University of Groningen Enabling Darwinian evolution in chemical replicators Mattia, Elio

University of Groningen

Enabling Darwinian evolution in chemical replicators

Mattia, Elio

IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from

it. Please check the document version below.

Document Version

Publisher's PDF, also known as Version of record

Publication date:

2017

Link to publication in University of Groningen/UMCG research database

Citation for published version (APA):

Mattia, E. (2017). Enabling Darwinian evolution in chemical replicators. Rijksuniversiteit Groningen.

Copyright

Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).

Take-down policy

If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum.

5

5

1.

REPLICATION

AND

EVOLUTION

Understanding how life can be created de novo is extremely interesting and a challenge at the frontiers of knowledge. From systems chemistry to mathematics and from supramolecular chemistry to information theory, many are the branches that can yield fundamental insights into what makes living systems alive, into how life could be originated from inorganic material and into the fundamental relationship between evolution and the replication reaction. This chapter provides an overview of the main fields involved in the studies on the origins of life and on chemical evolution and serves as a starting point for the interested reader to explore these topics further. It also introduces the themes and the findings developed in the following chapters – exponential growth, far-from-equilibrium replication, and information transfer – and puts the experimental and computational results described there into a broader perspective. A short introduction to computational modelling, extensively employed in the work described in this thesis, concludes the chapter.

Parts of this chapter have been published:

Elio Mattia & Sijbren Otto. Supramolecular Systems Chemistry. Nat. Nanotech.

6

on 1.1. EVOLUTION AND THE THEORY OF LIVING SYSTEMS

Evolution is nowadays the focus of multiple research areas ranging from mathematics and physics to chemistry and biology, up to the social sciences, as subdisciplines such as evolutionary psychology and evolutionary economics confirm. Whereas its evidence is clear, resulting in features such as cooperation, speciation, and extinction, reproducing it de novo is a major challenge and the hardships scientists are confronted with indicate that we lack a fundamental understanding of the underlying structure of evolution.

Yet the topic is of extreme interest. Life appears to be complex, i.e., endowed with emergent properties that are not predictable based on information regarding its constituting parts alone. 1-3 _{Many definitions of life exist, such as the one provided} by Nasa of “a self-sustaining chemical system capable of Darwinian evolution”, yet none provides a conclusive insight into what makes living systems alive and how to create them from inert matter. Simple features such as replication, mutation and selection can result in a combinatorial explosion of complex behaviour and diversity of species.4-6 _{Understanding the emergent properties necessary for} evolution could allow us to predict the exact basic ingredients and pathways to create life de novo.

As mentioned above, evolution involves selection, i.e., survival of the fittest but also extinction of the weakest due to contingency or specific fitness in a given environment.7-11 _{Any analysis of genealogies, as Figure 1.1.1 illustrates, reminds us} that many species only persisted up to a given point in time, after which they became extinct.

Figure 1.1.1 | Genealogy tree of a select few early species, distributed on a timeline. The ubiquity

7

Biology however shows that survival and extinction are compatible with cooperation: species can organize themselves and by doing that they can become fitter in order to survive in the face of adverse conditions, e.g., forces that push towards extinction.13

Within the chemical sciences, studies on biological evolution merge with origins of life studies, namely on every possible way that life could have originated from simple chemicals, as opposed to strictly investigating the single way this process effectively took place along Earth’s history.14-22 _{We will focus on a few historical} aspects of studies into the origins of life in Section 1.4 of this first chapter.

The field of the origins of life has tight relations to various theoretical areas, including but not limited to mathematics, non-classical thermodynamics and computer science.

Numerous theoretical models have been developed to explain the complexity of life and its origins, namely the onset of evolution from absence of organization.23,24 Autocatalytic sets represent one possible formulation of the fundamental unit from which further evolution can take place.25-27 _{The autocatalytic set in Figure 1.1.2} illustrates a series of reactions (empty nodes) and chemicals (filled nodes), some of which act as catalysts for some reactions (dashed lines).

Figure 1.1.2 | Catalytic reaction system (CRS) with food set F=(a,b) containing a reflexively

autocatalytic and F-generated (RAF) set R=(r1,r2).25 _{Such a set constitutes a tight chemical}

cooperation model that might have played a prominent role in the early stages of the evolution of life from non-living material.

As noticeable from the diagram, species a and b can alone generate the whole

reaction network. The set (a,b) is therefore said to be the food set (F) of this catalytic

reaction system (CRS). Furthermore, catalytic processes in the network are such that reactions r1 and r2 are catalysed by species within the reactants of products of these same reactions. Therefore the set (r1,r2) is said to be reflexively autocatalytic

and F-generated, i.e., a RAF set.

The concept of autocatalytic sets is of importance to the field of the origins of life in that it represents a set of reactions that cooperatively, i.e., by means of autocatalysis, generate a series of products that are themselves actively involved

8

on in the formation of other species in the set. These constitute a robust set that is likely to resist adverse destructive forces and undergo replication, i.e., autocatalysis, thereby propagating information efficiently. These concepts are furthermore important in theories on autopoiesis.24,28-32

Non-classical thermodynamics, a field developed among others by Kondepudi and Prigogine, while not constituting an encompassing theory for the inherent difficulties of the underlying themes, has contributed many important breakthroughs such as the discovery of dissipative structures. Important to mention are the results on far-from-equilibrium chemical systems,33 _{which are} difficult to model and are thought to obey special laws as well as the standard thermodynamic laws: microscopic reversibility must also be maintained in individual equilibrium processes.34,35 _{While systems close enough to equilibrium} tend to minimize entropy production in their approach to the steady state (hence, in their transient states),36-41 _{it is postulated that far-from-equilibrium systems tend} to be attracted to a steady state where the rate of entropy production is maximized,42-46 _{illustrating the complexities and the current challenges within the} field. It is therefore often appropriate to state that far-from-equilibrium systems will tend towards a steady state that is an attractor in a suitable phase space.

Some theoretical problems are mathematically hard to solve.47-50 _{Despite a variety} of theories that inform us on important aspects of life,51-53 _{an encompassing vision} that also enables scientists to create de novo life is lacking. Experimentalists are therefore largely dependent on disparate results on often very different systems to progress in the area.

1.2. FROM EXPONENTIAL REPLICATION TO DYNAMIC KINETIC STABILITY

Exponential replication and dynamic kinetic stability are at the heart of evolutionary systems and are therefore key phenomena in origins of life studies. In the following we will describe the role they play in gaining a better understanding on how life could have emerged.

