Non-equilibrium self-assembly for living matter-like properties

The soft and wet machines of life emerged as the spatially enclosed ensemble of biomolecules with replicating capabilities integrated with metabolic reaction cycles that operate at far-from-equilibrium. A thorough step-by-step synthetic integration of these elements, namely metabolic and replicative properties all confined and operating far-from-equilibrium, can set the stage from which we can ask questions related to the construction of chemical-based evolving systems with living matter-like properties - a monumental endeavour of systems chemistry. The overarching concept of this Review maps the discoveries on this possible integration of reaction networks, self-reproduction and compartmentalization under non-equilibrium conditions. We deconvolute the events of reaction networks and transient compartmentalization and extend the discussion towards self-reproducing systems that can be sustained under non-equilibrium conditions. Although enormous challenges lie ahead in terms of molecular diversity, information transfer, adaptation and selection that are required for open-ended evolution, emerging strategies to generate minimal metabolic cycles can extend our growing understanding of the chemical emergence of the biosphere of Earth.

Generalist versus Specialist Self-Replicators

Darwinian evolution, including the selection of the fittest species under given environmental conditions, is a major milestone in the development of synthetic living systems. In this regard, generalist or specialist behavior (the ability to replicate in a broader or narrower, more specific food environment) are of importance. Here we demonstrate generalist and specialist behavior in dynamic combinatorial libraries composed of a peptide-based and an oligo(ethylene glycol) based building block. Three different sets of macrocyclic replicators could be distinguished based on their supramolecular organization: two prepared from a single building block as well as one prepared from an equimolar mixture of them. Peptide-containing hexamer replicators were found to be generalists, i. e. they could replicate in a broad range of food niches, whereas the octamer peptide-based replicator and hexameric ethyleneoxide-based replicator were proven to be specialists, i. e. they only replicate in very specific food niches that correspond to their composition. However, sequence specificity cannot be demonstrated for either of the generalist replicators. The generalist versus specialist nature of these replicators was linked to their supramolecular organization. Assembly modes that accommodate structurally different building blocks lead to generalist replicators, while assembly modes that are more restrictive yield specialist replicators.

Multistable Protocells Can Aid the Evolution of Prebiotic Autocatalytic Sets

We present a simple mathematical model that captures the evolutionary capabilities of a prebiotic compartment or protocell. In the model, the protocell contains an autocatalytic set whose chemical dynamics is coupled to the growth-division dynamics of the compartment. Bistability in the dynamics of the autocatalytic set results in a protocell that can exist with two distinct growth rates. Stochasticity in chemical reactions plays the role of mutations and causes transitions from one growth regime to another. We show that the system exhibits 'natural selection', where a 'mutant' protocell in which the autocatalytic set is active arises by chance in a population of inactive protocells, and then takes over the population because of its higher growth rate or 'fitness'. The work integrates three levels of dynamics: intracellular chemical, single protocell, and population (or ecosystem) of protocells.

The ecology-evolution continuum and the origin of life

Prior research on evolutionary mechanisms during the origin of life has mainly assumed the existence of populations of discrete entities with information encoded in genetic polymers. Recent theoretical advances in autocatalytic chemical ecology establish a broader evolutionary framework that allows for adaptive complexification prior to the emergence of bounded individuals or genetic encoding. This framework establishes the formal equivalence of cells, ecosystems and certain localized chemical reaction systems as autocatalytic chemical ecosystems (ACEs): food-driven (open) systems that can grow due to the action of autocatalytic cycles (ACs). When ACEs are organized in meta-ecosystems, whether they be populations of cells or sets of chemically similar environmental patches, evolution, defined as change in AC frequency over time, can occur. In cases where ACs are enriched because they enhance ACE persistence or dispersal ability, evolution is adaptive and can build complexity. In particular, adaptive evolution can explain the emergence of self-bounded units (e.g. protocells) and genetic inheritance mechanisms. Recognizing the continuity between ecological and evolutionary change through the lens of autocatalytic chemical ecology suggests that the origin of life should be seen as a general and predictable outcome of driven chemical ecosystems rather than a phenomenon requiring specific, rare conditions.

The modular biochemical reaction network structure of cellular translation

Translation is an essential attribute of all living cells. At the heart of cellular operation, it is a chemical information decoding process that begins with an input string of nucleotides and ends with the synthesis of a specific output string of peptides. The translation process is interconnected with gene expression, physiological regulation, transcription, and responses to signaling molecules, among other cellular functions. Foundational efforts have uncovered a wealth of knowledge about the mechanistic functions of the components of translation and their many interactions between them, but the broader biochemical connections between translation, metabolism and polymer biosynthesis that enable translation to occur have not been comprehensively mapped. Here we present a multilayer graph of biochemical reactions describing the translation, polymer biosynthesis and metabolism networks of an Escherichia coli cell. Intriguingly, the compounds that compose these three layers are distinctly aggregated into three modes regardless of their layer categorization. Multimodal mass distributions are well-known in ecosystems, but this is the first such distribution reported at the biochemical level. The degree distributions of the translation and metabolic networks are each likely to be heavy-tailed, but the polymer biosynthesis network is not. A multimodal mass-degree distribution indicates that the translation and metabolism networks are each distinct, adaptive biochemical modules, and that the gaps between the modes reflect evolved responses to the functional use of metabolite, polypeptide and polynucleotide compounds. The chemical reaction network of cellular translation opens new avenues for exploring complex adaptive phenomena such as percolation and phase changes in biochemical contexts.

