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

University of Groningen

Enabling Darwinian evolution in chemical replicators

Mattia, Elio

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ENABLING

DARWINIAN EVOLUTION

IN CHEMICAL REPLICATORS

The research described in this thesis was performed within the laboratories of the Stratingh Institute for Chemistry, University of Groningen, the Netherlands.

This research was financially supported by the Netherlands Organization for Scientific Research (NWO, ECHO grant, project 700.59.021).

Enabling Darwinian evolution in chemical replicators Copyright © 2017, Elio Mattia, Groningen, the Netherlands

All rights reserved. No part of this work may be reproduced by print, photocopy or any other means without prior written permission of the author.

ISBN: 978-90-367-9615-6

eISBN: 978-90-367-9614-9

Cover design: Elio Mattia (watercolor art by Barbara Fojkar)

Enabling Darwinian evolution

in chemical replicators

Proefschrift

ter verkrijging van de graad van doctor aan de Rijksuniversiteit Groningen

op gezag van de

rector magnificus prof. dr. E. Sterken en volgens besluit van het College voor Promoties.

De openbare verdediging zal plaatsvinden op maandag 22 mei 2017 om 12.45 uur

door

Elio Mattia

geboren op 27 oktober 1986 te Monopoli (Bari), Italië

Promotor

Prof. dr. S. Otto

Beoordelingscommissie

Prof. dr. R. C. Chiechi

Prof. dr. ir. J. Huskens

Prof. dr. A. Pross

i i

1. REPLICATION AND EVOLUTION ... 5

1.1. Evolution and the theory of living systems ... 6

1.2. From exponential replication to dynamic kinetic stability ... 8

1.2.1. Autocatalysis and replicators ... 8

1.2.2. Replication regimes: exponential, hyperbolic, parabolic ...9

1.2.3. Replicating systems in far-from-equilibrium conditions ... 13

1.2.4. Dynamic kinetic stability and evolution ...14

1.3. Supramolecular systems chemistry in far-from-equilibrium replication conditions ... 19

1.3.1. Systems under thermodynamic control ... 22

1.3.2. Systems under kinetic control: kinetic traps ... 23

1.3.3. Systems under kinetic control: far-from-equilibrium regime ... 27

1.3.4. An experimental toolset for origins of life studies ... 32

1.4. The origins of life and the role of information transfer ... 33

1.4.1. Prebiotic chemistry and the RNA world... 34

1.4.2. Compartments and metabolic networks ... 35

1.4.3. Information transfer ... 36 1.5. Computational modelling ... 40 1.5.1. Deterministic models ...41 1.5.2. Stochastic models ...41 1.6. References ... 43 2. EXPONENTIAL REPLICATION ... 51 2.1. Experimental framework ... 52 2.2. Experimental results ... 54