1.2.1 Autocatalysis and replicators

Replication of information-containing molecules is of utmost importance in life as we know it. Autocatalytic processes are at the core of molecular replication.54-56 _The existence of replicators ensures that the chemical identity of a given species is propagated by successive rounds of replication to the offspring. Replication is the fundamental process of life that enables persistence of living systems, as opposed to continuous and fast random formation and decay of living structures that in this way would not have the means to undergo evolution.

9

While in biology replication is mediated by complex biomolecular machinery, in the prebiotic world this process must have occurred through much simpler mechanisms. This postulate has spurred the development of relatively simple self-replicating and cross-self-replicating molecules57,58 _{based on nucleic acids,}59,60 peptides61,62 _{or fully synthetic structures.}63-66

The typical design of self-replicating systems is based on template-directed ligation of two halves of the replicator, to produce a noncovalent dimer of the autocatalyst. Subsequent dissociation of this duplex will liberate two replicators that can each mediate another round of replication, potentially enabling exponential growth of the replicator (Figure 1.2.1).

Figure 1.2.1 | Common replication mechanism. Template-directed ligation of two replicator precursors leads to the formation of a termolecular complex that reacts and subsequently dissociates, liberating two free replicator molecules. The duplex dissociation equilibrium influences the capability of the replicator to undergo fast and competitive replication.

Figure 1.2.2 illustrates a few examples of such replicating systems. Replication, which is mostly based on duplex formation, is generally highly irreversible. 1.2.2 Replication regimes: exponential, hyperbolic, parabolic

Exponential replication is only rarely realised, because achieving sufficient duplex dissociation is in most cases problematic. Von Kiedrowski demonstrated that, when a significant proportion of the replicator resides in the inactive duplex state, replicator growth is typically parabolic; the reaction has an order of 0.5 in the autocatalyst.67-73 _{Exponential growth occurs only when the order in autocatalyst is} 1. This difference in replication kinetics has important consequences for evolutionary scenarios where several replicators compete for a common resource. Equations 1.1-3 describe the kinetics of a simple competition:68-69,74

𝐹𝐹→ 𝑅𝑅 𝑅𝑅 (1.1)

𝑅𝑅 + 𝐷𝐷 → 𝐹𝐹 + 𝑊𝑊 (1.2) 𝑑𝑑[𝑅𝑅]

10

on where F is a food molecule, R is a replicator, D is a destroying agent and W a waste

molecule.

Figure 1.2.2 | Replicator examples: a hexanucleotide (top left),59 _{a peptide (top right and bottom}

left),62 _{and a fully synthetic system (bottom right).}64

Without the effects of a destroying agent, the order of replication r in the replicator

11

importance of the consequences in the following. For these purposes, let us consider Equation 1.1 individually and its corresponding rate equation:

𝑑𝑑[𝑅𝑅]

𝑑𝑑𝑑𝑑 = 𝑘𝑘𝑅𝑅[𝐹𝐹]𝑓𝑓[𝑅𝑅]𝑟𝑟 (1.4) If r=1, the growth in concentration of replicator R is said to be exponential. As a consequence, the competition between two exponential replicators feeding upon the same food molecules ends up in the death by dilution of the one with lowest kR:

[𝑅𝑅1](𝑑𝑑) [𝑅𝑅2](𝑑𝑑)=

[𝑅𝑅1]0𝑒𝑒𝑘𝑘𝑅𝑅1𝑡𝑡

[𝑅𝑅2]0𝑒𝑒𝑘𝑘𝑅𝑅2𝑡𝑡= 𝐶𝐶𝑒𝑒

(𝑘𝑘𝑅𝑅1−𝑘𝑘𝑅𝑅2)𝑑𝑑 (1.5) This situation is known as survival of the fittest.72

If r>1, the growth in concentration of replicator R is said to be hyperbolic. If food supply is unlimited, infinite concentrations are reached in finite times. Integrating the equations for r=2, the prevailing replicator is the one with the highest initial concentration [Ri]0 times the replication constant kR.

This situation is known as survival of the common: the intrinsic replicating fitness

is masked by the initial availability due to the replication kinetics.72

If r<1, the growth in concentration of replicator R is said to be parabolic. Solving for r=0.5, the “square root of autocatalysis” is obtained. The relative concentrations of two competing replicators is stable in the long run:

lim 𝑑𝑑→∞ [𝑅𝑅1](𝑑𝑑) [𝑅𝑅2](𝑑𝑑)= 𝑘𝑘12 𝑘𝑘22 (1.6)

This situation is known as survival of everybody.72 _{All species coexist. This situation} can favour cooperation between species but at the same time limits evolution as extinction is not possible.

It is important to notice that a replicator can be constituted by a single molecule, as well as by a network of reactions globally displaying replication behaviour, as shown in the scheme in Figure 1.2.3.

Figure 1.2.3 | Replication network. A small network replicates upon food molecule X and produces waste molecule Y. The formation of additional A1 species results in an increased rate of reaction for the entire autocatalytic network.

12

on As mentioned above, replicators following the standard duplex paradigm can display orders of replication between 0.5 and 1. However reaching an order of 1 is difficult if the association in the duplex is stable enough. In the following we will illustrate in which specific conditions the order can vary.

Most replicators follow the general reaction scheme in Equation 1.7 and are known as minimal replicators.

𝐴𝐴 + 𝐵𝐵 + 𝐶𝐶𝐾𝐾⇌1𝐴𝐴𝐵𝐵𝐶𝐶 → 𝐶𝐶2 𝐾𝐾2

⇌2𝐶𝐶 (1.7)

A termolecular complex ABC is formed from replicator C and food molecules A and B. It is assumed that the subsequent irreversible formation of C2 be the rate limiting step. The latter complex then dissociates to form two copies of the replicator.

Depending on equilibrium constants and temperature, the replication order in this reaction model can vary between 0.5 and 1.

In the hypothesis of rapid equilibration, the values of the equilibrium constants of formation of complexes ABC (K1) and C2 (K2) allow the observation of three limit regimes, i.e., parabolic, weak exponential and strong exponential growth.67

— Parabolic growth (r=0.5). If K1 is relatively low and K2 is relatively high, association of complex ABC is disfavoured while complex C2 tends not to dissociate after formation. Growth depends upon the concentration of A and B and upon the concentration of C2, i.e., it is parabolic (it has an order of 0.5) in the replicator C.

— Weak exponential growth (r=1). If both K1 and K2 are relatively low, formation is ABC is disfavoured, but after the irreversible step the duplex tends to dissociate to individual C molecules. Growth is first order in the replicator C and also depends upon the concentration of food molecules A and B.

— Strong exponential growth (r=1). If K1 is relatively high and K2 is relatively low, complex ABC easily associates and complex C2 easily dissociates. The same situation is obtained for high relative values of K2 as long as K1 is proportionally high. Growth uniquely depends upon the concentration of the replicator C.