Kinetic Modeling and Parameter Estimation of a Prebiotic Peptide Reaction Network

Although our understanding of how life emerged on Earth from simple organic precursors is speculative, early precursors likely included amino acids. The polymerization of amino acids into peptides and interactions between peptides are of interest because peptides and proteins participate in complex interaction networks in extant biology. However, peptide reaction networks can be challenging to study because of the potential for multiple species and systems-level interactions between species. We developed and employed a computational network model to describe reactions between amino acids to form di-, tri-, and tetra-peptides. Our experiments were initiated with two of the simplest amino acids, glycine and alanine, mediated by trimetaphosphate-activation and drying to promote peptide bond formation. The parameter estimates for bond formation and hydrolysis reactions in the system were found to be poorly constrained due to a network property known as sloppiness. In a sloppy model, the behavior mostly depends on only a subset of parameter combinations, but there is no straightforward way to determine which parameters should be included or excluded. Despite our inability to determine the exact values of specific kinetic parameters, we could make reasonably accurate predictions of model behavior. In short, our modeling has highlighted challenges and opportunities toward understanding the behaviors of complex prebiotic chemical experiments.

Self-organization of primitive metabolic cycles due to non-reciprocal interactions

One of the greatest mysteries concerning the origin of life is how it has emerged so quickly after the formation of the earth. In particular, it is not understood how metabolic cycles, which power the non-equilibrium activity of cells, have come into existence in the first instances. While it is generally expected that non-equilibrium conditions would have been necessary for the formation of primitive metabolic structures, the focus has so far been on externally imposed non-equilibrium conditions, such as temperature or proton gradients. Here, we propose an alternative paradigm in which naturally occurring non-reciprocal interactions between catalysts that can partner together in a cyclic reaction lead to their recruitment into self-organized functional structures. We uncover different classes of self-organized cycles that form through exponentially rapid coarsening processes, depending on the parity of the cycle and the nature of the interaction motifs, which are all generic but have readily tuneable features.

Multispecies autocatalytic RNA reaction networks in coacervates

Robust localization of self-reproducing autocatalytic chemistries is a key step in the realization of heritable and evolvable chemical systems. While autocatalytic chemical reaction networks already possess attributes such as heritable self-reproduction and evolvability, localizing functional multispecies networks within complex primitive phases, such as coacervates, has remained unexplored. Here, we show the self-reproduction of the Azoarcus ribozyme system within charge-rich coacervates where catalytic ribozymes are produced by the autocatalytic assembly of constituent smaller RNA fragments. We systematically demonstrate the catalytic assembly of active ribozymes within phase-separated coacervates-both in micron-sized droplets as well as in a coalesced macrophase, underscoring the facility of the complex, charge-rich phase to support these reactions in multiple configurations. By constructing multispecies reaction networks, we show that these newly assembled molecules are active, participating both in self- and cross-catalysis within the coacervates. Finally, due to differential molecular transport, these phase-separated compartments endow robustness to the composition of the collectively autocatalytic networks against external perturbations. Altogether, our results establish the formation of multispecies self-reproducing reaction networks in phase-separated compartments which in turn render transient robustness to the network composition.

Abiogenesis through gradual evolution of autocatalysis into template-based replication

How life emerged from inanimate matter is one of the most intriguing questions posed to modern science. Central to this research are experimental attempts to build systems capable of Darwinian evolution. RNA catalysts (ribozymes) are a promising avenue, in line with the RNA world hypothesis whereby RNA pre-dated DNA and proteins. Since evolution in living organisms relies on template-based replication, the identification of a ribozyme capable of replicating itself (an RNA self-replicase) has been a major objective. However, no self-replicase has been identified to date. Alternatively, autocatalytic systems involving multiple RNA species capable of ligation and recombination may enable self-reproduction. However, it remains unclear how evolution could emerge in autocatalytic systems. In this review, we examine how experimentally feasible RNA reactions catalysed by ribozymes could implement the evolutionary properties of variation, heredity and reproduction, and ultimately allow for Darwinian evolution. We propose a gradual path for the emergence of evolution, initially supported by autocatalytic systems leading to the later appearance of RNA replicases.

Stoechiometric and dynamical autocatalysis for diluted chemical reaction networks

Autocatalysis underlies the ability of chemical and biochemical systems to replicate. Recently, Blokhuis et al. (PNAS 117(41):25230-25236, 2020) gave a stoechiometric definition of autocatalysis for reaction networks, stating the existence of a combination of reactions such that the balance for all autocatalytic species is strictly positive, and investigated minimal autocatalytic networks, called autocatalytic cores. By contrast, spontaneous autocatalysis-namely, exponential amplification of all species internal to a reaction network, starting from a diluted regime, i.e. low concentrations-is a dynamical property. We introduce here a topological condition (Top) for autocatalysis, namely: restricting the reaction network description to highly diluted species, we assume existence of a strongly connected component possessing at least one reaction with multiple products (including multiple copies of a single species). We find this condition to be necessary and sufficient for stoechiometric autocatalysis. When degradation reactions have small enough rates, the topological condition further ensures dynamical autocatalysis, characterized by a strictly positive Lyapunov exponent giving the instantaneous exponential growth rate of the system. The proof is generally based on the study of auxiliary Markov chains. We provide as examples general autocatalytic cores of Type I and Type III in the typology of Blokhuis et al. (PNAS 117(41):25230-25236, 2020) . In a companion article (Unterberger in Dynamical autocatalysis for autocatalytic cores, 2021), Lyapunov exponents and the behavior in the growth regime are studied quantitatively beyond the present diluted regime .