2.2.1. Determination of the replication order in the replicator ... 54

2.2.2. Mechanistic insights into the elongation/breakage process ... 55

2.3. Computational results ...57

2.3.1. Modelling of the elongation/breakage mechanism... 58

ii

nts 2.3.3. Breakage-free mechanism: main results and discussion ... 60

2.3.4. Replication orders: summary ... 60

2.3.5. Model implementation details: systems of ODEs ... 64

2.4. Conclusions ... 67

2.5. Experimental methods ... 68

2.6. References ... 70

3. FAR-FROM-EQUILIBRIUM REPLICATION ... 71

3.1. An experimental platform for far-from-equilibrium replication ... 73

3.1.1. Replication and reversible redox chemistry ... 73

3.1.2. The individual effects of reduction and oxidation ... 74

3.1.3. Replicator destruction in simultaneous batch processes ... 75

3.1.4. Replicator destruction in a flow setup ... 76

3.1.5. Feedback systems ... 79

3.1.6. The effects of concentration ...80

3.1.7. Conclusions – Experimental far-from-equilibrium replication ...80

3.1.8. Experimental methods ... 81

3.2. Deterministic modelling – Efficient replicator recycling conditions .... 83

3.2.1. Thermodynamic equilibration conditions ... 83

3.2.2. Far-from-equilibrium replicator recycling conditions ... 87

3.2.3. Flux analysis and selectivity studies ... 94

3.2.4. Conclusions and perspectives – Far-from-equilibrium replication ... 110

3.2.5. Concentration experiments ... 112

3.3. Stochastic modelling – A platform for multi-building-block systems ... 115

3.3.1. Implementation ... 117

3.3.2. Results and discussion ... 118

3.3.3. Conclusions – Stochastic modelling ... 120

3.4. References ... 121

4. INFORMATION PROPAGATION AND LOSS BY REPLICATION AND EXCHANGE ... 123

4.1. Pathway complexity of replication/exchange ... 126

4.2. Mechanistic studies by means of reduction experiments ... 130

4.3. Conclusions ... 139

4.4. Experimental methods ... 140

Ta bl e of c on te nts

iii

5. CONCLUSIONS AND PERSPECTIVES ... 145

A. APPENDIX – SOURCE CODE ... 149

A.1. C++ deterministic model, exponential replication (Chapter 2) ... 150

A.2. MATLAB deterministic model, far-from-equilibrium replication (Chapter 3, Section 3.2) ... 158

A.2.1. Main code (single and multiple parameter sets)... 158

A.2.2. Kinetic equation set ... 163

A.2.3. Flux equation set ... 165

A.2.4. 3D plot toolset ... 166

A.2.5. Parameters panels ... 174

A.3. C++ stochastic model (Chapter 3, Section 3.3) ... 182

SUMMARY ... 185

SAMENVATTING ...187

1

1

I.

INTRODUCTION

Self-replicating molecules, or replicators, play a fundamental role in origins of life studies.

In Chapter 2, experimental and computational evidence is provided that certain replicators are capable of growing exponentially. This is a very important breakthrough: exponentially growing replicators are particularly prone to survive during Darwinian evolution. Almost all replicators discovered up to the latest years were not capable of exponential growth.

Primordial life likely resulted from repeated attempts of replication in a destructive environment. Such a replication/destruction scenario is at the core of Darwinian

evolution. In Chapter 3, a replication/destruction system is studied experimentally

and computationally. Based on these studies, it is now possible to set up an experimental system where the replicators are constantly broken down into building blocks, and where the latter replicate again. Computer simulations allow the determination of optimal energy coupling conditions for such systems. In Chapter 4, information exchange pathways in peptide fibres were studied. The experimental results show that the exchange of building blocks from one fibre to another one takes place at the extremities thereof, while building blocks in the fibre cores are hardly used in the replication of other fibres. These are therefore protected from replication and the information that they carry can hardly be exchanged, unless the fibres continuously break into smaller pieces.

While in our experiments Darwinian evolution does not yet take place, we could observe significant processes for enabling Darwinian evolution in chemical replicators: exponential growth of fibres, destruction of replicators and selective exchange of building blocks.

2

In

tr

od

uc

tion Evolution is a trending topic in chemistry. Understanding its meaning and _{implications allows us to gain greater insights not only into the biological evolution}

of simple chemical systems and ultimately into the origins of life, but prominently about how complex systems endowed with emergent properties behave and evolve, including, e.g., social or financial systems. Grasping evolution involves understanding what the structure of life itself is and building a theory of living systems, which implies more than the awareness of what the material building blocks of life as we know it are and how they can be synthesized individually. Two fundamental concepts at the core of evolution are replication and dynamic kinetic stability, namely the interplay between the tool that allows for identity to be propagated and altered and the concept behind preservation of identity under conditions of constant change, respectively. Chemical replicators are autocatalysts, i.e., species that catalyse their own formation from underlying constituent materials. They vary in their capability to promote the formation of copies of themselves – a characteristic that can be measured and expressed via the tools of chemical kinetics – and this affects their evolutionary capabilities: exponential replicators, for example, tend to be favoured in the competition race. Nonetheless, exponential replicators themselves cannot sustain their replication process indefinitely: in general, either stable species or kinetically trapped “frozen” products are formed. In order to promote continuous evolution, replicators have to be brought in conditions of destruction, i.e., of constant change, namely far-from-equilibrium replication. The latter is the key towards sustained evolution and dynamic kinetic stability, as it involves survival of the species that can undergo constant replication notwithstanding the destructive processes.