Intermediate situations are also found between these limit laws, as shown in Figure 1.2.4. Temperature also plays an important role in establishing the replication order, as Figure 1.2.5 illustrates. In particular, it is found that parabolic growth prevails at intermediate temperatures between a strong exponential growth regime at low temperatures and a weak exponential growth regime at high temperatures. The generally neglected association of A and B into a complex AB results in the fact that the order of replication is lower than 1 at low temperatures, i.e., the strong exponential growth regime at low temperatures can hardly be observed. Furthermore, the models generally assume that the reaction of ABC to form C2 be the rate limiting step. At relatively low temperatures, dissociation of C2 becomes

13

rate limiting, contributing to replication orders lower than 1, i.e., parabolic instead of exponential.

Figure 1.2.4 | Replication order as a function of equilibrium constants. Depending on the strength

of the equilibria, the duplex model can display replication orders varying between 0,5 and 1.67

Figure 1.2.5 | Replication order as a function of temperature. Left, cooperative formation of complex ABC. Right, non-cooperative formation of complex ABC. Reaction orders of 1, i.e., exponential replication, are observed at very high temperatures or at very low temperatures,

compared to the temperatures most current carbon-based life thrives at.67

1.2.3 Replicating systems in far-from-equilibrium conditions

In the previous discussion, replication has been considered as the only active reaction pathway. If a destruction pathway is added to the system, the rate of replicator formation is given by Equation 1.3, in which kR and kD are the rate

constants for the replication and destruction reactions, respectively. The order of the replication process in food and replicator are given by f and r, respectively, and

the order of the destruction process in replicator and destroying agent are given by

d and x, respectively. Destruction forces alter the selection laws in the replicating

system, while at the same time introducing an important recycling factor that allows for evolution to take place by continuous destruction of the weakest replicator and reutilization of their building blocks for the faster production of a

14

on competitor, instead of by dilution of the worse growing population at the asymptotic limit in excess of food material.75

A fundamental result for replicating systems in far-from-equilibrium conditions is that in order for competition to result in destruction of the weakest replicator (a

necessary but not sufficient requirement for Darwinian evolution), the order of the replication reaction in the replicator has to be higher than or equal to the order of the destruction reaction in the replicator:74

𝑟𝑟 ≥ d (1.8)

In the most plausible replicator/destruction scenarios d equals 1, e.g., by a

bimolecular reaction with a destroying agent as shown in Equation 1.2 or by removal of products through flowing part of the solution out of the system. Therefore, for most common competition/destruction scenarios, an order in replicator of at least 1 (i.e., exponential replication) is required to achieve Darwinian evolution. Hyperbolic replicators are even rarer, due to the fact that a mechanism should be at play by which autocatalysis should accelerate upon formation of more replicator.

Exponential replicators are particularly able to take over competitively in an evolutionary race. While destruction of the weakest is not needed for evolution, should all replicating systems coexist, food resources would be limiting and there would not be many copies of the same species. As destruction of the weakest simply happens empirically, and when it does the exponential replicators prevail, it is important to understand the underlying causes, mechanisms and consequences. While systems have been reported that range from parabolic towards exponential replication,76-79 _{few systems have been reported which achieve r ≥ 1} non-autonomously80-82 _{or autonomously,}60,83 _{but even in these examples no general} mechanism for exponential growth was reported. The lack of design criteria for self-replicators capable of exponential growth constitutes a major problem that needs to be solved before approaches to Darwinian evolution of synthetic molecules can become mainstream.

We report in Chapter 2 a new mechanism by which exponential replication can be achieved based on a fibre growth/breakage mechanism acting on self-assembling replicators.

1.2.4 Dynamic kinetic stability and evolution

While replication plays a fundamental role in the origins of life, simple replicators cannot by themselves bring about evolution. A replication reaction is highly irreversible in its exponential growth regime, before scarcity of food molecules brings it towards a thermodynamically stable state. In the latter, the reaction is highly shifted towards the formation of the replication products, which generally display a high thermodynamic stability. Stable products in the classical thermodynamic sense are relatively inert to further transformations, unless a

15

pathway towards even more stable products is available. Therefore, replication generally produces inert chemicals that do not evolve further.

As shown in Figure 1.2.6, replication does however display unique characteristics that set it apart from other reactions.84-86 _{Common reactions head towards a} thermodynamic sink, resulting in the convergence of many pathways towards a common state, which in turn makes reaction history not relevant for the final result. On the other hand, replication reactions, being autocatalytic and nonlinear in nature, have the potential to diverge towards multiple possible outcomes. The final product is dictated by kinetic factors and by the history of the previous reactions.

Figure 1.2.6 | Thermodynamic and kinetic reaction spaces. Approach to thermodynamic equilibrium involves reaching a thermodynamic sink, i.e., a stable, non-reactive state; reaction history does not have any effects on the outcome. In systems governed by kinetics and far from equilibrium, such as replicating systems, a divergent behaviour can be observed: reaction history

influences the final/steady state of the system and the products that are obtained.86

An example of such a behaviour is also found in phenomena such as chiral symmetry breaking, a feature of kinetic systems and dynamic systems alike which derives from nonlinear effects, in particular exponential growth. Figure 1.2.7 shows the kinetic profile of an autocatalytic system displaying chiral symmetry breaking due to the nonlinear nature of the underlying reactions,75 _{an example of the kinetics} of the system randomly dictating the outcome of the reaction (any of the enantiomers can prevail) and of the equilibrium prevailing at long enough times. Replication reactions can also evolve towards the thermodynamic minimum, even though kinetic barriers can make that process significantly slow. However, the normal outcome of a simple replication reaction is a relatively stable product that does not exhibit significant further reactivity.

For evolution to happen, then, systems must be brought in states that continuously allow for change but at the same time are stable enough to retain the current results of evolution. Figure 1.2.8 shows schematically the basic processes required for such conditions, i.e, replication and destruction.

Dynamic kinetic stability (DKS) aptly represents the status that should be attained in order for continuous evolutionary transitions to occur.84-89 _{DKS indicates a state}

16

on of a replicator in which replication and destruction occur at the same time, thereby resulting in a macroscopically stable state. DKS states are therefore by definition far-from-equilibrium, as approach to equilibrium would mean either evolution towards a thermodynamically stable, and thus inert, state, or kinetic entrapment in a state that is protected towards further reactivity by high kinetic barriers.