The Origin of Life: What Is the Question?

The question of the origin of life is a tenacious question that challenges many branches of science but is also extremely multifaceted. While prebiotic chemistry and micropaleontology reformulate the question as that of explaining the appearance of life on Earth in the deep past, systems chemistry and synthetic biology typically understand the question as that of demonstrating the synthesis of novel living matter from nonliving matter independently of historical constraints. The objective of this contribution is to disentangle the different readings of the origin-of-life question found in science. We identify three main dimensions along which the question can be differently constrained depending on context: historical adequacy, natural spontaneity, and similarity to life-as-we-know-it. We argue that the epistemic status of what needs to be explained-the explanandum-varies from approximately true when the origin-of-life question is the most constrained to entirely speculative when the constraints are the most relaxed. This difference in epistemic status triggers a shift in the nature of the origin-of-life question from an explanation-seeking question in the most constrained case to a fact-establishing question in the lesser-constrained ones. We furthermore explore how answers to some interpretations of the origin-of-life questions matter for other interpretations.

Thermodynamic and Kinetic Sequence Selection in Enzyme-Free Polymer Self-Assembly Inside a Non-Equilibrium RNA Reactor

The RNA world is one of the principal hypotheses to explain the emergence of living systems on the prebiotic Earth. It posits that RNA oligonucleotides acted as both carriers of information as well as catalytic molecules, promoting their own replication. However, it does not explain the origin of the catalytic RNA molecules. How could the transition from a pre-RNA to an RNA world occur? A starting point to answer this question is to analyze the dynamics in sequence space on the lowest level, where mononucleotide and short oligonucleotides come together and collectively evolve into larger molecules. To this end, we study the sequence-dependent self-assembly of polymers from a random initial pool of short building blocks via templated ligation. Templated ligation requires two strands that are hybridized adjacently on a third strand. The thermodynamic stability of such a configuration crucially depends on the sequence context and, therefore, significantly influences the ligation probability. However, the sequence context also has a kinetic effect, since non-complementary nucleotide pairs in the vicinity of the ligation site stall the ligation reaction. These sequence-dependent thermodynamic and kinetic effects are explicitly included in our stochastic model. Using this model, we investigate the system-level dynamics inside a non-equilibrium ‘RNA reactor’ enabling a fast chemical activation of the termini of interacting oligomers. Moreover, the RNA reactor subjects the oligomer pool to periodic temperature changes inducing the reshuffling of the system. The binding stability of strands typically grows with the number of complementary nucleotides forming the hybridization site. While shorter strands unbind spontaneously during the cold phase, larger complexes only disassemble during the temperature peaks. Inside the RNA reactor, strand growth is balanced by cleavage via hydrolysis, such that the oligomer pool eventually reaches a non-equilibrium stationary state characterized by its length and sequence distribution. How do motif-dependent energy and stalling parameters affect the sequence composition of the pool of long strands? As a critical factor for self-enhancing sequence selection, we identify kinetic stalling due to non-complementary base pairs at the ligation site. Kinetic stalling enables cascades of self-amplification that result in a strong reduction of occupied states in sequence space. Moreover, we discuss the significance of the symmetry breaking for the transition from a pre-RNA to an RNA world.

A Mutation Threshold for Cooperative Takeover

One of the leading theories for the origin of life includes the hypothesis according to which life would have evolved as cooperative networks of molecules. Explaining cooperation—and particularly, its emergence in favoring the evolution of life-bearing molecules—is thus a key element in describing the transition from nonlife to life. Using agent-based modeling of the iterated prisoner’s dilemma, we investigate the emergence of cooperative behavior in a stochastic and spatially extended setting and characterize the effects of inheritance and variability. We demonstrate that there is a mutation threshold above which cooperation is—counterintuitively—selected, which drives a dramatic and robust cooperative takeover of the whole system sustained consistently up to the error catastrophe, in a manner reminiscent of typical phase transition phenomena in statistical physics. Moreover, our results also imply that one of the simplest conditional cooperative strategies, “Tit-for-Tat”, plays a key role in the emergence of cooperative behavior required for the origin of life.

Semi-Adaptive Evolution with Spontaneous Modularity of Half-Chaotic Randomly Growing Autonomous and Open Networks

Up until now, studies of Kauffman network stability have focused on the conditions resulting from the structure of the network. Negative feedbacks have been modeled as ice (nodes that do not change their state) in an ordered phase but this blocks the possibility of breaking out of the range of correct operation. This first, very simplified approximation leads to some incorrect conclusions, e.g., that life is on the edge of chaos. We develop a second approximation, which discovers half-chaos and shows its properties. In previous works, half-chaos has been confirmed in autonomous networks, but only using node function disturbance, which does not change the network structure. Now we examine half-chaos during network growth by adding and removing nodes as a disturbance in autonomous and open networks. In such evolutions controlled by a ‘small change’ of functioning after disturbance, the half-chaos is kept but spontaneous modularity emerges and blurs the picture. Half-chaos is a state to be expected in most of the real systems studied, therefore the determinants of the variability that maintains the half-chaos are particularly important in the application of complex network knowledge.

