Chemically Fueled Self‐Assembly in Biology and Chemistry

Abstract Life is a non‐equilibrium state of matter maintained at the expense of energy. Nature uses predominantly chemical energy stored in thermodynamically activated, but kinetically stable, molecules. These high‐energy molecules are exploited for the synthesis of other biomolecules, for the activation of biological machinery such as pumps and motors, and for the maintenance of structural order. Knowledge of how chemical energy is transferred to biochemical processes is essential for the development of artificial systems with life‐like processes. Here, we discuss how chemical energy can be used to control the structural organization of organic molecules. Four different strategies have been identified according to a distinguishable physical‐organic basis. For each class, one example from biology and one from chemistry are discussed in detail to illustrate the practical implementation of each concept and the distinct opportunities they offer. Specific attention is paid to the discussion of chemically fueled non‐equilibrium self‐assembly. We discuss the meaning of non‐equilibrium self‐assembly, its kinetic origin, and strategies to develop synthetic non‐equilibrium systems.


Introduction
Theq uestion of how life originated on earth touches the essence of humankind and has led to profound existential reflections by theologists,philosophers,and scientists over the course of human history.Scientists marvel at the observation that living matter is able to defy the second law of thermodynamics by maintaining local order in au niversal context of acontinuous increase in entropy. [1][2][3] This astonishing feature implies that the acquisition of the ability to exploit energy from the surroundings to create and maintain structure must have played ak ey part in the transition from inert to living matter. [4,5] Energy is abundantly available on earth in the form of photons that are generated by nuclear fusion processes occurring in the sun and in the form of geothermal energy originating from the earthsc ore. Although other energy sources are available,the importance of solar and geothermal energy is that they can directly activate molecules and facilitate chemical reactions.T he photo-or thermal activation of molecules enables their conversion into new molecules with increased chemical potential. [6] Thes torage of solar energy in high-energy molecules through photosynthesis is the process that sustains life on earth. [7,8] Thec hemical energy stored in thermodynamically activated but kinetically stable molecules drives the entire biological machinery. [9] Thenon-equilibrium nature of life is manifest in the cell, the smallest organizational unit that expresses the characteristics of life. [10] Cells grow and divide,r eproduce,c ommunicate with the environment, and adapt to changes therein. [11] Theexpression of these features requires acontinuous supply of energy,which arrives at the cell in the form of high-energy nutrients;d eath follows when the energy supply ceases.T he energy released from the breakdown of nutrients is used for the synthesis of lipids,peptides,and nucleic acids,which self-assemble in athermodynamically controlled manner to form the constitutional structures of the cell, including membranes, proteins,and the genome.Importantly,energy is also used to synthesize molecules with ah igh chemical potential-for example,ATP,NADH, acetyl-CoA-whichserve as chemical fuels that keep the biological engine running. [9] Thee nergy released from these molecules upon their conversion into waste molecules with al ower chemical potential drives molecular pumps and motors,w hich results in sustained concentration gradients and directional motion;t hese are evident signatures of an on-equilibrium system. [12][13][14][15] At the same time,c hemical fuels also play ad irect role in the structural organization of the cell by controlling self-assembly processes in time and space. [16][17][18] Through adirect coupling of self-assembly processes and energy dissipation processes, Life is anon-equilibrium state of matter maintained at the expense of energy.Nature uses predominantly chemical energy stored in thermodynamically activated, but kinetically stable,m olecules.T hese high-energy molecules are exploited for the synthesis of other biomolecules,f or the activation of biological machinery such as pumps and motors,and for the maintenance of structural order.Knowledge of howc hemical energy is transferred to biochemical processes is essential for the development of artificial systems with life-like processes.Here,wediscuss howchemical energy can be used to control the structural organization of organic molecules.F our different strategies have been identified according to ad istinguishable physical-organic basis.F or each class,o ne example from biology and one from chemistry are discussed in detail to illustrate the practical implementation of each concept and the distinct opportunities they offer. Specific attention is paid to the discussion of chemically fueled nonequilibrium self-assembly.Wediscuss the meaning of non-equilibrium self-assembly,i ts kinetic origin, and strategies to develop synthetic non-equilibrium systems.
From the Contents 1. Introduction 20121 chemical fuels also allow the formation of high-energy structures,w hich is another signature of the non-equilibrium nature of life. [19] Driven by the desire to understand how life could have originated in ap rebiotic context, chemists have had al ongstanding interest in the origin-of-life question. [20][21][22][23][24][25][26][27] In more recent years,interest in the chemistry of life has gained even more traction, as chemistry has advanced to such alevel that the installation of emergent properties in complex synthetic mixtures of interacting molecules,j ust as in the cell, has become within experimental reach from as ynthetic and analytical point of view. [28][29][30] Thei mplementation of life-like properties in synthetic systems offers the prospective of unprecedented materials and, in the future,the development of artificial entities that may be recognized as being alive. [31] In these studies,t he development of synthetic chemical systems that operate out-of-equilibrium form ac entral focus. [32][33][34][35] Great strides have been made in the design of artificial molecular machines that exploit energy to function. [36][37][38][39][40][41][42][43][44][45][46][47] Although light has most frequently been used as an energy source,t he first molecular machines that exploit chemical energy have also been recently reported. [48][49][50][51][52] Compared to molecular machines,t he self-assembly of nonequilibrium structures is still in its infancy. [53][54][55][56][57][58][59][60][61] Although highly interesting systems with novel properties have been described, progress towards systems that can mimic natural non-equilibrium self-assembly in all its facets could be improved by abetter understanding of the physical-chemical principles that govern the transfer of energy from achemical fuel to the self-assembly process. [62,63] In this Review,w ed iscuss in as ystematic manner how chemical fuels can be used to control the self-assembly of organic molecules.T he objective of this Review is to provide as ystematic,a ccessible treatment that extends on the more technical analysis that we and others have reported previously on the topic of chemically fueled non-equilibrium selfassembly. [62][63][64] We have identified four different classes that differ in the way chemical energy stored in molecules is transferred to the self-assembly process.Class 1describes the use of templates to control self-assembly processes at thermodynamic equilibrium. Class 2d escribes templated self-assembly under dissipative conditions,w hich implies that the template is gradually converted into anontemplating waste molecule by an external agent that does not participate in the self-assembly process.C lass 3d escribes systems in which the self-assembling components play an active role in the conversion of fuel into waste.C lass 4d escribes systems similar to Class 3b ut with the additional feature that the released chemical energy is used to drive the system out-ofequilibrium.
These classes will be presented in order of increasing complexity and for each of them aconceptual analysis will be provided followed by two representative examples:one from biology and one from chemistry.T he reason for this setup is that the illustration of the concept with practical examples shows how an abstract concept can be translated to molecular systems.T he direct comparison of examples from nature and the laboratory provides insight into how the same concept can be applied to chemical systems with very different levels of complexity.W ewould like to point out that this Review is not intended to be comprehensive;k ey examples were selected from the rich literature based on their suitability to illustrate the concept. Excellent and comprehensive reviews of the respective research areas that will be discussed herein are available in the literature and references to these have been inserted to guide the reader.
To facilitate the analysis and comparison between the different classes,w eh ave chosen the self-assembly of two identical monomers (M) into dimer M 2 as the framework for the conceptual analysis ( Figure 1). Dimerization represents the simplest example of the organization of molecules.T he composition at thermodynamic equilibrium is defined by an equilibrium constant, K 4 ,which in our analysis is chosen such that the equilibrium composition resides on the side of the monomers.This implies that dimer M 2 is higher in energy than monomer Ma nd that self-assembly does not occur spontaneously.

Concept
An evaluation of templated self-assembly forms the best starting point for our analysis,e ven though no energy is dissipated by the chemical conversion of fuel into waste. Te mplated self-assembly sets the proper framework for the analysis of the other classes,inwhich energy dissipation does take place.T he distribution of species under equilibrium conditions is defined by the thermodynamic cycledepicted in Figure 2a.T he interaction of template Tw ith Ml eads to acomplex M*, which is activated for dimerization to give the thermodynamically more stable dimer M* 2 .D issociation of the template from M* 2 results in the formation of the highenergy species M 2 ,w hich dissociates to give M. Them ost populated species at equilibrium is M* 2 ,which has the highest thermodynamic stability.
Microscopic reversibility implies that the reaction path in the reverse direction must in every detail be the identical reverse of the reaction path in the forward direction. [65,66] To emphasize this aspect, in this Review we consistently describe all reactions as equilibria, even those that, from ap ractical point of view,w ould typically be considered unidirectional. At the molecular level, microscopic reversibility leads to the concept of detailed balance,w hich states that in as ystem at thermodynamic equilibrium the rate of the forward reaction must be identical to the rate of the backward reaction. A consequence of microscopic reversibility for the thermodynamic cycle depicted in Figure 2a is Equation (1).
This equation implies that, from an energetic point of view,t here is no difference if the activated assembly M* 2 is populated by dimerization of Mfollowed by association of the template or by activation of Mf ollowed by the dimerization of M*. In other words,from an energetic point of view,there is no difference in following at hermodynamic cycle in the clockwise or counterclockwise direction.
Fora ll the different classes of fueled self-assembly that will be discussed we have added energy diagrams containing the relative energy levels of the different states.T hese schemes serve to facilitate an understanding of how the population of the states is affected by the addition of fuel/ template and the conversion of fuel into waste (for the successive classes). ForC lass 1, this results in af our-state diagram (Figure 2b)w ith the distribution of Ma mongst the four states represented by the size of the dark red circles.The Figure 1. The equilibriumbetween Mand M 2 that is used as areference throughout the Review.T he composition at equilibrium is defined by the equilibrium constant K 4 (m À1 ). The notation for the equilibrium constant (K 4 )i sused to facilitate the comparisono fthe discussion in this Review with aprevious publication. [62] Figure 2. Class 1: Templated self-assembly.a )The reaction scheme describes the chemical connectivity between the components of the system. b) Energy diagram in which the dark red circles indicate the composition of the system in the presence of template T.
reported (arbitrary) distribution is based on simulations reported previously. [62] From the scheme it is evident that the distribution is completely dictated by the relative thermodynamic stabilities.