The field of systems chemistry, especially dynamic combinatorial chemistry, offers an excellent platform for these studies and is at the centre of this thesis, together with self-organization and self-assembly.

An important role in aiding discoveries in these areas is played by computational modelling of both theoretical and experimental systems.

Traditional origins of life research has been focusing on molecular building blocks, i.e., prebiotic chemistry research, or on components thought to be fundamental for life, e.g., the RNA world as well as compartmentalization and metabolism. These represent important ingredients of life, but they mostly ignore the involvement of far-from-equilibrium conditions. Propagation of information is a concept that is key to understanding evolution, as replication must maintain the chemical identity of the species in order to prevent diffusion and loss of information, and at the same time allow for mutation of information as the means to explore sequence space and to enable evolution.

This thesis has a structure that follows the thread presented above. It presents experimental and computational results that deepen our understanding of chemical evolution.

In particular, the first chapter explains and expands on the concepts mentioned

3

common elements of much of the work in this thesis are presented there: the first introductory Section 1.1 focuses on theoretical approaches to understand and study living systems. The experimental supramolecular replicator arising from self-assembled peptide building blocks upon which the work in this thesis is based is introduced in Section 1.3.2. Computational modelling methods are briefly presented in Section 1.5. The remaining sections of Chapter 1 relate directly to the work that is described in the individual chapters 2-4.

Chapter 2 presents results on exponential replication: we found experimentally and confirmed by computational means that supramolecular replicators based on self-assembled peptidic macrocyles follow an exponential growth law. This character makes them good candidates to win the evolutionary game. The introductory Section 1.2 explains how exponential replication is key to the understanding of evolution and illustrates that dynamic conditions such as those implied by the concept of dynamic kinetic stability are equally fundamental. Chapter 3 explores far-from-equilibrium replication and dynamic kinetic stability: we developed experimental conditions in which to operate the replicators under a regime of simultaneous replication and destruction. We also modelled computationally its kinetic states space in order to identify the parameters under which the efficiency of replicator recycling is maximized. Taken together, these far-from-equilibrium conditions represent a platform for studies on competition and evolution of chemical replicators. Section 1.3 of the first chapter expands on the previous concepts by describing an experimental toolset that has revealed itself extremely versatile for the purpose of origins of life studies, namely supramolecular systems chemistry; particular attention is given to far-from-equilibrium conditions, which need to be applied to a replicating system in the quest for systems displaying high dynamic kinetic stability. Section 1.3.2 introduces the experimental system upon which much of the rest of this thesis is based. The introductory Section 2.1 of Chapter 2 describes this system in further detail.

Chapter 4 focusses on information transmission during replication: we studied experimentally the pathway complexity of growth, breakage and destruction of the replicators and indirectly observed to which extent a macrocycle localized within a fibre is able to escape the latter and access the building block pool. The next introductory Section 1.4 of Chapter 1 explains the role of information transfer as the way living systems preserve and propagate their identity and puts this topic in its historical context as one of the fundamental concepts of origins of life studies, together with metabolism and compartmentalization. Prebiotic chemistry and the RNA world are also briefly touched upon.

The fifth and final chapter summarizes the work and presents the future perspectives in the area.

4

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 of extinction in modern life is repeatedly confirmed by paleontological studies.12

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

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

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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

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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. DKS theory aims to serve as a bridging theoretical framework for both evolutionary phases.86-88

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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.

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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

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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:

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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

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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

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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

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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}

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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} switch the system between two relatively stable conformations of different molecular length.108

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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 image); different enzyme concentrations yield different gel strengths.129

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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