Automated Exploration of Prebiotic Chemical Reaction Space: Progress and Perspectives

Prebiotic chemistry often involves the study of complex systems of chemical reactions that form large networks with a large number of diverse species. Such complex systems may have given rise to emergent phenomena that ultimately led to the origin of life on Earth. The environmental conditions and processes involved in this emergence may not be fully recapitulable, making it difficult for experimentalists to study prebiotic systems in laboratory simulations. Computational chemistry offers efficient ways to study such chemical systems and identify the ones most likely to display complex properties associated with life. Here, we review tools and techniques for modelling prebiotic chemical reaction networks and outline possible ways to identify self-replicating features that are central to many origin-of-life models.

Long-term behaviours of Autocatalytic Sets

Autocatalytic Sets are reaction networks theorised as networks at the basis of life. Their main feature is the ability of spontaneously emerging and self-reproducing. The Reflexively and Food-generated theory provides a formal definition of Autocatalytic Sets in terms of graphs with peculiar topological properties. This formalisation has been proved to be a powerful tool for the study of the chemical networks underlying life, and it was able to identify autocatalytic structures in real metabolic networks. However, the dynamical behaviour of such networks has not been yet complitely clarified. In this work, I present a first attempt to connect the topology of an Autocatalytic Set with its dynamics. For this purpose, I represent Autocatalytic Sets in terms of Chemical Reaction Networks, and I use the Chemical Reaction Network theory to detect motifs in the networks'structure, that allow to determine the long-term behaviour of the system.

Kinetic Selection in the Out-of-Equilibrium Autocatalytic Reaction Networks that Produce Macrocyclic Peptides

Autocatalytic reaction networks are instrumental for validating scenarios for the emergence of life on Earth and for synthesizing life de novo. Here, we demonstrate that dimeric thioesters of tripeptides with the general structure (Cys-Xxx-Gly-SEt)₂ form strongly interconnected autocatalytic reaction networks that predominantly generate macrocyclic peptides up to 69 amino acids long. Some macrocycles of 6-12 amino acids were isolated from the product pool and were characterized by NMR spectroscopy and single-crystal X-ray analysis. We studied the autocatalytic formation of macrocycles in a flow reactor in the presence of acrylamide, whose conjugate addition to thiols served as a model "removal" reaction. These results indicate that even not template-assisted autocatalytic production combined with competing removal of molecular species in an open compartment could be a feasible route for selecting functional molecules during the pre-Darwinian stages of molecular evolution.

A robotic prebiotic chemist probes long term reactions of complexifying mixtures

To experimentally test hypotheses about the emergence of living systems from abiotic chemistry, researchers need to be able to run intelligent, automated, and long-term experiments to explore chemical space. Here we report a robotic prebiotic chemist equipped with an automatic sensor system designed for long-term chemical experiments exploring unconstrained multicomponent reactions, which can run autonomously over long periods. The system collects mass spectrometry data from over 10 experiments, with 60 to 150 algorithmically controlled cycles per experiment, running continuously for over 4 weeks. We show that the robot can discover the production of high complexity molecules from simple precursors, as well as deal with the vast amount of data produced by a recursive and unconstrained experiment. This approach represents what we believe to be a necessary step towards the design of new types of Origin of Life experiments that allow testable hypotheses for the emergence of life from prebiotic chemistry.

Social Networking of Quasi-Species Consortia drive Virolution via Persistence

The emergence of cooperative quasi-species consortia (QS-C) thinking from the more accepted quasispecies equations of Manfred Eigen, provides a conceptual foundation from which concerted action of RNA agents can now be understood. As group membership becomes a basic criteria for the emergence of living systems, we also start to understand why the history and context of social RNA networks become crucial for survival and function. History and context of social RNA networks also lead to the emergence of a natural genetic code. Indeed, this QS-C thinking can also provide us with a transition point between the chemical world of RNA replicators and the living world of RNA agents that actively differentiate self from non-self and generate group identity with membership roles. Importantly the social force of a consortia to solve complex, multilevel problems also depend on using opposing and minority functions. The consortial action of social networks of RNA stem-loops subsequently lead to the evolution of cellular organisms representing a tree of life.

Self-Reproduction and Darwinian Evolution in Autocatalytic Chemical Reaction Systems

Understanding the emergence of life from (primitive) abiotic components has arguably been one of the deepest and yet one of the most elusive scientific questions. Notwithstanding the lack of a clear definition for a living system, it is widely argued that heredity (involving self-reproduction) along with compartmentalization and metabolism are key features that contrast living systems from their non-living counterparts. A minimal living system may be viewed as "a self-sustaining chemical system capable of Darwinian evolution". It has been proposed that autocatalytic sets of chemical reactions (ACSs) could serve as a mechanism to establish chemical compositional identity, heritable self-reproduction, and evolution in a minimal chemical system. Following years of theoretical work, autocatalytic chemical systems have been constructed experimentally using a wide variety of substrates, and most studies, thus far, have focused on the demonstration of chemical self-reproduction under specific conditions. While several recent experimental studies have raised the possibility of carrying out some aspects of experimental evolution using autocatalytic reaction networks, there remain many open challenges. In this review, we start by evaluating theoretical studies of ACSs specifically with a view to establish the conditions required for such chemical systems to exhibit self-reproduction and Darwinian evolution. Then, we follow with an extensive overview of experimental ACS systems and use the theoretically established conditions to critically evaluate these empirical systems for their potential to exhibit Darwinian evolution. We identify various technical and conceptual challenges limiting experimental progress and, finally, conclude with some remarks about open questions.