Biology-Templated Self-Assembly of Virus Capsids
Self-assembly is extensively used in nature for the structural organization of matter.T he formation of selfassembled structures that need to persist in time typically involve building blocks (phospholipids,n ucleic acids,p eptides) that spontaneously assemble through athermodynamically controlled process.N ature makes such building blocks by exploiting the energy released from the degradation of nutrients in catabolic pathways.H owever,o nc ertain occasions the use of templates in the self-assembly of thermodynamically stable structures provides additional benefits,which is illustrated by taking the self-assembly of virus capsids templated by nucleic acids as an example.
Viruses are dynamic assemblies of nucleic acids and proteins that use their own components and the biological machinery of ac ell to multiply and propagate. [67] Virionssingle infectious viral particles-exist with various sizes, shapes,a nd levels of complexity. [68] Virions range from very simple structures composed of just the viral nucleic acid and as urrounding protein shell, called ac apsid, to complex enveloped structures in which al ipid membrane surrounds the capsid and which contain additional proteins both inside the capsid and expressed on the envelope. [69] Capsid formation is ab eautiful example of as elf-assembly process; hundreds of copies of ac apsid protein spontaneously assemble to form an object that can reach even micrometersized dimensions. [70] Generally,v iral capsids have either ar odlike shape,i nw hich the capsid proteins are arranged in ahelical fashion around the nucleic acid, or aspherical shape, in which the capsid proteins are arranged with icosahedral symmetry.S ince ah elix is,i np rinciple,a ni nfinite structure, rod-shaped capsids can, in principle,a ccommodate nucleic acids of any length. On the other hand, the geometrical constraints of the icosahedral lattice require the spherical capsids to be composed of 60T subunits,i nw hich T is the triangulation number, which is equal to the number of distinct conformations of the capsid protein that can be found in the lattice.
Virions can form as empty capsids,s o-called procapsids, which are successively loaded with nucleic acids through ap ortal protein complex using an ATP-driven molecular pump.T his is typically the case for double-stranded DNA (dsDNA) or dsRNAviruses,which have such ahigh stiffness and charge density that spontaneous encapsulation is precluded. However,here we want to focus on those virions that form through ap rocess in which the nucleic acid, typically aflexible single nucleic acid strand (mostly ssRNA), serves as the template for the self-assembly of the capsid and discuss the advantages of templation. [71,72] One of the mechanisms for the templated self-assembly of capsids is anucleation-and-growth sequence,inwhich asmall cluster of capsid proteins engages in interactions with ssRNA ( Figure 3). [73] Electrostatic interactions between the negatively charged nucleic acid strand and the flexible N-terminal domain of ac apsid protein rich in basic amino acids-called arginine-rich motifs (ARMs)-form the thermodynamic driving force for the formation of the nucleation complex. Thefavorable contribution of the ssRNAtothe formation of this complex allows self-assembly of the nucleation complex to occur at lower concentrations compared to the threshold concentration required for empty capsid assembly (c templated < c empty ). Formation of the nucleation complex frequently involves specific short RNAs equences of the nucleic acid strand with aw ell-defined secondary structure,s o-called packaging signals.Nucleation is followed by the condensation of additional capsid proteins.Inthis growth step,interactions between RNAa nd the capsid protein serve not only to promote oligomerization, but also to direct the self-assembly pathway.B oth specific and nonspecific interactions lead to the simultaneous packaging of the nucleic acid strand and conformational changes in the capsid protein required to form as table assembly.T he selectivity of the interaction between the nucleic acid strand and capsid proteins in this templated self-assembly process is part of the reason why virions can assemble with specificities up to 99 %around the viral genome in ac ellular context that contains am yriad of nonviral RNAm olecules.

Chemistry-Dynamic Combinatorial Chemistry
Theserendipitous discovery by Pedersen that Na + cations templated the formation of crown ethers initiated the era of supramolecular chemistry. [74][75][76] Since its inception, the use of templates to control self-assembly processes has maintained aprominent position in supramolecular chemistry,eventually culminating in the development of dynamic combinatorial chemistry (DCC) as at ool for the discovery of receptors, catalysts,a nd materials (Figure 4a). [77][78][79][80][81][82][83][84] DCC relies on the

Angewandte Chemie
Reviews use of dynamic combinatorial libraries,w hich are composed of dynamic members that can interconvert because the building blocks interact through reversible bonds (either noncovalent or covalent). These libraries are at thermodynamic equilibrium, which implies that the library composition is dictated by the relative stability of each library member in the global energy landscape.T he central concept of DCC is the adaptation of the system to ap erturbation in the energy landscape caused by an external stimulus.F or example,t he addition of atemplating molecule will spontaneously lead to ac hange in the library composition, enriched in the library member with, in principle,t he highest affinity for the template.That library member can be identified in astraightforward manner simply by comparing the library compositions before and after addition of the stimulus.The attractiveness of DCC is that screening is carried out by the molecules themselves,w hich overcomes the limitations of rational design.
Thepotential of DCC has been nicely illustrated by Otto et al.,who demonstrated that asingle dynamic combinatorial library can evolve in different directions depending on the molecular structure of the added template ( Figure 4b). [85] A dynamic library was obtained by mixing three different dithiol building blocks 1-3,w hich under slowly oxidizing conditions formed am yriad of disulfide macrocycles of different sizes and composition. ESI-MS measurements of the library revealed the presence of 45 library members with ad istinct mass.E xposure of the library to 2-methylisoquinolinium iodide resulted in amajor change in the library composition, as observed by HPLC analysis.Astrong amplification was observed for macrocycle 1 2 3,w hich was al ibrary member hardly detectable in the template-free library.N otably, exposure of the same library to ad ifferent template-Nmethylated morphine-led to strong amplification of ac om-pletely different macrocycle,n amely 1 3 .I ti sw orth noticing that the template-induced increase in macrocycles enriched in building block 1 is accompanied by ad ecrease in other macrocycles containing 1,w hich illustrates that the amplification process indeed occurs at the expense of competing library members.Respective binding constants of 2.5 10 5 m À1 and 7.1 10 5 m À1 were determined for complexes between macrocycles 1 2 3 and 1 3 and their respective guests,w hich illustrate that DCC permits high-affinity receptors to be identified from amixture of structurally related structures.

Concept
Te mplates favor self-assembly processes because the interaction with the self-assembling components is an energetically downhill process.I nt he example of virion selfassembly,wehave seen that the association of capsid proteins to the nucleic acid strand increases their local concentration, which permits self-assembly to occur at lower concentrations. There is ac lear entropic contribution to this process which results from the exchange of multiple counteranions from the positively charged amino acid residues in the capsids by as ingle one-the nucleic acid strand. It is important to note that the biochemical synthesis of such as ingle multicharged counteranion is an energetically uphill process.F rom this analysis it follows that templates of this kind can be regarded as high-energy molecules.I np rinciple,t his energy can be released through an independent chemical reaction that breaks down the template,w hich consequently loses its templating ability.T his situation defines Class 2: Te mplated self-assembly under dissipative conditions.
As ystem displaying templated self-assembly under dissipative conditions contains the identical set of equilibria as Class 1 ( Figure 5a). Thed ifference lies in the fact that an additional process is present that slowly degrades the template into awaste product (W) without templating ability. Thedegradation process is caused by an external element (for example,a ne nzyme or reactant) or by the experimental conditions;the monomers and assemblies do not play arole in this process.A ni mportant consequence of template degradation is that, just as in Cass 1, after the initial change in the energy landscape upon the addition of ab atch of template, the energy landscape gradually reverts to the original energy landscape (assuming that the waste molecules do not interfere in the self-assembly process).
This difference with Class 1i sr epresented in the energy diagram by the presence of two novel energy states corresponding to M + Wand M 2 + W (Figure 5b). These states are lower in energy compared to all other states-which involve intact template-indicative of the lower chemical potential of the waste compared to the template.T he difference in the chemical potential between the fuel and waste corresponds to the energy difference between states M + Fand M + Winthe diagram (or between M 2 + Fand M 2 + W). It should be noted that in the scheme we have changed the label for the chemical  [85] trigger from T( template) to F( fuel). It is worth spending af ew words on the term "fuel", which in the literature on chemically fueled processes is used with ambiguity. [41,86] In the restricted interpretation, the word fuel is used exclusively for those cases in which the energy released from the chemical trigger is exploited by the system to carry out work. This implies that fuel consumption must drive the system to anonequilibrium composition. Within the Classes that we have identified in this Review,o nly Class 4s atisfies this criterion. In am uch broader interpretation, though, the term fuel is used for any chemical stimulus that induces atransient change in the system as aresult of conversion into waste,irrespective of whether this allows the system to perform work. Aware of this difference,t hroughout this Review we adhere to this broad interpretation because the usefulness of chemically fueled systems is not just limited to those systems that can exploit chemical energy to perform work (see Classes 2a nd 3).
Before analyzing the systemsresponse to the addition of af uel, it is important to distinguish between situations in which the fuel is added batchwise and those in which the fuel concentration is kept constant. This represents the difference between aclosed system and an open system in which fuel and waste are continuously exchanged with the environment. The energy diagram in Figure 5b serves to visualize the composition of the system under stationary conditions,that is,inan open system. Theg reen arrows indicate the processes that convert fuel into waste.B oth start from the Ma nd M 2 (+ F) energy levels,b ecause fuel-to-waste conversion in Class 2 occurs after dissociation of Ff rom M* and M* 2 .T he red spheres indicate the relative population of each state and correspond to arbitrary values for K 1 -K 4 used in previously reported simulations. [62] Forreasons of clarity,the populations of the Ma nd M 2 states are indicated just on the waste level (identical shaded spheres are inserted on the fuel level). Under stationary conditions,that is,atconstant fuel and waste concentrations,t he distribution is completely dictated by thermodynamics and M* 2 is the most populated species. Importantly,b ecause the self-assembly and fuel-to-waste conversion processes are independent, energy consumption cannot affect the ratio between Ma nd M 2 ,w hich always corresponds to the ratio at thermodynamic equilibrium.
It is nonetheless possible to observe the high-energy assembly M 2 ,but only if fuel is added batchwise to the system and if assembly M 2 has ah igh kinetic stability.U nder these circumstances it is possible that assembly M 2 temporarily persists in the system after the dissociation and destruction of F. The( spontaneous) switching of the environmental conditions (no fuel-fuel-no fuel) leads to atemporary alteration of the energy landscape and this can lead to the population of ah igh-energy state.T his mechanism of energy transferreferred to as an energy ratchet-has been frequently applied to populate high-energy states of molecular pumps. [32,49,52,87] However,under stationary conditions this mechanism cannot be effective,asit intrinsically relies on the switching between different conditions.I ndeed, we will show later that under stationary conditions M 2 can be populated by an entirely different mechanism (Class 4).
Although the systems composition is determined by the same set of thermodynamic equilibria that govern Class 1, the transient change in the energy landscape upon the addition of ab atch of fuel introduces the possibility of gaining temporal control over the composition. Thee xtent at which the M* 2 state is populated and the duration of this populated state can be controlled by the amount of fuel that is added;systems that operate according to this scheme are exploited for the activation of functions associated with the M* 2 state with temporal and quantitative control.