Figure 1.2.7 | Far from equilibrium chiral symmetry breaking followed by approach to equilibrium in a nonlinear autocatalytic reaction system: achiral reactant A produces enantiomeric products R and S in starkly different amounts, generating an enantiomeric eccess; in the approach to thermodynamic equilibrium R and S can convert into each other, eventually reducing the

enantiomeric eccess to 0.75

Figure 1.2.8 | Minimal far-from-equilibrium replication scheme: food molecules can be converted into replicators by means of an autocatalytic replication reaction; replicators can be converted back into food molecules by means of a destruction reaction. Both reactions, i.e., replication and destruction, are irreversible and fuelled by external energy.

The DKS concept has gained interest in recent times and differs from a simple far-from-equilibrium states in that distance from equilibrium is maintained continuously and mainly in that it involves replication reactions. The autocatalytic

17

nature of the latter implies that replicators will hardly be destroyed completely, as shown in Figure 1.2.9. DKS conditions are therefore a platform for continuous evolution to occur: improbable events dictated by kinetics constantly have the chance to occur and will be stored in the current state of the chemical system if they are kinetically stable, i.e., if the replication/destruction conditions allow for a given set of concentrations to sustain themselves.

Figure 1.2.9 | Kinetics of replication and destruction: in the limit case of zeroth order destruction, when the concentration (or molar fraction) of the replicator is higher than a full destruction threshold (a molar fraction close to 0.3 in the illustration), DKS conditions will result in continuous replication/destruction with survival of replicator. The blue areas indicate states for which destruction will prevail, thereby decreasing replicator concentration. The grey area indicates states for which replication will prevail, thereby increasing replicator concentration.

DKS is meant to provide a bridging platform between chemistry and biology. As shown in Figure 1.2.10, Darwinian theory only covers later stages of evolution. DKS is meant to serve as a conceptual framework to explain the transition from non-life to simple life, as well as the later evolutionary stages.

Figure 1.2.10 | Evolution from non-life to simple life happened through a non-identified chemical evolution phase. Darwinian theory explains evolution from such simple life towards complex life.

18

on The DKS concept is related to many properties of life, such as:

1. Diversity and adaptation: as shown in Figure 1.2.6, systems governed by

kinetics show divergence in the reaction pathways, as opposed to systems governed by thermodynamics that converge to an equilibrium state. This characteristic results in the development of diverse systems in kinetic conditions.

2. Complexity: dissipative structures are known to bring about complexity.

3. Homochiral character: homochirality can be achieved in a nonlinear replicating

system far from equilibrium.75,89

4. Teleonomic (purposeful) character: purpose is only achieved once a replicating

system becomes capable of gathering energy by kinetic selection, hence freeing itself from thermodynamic constraints. At this stage the system can be said to have become purposeful.

5. Dynamic character: continuous replication and destruction allows for

evolution, whereas thermodynamically stable or kinetically trapped states do not show dynamicity.

6. Far-from-equilibrium state: DKS states are continuously involving irreversible

processes, namely replication and destruction, hence are far-from-equilibrium. The DKS concept is useful to explain the origins of life. However, a sudden evolutionary transition is highly unlikely and not needed. As Figure 1.2.11 shows, many steps can have brought about life, each of them progressively increasing the DKS of the system.

Figure 1.2.11 | Transitions towards life imply an increase of information content and therefore a decrease in entropy for the individual system, accompanied by an overall increase in entropy for

the universe.87 _{(a) Large transitions are very unlikely events, as a large decrease in entropy}

corresponds to a large increase of the improbability of the system. (b) Smaller intermediate steps with steadily higher DKS are more likely and might help to explain the formation of living systems from inanimate matter.

19

In Chapter 3 we show how a system reaching DKS may be implemented experimentally and how kinetic modelling aids to find the optimal conditions to expect evolutionary behaviour.

One of the major drawbacks of DKS is the inherent difficulty in quantifying it. We therefore try to provide a conceptual framework for the quantification of DKS. It is fundamental to consider that the state of a system under kinetic control can be depicted in an n-dimensional phase space involving chemical concentrations, rates of chemical reactions, bits of information, quantum states, configuration parameters such as distances, and any other parameter defining a system.

The DKS of the system could be defined quantitatively as the logarithm of the modulus of the surface integral (or flow integral) of the entropy production gradient field of such a phase space across the n-dimensional subspace of all microstates defining a given macroscopic state, integrated with a normal vector pointing inside the subspace, divided by the area integral of the (n-1)-dimensional surface bordering the aforementioned subspace of the phase space.

The aforementioned definition refers to the theory that assumes gradient in entropy production to indicate stability in a far-from-equilibrium system. This theory is currently under discussion,33 _{hence the definition of DKS should be} updated accordingly as new theory is produced and proven.

The variation in DKS between any two given states can therefore be theoretically expressed quantitatively using the definition above.

This framework, while setting the bases for the quantification of DKS, does not make the actual task consistently easier. Complex systems such as the ones displaying chaotic behaviour are on the other hand known for eluding simple quantification techniques: such systems are extremely sensitive to initial conditions and while approachable theoretically, simulating their behaviour is often problematic.

1.3. SUPRAMOLECULAR SYSTEMS CHEMISTRY IN FAR-FROM-EQUILIBRIUM REPLICATION CONDITIONS

Experimentalists use a variety of techniques and frameworks for studies in the origins of life. In the following we will review the common experimental toolset and related concepts.

The field of supramolecular chemistry focusses on noncovalent interactions between molecules, which give rise to molecular recognition and self-assembly processes.90 _{Since most noncovalent interactions are relatively weak and form and} break without significant activation barriers, many supramolecular systems are under thermodynamic control. Hence, traditionally, supramolecular chemistry has focused predominantly on systems at equilibrium. However, more recently, self-assembly processes that are governed by kinetics are becoming topical, where the

20

on outcome of the assembly process is dictated by the assembly pathway rather than the free energy of the final assembled state. The kinetic regime allows, in principle, for more elaborate structural and functional diversity of self-assembled systems. Within the kinetic regime one can distinguish between systems that reside in a kinetic trap and far-from-equilibrium systems that require a continuous supply of energy to maintain a stationary state. In particular, the latter systems have vast functional potential (life is a prime example), and the design and exploitation of such systems represents a promising new research direction. Specifically, we will compare the different thermodynamic regimes using some selected examples and discuss some of the challenges that need to be addressed when developing new functional supramolecular systems.

Supramolecular chemistry is in many aspects inspired by biology.91-93 _Indeed, supramolecular assemblies are an essential element of biological function. Compelling illustrations of complex assemblies carrying out important cellular tasks abound; e.g., bilayer membranes, ribosomes and nucleic acid transcription machinery. In some cases, thermodynamically driven molecular assembly processes are sufficient for biological functions. Examples include the self-assembly of lipids giving rise to a cell membrane or the formation of a stable host-guest complex that triggers a given biomolecular process. However, for many of the more advanced biological processes self-assembly processes that are by themselves thermodynamically downhill are insufficient and function only emerges by processes that continuously dissipate energy. Continuous free energy consumption activates the biological supramolecular machinery and thereby enables the chemical reactions that make cells alive. Hence, life is far from equilibrium.