Darwinian properties and their trade-offs in autocatalytic RNA reaction networks

Discovering autocatalytic chemistries that can evolve is a major goal in systems chemistry and a critical step towards understanding the origin of life. Autocatalytic networks have been discovered in various chemistries, but we lack a general understanding of how network topology controls the Darwinian properties of variation, differential reproduction, and heredity, which are mediated by the chemical composition. Using barcoded sequencing and droplet microfluidics, we establish a landscape of thousands of networks of RNAs that catalyze their own formation from fragments, and derive relationships between network topology and chemical composition. We find that strong variations arise from catalytic innovations perturbing weakly connected networks, and that growth increases with global connectivity. These rules imply trade-offs between reproduction and variation, and between compositional persistence and variation along trajectories of network complexification. Overall, connectivity in reaction networks provides a lever to balance variation (to explore chemical states) with reproduction and heredity (persistence being necessary for selection to act), as required for chemical evolution.

Prebiotic Peptide Synthesis and Spontaneous Amyloid Formation Inside a Proto-Cellular Compartment

Cellular life requires a high degree of molecular complexity and self-organization, some of which must have originated in a prebiotic context. Here, we demonstrate how both of these features can emerge in a plausibly prebiotic system. We found that chemical gradients in simple mixtures of activated amino acids and fatty acids can lead to the formation of amyloid-like peptide fibrils that are localized inside of a proto-cellular compartment. In this process, the fatty acid or lipid vesicles act both as a filter, allowing the selective passage of activated amino acids, and as a barrier, blocking the diffusion of the amyloidogenic peptides that form spontaneously inside the vesicles. This synergy between two distinct building blocks of life induces a significant increase in molecular complexity and spatial order thereby providing a route for the early molecular evolution that could give rise to a living cell.

Radiolysis generates a complex organosynthetic chemical network

The architectural features of cellular life and its ecologies at larger scales are built upon foundational networks of reactions between molecules that avoid a collapse to equilibrium. The search for life’s origins is, in some respects, a search for biotic network attributes in abiotic chemical systems. Radiation chemistry has long been employed to model prebiotic reaction networks, and here we report network-level analyses carried out on a compiled database of radiolysis reactions, acquired by the scientific community over decades of research. The resulting network shows robust connections between abundant geochemical reservoirs and the production of carboxylic acids, amino acids, and ribonucleotide precursors—the chemistry of which is predominantly dependent on radicals. Moreover, the network exhibits the following measurable attributes associated with biological systems: (1) the species connectivity histogram exhibits a heterogeneous (heavy-tailed) distribution, (2) overlapping families of closed-loop cycles, and (3) a hierarchical arrangement of chemical species with a bottom-heavy energy-size spectrum. The latter attribute is implicated with stability and entropy production in complex systems, notably in ecology where it is known as a trophic pyramid. Radiolysis is implicated as a driver of abiotic chemical organization and could provide insights about the complex and perhaps radical-dependent mechanisms associated with life’s origins.

Constraint Closure Drove Major Transitions in the Origins of Life

Life is an epiphenomenon for which origins are of tremendous interest to explain. We provide a framework for doing so based on the thermodynamic concept of work cycles. These cycles can create their own closure events, and thereby provide a mechanism for engendering novelty. We note that three significant such events led to life as we know it on Earth: (1) the advent of collective autocatalytic sets (CASs) of small molecules; (2) the advent of CASs of reproducing informational polymers; and (3) the advent of CASs of polymerase replicases. Each step could occur only when the boundary conditions of the system fostered constraints that fundamentally changed the phase space. With the realization that these successive events are required for innovative forms of life, we may now be able to focus more clearly on the question of life's abundance in the universe.

Prebiotic Reaction Networks in Water

A prevailing strategy in origins of life studies is to explore how chemistry constrained by hypothetical prebiotic conditions could have led to molecules and system level processes proposed to be important for life's beginnings. This strategy has yielded model prebiotic reaction networks that elucidate pathways by which relevant compounds can be generated, in some cases, autocatalytically. These prebiotic reaction networks provide a rich platform for further understanding and development of emergent "life-like" behaviours. In this review, recent advances in experimental and analytical procedures associated with classical prebiotic reaction networks, like formose and Miller-Urey, as well as more recent ones are highlighted. Instead of polymeric networks, i.e., those based on nucleic acids or peptides, the focus is on small molecules. The future of prebiotic chemistry lies in better understanding the genuine complexity that can result from reaction networks and the construction of a centralised database of reactions useful for predicting potential network evolution is emphasised.

An organisational systems-biology view of viruses explains why they are not alive

Whether or not viruses are alive remains unsettled. Discoveries of giant viruses with translational genes and large genomes have kept the debate active. Here, a fresh approach is introduced, based on the organisational definition of life from within systems biology. It views living as a circular process of self-organisation and self-construction which is 'closed to efficient causation'. How information combines with force to fabricate and organise environmentally obtained materials, given an energy source, is here explained as a physical embodiment of informational constraint. Comparing a general virus replication cycle with Rosen's (M,R)-system shows it to be linear, rather than closed. Some viruses contribute considerable organisational information, but so far none is known to supply all required, nor the material nor energy necessary to complete their replication cycle. As a result, no known virus replication cycle is closed to efficient causation: unlike cellular obligate parasites, viruses do not match the causal structure of an (M,R)-system. Analysis based in identifying a Markov blanket in causal structure proved inconclusive, but using Integrated Information Theory on a Boolean representation, it was possible to show that the causal structure of a virocell is not different from that of the host cell.