Biology-Signal Transduction
An essential feature of ac ell is the possibility to communicate with the extracellular environment by receiving and transmitting signals. [88,89] Without communication, cells would not be able to organize themselves into structures of higher complexity. [90] Communication relies on the activation of signal transduction pathways by messenger molecules that selectively bind to extracellular receptor sites of transmembrane proteins embedded in the cell membrane.G enerally, the binding event leads to conformational changes or dimerization causing the activation of the intracellular domain for catalysis or the binding of intracellular components.M embrane receptors can be divided into three major groups based on the mechanism of signal transduction:G protein-coupled receptors,i on channel receptors,a nd enzyme-linked receptors.Asingle cell can have hundreds of different cell membrane receptors,w hich underlines the signaling power of ac ell and the importance of communication.
When studying signal transduction, the focus is generally on the signaling cascade that is triggered by the initial binding event. However,ofequalimportance is signal termination, as communication pathways are nearly always transient in nature.Signal termination requires elimination of the trigger, which can occur spontaneously through diffusion, but can also be an active process mediated by enzymes.A cetylcholine is an eurotransmitter that is released by nerve cells to send signals to other cells,such as other neurons and muscle cells. After release from the nerve cell, acetylcholine binds to receptor proteins embedded in the membrane of the receiving cell. Acetylcholine receptors can be divided into two major classes,n icotinic acetylcholine receptors (nAChR) [91] and muscarinic acetylcholine receptors (mAChR), [92] both of which respond to acetylcholine,b ut with different response mechanisms.H ere,w ef ocus in detail on nAChR, as it provides afascinating example of how nature uses achemical fuel-acetylcholine-under dissipative conditions to transiently activate function ( Figure 6). At the neuromuscular junction, nAChR plays ak ey role in the transfer of signals from the nervous system to skeletal muscle cells.n AChR is a2 90 kDa transmembrane protein made up of five subunits that are symmetrically arranged around ac entral pore. [93] Binding of acetylcholine leads to ac onformational change, which opens ac hannel that permits the permeation of Na + and K + ions through the membrane at as taggering rate of around 15 000-30 000 ions per millisecond. [11] This induces ad epolarization of the muscle membrane,w hich is the triggering event that leads to the release of Ca 2+ ions stored intracellularly in the sarcoplasmic reticulum. Then earinstantaneous increase in the cytosolic Ca 2+ concentration activates enzymes involved in muscle contraction (see also Section 5.1). Communication between the nervous system and skeletal muscles must be regulated at extremely short time intervals to allow an immediate reaction by the organism. This necessity is reflected by the rates of acetylcholine-mediated activation of nAChR and its subsequent deactivation. Upon activation of the nervous system, acetylcholine is released in ab urst-wise fashion into the synaptic cleft from synaptic vesicles present in the nerve cell-each containing around 5000-10 000 molecules-causing an increase in the acetylcholine concentration in the synaptic cleft to around 0.3 mm. [94,95] Acetylcholine binds nAChR with ar elatively low dissociation constant (K d )o fa round 0.2 mm, which implies the binding sites are only partly occupied. [96] Of importance is also the high dissociation rate constant of 5 10 4 s À1 ,w hich implies acetylcholine occupies the binding site for very short times.T ogether, the low binding site occupancy and the short lifetime of the complex are essential to control ion-channel opening and closure on the millisecond timescale and allows for av ery fast deactivation pathway.T ermination of the signal requires elimination of acetylcholine from the synaptic cleft. This role is carried out by the enzyme acetylcholinesterase,which cleaves acetylcholine into choline and acetate.Acetylcholinesterase is abundantly present in the synaptic cleft and cleaves acetylcholine at ar ate of around 25 000-30 000 molecules per second, which approaches the limit set by substrate diffusion. [97] This enzyme installs the dissipative conditions required to terminate the signal activation pathway by clearing the neurotransmitter from the synaptic cleft. In the context of this discussion, it is true that this example falls to some extent short in the sense that acetylcholine-binding induces an intra-rather than intermolecular self-assembly process in nAChR. However,w eh ave selected this example because it demonstrates clearly how nature exploits dissipative conditions to temporally regulate chemical functions in an extraordinary way.E xamples in which ac hemical trigger transiently activates as ignal transduction pathway by triggering changes in self-assembly processes are abundant and involve,f or example,Gproteincoupled receptors [98] and integrin clustering on cell membranes. [99] 3.3. Chemistry-Transient Self-Assembly of Nanoreactors In ac hemical context, templated self-assembly under dissipative conditions has emerged as at ool to control the lifetime of self-assembled structures and, importantly,t he functional properties exerted by templated assembly. [58,[100][101][102][103][104][105]  This requires that initial conditions are chosen such that the building blocks reside in the unassembled state (M) in the absence of fuel and that the waste molecules have no templating ability.Our group has illustrated how multivalency can be used to design as ystem that meets these criteria. [106] Previously,w ed emonstrated that the interaction of adenine nucleotides (AXP, with X = M, D, or T) with the monolayer surface of gold nanoparticles covered with am onolayer of alkylthiols terminating with a1 ,4,7-triazacyclononane·Zn 2+ (TACN·Zn 2+ )c omplex strongly increased as the number of phosphate groups present in the nucleotide increased. [107,108] Them ultivalent effect originates from the establishment of multipoint interactions between the phosphate groups and Zn 2+ metal ions embedded in the monolayer and the substitution of multiple-smaller-counteranions surrounding the monolayer with as ingle multivalent one.T he observation of astrong multivalent effect in the nanoparticle system led us to explore its use for the templated selfassembly of vesicles under dissipative conditions ( Figure 7). [109] Thea ddition of ATPt oas olution of C 16 TACN·Zn 2+ -in which the TACN·Zn 2+ complex is attached to asaturated C 16 chain-at aconcentration below the critical micellar concentration resulted in the formation of ATP-templated vesicles.H owever,t he solution also contained potato apyrase,a ne nzyme that hydrolyzes ATPi nto AMP and two phosphate ions.A saconsequence of the conversion of ATPi nto waste products,w hich are unable to stabilize the vesicles,t he latter gradually dissociated in time. Anew cycle of transient vesicle formation could be triggered by the addition of an ew batch of ATP. In this system, the lifetime of the assemblies can be regulated by varying the concentration of ATPorthe concentration of the enzyme.
Thetransient formation of ATP-templated vesicles offers an ew possibility to control chemical reactivity in the time domain. [109][110][111] Vesicles are characterized by an apolar bilayer, which can be used to trap apolar reactants that are poorly soluble in the aqueous medium. [112,113] Uptake into aconfined space leads to an increased local concentration, which favorably affects the reaction rates.T he limited lifetime of the vesicles under dissipative conditions implies that alimited timeframe is available for observing such arate acceleration. Tr ansient upregulation of ac hemical reaction was illustrated by using asystem in which two hydrazone-forming reactions I and II can take place contemporarily (Figure 7). [110] Ther ate of reaction I is not affected by the presence of vesicles, whereas reaction II-which involves the apolar cinnamaldehyde-is characterized by as low background reaction in water and as trong rate acceleration when vesicles are present. Reaction I dominates in as olution containing just the amphiphile,b ut the addition of ATPr esults in strong upregulation of reaction II and the corresponding hydrazone becomes the major product. However,r eaction II gradually slows down as ATPi sh ydrolyzed by the enzyme and the product of reaction I becomes again the major species in the system. Inversion of the reaction selectivity can be retriggered by adding anew batch of ATP.
Te mplated assembly under dissipative conditions introduces the possibility to use time as ad esign criterion for developing complex systems.A lthough the distribution of species is still controlled by thermodynamics,t he system responds dynamically to ag radual change in the fuel concentration. It must be noted, though, that this possibility requires the fuel to be added batchwise.I nahypothetical open system, the constant fuel concentration would ensure ap ermanent presence of the templated assembly and no difference from templated self-assembly at equilibrium composition would be observed.