In biological systems, energy is used in two complementary ways. Firstly, free energy from processes such as ATP hydrolysis is used to perform other chemical reactions that are otherwise thermodynamically unfavourable. Phosphorylation enzyme catalysis and transmembrane ion pumping are prominent examples of such pathways. Secondly, free energy is used in processes which not only represent a cellular function, but at the same time also produce more copies of the molecules which carry out that cellular function; e.g., protein synthesis in a ribosome. Far-from-equilibrium behaviour is ubiquitous in biology and at the heart of Darwinian evolution. By having biomolecules (and also entire organisms) constantly formed and broken down, the functions carried out by the molecular assemblies (or the organisms) can undergo a process of selection and adaptation. The stability of the resulting far-from-equilibrium supramolecular structures does not derive directly from thermodynamics, but from the degree of adaptation of their function to the environment.86-88

The predominance of far-from-equilibrium thermodynamics in biology contrasts starkly with the mode of operation in the vast majority of man-made supramolecular systems. Three different thermodynamic regimes (Figure 1.3.1) may be identified for supramolecular assemblies:

21

1. Equilibrium assemblies. A stable assembly, which is likely to persist for a long

time (e.g., years, or aeons) without undergoing any further spontaneous processes, due to its inherent thermodynamic stability.

2. Kinetically trapped assemblies. Systems that are transiently durable, trapped in

a local minimum of the energy landscape, but which could potentially access relatively more stable states. It would take time (e.g., minutes, or years), or the direct supply of an activation energy, for them to be converted into more stable structures.

3. Far-from-equilibrium supramolecular assemblies. These are assemblies that

require a continuous supply of energy to persist and could endure any period of time as long as energy is supplied. If the energy supply stopped, the system would fall apart (within, e.g., fractions of a second, or days) and end up in the thermodynamic minimum state (or in a kinetic trap en route). The continuous energy-driven transformations that these structures undergo makes it possible for them to have interesting (and sometimes unpredictable) emergent functions.

Figure 1.3.1 | Thermodynamic regimes of a chemical system. (a) Thermodynamic equilibrium: the final product distribution is pathway irrelevant and following the Boltzmann distribution. (b) Kinetic control: the final product distribution depends upon control over the synthetic pathway, the products are kinetically trapped in their state. (c) Far-from-equilibrium systems, dissipative and also under kinetic control: the final product distribution is essentially governed by control over synthesis and degradation pathways.

There has been a clear recent trend in supramolecular chemistry: the field started with the study of systems under thermodynamic control and is currently seeing a shift towards kinetically controlled systems. There is an important future for supramolecular systems far from equilibrium as these harness the richest functions: the capability of sustaining oscillations, concentration gradients, unidirectional movement, and other phenomena up to the most complex ones such as the functioning of living organisms and their evolution are in fact properties which can be observed only under far-from-equilibrium conditions; furthermore, the inherent added complexity of a system far from equilibrium, which is due to the continuous interconversion among multiple structures adds to the system the possibility of emergence of entirely new unpredictable functions, albeit not

22

on guaranteeing their existence. This trend from thermodynamic towards kinetic control and far-from-equilibrium conditions is reflected in an increase in complexity of supramolecular structures that are currently being investigated, increasing the impact of supramolecular chemistry in systems chemistry.

Systems chemistry emerged in recent years as a new field that studies chemical systems endowed with a high degree of complexity, which allows them to show emergent properties, i.e., properties of a whole system which are not predictable solely from the properties of its constituting parts.4,6,94-95 _{Examples of emergent} properties of chemical systems range from oscillatory behaviour to self-replication and from chiral symmetry breaking to molecular recognition.5,96-98 _{Supramolecular} systems present many possibilities to show emergent behaviour, particularly when under far-from-equilibrium conditions.

However, thus far, very few experimental examples of far-from-equilibrium supramolecular systems have appeared in the literature.

The structure of this section will follow the development of supramolecular chemistry from thermodynamically controlled, via kinetically controlled to far-from-equilibrium systems. We will highlight a few selected examples from the literature for each of these thermodynamic regimes that are, in our (inevitably rather personal) opinion, representative of the current state of the art in the field. 1.3.1 Systems under thermodynamic control

Structures under thermodynamic control represent stable systems with properties that result from the molecular structure that they adopt and the corresponding supramolecular interactions within it. Structures of impressive architectural complexity have become accessible, based a continuously improving understanding of non-covalent interactions. We have selected a few examples to illustrate the current state of the art. Among them are mechanically interlocked molecular structures that may be accessed by making use of template-directed synthesis. An appropriate example in this context is the very elegant synthesis of Borromean rings as shown in Figure 1.3.2a.99 _{Borromean rings are an arrangement} of three macrocycles which cannot be separated without breaking one of the rings. This structure was templated by transition metals and relied on reversible imine bond formation for its synthesis.

Another important class of thermodynamically stable structures are supramolecular polymers, in which the monomer units are held together by noncovalent interactions such as hydrogen bonds.100 _{The properties of the} monomers which form such supramolecular polymers and the effects of the intermolecular interactions that the latter form are directly translated into mechanical properties which are observable at the macroscopic level, i.e., polymer rigidity or flexibility. These materials differ from traditional covalent polymers in that the molecular weight distribution of supramolecular polymers is not fixed during their synthesis, but defined by the experimental conditions including

23

monomer concentration, temperature and the medium. An example of such structure and the underlying H-bond interactions is shown in Figure 1.3.2b. A recent tool which has proven very useful for discovering and studying thermodynamically stable supramolecular systems is dynamic combinatorial chemistry,101-105 _{whereby building blocks are allowed to undergo dynamic covalent} exchange leading to the formation of library members which stability will determine their relative abundance within the dynamic combinatorial library that they create. Dynamic combinatorial chemistry has been used for the exploration and discovery of stable host-guest interactions106 _{and mechanically interlocked} structures.107 _{For example, the Sanders lab recently discovered a trefoil knot in a} dynamic combinatorial library based on a building block containing three naphthalenediimide units (Figure 1.3.2c). This iconic structure formed spontaneously simply by allowing the dithiol building block to oxidize in an aqueous solution, giving rise to an equilibrium mixture of disulfides which was dominated by the knot.