Impact of composition on the dynamics of autocatalytic sets

Autocatalytic sets are sets of entities that mutually catalyse each other's production through chemical reactions from a basic food source. Recently, the reflexively autocatalytic and food generated theory has introduced a formal definition of autocatalytic sets which has provided promising results in the context of the origin of life. However, the link between the structure of autocatalytic sets and the possibility of different long-term behaviours is still unclear. In this work, we study how different interactions among autocatalytic sets affect the emergent dynamics. To this aim, we develop a model in which interactions are presented through composition operations among networks, and the dynamics of the networks is reproduced via stochastic simulations. We find that the dynamical emergence of the autocatalytic sets depends on the adopted composition operations. In particular, operations involving entities that are sources for autocatalytic sets can promote the formation of different autocatalytic subsets, opening the door to various long-term behaviours.

From self-replication to replicator systems en route to de novo life

The process by which chemistry can give rise to biology remains one of the biggest mysteries in contemporary science. The de novo synthesis and origin of life both require the functional integration of three key characteristics - replication, metabolism and compartmentalization - into a system that is maintained out of equilibrium and is capable of open-ended Darwinian evolution. This Review takes systems of self-replicating molecules as starting points and describes the steps necessary to integrate additional characteristics of life. We analyse how far experimental self-replicators have come in terms of Darwinian evolution. We also cover models of replicator communities that attempt to solve Eigen's paradox, whereby accurate replication needs complex machinery yet obtaining such complex self-replicators through evolution requires accurate replication. Successful models rely on a collective metabolism and a way of (transient) compartmentalization, suggesting that the invention and integration of these two characteristics is driven by evolution. Despite our growing knowledge, there remain numerous key challenges that may be addressed by a combined theoretical and experimental approach.

A continuous reaction network that produces RNA precursors

Continuous reaction networks, which do not rely on purification or timely additions of reagents, serve as models for chemical evolution and have been demonstrated for compounds thought to have played important roles for the origins of life such as amino acids, hydroxy acids, and sugars. Step-by-step chemical protocols for ribonucleotide synthesis are known, but demonstrating their synthesis in the context of continuous reaction networks remains a major challenge. Herein, compounds proposed to be important for prebiotic RNA synthesis, including glycolaldehyde, cyanamide, 2-aminooxazole, and 2-aminoimidazole, are generated from a continuous reaction network, starting from an aqueous mixture of NaCl, NH4Cl, phosphate, and HCN as the only carbon source. No well-timed addition of any other reagents is required. The reaction network is driven by a combination of γ radiolysis and dry-down. γ Radiolysis results in a complex mixture of organics, including the glycolaldehyde-derived glyceronitrile and cyanamide. This mixture is then dried down, generating free glycolaldehyde that then reacts with cyanamide/NH3 to furnish a combination of 2-aminooxazole and 2-aminoimidazole. This continuous reaction network models how precursors for generating RNA and other classes of compounds may arise spontaneously from a complex mixture that originates from simple reagents.

Spontaneous formation of autocatalytic sets with self-replicating inorganic metal oxide clusters

Self-replication is an important property of life, yet no one knows how it arose, and the machinery found in modern cells is far too complex to have formed by chance. One suggestion is that simple networks may become able to cooperate and hence replicate together forming autocatalytic sets, but no simple systems have been found. Here we present an inorganic autocatalytic, based on molybdenum blue, that is formed spontaneously when a simple inorganic salt of sodium molybdate is reduced under acidic conditions. This study demonstrates how autocatalytic sets, based on simple inorganic salts, can lead to the spontaneous emergence of self-replicating systems and solves the mystery of how gigantic molecular nanostructures of molybdenum blue can form in the first place.

Here we show how a simple inorganic salt can spontaneously form autocatalytic sets of replicating inorganic molecules that work via molecular recognition based on the {PMo₁₂} ≡ [PMo₁₂O₄₀]^3– Keggin ion, and {Mo₃₆} ≡ [H₃Mo₅₇M₆(NO)₆O₁₈₃(H₂O)₁₈]^22– cluster. These small clusters are able to catalyze their own formation via an autocatalytic network, which subsequently template the assembly of gigantic molybdenum-blue wheel {Mo₁₅₄} ≡ [Mo₁₅₄O₄₆₂H₁₄(H₂O)₇₀]^14–, {Mo₁₃₂} ≡ [Mo^VI₇₂Mo^V₆₀O₃₇₂(CH₃COO)₃₀(H₂O)₇₂]^42– ball-shaped species containing 154 and 132 molybdenum atoms, and a {PMo₁₂}⊂{Mo₁₂₄Ce₄} ≡ [H₁₆Mo^VI₁₀₀Mo^V₂₄Ce₄O₃₇₆(H₂O)₅₆ (PMo^VI₁₀Mo^V₂O₄₀)(C₆H₁₂N₂O₄S₂)₄]^5– nanostructure. Kinetic investigations revealed key traits of autocatalytic systems including molecular recognition and kinetic saturation. A stochastic model confirms the presence of an autocatalytic network involving molecular recognition and assembly processes, where the larger clusters are the only products stabilized by the cycle, isolated due to a critical transition in the network.