From Equilibrium to Non-equilibrium Self-Assembly
In our model self-assembly process,t he formation of M 2 from Mi se nergetically uphill. Therefore,t he population of the M 2 state-and the maintenance of that populated staterequires continuous consumption of energy.A nalysis of Class 2illustrates that in this case,itisnot possible to exploit the chemical energy released during fuel-to-waste conversion to shift the equilibrium from Mt oM 2 when the system is governed by at hermodynamic cycle.T he reason for this is that self-assembly and fuel-to-waste conversion in Class 2are fully independent processes,which implies that energy transfer between these processes cannot take place.Itfollows that coupling of the self-assembly and fuel consumption processes is required if the energy stored in chemical fuels is to be used to shift the equilibrium between Ma nd M 2 .C lasses 3a nd 4 describe systems in which such ac oupling is present. However,a sw ew ill discuss next, the coupling between selfassembly and fuel consumption processes by itself is not sufficient to install an on-equilibrium composition, which depends on the presence (Class 4) or not (Class 3) of kinetic asymmetry in the energy consumption pathway.A saresult, fuel consumption changes the equilibrium composition between Mand M 2 in Class 4(driven self-assembly), but not in Class 3( dissipative self-assembly). It is noted that in our previous contribution, Classes 3a nd 4w ere referred to as symmetric and asymmetric dissipative self-assembly,r espectively. [62] Thed ifference between Classes 2a nd 3/4 is immediately clear from ac omparison of the reaction schemes ( Figure 5a: Class 2, Figure 8a:C lass 3, Figure 11 a: Class 4). In Classes 3 and 4, an additional connection exists between Mand M 2 and their activated counterparts M* and M* 2 ,respectively,which involve the waste.T his new connection implies that the selfassembly components play arole in the conversion of fuel into waste.T his can occur in two ways depending on whether the fuel interacts in ac ovalent or noncovalent manner with the building blocks.Inthe first case,achemical reaction between Ma nd Fl eads to product M*, which self-assembles to give M* 2 in at hermodynamically driven process.Asecond, different reaction converts M* back into Ma nd generating waste.S imilar activation and deactivation pathways are present on the other side of the equilibrium involving the interconversion between M 2 and M* 2 .A lternatively,i nc ases where the interaction between the fuel and the building blocks is noncovalent, M( and M 2 )p lay the role of catalysts for the fuel-waste conversion. Complex formation between M(or M 2 )and Fleads to the activated complex M* with the capacity to catalyze the conversion of fuel into waste.
Thepresence of two chemically distinct pathways between Ma nd M* (and M 2 and M* 2 )i se ssential for overcoming the problem of detailed balance,w hich prevents any nonequilibrium composition of at hermodynamic cycle (Class 1) under stationary conditions.Indeed, because of the presence of two pathways in steps 1and 3, the distribution of species in the system is now defined by Equation (2).
Here,t he equilibrium constants for steps 1a nd 3h ave been replaced by the kinetic constants for the forward (f)a nd backward (b)r eactions involving fuel (F) and waste (W). It should be noted that some of the rate constants are apparent first order rate constants that include the concentrations of fuel and waste. [62] Thef undamental difference with the thermodynamic cycle is that the product of the terms on the left-hand side of the equation does not have to be equal to 1, which is adirect consequence of the fact that the fuel-to-waste conversion releases energy into the system. This implies that-in contrast to the thermodynamic cycles of Class 1detailed balance can be broken. Under stationary conditions, the rates of the forward and backward reactions in equilibria 4a nd 2m ay be different, thereby leading to currents, which are defined as the difference between the forward and backward rates.T he presence of currents implies that more molecules follow the cycle in one direction than the other.W e will see that the reason for this preferential directionality is that the energy barriers encountered in one direction are lower than the energy barriers encountered when following the cycle in the opposite direction. Theproduct of the terms in Equation (2) can be defined as ar atcheting constant, K r , which can be interpreted as ad irectionality parameter that indicates whether apreference exists for the counterclockwise (K r > 1) or clockwise direction (K r < 1). For K r = 1, no preferential directionality is present.  Figure 8a.The dark colored arrows correspond to the processes during which waste molecules are generated.The size of the dark red circles indicates the relative populations of the respective states reported in previous simulations. [62] Angewandte Chemie Reviews 5. Class 3: Dissipative Self-Assembly (K r = 1)

Concept
Thei mportance of the ratcheting constant emerges from simulations that we have reported previously. [62] In af irst set of simulations we analyzed the composition of the system in cases where the rate constants for the fuel-waste reactions 1 and 3were imposed such that K r = 1; in this case the system is said to display kinetic symmetry.T he result of kinetic symmetry is that in as tationary state-that is,a tc onstant fuel and waste concentrations in an open system-at any given time,the number of molecules that follow the clockwise pathway (orange) is equal to the number of molecules that follow the counterclockwise pathway (green;F igure 8a). Both trajectories are also indicated in the corresponding energy diagram (Figure 8b). Under these conditions,asituation is installed that is similar to the thermodynamic cycle of Class 1; no currents are present in the system. Indeed, simulations show that in the case of kinetic symmetry,t he composition of the system is entirely dictated by the relative thermodynamic stabilities,and the assembled structure M* 2the thermodynamically most stable species-is the most populated species in the system under stationary conditions ( Figure 8b). Importantly,for K r = 1, the rates at which Mand M 2 are consumed and reformed as ar esult of the activation (+ F) and deactivation (-W) pathways are such that the ratio between Ma nd M 2 always corresponds to the ratio at thermodynamic equilibrium. In other words,i nasystem that displays kinetic symmetry,e nergy is continuously being dissipated, but without affecting the composition of the system, which remains fully dictated by the relative thermodynamic stabilities.

Biology-Smooth Muscle Contraction
As an illustration of abiological dissipative self-assembly process with kinetic symmetry,wehave chosen an example of the most common way chosen by nature to regulate chemical processes-the reversible phosphorylation of proteins. [114] Protein phosphorylation is the covalent post-translational modification of proteins in which an amino acid residue (Ser, Ty r, or Thr) is phosphorylated through ak inase-catalyzed transfer of the g-phosphate group of ATP. As econd class of enzymes,phosphatases,reverses this modification by catalyzing the opposite dephosphorylation reaction. Protein phosphorylation plays ar ole in nearly all cellular functions, ranging from enzyme activation, signal transduction, subcellular localization, to apoptosis. [115] Thewidespread use of this post-translational modification as ar egulatory tool emerges from the fact that the human genome encodes roughly 500 kinases and 200 phosphatases,w hich have been estimated to act on over 13 000 human proteins. [116] Theu se of reversible protein phosphorylation as as witch is attractive for several reasons.P ost-translational modification implies that activation and deactivation does not require the synthesis or degradation of the protein. Thep hosphate group can be rapidly introduced and removed. Theselectivity of kinases in terms of substrate recognition implies that, in principle, as ingle energy currency-ATP-can be used to drive the entire biological machinery.P hosphorylation of key amino acids leads to the introduction of ah ighly polar phosphate group with negative charge,w hich can induce structural reorganization of the protein or affect the interaction with other proteins.R eversible phosphorylation thus succinctly illustrates how nature uses building block activation by chemical fuels to exert temporal control over chemical functions.T he concentration of the activated building blocks is determined by the relative rates of the chemically distinct forward and backward reactions which are regulated by kinases and phosphatases,respectively.
In line with the focus of this work on structural organization, we have chosen to discuss in detail an example in which the phosphorylation state of the protein affects its self-assembly properties.O nt he molecular level, muscle contraction is caused by the ATP-driven sliding of tiny filaments composed of the proteins actin and myosin II. [11] In cardiac and skeletal muscle cells,these filaments are arranged in well-defined contractile units,called sarcomeres,which line up and are bundled into myofibrils,thereby giving acharacteristic striated appearance when imaged under amicroscope. [117] In these cells,contraction is activated by asudden rise in the cytosolic Ca 2+ concentration triggered by as ignal from the nervous system (Section 3.2). Thei ncrease in the Ca 2+ concentration is transient because Ca 2+ is rapidly pumped outside of the cells;w ithin around 30 ms the cytosolic Ca 2+ concentration is restored and the myofibrils relax. The structural organization of actin and myosin and the Ca 2+regulatory mechanism in these cells have evolved to permit the fast generation of force.Incontrast, smooth muscle tissue is responsible for the slow and sustained contraction of, amongst others,the intestines,artery walls,and the uterus. [118] This different function is reflected by the lower structural order of actin and myosin-the name smooth derives indeed from the fact that these cells lack the striated appearance of cardiac and skeletal muscle cells-and possess ad ifferent (slower) activation mechanism that relies on the phosphorylation of myosin. Asimilar mechanism also regulates myosin activity in non-muscle cells and provides control over the actin cytoskeleton present in nearly all eukaryotic cells.
Myosin II in smooth muscle cells and non-muscle cells are structurally very similar ( Figure 9). [119] Myosin II is composed of three pairs of peptides-two heavy chains (230 kDa), two regulatory light chains (RLCs,2 0kDa), and two essential light chains (ELCs,1 7kDa)-and several domains are notable in the myosin II structure. [120] Twog lobular head domains are involved in binding to actin and each of them contains acatalytic site for hydrolysis by ATP, which provides the energy for myosin II movement along the actin tracks. ATPb inding and hydrolysis reorganizes the neck domain, which generates motion in asimilar way as kinesin, which will be discussed later in detail (Section 8.2). Each neck domain also binds the RLC and ELC light chains.F inally,along ahelical coiled-coil rod domain is present which ensures dimerization of the two heavy chains.
Conversion of the energy stored in ATP-activated myosin into movement along the actin track during contraction requires crosslinking between different actin tracks.I n cardiac and skeletal muscles,t he permanent organization of myosin and actin filaments in sarcomeres ensures that these muscle cells are always ready for contraction. In contrast, this permanent predisposition of myosin within myofilaments is absent in smooth muscle and non-muscle cells.I ndeed, in these cells,m yosin adopts ac ompact, folded conformation through ah ead-to-tail interaction. [121] In this resting state, myosin has alow affinity for actin and does not self-assemble into filaments.Myosin II activation requires phosphorylation of residue Ser19 on the regulatory light chain (RLC) by myosin light-chain kinase (MLCK). In vitro experiments have shown that phosphorylation opens up the myosin II structure, which leads to actin-binding by the head domains and, importantly,self-assembly of myosin II into filaments through association of rod domains. [122] MLCK activity requires binding of the Ca 2+ -calmodulin complex, which implies that, just as in cardiac and skeletal muscles,contraction is regulated by Ca 2+ ions.H owever,t he kinase activation pathway is much slower and maximum contraction can require almost asecond compared to afew milliseconds for striated muscle cells. [11] A second major difference with the striated muscle cells occurs in the relaxation phase.W hereas striated muscle relaxes within milliseconds after contraction because of the rapid reduction in the cytosolic Ca 2+ concentration, smooth muscle remains in the contracted form as long as myosin II remains phosphorylated. Dephosphorylation catalyzed by myosin light-chain phosphatase (MLCP) makes myosin return to the folded conformation, and dissociation of the filaments takes place. [123] Although much slower compared to the activation and deactivation of striated muscle,t his type of regulation is better suited to serve the purpose of smooth muscle,w hich is to maintain force for ap rolonged period of time with minimal energy consumption.
Theo perating mechanism of myosin II makes sense within the framework of Class 3. Protein (de-)phosphorylation controls the ability of myosin II to self-assembly and, consequently,exert its biological function. However,the selfassembly of phosphorylated myosin II (M* in Figure 8a)itself is at hermodynamically controlled process.T his permits the structure (M* 2 )t ob em aintained without additional energy consumption. Fort he biological function of myosin II, the hypothetical use of ahigh-energy assembly M 2 would not add any value,but rather would imply an unnecessary expense of energy.