Building on work from other groups (Sauvage, Stoddart), thermodynamically stable structures were also exploited at the macroscopic level by engineering multistable systems such as muscle-like supramolecular polymers.108 _{The rotaxane shown in} Figure 1.3.2d is held together by the crown ether binding to the protonated benzylic amines. Deprotonation of these amines causes the crown ester to shift to the triazonium ring, extending the length of the molecule. Several of these rotaxanes were linked together through coordination of the tripyridyl termini with a metal ion. The possibility to use different pH conditions to induce a length change of the polymer by switching between two stable structures is also a result of the supramolecular interactions that keep together the individual building blocks within such a polymer. In this example, an emergent property, i.e., macroscopic length change, arises not just from one single molecular or supramolecular structure but from the possibility for a system to transition between two states (Figure 1.3.2d).

Equilibrium supramolecular systems, as we have seen from the examples above, reside in their lowest free energy state. The only way for making these systems move away from that state is to change the free-energy landscape such that a new energy minimum is created. In the example in Figure 1.3.2d the free energy landscape was changed by altering the pH allowing the transition to a new state. By creating these two different best states it is possible to harness the transition between them as a macroscopic length change, which is an emergent property of the transition itself but not of any of the two states as such.

1.3.2 Systems under kinetic control: kinetic traps

In the following we will turn our attention towards kinetically controlled assembly processes. Kinetic states are different from the thermodynamic minimum of the system and are therefore endowed with interesting properties arising from possible transitions to the thermodynamic minimum. Their properties arise from the one

24

on single defined chemical structure that they adopt. In principle, many different kinetically trapped states can exist for a given system.

Most bilayer vesicles formed from phospholipids are examples of supramolecular systems under kinetic control, i.e., they form rapidly under certain conditions, but are usually transient products, that convert, with time, to the more stable hydrated crystals. Depending on the conditions of formation, control can be exerted over the shape and size of the vesicles, reflecting different kinetically trapped states. Transitions between states are possible, for example by allowing for vesicles to fuse. However, such transitions are only feasible if the new state has a lower thermodynamic stability than the old state.109-111

Many examples exist of kinetically controlled vesicle formation and the topic is of fundamental importance in the field of the origins of life.112-121

The kinetics of formation of a supramolecular system might also give rise to pathway complexity where the assembly process passes through metastable structures at first, followed by their conversion into the more thermodynamically stable structure later.122,123 _{This scenario was recently described for a unstable} supramolecular polymer that undergoes helicity inversion into the final stable product (Figure 1.3.3a). The chiral SOPV monomer contains a self-complementary H-bonding unit that dimerizes. The dimers then stack to form helical aggregates. If one is able to control the kinetics of formation of kinetically trapped supramolecular structures it becomes possible to access many different metastable structures from the same building blocks, by carrying out the assembly process under different experimental conditions.124-128 _{Oligothiophene derivatives, for} example, can produce various polymorphic self-assembled structures all based on hydrogen bonding between the amide groups,124 _{shown in Figure 1.3.3b.}

Catalysis is an exquisite instrument for exerting control over kinetic pathways and thereby accessing kinetically trapped systems. Examples include catalysis performed by external molecules, or autocatalysis, in which the assembly product accelerates its own synthesis. Both can determine which structure forms at a higher rate and therefore with higher abundance.

Using catalysis, transiently stable structures with particular useful properties can be produced. For example, gel strength can be controlled by use of enzymatic catalysis to generate different supramolecular products by varying enzyme concentration.129-131 _{These products are transiently stable for a sufficiently long} time for their properties to be analyzed and exploited. Figure 1.3.3c shows an example where enzymes (visible in the AFM image) that hydrolyze esters produce gelators which form gels of different strengths depending on the enzyme concentration.132,133

Autocatalysis can further expand the range of interesting properties that can be attained in kinetically trapped supramolecular systems. One of them is chiral symmetry breaking, which is a major phenomenon of interest in the study of natural homochirality.134-140 _{The catalytic activity of peptidic systems is of special interest} in the field of the origins of life.141,142

25

Figure 1.3.2 | Supramolecular systems under thermodynamic control. (a) Molecular Borromean

rings, illustrations of the corresponding topology, coordination sphere and retrosynthesis.99 _(b)

Supramolecular polymers, schematic representation and depiction of the hydrogen-bonding

patterns responsible of the macroscopic properties of the polymers.100 _{(c) Stable trefoil knot}

discovered by dynamic combinatorial chemistry, illustration of the formation equilibria and

schematic topology.107 _{(d) Muscle-like supramolecular polymers, for which a pH-stimulus can}

26

Figure 1.3.3 | Supramolecular systems under kinetic control (kinetic traps). (a) Supramolecular polymers of dimers of the SOPV building block; the right-handed helicity is obtained as a transiently

stable product.122 _{(b) Polymorphs of the same polythiophene derivative (in the EM pictures) are}

obtained under kinetic control by using different experimental conditions.124 _{(c) Hydrolytic enzymes}

convert a methyl ester into a gelating carboxylic acid (which forms fibres as shown in the AFM

27

Replication of supramolecular structures or of molecules thanks to the formation of supramolecular assemblies is another prominent phenomenon that directly results from autocatalysis and which is of fundamental importance in the studies on the origins of life.59,61,63,143

Where above we have discussed the use of dynamic combinatorial chemistry at equilibrium, we recently reported that the same technique can also be used for the development of kinetically trapped supramolecular fibres which show autocatalysis through a fibre elongation and breakage mechanism. Specifically, thiol-functionalized peptides shown in Figure 1.3.4a undergo air oxidation, initially forming a library dominated by interconverting trimeric and tetrameric disulfide macrocycles. A nucleation-growth mechanism subsequently leads to the formation of fibres of larger macrocycles, such as hexamers, within two weeks from the start of the experiment. These larger macrocycles are only stable in the aggregated form. Interestingly, the aggregates form only when the samples are agitated. Mechanically-induced fibre breakage turned out to be crucial for converting primary nuclei into secondary ones, which enabled the autocatalytic, exponential growth of the fibres, eventually resulting in the total depletion of the smaller macrocycles (Figure 1.3.4a). Experiments which yield different macrocycle distributions under different initial conditions have confirmed the kinetic nature of the self-replication process.144,145 _{This system represents the experimental basis} upon which much of the work in this thesis is based. A more detailed description of the system is provided in the introductory Section 2.1 of Chapter 2.