Autocatalytic networks in biology: structural theory and algorithms

Self-sustaining autocatalytic networks play a central role in living systems, from metabolism at the origin of life, simple RNA networks and the modern cell, to ecology and cognition. A collectively autocatalytic network that can be sustained from an ambient food set is also referred to more formally as a 'reflexively autocatalytic food-generated' (RAF) set. In this paper, we first investigate a simplified setting for studying RAFs, which is nevertheless relevant to real biochemistry and which allows an exact mathematical analysis based on graph-theoretic concepts. This, in turn, allows for the development of efficient (polynomial-time) algorithms for questions that are computationally intractable (NP-hard) in the general RAF setting. We then show how this simplified setting for RAF systems leads naturally to a more general notion of RAFs that are 'generative' (they can be built up from simpler RAFs) and for which efficient algorithms carry over to this more general setting. Finally, we show how classical RAF theory can be extended to deal with ensembles of catalysts as well as the assignment of rates to reactions according to which catalysts (or combinations of catalysts) are available.

The Future of Origin of Life Research: Bridging Decades-Old Divisions

Research on the origin of life is highly heterogeneous. After a peculiar historical development, it still includes strongly opposed views which potentially hinder progress. In the 1st Interdisciplinary Origin of Life Meeting, early-career researchers gathered to explore the commonalities between theories and approaches, critical divergence points, and expectations for the future. We find that even though classical approaches and theories-e.g. bottom-up and top-down, RNA world vs. metabolism-first-have been prevalent in origin of life research, they are ceasing to be mutually exclusive and they can and should feed integrating approaches. Here we focus on pressing questions and recent developments that bridge the classical disciplines and approaches, and highlight expectations for future endeavours in origin of life research.

Probing complexity: thermodynamics and computational mechanics approaches to origins studies

This paper proposes new avenues for origins research that apply modern concepts from stochastic thermodynamics, information thermodynamics and complexity science. Most approaches to the emergence of life prioritize certain compounds, reaction pathways, environments or phenomena. What they all have in common is the objective of reaching a state that is recognizably alive, usually positing the need for an evolutionary process. As with life itself, this correlates with a growth in the complexity of the system over time. Complexity often takes the form of an intuition or a proxy for a phenomenon that defies complete understanding. However, recent progress in several theoretical fields allows the rigorous computation of complexity. We thus propose that measurement and control of the complexity and information content of origins-relevant systems can provide novel insights that are absent in other approaches. Since we have no guarantee that the earliest forms of life (or alien life) used the same materials and processes as extant life, an appeal to complexity and information processing provides a more objective and agnostic approach to the search for life's beginnings. This paper gives an accessible overview of the three relevant branches of modern thermodynamics. These frameworks are not commonly applied in origins studies, but are ideally suited to the analysis of such non-equilibrium systems. We present proposals for the application of these concepts in both theoretical and experimental origins settings.

Survival of Self-Replicating Molecules under Transient Compartmentalization with Natural Selection

The problem of the emergence and survival of self-replicating molecules in origin-of-life scenarios is plagued by the error catastrophe, which is usually escaped by considering effects of compartmentalization, as in the stochastic corrector model. By addressing the problem in a simple system composed of a self-replicating molecule (a replicase) and a parasite molecule that needs the replicase for copying itself, we show that transient (rather than permanent) compartmentalization is sufficient to the task. We also exhibit a regime in which the concentrations of the two kinds of molecules undergo sustained oscillations. Our model should be relevant not only for origin-of-life scenarios but also for describing directed evolution experiments, which increasingly rely on transient compartmentalization with pooling and natural selection.

Emergence of Function and Selection from Recursively Programmed Polymerisation Reactions in Mineral Environments

Living systems are characterised by an ability to sustain chemical reaction networks far-from-equilibrium. It is likely that life first arose through a process of continual disruption of equilibrium states in recursive reaction networks, driven by periodic environmental changes. Herein, we report the emergence of proto-enzymatic function from recursive polymerisation reactions using amino acids and glycolic acid. Reactions were kept out of equilibrium by diluting products 9:1 in fresh starting solution at the end of each recursive cycle, and the development of complex high molecular weight species is explored using a new metric, the Mass Index, which allows the complexity of the system to be explored as a function of cycle. This process was carried out on a range of different mineral environments. We explored the hypothesis that disrupting equilibrium via recursive cycling imposes a selection pressure and subsequent boundary conditions on products. After just four reaction cycles, product mixtures from recursive reactions exhibit greater catalytic activity and truncation of product space towards higher-molecular-weight species compared to non-recursive controls.

Mathematical Analysis of a Prototypical Autocatalytic Reaction Network

Network autocatalysis, which is autocatalysis whereby a catalyst is not directly produced in a catalytic cycle, is likely to be more common in chemistry than direct autocatalysis is. Nevertheless, the kinetics of autocatalytic networks often does not exactly follow simple quadratic or cubic rate laws and largely depends on the structure of the network. In this article, we analyzed one of the simplest and most chemically plausible autocatalytic networks where a catalytic cycle is coupled to an ancillary reaction that produces the catalyst. We analytically analyzed deviations in the kinetics of this network from its exponential growth and numerically studied the competition between two networks for common substrates. Our results showed that when quasi-steady-state approximation is applicable for at least one of the components, the deviation from the exponential growth is small. Numerical simulations showed that competition between networks results in the mutual exclusion of autocatalysts; however, the presence of a substantial noncatalytic conversion of substrates will create broad regions where autocatalysts can coexist. Thus, we should avoid the accumulation of intermediates and the noncatalytic conversion of the substrate when designing experimental systems that need autocatalysis as a source of positive feedback or as a source of evolutionary pressure.