Chemistry-Transient Self-Assembly of Hydrogels
In recent years,t he development of synthetic chemically fueled self-assembly processes that mimic the phosphorylation-dephosphorylation scheme of biological fuel-activated processes has truly taken flight. [124][125][126][127][128][129][130][131][132][133][134][135][136] Many systems have now been described that rely on the fuel-mediated activation of building blocks for self-assembly under conditions where ac oncurrent and chemically distinct pathway causes deactivation. It was quickly realized that this provides away to form nanostructures and materials with acontrolled lifetime,which is not possible for thermodynamically controlled self-assembly processes.I nt he vast majority of cases,h owever,t he attention has been primarily focused on the self-assembly process and the properties of the thermodynamically stable assembly composed of activated building blocks,w hich corresponds to assembly M * 2 in our scheme.T he presence of high-energy assemblies composed of non-activated building blocks,that is,M 2 ,has so far not been specifically searched for, and detailed kinetic studies that would prove the installation of kinetic asymmetry have not been reported. In the absence of this information it is,therefore,not possible to unequivocally assign the reported systems to Class 1o r2 .
Here,w ed iscuss as ystem reported by Ulijn and co-workers for which no particular properties have been reported that would indicate the formation of ah igh-energy assembly ( Figure 10). [124] In addition, the fact that activation and deactivation of the building blocks occurs in the active site of enzymes combined with the fact that bond making and breaking involves an internal bond of the building block, make it more likely that the conversion of fuel into waste

Angewandte Chemie
Reviews involves the free building blocks rather than the assembled ones.
Ther eported system exploits the ability of proteases to catalyze the formation (rather than hydrolysis) of peptide bonds under specific experimental conditions.F or example, chymotrypsin efficiently catalyzes the formation of apeptide bond when an ester precursor is used, rather than acarboxylic acid. This property was exploited for the transient formation of ah ydrogel from dipeptide gelators.C -Terminal-amidated l-tyrosine (Y-NH 2 )w as used as ab uilding block and converted into ad ipeptide gelator upon reaction with the methyl ester of l-tyrosine,f unctionalized at the N-terminus with an apolar naphthoxyacetyl group (Nap-Y-OMe). The latter species can be described as achemical fuel, because this compound drives the process and eventually ends up as ac arboxylic acid waste molecule.T he chymotrypsin-catalyzed reaction between the building block and the fuel leads to the rapid formation-within 2-3 minutes-of the dipeptide Nap-YY-NH 2 .T his dipeptide has as trong tendencyt o assemble into nanofibers through ac ombination of p-p stacking interactions between the naphthyl groups and hydrogen bonding between the amide bonds.T he selfassembly of fibers is evidenced on the macroscopic level by hydrogel formation. However,o ver time,c hymotrypsin slowly hydrolyzes the amide bond between the tyrosine residues in Nap-YY-NH 2 to yield the original building block Y-NH 2 and the waste molecule Nap-Y-OH. This reaction is actually an equilibrium, but the composition at equilibrium lies so far to the product side that the final concentration of Nap-YY-NH 2 is negligible.I tw as shown that transient hydrogels were obtained in cases where the gelator Nap-YY-NH 2 could be produced and maintained above the critical gelator concentration for ac ertain time interval before the final state was eventually reached. Importantly,the lifetime of the gel could be controlled by regulating the kinetics of the chemical reactions (pH, enzyme concentration), which is an important general feature of systems that display dissipative self-assembly.
Many conceptually related examples have followed this early report and have convincingly demonstrated that the properties of materials,a mongst others,c an indeed be controlled using as imple set of orthogonal chemical reactions. [124][125][126][127][128][129][130][131][132][133][134][135][136] This bears astrong resemblance to the activation of biological functions through transient chemical modification of proteins.Chemical fuel is consumed, but the released energy is not transferred to the self-assembly process in the sense that it does not lead to the population of ahigh-energy assembled state.Indeed, from aconceptual point of view,no new properties appear compared to thermodynamically controlled templated self-assembly under dissipative conditions.

Concept
Ar adically different situation is obtained in cases where kinetic asymmetry is present in the system (K r ¼ 6 1; Figure 11). This emerged from as econd simulation that we reported previously, [62] in which the rate constants for the fuel-and waste-mediated reactions 1and 3were imposed in such away that K r > 1. This value for the ratcheting constant implies that, under stationary conditions,more molecules follow the cycle in the counterclockwise direction (green arrow) compared to the clockwise direction (orange arrow). Such kinetic asymmetry was achieved by lowering the energy barriers for equilibria 1F and 3W (simulated by increasing k 1,Ff ,k 1,Fb , k 3,Wf , and k 3,Wb )and by increasing the energy barriers for equilibria 1W and 3F (simulated by decreasing k 1,Wf, k 1,Wb , k 3,Ff ,and k 3,Fb ). states. b) Energy diagramillustrating how kinetic asymmetry creates the conditionsr equired for the permanentp opulation of the highenergy assembly M 2 under stationary conditions. The green trajectory represents the counterclockwise (green) direction of the cycle depicted in Figure 11 a. The dark green arrow corresponds to the process during which waste molecules are generated.T he size of the dark red circles indicate the relative population of the respective state reported in previous simulations. [62] In practice,this implies that the fuel reacts faster with Mthan M 2 and that waste is more rapidly produced by M* 2 than M*. Importantly,t his creates ap referential pathway (green) that includes the formation of the high-energy assembly M 2 from M* 2 (Figure 11 b) as ak ey passage in the energy dissipating process.I ndeed, simulations show that, as ar esult of kinetic asymmetry,t he high-energy assembly M 2 becomes the most populated species in the system under stationary conditions.It should be noted that this requires fuel-to-waste conversion to occur more rapidly than the equilibration in steps 2and 4(for adiscussion on the importance of kinetic stabiity of assembly M 2 see also Section 9). Theo bservation that equilibrium 4 between Ma nd M 2 has shifted towards the energetically uphill assembly of M 2 unequivocally demonstrates that the energy released from fuel-to-waste conversion is used to sustain the stationary non-equilibrium composition of the system. Thes ame insight emerges from an analysis of the kinetically preferred pathway in the system [Eqs (3)-(5)]: This set of equilibria provides,a ss um, the overall equilibrium is described by Equation (6): This equilibrium illustrates that the self-assembly of Mto form M 2 is now coupled to fuel consumption, thus permitting at ransfer of energy between the two processes.K inetic asymmetry in the system creates as ituation in which ac hemical fuel drives the self-assembly of Mi nto M 2 .I n this case,t he identification of the high-energy molecule as a" fuel" that drives the system to an on-equilibrium state leaves no room for ambiguity. [41]

Biology-Microtubule Formation
Microtubules are noncovalent protein polymers that play an essential role in intracellular organization. Microtubule filaments give structure and shape to eukaryotic cells,serve as tracks for intracellular transport, and are involved in chromosome segregation during cell division. Microtubule networks are highly dynamic structures which are continuously being remodeled through stochastic length fluctuations at the ends of the individual microtubules,aproperty referred to as dynamic instability. [137,138] Dynamic instability manifests itself through periods of persistent microtubule growth which are occasionally interrupted by moments of rapid shrinkage (called "catastrophe"), followed by aswitch back to polymer growth (called "rescue"). We will illustrate here that dynamic instability is aproperty that originates from kinetic asymmetry in the energy consumption pathway of this chemically fueled self-assembly process.
Microtubules are stiff,n anotubular structures with an outer diameter of around 25 nm (Figure 12). [19,139] Thesubunit of microtubules is ah eterodimer of a-a nd b-tubulin proteins-each with am ass of around 50 kDa-which associate in ahead-to-tail manner to form linear structures called protofilaments.T ypically,1 3s uch protofilaments engage in lateral interactions to form amicrotubule.Inthe microtubule lattice,l ateral interactions between protofilaments are a to a and b to b,e xcept at the seam, where a-tubulin binds btubulin. As ar esult of the longitudinal arrangement of abtubulins in protofilaments,m icrotubules have one end (À) where the a-subunits are exposed, and one end (+ +)where the b-subunits are exposed. Frequently,t he (À)-end of microtubules is anchored to microtubule organizing centers,such as the centrosome.Dynamic instability occurs predominantly at the (+ +)-end of microtubules.
Microtubule assembly and disassembly is regulated by guanosine triphosphate (GTP;F igure 12 a). Both a-a nd btubulin have abinding site for GTP,but these sites have very different properties and functions. [140] Theb inding site in atubulin (N-site) is buried within the tubulin dimer at the interface between a-and b-tubulin. GTP bound to the N-site plays as tructural role and is non-exchangeable and nonhydrolysable.Onthe other hand, the binding site in b-tubulin (E-site) is exposed on the surface of free tubulin and on the terminal tubulin subunits located at the (+ +)-end of microtubules.T he properties of this binding site change dramatically upon the incorporation of free tubulin onto the microtubule.With free tubulin, nucleotide exchange at the E-site is possible and the bound GTP is chemically stable.H owever, upon inclusion in the microtubule,n ucleotides bound to the

