is indeed hierarchical as described above (i.e., pacrteatin → TCEP → PEG → DTAB → safranin).

image file: c7cs00089h-f22.tif
Fig. 22 (a) Illustration of the system of mesoporous NPs relaying chemical information. Red cargo (TCEP) released from the first type of particles opens the pores of a second type of particles, which release green cargo (DTAB) to open the pores of the third type of particle and to release it safranin cargo (yellow balls). Enlarged images emphasizing the porosity of the NPs and the layers of capping molecules. (b) Structures of the capping molecules (sugar derivative, disulfide PEG, DOPC) and of the cargo/messenger molecules (TCEP, DTAB, safranin O). Figure reproduced with permission from ref. 43. Copyright 2013 Wiley-VCH.

In the above examples, the components of the system communicate with one another but they do not really self-assemble into ordered structures. In fact the first systems exhibiting both communication and DySA capabilities have been described only this year – this work, from the Rondelez group, builds on the toolkit of programmable DNA-enzyme “circuits”.256 In ref. 50, these authors used microparticles decorated with DNA template sequences that catalyze a positive feedback loop with the help of a DNA polymerase, an exonuclease, and a nickase set of enzymes. The on-particle templates bind shorter input strands from solution which then prime DNA synthesis with the help of the polymerase. The double-stranded intermediates thus produced have sites recognizing the nickase – this enzyme cleaves one of the strands to regenerate the input and the template strands and liberating a new output strand, thus completing the catalytic cycle (Fig. 23a). The role of the third enzyme, the exonuclease, is to degrade non-specifically all unprotected strands (i.e., other than the on-particle templates), creating concentration gradients and effectively maintaining the system in a responsive out-of-equilibrium state. Overall, owing to this complex mechanism the particles (1) are bistable and can exist in activated “ON” and deactivated “OFF” states; (2) can communicate with one another by the input and output DNA signals they receive and emit; and (3) can be programmed for different tasks depending on the specific DNA sequences used.

image file: c7cs00089h-f23.tif
Fig. 23 (a) Upon input in the form of short DNA strands, nanoparticles covered with DNA templates can be “activated” into a double-strand form which then “emits” output-strand “signals”. DNA-polymerase elongates input strands that hybridize to matching on-particle templates (encoding “αto2α”); a nickase recognizes and cuts the resulting full duplex, releasing both the input and a new output DNA. The exonuclease non-specifically degrades all unprotected oligonucleotides (templates are protected by backbone modifications), maintaining the system in a responsive out-of-equilibrium state. An activated particle can activate its neighbors triggering the propagation of an activation front as also illustrated in (b). Therein, images (1) and (2) are colorized representations of the front propagation where color represents the time of amplification (“ON” time) for each particle. The white spots indicate the positions of the monostable “ON” particles, which serve as triggers. In (3) these particles are barcoded in red, whereas bistable particles, which need an input signal to turn “ON”, are green dots. (c) When an autocatalytic loop illustrated in (a) is spilt into two templates (one encoding “γtoδ” and one “δtoγ”), which are separately attached to different microspheres, network requires oligonucleotides to be exchanged between both bead types. The activity within the majority population is directly related to the presence of a minority bead (red dots in experimental images) in their neighborhood. At low density of minority beads, the active colonies of beads are small and well defined. However, when the density of minority beads reaches a threshold, a sudden increase in the activity of most majority particles is observed suggesting a cooperative mechanism of colony-to-colony activation. Panels (b) and (c) adapted with permission from Macmillan Publishers Ltd: Nat. Nanotechnol., from ref. 50, copyright 2017.

The coupling between different particles via diffusion of the DNA signals gives rise to a variety of collective behaviors. For instance, activated particles can turn ON their inactive neighbors and propagate the activation front (Fig. 23b). When particles are of different types and emit orthogonal DNA signals (i.e., signals not affecting particles of other types), they can propagate activation fronts toward a “target” particle and then backwards – in effect, reporting the presence of this distant target. Most relevant to our discussion of DySA is the situation in which the autocatalytic machinery is not all residing on one type of NPs but is partitioned between particles of different types. In such a case, these particles must dynamically self-assemble to share their DNA and perform their signaling function together. As a result, such particles form local activation colonies (Fig. 23c) whose size is related to the steepness of the signal-concentration gradients emitted by the particles and is regulated by, for example, the concentrations of particles of different types.

One of the unique features of the Rondelez’ system is the ability to program its components for a specific mode of communication, either between particles of the same or different types (“autocrine” vs. “paracrine” communication). On the other hand, this design flexibility rests crucially on the use of DNA – in this light, while this system provides a clear and long-awaited demonstration of “networked DySA”, the main challenge that lies ahead will be to extend similar concepts to abiotic chemistries and non-aqueous solvents.

8. Conclusions and outlook

The last sentence of the preceding paragraph implies the future direction we envision for DySA research – namely, emphasis on completely non-biotic systems. With the already existing ability to reprogram living cells and microorganisms to perform desired tasks257 (e.g., synthesis of drug molecules,258 flavours,259 fragrances,260 fuels261 or even nanoparticles262), it would probably be of limited practical value to invest much effort into constructing, completely de novo, systems from isolated biological components. On the other hand, we see much value of designing “wired” DySA systems from abiotic parts and functioning in environments that would typically be incompatible with living matter. Such systems could use catalysts, solvents or reagents harmful to cells, operate at elevated temperatures and in organic solvents, etc. The big advantage of systems vs. their isolated parts is that the former could reconfigure to perform many different tasks depending on the external controls, much like a coffee maker is able to brew either espresso, or latte, or Americano depending on which button one pushes. The “buttons” in DySA systems could also be much smarter and versatile than the on/off switches in coffee machines, especially if the self-assembled state would feed back into the source of energy maintaining the non-equilibrium structure itself.263

A salient point – one we barely touched upon in this Review – is the importance of kinetics and multiple timescales inherent to any non-trivial systems. In a system supporting multiple alternative (or “competing”) processes, their timescales should generally be commensurate or else the fast pathways will rapidly outcompete the slow ones – for instance, if one dynamic catalyst (cf. Section 5 and Fig. 13b) self-assembles over seconds while the other over hours, then only the reactions driven by the former will be important on experimentally relevant timescales. One difficulty in such considerations is that of understanding the kinetics of truly complex systems – for instance, there is nothing in the kinetics of individual reactions of the BZ system that would predict oscillations when all these reactions are wired together. Such examples illustrate that when we think about systems, our chemical intuition alone will generally be insufficient – instead, we will need to increasingly rely on mathematical approaches/models to understand the kinetics/dynamics of complex systems. In fact, we see the development of user-friendly software with which chemists, not only physicists and mathematicians, could model systems’ kinetics as the urgent next step in the development of the field.


This work was supported by Korea's Institute for Basic Science, IBS, project code IBS-R020-D1.


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