Autocatalysis is also important in information propagation. In a recently reported system82 _{based on DNA origami, transient replicating structures were found to be} capable of propagating and maintaining a particular sequence of nucleic acids (Figure 1.3.4b), thereby preventing the sequence from being lost even if the transient nature of the assembly could make some of the sequences undergo degradation. The experimental system involved a pool of different DNA tiles characterized by specific sequences on their sticky ends; the tiles could nucleate larger aggregates which could laterally replicate following a set of rules dictated by sequence complementarity between the available tiles in the pool. In the presence of a seeded tile sequence, growth and breakage would ensure that the initial sequence would dominate as the kinetic product in the final product distribution. 1.3.3 Systems under kinetic control: far-from-equilibrium regime

Neither the thermodynamically stable, nor the kinetically trapped systems discussed above use energy to maintain their integrity. The interest in such systems derives mostly from the properties of the state (i.e. supramolecular structure) that the molecules adopt. In some cases, the transition between structures can give rise to interesting behaviour. For kinetically controlled systems the selective reduction of energy barriers can allow the system to move to thermodynamically more stable states on the same energy landscape. For thermodynamically controlled systems a change between states requires changing

28

on the free-energy landscape. Let us now turn our attention to far-from-equilibrium supramolecular systems chemistry. Far-from-equilibrium supramolecular systems have intrigued experimental scientists but their realization has often been elusive, due to the intrinsic difficulties in imagining systems which exist only in far-from-equilibrium conditions. Also the lack of understanding of the fundamental differences that exist between equilibrium assemblies and far-from-equilibrium systems and a lack of appreciation of their fundamental importance has hampered progress. A few examples however exist and illustrate well the role of far-from-equilibrium conditions in the realization of a supramolecular system.146

Figure 1.3.4 | Supramolecular systems under kinetic control (kinetic traps): replicators. (a) Thiol-functionalized peptide replicator which forms a dynamic combinatorial library of macrocycles, the larger of which nucleate into fibres, which elongate and break thanks to mechanical forces, yielding

exponential growth of the replicating fibres.144,145 _{(b) DNA origami tiles endowed with sticky ends}

hybridize selectively with complementary ends on adjacent tiles. In the presence of an initial seed with a predefined tile sequence, sticky end complementarity induces the lateral replication of the initial sequence from a pool of tiles. Further growth of building blocks from solution and crystal breakage of the larger aggregate ensure exclusive kinetically controlled replication of the initial

sequence seed; other possible sequences are not copied competitively.82

The experimental realization of a far-from-equilibrium system is in principle straightforward. The fact that a system is in far-from-equilibrium conditions does however not guarantee per se the emergence of qualitatively new properties. The simplest paradigm for far-from-equilibrium chemistry is to study a reaction during its approach to equilibrium; an example where a characteristic new emergent property does arise is the well-known Belousov-Zhabotinsky reaction, which features concentration oscillations in time and space; such a system would spontaneously evolve towards either equilibrium or a kinetic trap eventually, hence not allowing the emergence of persistent properties. In order to observe stable features in a far-from-equilibrium system it is therefore necessary to allow it to

29

reach a steady state (this is in some cases intrinsically not possible), e.g., by operating it under continuous flow of matter into and out of the system itself; microfluidic setups technically enhance the tuning and controlling possibilities in the experimentalists’ hands in such cases. Far-from-equilibrium conditions are however possibly best understood with a minimalist approach to the necessary ingredient, i.e., adding a continuous source of energy, and removing exchange of matter. Energy flow is the most fundamental element to create far-from-equilibrium conditions and can already be attained by employing photons only; the area of photochemistry has therefore a privileged role in the contribution to the development of far-from-equilibrium systems chemistry.

In the following, we will have a look at a few examples, focusing on a few important points:

1. What the far-from-equilibrium emergent property characteristic of that system is.

2. Whether that property is unique to far-from-equilibrium conditions.

3. Why the system is far from equilibrium, i.e., what are the continuous energy-driven irreversible processes that keep it far from equilibrium and without which the system with its peculiar properties would fall apart.

4. The role of at least two different structures in the realization of far-from-equilibrium conditions.

5. What state the system would fall to in absence of energy consumption. The first example involves nanoparticles functionalized with azobenzene-containing thiol derivatives as shown in Figure 1.3.5a. This system self-assembles only when subjected to UV irradiation, thanks to the change in polarity that occurs due to light-induced azobenzene E/Z isomerization.147 _{When the UV irradiation is} turned off, the self-assembled structures fall apart spontaneously within a few minutes and the nanoparticles disperse again into the solution. In order to keep the reverse Z-to-E isomerization process steadily active and fast at all times, continuous irradiation with visible light is required. The far-from-equilibrium self-assembly process may be exploited for the producing light-sensitive inks: due to plasmon resonance, the aggregates have a different apparent colour than the dispersed nanoparticles.

The far-from-equilibrium emergent property which arises in this system is the formation of supramolecular self-assemblies only in the presence of UV light. Of course, equilibrium or kinetically trapped self-assembled systems also exist, however in the present case the structures are kept together by the utilization of energy in the form of light and fall apart without. The self-assembled structures exist thanks to the continuous transformation of two different chemical structures, i.e., the E and Z isomers, into each other. Without this continuous transformation, the more stable E isomer would prevail and the assembly would fall apart. The second example deals with gelation. A gel was obtained by continuous methylation of a carboxylic acid precursor (which does not form gels itself due to electrostatic repulsion) by using methyl iodide as the fuel.148 _{The gel falls apart}

30

on when the fuel is consumed (Figure 1.3.5b). Energy provided by the fuel in this case keeps the supramolecular system in the gel state and the system could be cycled between the solution state and the gel state by subsequent addition of new fuel. The far-from-equilibrium emergent property which arises in this system is the formation of a gel only in the presence of fuel. Gels can also be produced by catalysis, as shown before, and are in many cases kinetically trapped systems. However, the gel structure in the present example exists thanks to the utilization of energy in the form of fuel, i.e., methyl iodide, and falls apart without. The gel structure persists thanks to the continuous transformation of two different chemical structures, i.e., the free carboxylic acid and the methylated derivative, into each other. Without this continuous transformation, i.e., in the absence of methyl iodide, the carboxylic acid would be the most stable species and the gel would disintegrate. An analogous system based on two competing enzymatic reactions has also been recently reported by the Ulijn group.149

Reaction/diffusion systems also represent far-from-equilibrium setups where supramolecular organization can be obtained by dissipation of energy. It is possible to use UV light to obtain steady states which involved pH gradients by using an appropriate diazobenzene derivative (Figure 1.3.5c) which is more acidic in its Z-isomer than in its E-isomer due to breakage of a H-bond.150 _The far-from-equilibrium emergent property which arises in this system is long-range supramolecular order, i.e., gradients in concentration, only in the continuous presence of energy inputs such as UV light. Stable chemical gradients are another emergent property which is attainable only in far-from-equilibrium conditions, lacking which, homogeneous chemical systems would be obtained. Gradients are ubiquitous in nature and serve diverse and important functions. This dynamic system is far from equilibrium since it involves continuous isomerization processes thanks to the utilization of energy in the form of photons and this state ceases to exist when energy is not supplied to the system any longer. Even though in this case there is no traditional supramolecular assembly based on non-covalent interactions, a long-range supramolecular structure arising from the competitive redox reactions and diffusion processes emerges when UV light is constantly supplied to the system. Gradients in this chemical system only arise thanks to the continuous transformation of the two isomers into each other. Without energy consumption, the most stable isomer would prevail, cancelling out any gradient in the system.