Angewandte Chemie
Reviews E-site become non-exchangeable and GTP is rapidly converted into GDP + P i . [141,142] Thed ifference in the properties of the E-site between free and polymerized tubulin constitutes the basis for kinetic asymmetry in this process and for that reason it is relevant to discuss what happens upon polymerization from as tructural point of view.
Microtubule formation initiates with an exchange of GDP by GTP in free tubulin. GDP-tubulin does not polymerize, but the exchange of GDP with GTP causes aconformational change in the T5 loop of b-tubulin, which activates tubulin for polymerization (Figure 12 b). [143,144] Polymerization of GTPtubulin is at hermodynamically favored process,w hich is evidenced by the fact that the use of non-hydrolysable analogues of GTP results in the formation of thermodynamically stable microtubules that do not display dynamic instability. [145] Tw oi mportant processes occur when GTPactivated tubulin attaches to the microtubule (+ +)-end. Firstly, lateral and longitudinal interactions with the microtubule lattice cause as traightening of the tubulin, which in the free form is curved with a1 2 8 8 kink at the dimer interface. Secondly,b inding to the polymer activates the E-site for the catalytic cleavage of GTP into GDP + P i ,which occurs rapidly after association of GTP-tubulin with the microtubule following first order kinetics .C onsequently,m icrotubules are composed mostly of GDP-tubulin, even though that unit by itself does not polymerize under equilibrium conditions. Importantly,t he conversion of GTP into GDP compacts the tubulin structure,leading to an increase in lattice strain in the microtubule.T he presence of lattice strain implies that these are high-energy structures composed of "spring-loaded" GDP-tubulin. Thereason why the structure does not collapse originates from the presence of as tabilizing GTP cap at the (+ +)-end of the microtubule.A lthough the precise nature of the GTP cap is still under debate,there is consensus that the microtubule end must be regarded as ad ynamic structure, where the amount of GTP-tubulin depends on the availability of free GTP-tubulin. [146] Ar educed influx lowers the amount of stabilizing GTP-tubulin in the cap and increases the possibility that the entire microtubule will collapse ("catastrophe").
Within the context of this Review,i ti so fr elevance to recognize the elements that install kinetic asymmetry in the cycle that describes GTP-fueled microtubule formation. The observation that GDP-GTP exchange can only occur in the E-site of free tubulin implies that fuel activation involves only the building block and not the assembly.Inaddition, only the E-site of assembled tubulin is catalytically active,w hich implies that energy dissipation leads to the formation of ah igh-energy assembly composed of GDP-tubulin. Consequently,akinetic preference for counterclockwise directionality exists in the system, which shows that GTP-GDP conversion and microtubule self-assembly are coupled processes.T he structural analysis illustrates that the energy released from GTP is stored as lattice strain in the GDP-rich assembly.

Chemistry-Self-Assembled Fibers with Dynamic Instability
Thei nstallation of kinetic asymmetry has so far rarely been considered in the design of synthetic dissipative selfassembly processes.A sd iscussed above,t he main focus has been on the formation of the self-assembled structure,which in nearly all cases regards the thermodynamically stable selfassembly corresponding to M* 2 in our general scheme.I n most cases,l ittle attention has been paid to the potential presence of the high-energy assembly M 2 ,a lthough, as we have seen in this section, it is the fuel-driven formation of this species that leads to valuable properties,such as the dynamic instability of microtubules.H owever,a lthough kinetic asymmetry has not been actively sought for, experimental observations strongly suggest that some systems behave in asimilar manner as microtubules.
Va nE sch and co-workers reported on the chemically fueled self-assembly of fibers which displayed properties that strongly resembled the dynamic instability of microtubules ( Figure 13). [147,148] This system relied on the activation of N,N'dibenzoyl-l-cysteine (DBC) for self-assembly by means of an esterification reaction with dimethyl sulfate.DBC by itself did not assemble under the experimental conditions (basic pH) because of electrostatic repulsion between the carboxylate groups.T he addition of dimethyl sulfate,w hich is as trong methylating agent, caused the formation of the monoester of DBC,w hich self-assembled into bundles of fibers with micrometer dimensions,t hereby leading to gelation of the aqueous solution. However,a tt he high experimental pH values,g radual hydrolysis of the methyl ester took place, which caused re-formation of the starting compound DBC, and spontaneous dissolution of the gel was observed over time.S imilar to the example discussed in the Section 5.3, it was observed that the lifetime of the gel could be regulated by tuning the rates of the forward (fuel concentration) and backward reactions (pH).
Tw oobservations strongly suggested that the properties of the system were not solely governed by the thermodynami- Figure 13. Chemically fueled driven self-assembly of fibers that show features reminiscento fthe catastrophic collapse of microtubules.

Angewandte Chemie
Reviews cally stable fibers (M* n )composed of the monoester of DBC, but that also the unactivated building block DBC played ar ole in the self-assembly process.F irstly,adelay was observed between changes in the concentration of the monoester and the rheological behavior of the gel in the decay phase.F or example,a tp H11, ag el state was still observed after 10 hours,w hereas the concentration of the monoester had already dropped to 0.6 mm after 5hours.T he second observation came from ac onfocal microscopy study, which provided insight into the behavior of single fibers during the dissipative cycle.T he addition of dimethyl sulfate at pH 11 resulted in the rapid formation of fibers,w hich reached amaximum length in atime that corresponded with the time required for the gel to reach the maximum storage modulus.N ext, the fibers entered as hrinking regime and decreased in length. However, rather than the expected gradual and simultaneous shrinking of all fibers,astochastic abrupt collapse of the fibers was observed, reminiscent of the collapse of microtubules.T he fibers shrunk only from their ends;afracturing or homogeneous dissolution of the fibers was not observed. Atime regime existed in which the growing and shrinking of fibers occurred simultaneously.A ltogether, these observations are coherent with the formation of highenergy fibers that are (partially) composed of the nonactivated building block DBC,o btained through the hydrolysis of the methyl esters of the building blocks in the fibers. Thes trong similarity with the dynamic instability of microtubules suggests that the fuel-driven cycle is regulated by as imilar kinetic scheme.Adetailed kinetic analysis of the activation and deactivation reaction steps would serve to unequivocally demonstrate the presence of kinetic asymmetry in this system.

Information Ratchet
In the previous sections we have discussed the different ways in which high-energy molecules regulate self-assembly processes.T he different scenarios have been presented in an order of increasing complexity ranging from straightforward templated self-assembly to the sophisticated kinetic schemes of driven self-assembly.The examples taken from biology and chemistry have illustrated that ac orrelation exists between the level of complexity in the energy consumption pathway and the functional complexity of the system. Compared to thermodynamically driven self-assembly (Class 1), the introduction of an energy dissipation element into the system permitted temporal control over the functions of the selfassembled material (Classes 2and 3). Thepresence of kinetic asymmetry in the energy consumption pathway permitted storage of the energy released from fuel-to-waste conversion in an on-equilibrium high-energy structure (Class 4). It appears that, if chemists are to harness the full potential of chemical fuel driven self-assembly,a ttention should be focused on this final class of systems.F or that reason, in this section we explore the chemical origins of kinetic asymmetry in more detail and show that the same kinetic asymmetry drives biomolecular machinery and synthetic molecular machines.
It is important to realize that Equation (2), which provides the composition of the system at constant chemical potential, can be rewritten as Equation (7) This shows that the ratcheting constant, K r ,i se xclusively determined by the rate constants of the fuel and waste reactions in steps 1a nd 3. Some of the rate constants are apparent first order rate constants that include the fuel and waste concentrations,w hich are constant under stationary conditions. [62] Thepotential installation of kinetic asymmetry (K r ¼ 6 1) in the system does not at all depend on the equilibrium constants for steps 2a nd 4, but exclusively on differences in the transition states of steps 1and 3. This shows that the ratcheting constant has an exclusively kinetic origin. Theo ccurrence of kinetic asymmetry in the system implies the presence of an information ratchet. In the case of selforganization, an information ratchet can be defined as as ituation in which the capacity of the building block to catalyze the fuel-to-waste reaction is different for the unassembled (M) and assembled (M 2 )s tates.

Information Ratchets Cause Unidirectional Motion
Information ratchets are well-known to cause unidirectional motion in biological and synthetic machines. [149][150][151][152][153] Unidirectional motion is an on-equilibrium phenomenon; random Brownian motion can only be overcome at the expense of energy consumption. [154] Therefore,t he information ratchet forms alink between chemically fueled unidirectional motion and the self-assembly of non-equilibrium molecular systems.A lthough this Review is dedicated to self-assembly processes,a nd although information ratchets have been extensively described within the context of molecular machines,wehave nonetheless preferred to discuss chemically fueled unidirectional motion in the same way we have discussed self-assembly to facilitate recognition of the analogy between directional motion and driven self-assembly.

Concept
An information ratchet in am olecular machine implies that the position of amoving unit determines the direction of its movement. [150][151][152][153] As one possible model to illustrate chemically fueled directional movement, we have taken al inear polymer composed of identical building blocks that contain abinding site for aguest (Figure 14 a). Theguest can move along the polymer track by hopping to an eighboring binding site on the left-(P i-1 )o rr ight-hand (P i+1 )s ide of the original position (P i ). However,m ovement of the guest is impeded by the presence of physical barriers between the binding sites.N ow,s uppose that the presence of ac hemical fuel triggers ac hemical reaction that causes the removal of the barriers,ap rocess indicated in Figure 14 aw ith the blue double-headed arrows.T his reaction-marked 1F and 3'Fleads to the transformation of the original structure P i into P* iR or P* iL ,respectively,depending on whether the barrier to the right-or left-hand side of the guest is removed. In the absence of the barrier, equilibration of the guest between two neighboring binding sites occurs,a nd-assuming that the binding sites are degenerate-both accessible binding sites will be occupied evenly (P* iR and P* i+1 on one side and P* iL and P* i-1 on the other side). Next, achemically distinct wastegenerating reaction reinstalls the barriers and, thus,r estores the original polymer,w here movement of the guest is blocked. Depending on which binding site was occupied in the activated structure,t his leads to the formation of structures P i-1 ,P i ,a nd P i+1 .A saresult of as ingle chemical activation-deactivation cycle,t he guest is now redistributed over the three binding sites P i-1 ,P i ,and P i+1 .
Theq uestion one needs to ask is how such af uel-driven cycle can lead to directional motion. Directional movement in the forward direction implies that, after one cycle,m ore guests have moved to position P i+1 compared to position P i-1 . It is evident that such as ituation can never be achieved for asystem that is fully symmetric,because in that case the cycles leading to P i+1 and P i-1 are identical and, consequently,a fter one cycle binding sites P i-1 ,P i ,a nd P i+1 must be occupied in as tatistically controlled 1:2:1r atio.A symmetry is required and in this model system, asymmetry is present in the structure of the building blocks that compose the polymer track. In our model, the structure is such that the binding site for the guest is closer to the barrier on the right-hand side than to the barrier on the left-hand side.I nc ases where the fuel-waste reactions that occur at the barriers are affected by the presence of ag uest in the binding site,t he asymmetry of the building block implies that the reactions occurring at the right-and left-hand barriers will be affected to different extents by the guest. In Figure 14 athis difference is indicated with the green tick and red cross above the blue doubleheaded arrows.I ti st his "communication" between the Figure 14. Chemically fueled unidirectional motion. a) Model used to illustrate how kinetic asymmetry leads to unidirectional motion. b) Energy diagram to explain how energy dissipation leads to motion in the forward direction. The green trajectory represents the preferential energy dissipation pathway leading to motion in the forward direction. The dark green arrow represents the step in which waste molecules are generated.
occupied binding site and the reactivity at the barriers that creates the conditions for the installation of an information ratchet, which drives directional motion. In our model, the binding of aguest enhances the rate at which the fuel removes the right-hand barrier (k 1,Ff @ k' 3,Ff ), causing am ore rapid population of P* iR than P* iL (see green trajectory in Figure 14 b). In the absence of the barrier,f ast equilibration between sites P* iR and P* i+1 occurs.However, the presence of guest in the binding site disfavors the backward reaction that re-installs the barrier (k 1,Wb ! k 3,Wb ), which implies the conversion of P* i+1 into P i+1 occurs faster than the conversion of P* iR back into P i .Asaconsequence of kinetic asymmetry in the cycle,the pathway that moves the guest from P i to P i+1 is much faster compared to any of the other possible pathways in the system that would either keep the guest in position P i or move it in the opposite direction to position P i-1 .The result of kinetic asymmetry is preferential motion in the forward direction.
In chemically driven self-assembly,c ontinuous energy supply is required to keep the high-energy assembly populated. [62] In chemically fueled directional motion, the situation is different because structures P i and P i+1 are identical on the molecular level. This difference emerges from an analysis of the energy flow in as ingle cycle.F uel activation can potentially lead to four different states,which are degenerate from an energetic point of view.H owever,a saresult of kinetic asymmetry in the activation pathway,t he activated structures P* iR and P* i+1 are predominantly populated. The presence of kinetic asymmetry in the deactivation pathway then leads to the preferential formation of P i+1 ,t hereby liberating waste.Ataconstant fuel concentration, this process repeats itself continuously and repetitive cycles drive the guest to position P i+2 ,P i+3 ,…, P i+n .

Biology-Unidirectional Motion of Kinesin
Kinesin 1i st he founding member of the kinesin superfamily of motor proteins that play an important role in many cellular processes,such as intracellular transport, mitosis and meiosis,and control over microtubule dynamics. [155] Kinesin 1 moves stepwise towards the (+ +)-end of the microtubule along single protofilament tracks (see Section 6.2). Each step bridges ad istance of around 8nm, which corresponds to the distance between two a/b-tubulin dimers. [156] Thed irectional movement of kinesin is driven by the conversion of ATPinto ADP + P i ,w hich proceeds at the expense of one ATPp er step.
Kinesin 1i sadimeric protein composed of two identical parts,e ach with am ass of around 120 kDa (Figure 15 a). Dimerization occurs through the formation of acoiled coil in the stalk domain, which positions two motor domains at one end and the cargo-binding domains at the opposite end of the structure.Akey element of the structure is the neck linker, asegment of 15 amino acids directly involved in ATP-induced structural rearrangement of the motor domains and the transduction of those changes to the translocation of cargo.
Them otor domains are responsible for directional motion, which is ac onsequence of the structural reorganiza-tion of three subdomains in response to ATPb inding and hydrolysis,a sw ell as ADP dissociation (Figure 15 b). [157][158][159] These structural changes affect three key processes:t he binding of the motor domain to the microtubule surface,t he exchange of nucleotides in the active site,and the movement of the neck linker. Ak ey role is played by the conserved "linchpin" residue (N255). Theinteraction of this residue with a-tubulin leads to the repositioning of the three subdomains. Disengagement of the N-terminal subdomain and the upper subdomain leads to opening of the so-called "nucleotide cleft", which allows dissociation of ADP.A tt he same time, alignment of the upper and lower subdomains strongly increases the affinity of the motor domain for the microtubule.S ubsequent binding of ATPt ot he active site of the microtubule-bound motor domain provides energy to organize the motor domain into an ew strained conformation. Through as eesaw motion, the N-terminal subdomain reconnects to the upper subdomain, which closes the nucleotide cleft, but also opens up ad ocking cleft for the neck linker, which subsequently binds in the direction of the microtubule (+ +)-end. This is akey step in the process,asitisthe moment where repositioning of the neck linker leads to directional movement of cargo along the microtubule.Atthe same time, the rearrangement leads to formation of the catalytic pocket and ATPi sr apidly hydrolyzed into ADP and P i. Following ATPh ydrolysis,P i dissociates but ADP remains trapped in the motor domain, as the nucleotide cleft remains closed. However,A DP is not able to maintain the motor domain in the strained conformation. Theinteraction between the upper and lower subdomains weakens and, as ac onsequence,t he motor domain loses its affinity for the microtubule surface and dissociates from the neck linker bound in the docking cleft.
Theq uestion here,i sh ow these processes combine to allow directional movement of kinesin 1a long the tubulin tracks.A sas tarting point, to describe as ingle step of kinesin 1onthe microtubule surface,wetake the state where both motor domains are strongly bound to the microtubule (Figure 15 c). [159] Strong affinity is assured by the presence of ATPinthe trailing head and the absence of nucleotide in the leading head. Then eck linker of the trailing head is con- Figure 15. Schematic representationo fkinesin 1. b) Structural changes in the motor domain as af unction of binding site occupancy by ADP and ATP. c) ATP-fueled directional motion of kinesin towards the (+ +)-end of amicrotubule. Figures (b) and (c) are inspired by Ref. [159].

Angewandte Chemie
Reviews strained in the docking cleft. Following the hydrolysis of ATP, dissociation of the trailing head from the microtubule takes places,b ut ADP remains trapped in the binding pocket and the neck linker remains positioned in the docking cleft. At this point, binding of ATPb yt he leading head promotes aforward step of the trailing head by docking the neck linker of the leading head. This movement also leads to release of the strained neck linker of the trailing head from the docking cleft. Attachment of the-former-trailingh ead to the forward tubulin causes the dissociation of ADP,w hich closes the cycle.T he astonishing perfection of this machine is evident from its performance:k inesin hydrolyzes ATPa t ar ate of around 100 molecules per second. [160] Considering the step size of 8nmp er molecule of ATP, this implies that kinesin moves along am icrotubule at as peed of around 800 nm s À1 ! Thed irectional movement of kinesin 1i sasophisticated process in which as eries of structural reorganizations follow each other in ah ighly orchestrated sequential manner. However,a sp reviously shown in av ery elegant manner by Astumian, [152] abstraction of the process by focusing on the kinetic scheme makes it apparent that kinetic asymmetry is the basis of directional movement. Thed imeric nature of kinesin 1isessential, as it creates an asymmetry between the two microtubule-bound motor domains.T he chemically distinct nature of the trailing and leading heads permits the installation of an information ratchet in which the binding and conversion of fuel is dependent on the position of the motor domain. Indeed, biochemical analysis shows that ATP hydrolysis occurs exclusively when the motor domain is in the backward position, but that the release of waste (ADP) occurs selectively from the forward position. Thecoupling of the activation and deactivation reactions to the relative position of the motor domains installs the information ratchet that drives unidirectional motion.

Chemistry-Unidirectional Motion in aNanomachine
In recognition of the fact that the biological machinery composed of protein-based motors and pumps is essential for maintaining the cell in anon-equilibrium state,chemists have been fervently dedicated to the development of artificial molecular machines for applications in materials science, nanotechnology,a nd drug-delivery systems.O ver the past decades,e normous progress has been made and intricate molecular systems have been reported that indeed show directional motion. However,most of these systems use light as an energy source,whereas molecular machines that exploit chemical energy are only recently emerging.
Avery elegant demonstration of how chemical fuels can be used to drive directional motion using an information ratchet has been provided by Leigh and co-workers ( Figure 16). [48] They prepared a [ 2]catenane featuring two mechanically interlocked rings of different sizes.Inacomparable role as the protofilaments of microtubules,the large ring serves as ac yclic track for the movement of the smaller ring. Thes mall ring can shuttle between two binding sites on the track, but the passage is blocked by the presence of two bulky stoppers-fluorenylmethoxycarbonyl groups-that are attached in proximity to the binding sites.R emoval of the bulky stoppers in the presence of base eliminates the barriers to movement and the small ring can equilibrate between the two degenerate binding sites.Importantly,the bulky stoppers can be re-introduced by ac hemical reaction with Fmoc-Cl, which reinstates the barriers to movement. This reaction is orthogonal to the cleavage reaction, which implies that experimental conditions can be created in which the [2]catenane is subject to continuous cleavage and attachment of the stoppers as long as chemical fuel-Fmoc-Cl-is available.
Directional motion requires the installation of an information ratchet, which implies that the rate of the forward and/ or backward reactions must be sensitive to the position of the moving component on the track. In the [2]catenane,s uch as ituation occurs in the attachment reaction that (re-)introduces the stoppers on the large ring. Theb ulky size of Fmoc-Cl renders this reaction more difficult when the neighboring binding site is occupied by the small ring. The decrease in rate relative to the same reaction next to the unbound binding site is around fivefold (k far-attach > k close-attach ). On the other hand, the rate of the cleavage reaction is not sensitive to the presence of the small ring (k far-cleave = k closecleave ), because this reaction is mediated by the triethylaminetriggered abstraction of ap roton from the fluorenyl methine group that is five bonds remote from the attachment point.
Starting from the [2]catenane containing the stoppers,i t can be illustrated how as ingle cleavage-attachment cycle causes directional movement of the small ring (Figure 16 b). Considering that the cleavage reaction is insensitive to the presence of the ring, removal of the top and bottom stoppers occurs at the same rate.I nb oth cases removal of the barrier permits movement of the ring to the other binding site through ac ounterclockwise or clockwise movement. The binding sites are degenerate and, consequently,the small ring will occupy these sites equally.However,since subsequent reintroduction of the stoppers occurs more rapidly at the anchoring points that are more remote from the ring, the equilibrium structures are not evenly converted back into the [2]catenane with two stoppers.For the clockwise pathway,the major product is the [2]catenane containing the ring in the opposite position, whereas for the counterclockwise pathway, the [2]catenane with the ring in the original position dominates.T hus,a fter as ingle fuel-waste cycle the ring has either moved in aclockwise direction to the other position or has remained in the original position. Net cycling in the clockwise direction continues as long as Fmoc-Cl is present in the system. Evidently,t he efficiency and complexity of this system is still considerably far from that of kinesin 1. The calculated rate is around 12 hf or each 3608 8 rotation and al arge quantity of fuel is consumed without generating motion, because the cleavage pathway is not selective. Nonetheless,this system provides afundamental contribution to understanding how information ratchets can be implemented in chemically fueled molecular machines.