Gradients have also been obtained under electrochemical control.151 _{In this case,} the energy was supplied by constant redox processes at two electrodes. Ferrocene carboxylic acid was continuously oxidized and reduced at the two respective electrodes, thereby forming a concentration gradient in the solution between the electrodes. A surface that is functionalized with β-cyclodextrins was placed between the electrodes and brought in contact with the ferrocene solution. The cyclodextrins on the surface are capable of binding a fluorescently modified adamantane guest as well as the reduced (but not oxidized) ferrocene derivative.

31

Figure 1.3.5 | Far-from-equilibrium supramolecular systems. (a) Nanoparticles functionalized with diazobenzene derivative MUA are capable of self-assembly in a gel matrix only when continuously irradiated with UV light, due to the change in local dipole moments on the nanoparticle surfaces;

in absence of UV irradiation, the self-assembled structures fall apart.147 _{(b) A dicarboxylate precursor}

which exclusively gelates upon methylation is exposed to methyl iodide, which activates it, resulting

in the formation of a gel; when the fuel, i.e., methyl iodide, is consumed, the gel collapses.148 _{(c) A}

photoactive acidic phenol is exposed to UV irradiation in a specific region of a sample, resulting in

the formation of a pH gradient due to the continuous isomerization/diffusion processes.150 _{(d) An}

externally applied electric potential across two electrodes induces a surface concentration gradient in electrochemically active adamantane derivatives, which can be visualized by fluorescence

imaging techniques.151 _{(e) Excitation steps from an STM tip induces isomerizations that allow}

32

on Displacement of the adamantane groups by reduced ferrocene led to the formation of a gradient in the surface concentration of the adamantane derivative opposite to that of the reduced ferrocene derivative (Figure 1.3.5d). The gradient was observed by fluorescence microscopy.

The far-from-equilibrium emergent property which arises in this system is, again, long-range supramolecular order, i.e., gradients in concentration. The dynamic system is far-from-equilibrium since it persists only in the presence of continuous redox processes thanks to the utilization of energy in the form of electrical current and this state ceases to exist when the energy supply is stopped. Without a current, the most stable arrangement would prevail and gradients would disappear. Far-from-equilibrium systems can also result in directional motion on the molecular scale. Feringa et al. recently reported152 _{how energy for electronic and} vibrational excitations supplied through an STM tip leads to double bond isomerization and stereoisomerization inducing the directional motion of a four-wheeled molecule, a nanocar, across a Cu(111) surface (Figure 1.3.5e).

The far-from-equilibrium emergent property which arises in this system is molecular motion. Unidirectional movement is an example of an emergent property which cannot be obtained by one single stable or kinetically trapped structure and is unique to equilibrium conditions. The system is far-from-equilibrium since it results in molecular motion by the utilization of energy in the form of molecular excitations. This system also obtains its main property, movement, from continuously interchanging between many different electronic and spatial configurations, depicted in Figure 1.3.5e. In the absence of an energy supply, the four-wheeled molecule would remain anchored to the copper surface in one of these states. A similar paradigm involving the use of light to attain far-from-equilibrium conditions is now also being exploited with different chemistries by other research teams.153

Many other examples of far-from-equilibrium self-assembled chemical and biological systems have appeared.154-160 _{Nonetheless, the field is still in its infancy.} 1.3.4 An experimental toolset for origins of life studies

There has been a clear trend in supramolecular chemistry to move from thermodynamically controlled systems to ones under kinetic control and, more recently, also to systems that operate far from equilibrium.

Kinetically controlled systems have a structure that is generally one of many possibilities and its formation requires rather specific conditions, such as the presence of a catalyst or autocatalysis. Such systems may already give rise to interesting phenomena such as replication, chiral symmetry breaking and propagation of information. The use of kinetically controlled systems is limited by the intrinsically lower thermodynamic stability with respect to other more stable structures. Thermodynamically stable structures, on the other hand, are often sturdy and can be used for structural purposes or for their recognition properties, but are the most limited of all, when it comes to functional potential. Both

33

equilibrium and kinetically trapped systems are limited to the functions that correspond to the properties of the single relatively stable state in which they exist. Far-from-equilibrium systems owe their function to a continuous transitioning between different structures, rather than to the properties of one particular assembly and, most importantly, to the fact that they tap into an energy source. Notwithstanding the small number of examples that appeared in the literature up to now, far-from-equilibrium supramolecular systems can exhibit unique behaviour which emerges from the variety of states that these systems access, and that cannot be attained under more traditional thermodynamically or kinetically controlled regimes. Thus, when it comes to systems chemistry, supramolecular systems that operate far from equilibrium have by far the richest functional potential. The challenge for the coming decades is to unlock this potential.

Interestingly, the general trend that led scientific interest shift from equilibrium systems towards kinetically controlled ones is also to be found in the historic developments in the area of dynamic combinatorial chemistry. While the field of DCC was in its early years focused mainly on the discovery of new receptors and guests at equilibrium, new catalysts161,162 _{and replicators}163,164 _{(i.e., autocatalysts)} arising from dynamic combinatorial libraries have gradually entered the scene as systems under kinetic control. Far-from-equilibrium dynamic combinatorial chemistry would be the next logical step and will possibly play an even larger role in the near future, but has not yet been realized.

At present the most compelling illustrations of the functional richness of far-from-equilibrium systems are still found in biology. Yet efforts in supramolecular systems chemistry are increasing as evident from the recent examples discussed in this section. Probably one of the more appealing objectives in this area (and subject of this thesis) is to attain Darwinian evolution (and eventually de-novo life) via far-from-equilibrium supramolecular chemistry. Yet there are many other functional systems conceivable and systems chemistry is ultimately only limited by the imagination of the chemist.

1.4. THE ORIGINS OF LIFE

AND THE ROLE OF INFORMATION TRANSFER

An important lesson to be taken from traditional origins of life studies is that propagation of information plays an especially key role in life: living systems preserve, propagate, and change their identity through cycles of evolution.14-22 _As mentioned in Section 1.2 and illustrated in Figure 1.2.11, dynamic kinetic stability can be attained in progressive steps and each of them will depend upon the previous history of the system, as shown in Figure 1.2.6. A way to store and propagate information thus reflects this sensitivity to the previous history of the various evolutionary steps that increase the dynamic kinetic stability of the system.