The Design of Information Ratchets
Thed iscussions on driven self-assembly processes and unidirectional motion illustrate that information ratchets are essential to maintain ac hemical system away from equilibrium. [62] It is,therefore,important to take acloser look at the chemical origin of the information ratchet. Taking as reference the conceptual scheme used to introduce driven selfassembly,i ti si mportant to recognize that the reactions [Eq. (8) Thei mportance of this observation, which has been previously pointed out by Astumian, [63,152] is that the selfassembling building blocks involved in non-equilibrium chemistry must be catalysts for the conversion of fuel into waste. [161] However,for the installation of kinetic asymmetry, it is of crucial importance that the catalytic parameters of the building block, that is,the Michaelis-Menten parameters K M and k cat ,a re affected by the self-assembly process.K inetic asymmetry requires that fuel is bound preferentially by the unassembled monomer M-rather than by the assembly M 2but that catalysis is more efficient in the activated assembly M* 2 compared to the activated monomer M*. This is precisely what happens in microtubule formation (Section 6.2). GDP-GTP exchange is only possible when tubulin is in the unassembled form. Exchange does not occur when tubulin is embedded in the microtubule lattice.O nt he other hand, free tubulin is not catalytically active.The catalytic site is only formed when tubulin associates to form the microtubule.
It is important to realize that kinetic asymmetry is an essential condition to populate the high-energy assembly M 2 , but not sufficient by itself.Population of M 2 also requires that the fuel-to-waste conversion steps 1a nd 3o ccur faster than the equilibration steps 2a nd 4. In other words,M 2 must be populated at ah igher rate than the rate at which it disassembles into 2M.T he presence of ak inetic barrier to disassembly of the high-energy state is as econd essential requirement.
These insights provide avaluable piece of information for the design of chemically fueled driven self-assembly processes.B uilding blocks should be selected for their capacity to catalyze the conversion of fuel into waste.Itisworth pointing out that this does not necessarily need to occur through noncovalent interactions.T ransient covalent activation of the building block is equally possible,i na nalogy with covalent enzyme catalysis. [162] Thea ctivated building block should, of course,h ave the tendency to self-assemble in at hermodynamically controlled fashion, but, importantly,s elf-assembly should be accompanied by activation of the catalysis.Whereas catalyst activation in nature is extensively regulated by conformational changes in the enzyme,c hemists can achieve the same goal by using cooperative catalysis [163] and multivalency [164] (Figure 17). Cooperative catalysis implies that the catalytic site is composed of multiple catalytic units.T his can become apowerful tool if self-assembly can be used to bring those functional groups in proximity.R ecently,t he first examples have been described in which ac hemical fuel templates the formation of an assembly and, in doing so, creates the conditions for its own destruction. [165,166] On the other hand, the exploitation of multivalencyt oi nstall catalytic activity relies on changes in the local chemical environment (pH, polarity,ionic strength…) near the surface of am ultivalent assembly.T his may favorably affect the reaction rates or even open up different mechanistic pathways for fuel-to-waste conversion. [167] From an experimental point of view,astudy of the properties of the high-energy assembly M 2 would strongly benefit from the development of experimental set ups that allow the installation of anon-equilibrium steady state under continuous fuel consumption. An important step in this direction was reported by Hermans and co-workers,w ho developed am embrane reactor that permitted continuous exchange of fuel and waste,b ut not the building blocks. [131] Figure 17. Exploitation of cooperativity and multivalencyfor the installation of kinetic asymmetry.

Outlook
We have described how chemical fuels are used to control structural organization in both biology and chemistry.W e have identified different scenarios,w hich have been presented in an order of increasing complexity and, accordingly, with increased functionality.T he comparison between examples from biology and chemistry demonstrates the wide gap between the natural and synthetic worlds,inparticular related to the exploitation of chemical fuels to drive systems away from equilibrium. Evidently,this gap finds justification in the fact that chemists have only recently started to explore synthetic chemically fueled self-assembly processes with the precise purpose of creating artificial non-equilibrium systems. This initial phase is characterized by exploration, discovery, an increased understanding of the involved mechanisms,and al ogical discussion of key definitions.I ndeed, the precise meaning of non-equilibrium self-assembly is am atter of debate.W ew ould like to add to the debate the following reflections,w hich emerge from the conceptual treatments presented in this Review.
Equilibrium on the molecular level implies that the rate of the reaction in the forward direction equals the rate of the same reaction in the reverse direction. As ituation of nonequilibrium implies ad isparity between these rates;d etailed balance is broken. Such asituation can be established in two ways that, however,have afundamentally different origin and for that reason it is creating confusion. At ransient nonequilibrium situation is created when the concentration of one of the species involved in the reaction is changed (for example,t he fuel concentration). This leads to at ransiently higher reaction rate in the forward reaction until the systems evolves to the new equilibrium state.T his is what happens in any chemical reaction after mixing of the reactants.This is the basis of templated self-assembly under dissipative conditions (Class 2) and dissipative self-assembly (Class 3) when fuel is added batchwise.H owever,w eh ave discussed that, in these cases,the composition of the two equilibria (that is,between Mand M 2 (4) and between M* and M* 2 (2)) never changes as aconsequence of energy dissipation. Therelative ratio of free and assembled building blocks corresponds always to the composition at thermodynamic equilibrium. Tw ot hought experiments can be used to illustrate that the existence of anon-equilibrium state in these cases is indeed strictly related to variations in the fuel concentration. Firstly,i fo ne could imagine that at some moment in time all the fuel and waste reactions were instantly turned off,this would not lead to any shift in the concentrations of any species,because their ratios are entirely dictated by the equilibrium constants K 4 and K 2 . Secondly,i fs ystems from Class 2o r3would be studied at constant fuel and waste concentrations,t his would lead to ac omposition of the system that is entirely dictated by the relative thermodynamic stabilities of the systems components.U nder these conditions,a ll separate reaction steps would have identical rates for the forward and reverse directions.T he most populated species in the system would be M* 2 ,which is the thermodynamically most stable species in the system. Systems belonging to Classes 2a nd 3c an never develop as tationary non-equilibrium state for the selfassembly processes (equilibria 2a nd 4).
From an on-equilibrium point of view,a ne ntirely different situation is created when kinetic asymmetry in the energy dissipation pathway is present (Class 4). Likewise,inthis case, as tationary state is obtained under constant fuel and waste concentrations,b ut with ak ey difference in that detailed balance for equilibria 2and 4isbroken. In other words,under stationary conditions,p ersistent currents are present in the system, which indicates that as tationary non-equilibrium state is installed for the self-assembly processes.T his implies that only in this case do chemical fuels drive the formation of at ruly dissipative structure (M 2 ), according to the definition of Prigogine. [3] It marks the only case in which energy consumption is truly required to maintain structural order.
We would like to point out that this distinction is not an intent to value one class over the other. As illustrated by the examples from both biology and chemistry,a ll systems have their own specific utility.I ndeed, it is the entire ensemble of kinetically controlled processes that leads to the emergent properties of acell. From the origin-of-life perspective,aclear connection emerges with the concept of dynamic kinetic stability advanced by Pross and co-workers as being ac haracteristic feature of life. [5,168,169] It appears evident, though, that in terms of the development of synthetic systems with emergent properties,c hemical fuel driven self-assembly (Class 4) is potentially the most rewarding case.Itrepresents the only class in which chemical energy is transferred to aselfassembly process and stored in ahigh-energy organized state. It is,t herefore,w orth reflecting on the potential gain by focusing experimental attention on the formation of highenergy assemblies,such as M 2 ,rather than thermodynamically stable assemblies,s uch as M* 2 .M icrotubules use stored energy to do mechanical work by generating pushing and pulling forces.I nvitro studies have shown that as ingle depolymerizing microtubule can generate about ten times the force developed by amotor protein. [170] Dynamic instability of microtubules,w hich is ap roperty that derives from the accumulation of lattice strain, permits asearch and capture of kinetochores-which are specialized anchoring sites on the chromosomes-during cell division at arate that would not be possible for athermodynamically stable polymer. [171] In other words,the storage of energy can lead to improved properties. In this context it is worth adding that kinetic asymmetry is not limited to the molecular level, but can also emerge on the macroscopic level through spatially controlled energy delivery.F or example,w eh ave recently shown that ah ydrogel containing catalytic nanoparticles can be maintained in as tationary non-equilibrium state upon local irradiation with UV light. [172] Enhanced catalytic activity was observed under non-equilibrium conditions as ar esult of persistent concentration gradients in the gel. These observations indicate that the installation of kinetic asymmetry is an important tool that can be used to create non-equilibrium systems.E nergy storage in non-equilibrium systems leads to enhanced properties and this provides apowerful incentive to focus efforts on the development of synthetic self-assembly processes that display kinetic asymmetry in their energy dissipation pathways.