Robustness, Entrainment, and Hybridization in Dissipative Molecular Networks, and the Origin of Life

How simple chemical reactions self-assembled into complex, robust networks at the origin of life is unknown. This general problem-self-assembly of dissipative molecular networks-is also important in understanding the growth of complexity from simplicity in molecular and biomolecular systems. Here, we describe how heterogeneity in the composition of a small network of oscillatory organic reactions can sustain (rather than stop) these oscillations, when homogeneity in their composition does not. Specifically, multiple reactants in an amide-forming network sustain oscillation when the environment (here, the space velocity) changes, while homogeneous networks-those with fewer reactants-do not. Remarkably, a mixture of two reactants of different structure-neither of which produces oscillations individually-oscillates when combined. These results demonstrate that molecular heterogeneity present in mixtures of reactants can promote rather than suppress complex behaviors.

Prebiotic Oligomer Assembly: What Was the Energy Source?

Polymerization of nucleotides and amino acids to form large, complex, and potentially functional products was an early and essential event on the paths leading to life's origin. The standard Gibbs energies of the condensation reactions are uphill, however, and at equilibrium will yield only declining sequences of small, nonfunctional oligomers. Geochemically produced condensing agents such as carbonyl sulfide, cyanamide, and polyphosphates have been proposed to invert the unfavorable condensation Gibbs energies and thereby activate exergonic condensation. We argue, however, that although activators may provide modest yields of oligomers, the inherently episodic nature of their sources throttles their effectiveness, and the fundamental hydrolytic instabilities of oligonucleotides and peptides ultimately prevail to yield decreasing product sequences. Notably, the Gibbs energy governing oligomer formation is antientropic. Accordingly, we propose that declining progression can be surmounted in evaporating pools in which a favorable entropy change is produced when high surface/volume ratios concentrate reactants at the air/water interface in continuous cycles of wetting and drying. The severely reduced configurational freedom of the solutes then inverts the antientropic nature of the condensation reactions, pivoting them to exergonic states and thus to the production of ascending sequences of complex polymeric products.

Spontaneous advent of genetic diversity in RNA populations through multiple recombination mechanisms

There are several plausible abiotic synthetic routes from prebiotic chemical materials to ribonucleotides and even short RNA oligomers. However, for refinement of the RNA World hypothesis to help explain the origins of life on the Earth, there needs to be a manner by which such oligomers can increase their length and expand their sequence diversity. Oligomers longer than at least 10-20 nucleotides would be needed for raw material for subsequent natural selection. Here, we explore spontaneous RNA-RNA recombination as a facile means by which such length and diversity enhancement could have been realized. Motivated by the discovery that RNA oligomers stored for long periods of time in the freezer expand their lengths, we systematically investigated RNA-RNA recombination processes. In addition to one known mechanism, we discovered at least three new mechanisms. In these, one RNA oligomer acts as a splint to catalyze the hybridization of two other oligomers and facilitates the attack of a 5'-OH, a 3'-OH, or a 2'-OH nucleophile of one oligomer onto a target atom of another. This leads to the displacement of one RNA fragment and the production of new recombinant oligomers. We show that this process can explain the spontaneous emergence of sequence complexity, both in vitro and in silico.

Molecular Diversity Required for the Formation of Autocatalytic Sets

Systems chemistry deals with the design and study of complex chemical systems. However, such systems are often difficult to investigate experimentally. We provide an example of how theoretical and simulation-based studies can provide useful insights into the properties and dynamics of complex chemical systems, in particular of autocatalytic sets. We investigate the issue of the required molecular diversity for autocatalytic sets to exist in random polymer libraries. Given a fixed probability that an arbitrary polymer catalyzes the formation of other polymers, we calculate this required molecular diversity theoretically for two particular models of chemical reaction systems, and then verify these calculations by computer simulations. We also argue that these results could be relevant to an origin of life scenario proposed recently by Damer and Deamer.

Limited Sequence Diversity Within a Population Supports Prebiotic RNA Reproduction

The origins of life require the emergence of informational polymers capable of reproduction. In the RNA world on the primordial Earth, reproducible RNA molecules would have arisen from a mixture of compositionally biased, poorly available, short RNA sequences in prebiotic environments. However, it remains unclear what level of sequence diversity within a small subset of population is required to initiate RNA reproduction by prebiotic mechanisms. Here, using a simulation for template-directed recombination and ligation, we explore the effect of sequence diversity in a given population for the onset of RNA reproduction. We show that RNA reproduction is improbable in low and high diversity of finite populations; however, it could robustly occur in an intermediate sequence diversity. The intermediate range broadens toward higher diversity as population size increases. We also found that emergent reproducible RNAs likely form autocatalytic networks and collectively reproduce by catalyzing the formation of each other, allowing the expansion of information capacity. These results highlight the potential of abiotic RNAs, neither abundant nor diverse, to kick-start autocatalytic reproduction through spontaneous network formation.

Mathematical modeling reveals spontaneous emergence of self-replication in chemical reaction systems

Explaining the origin of life requires us to elucidate how self-replication arises. To be specific, how can a self-replicating entity develop spontaneously from a chemical reaction system in which no reaction is self-replicating? Previously proposed mathematical models either supply an explicit framework for a minimal living system or consider only catalyzed reactions, and thus fail to provide a comprehensive theory. Here, we set up a general mathematical model for chemical reaction systems that properly accounts for energetics, kinetics, and the conservation law. We found that 1) some systems are collectively catalytic, a mode whereby reactants are transformed into end products with the assistance of intermediates (as in the citric acid cycle), whereas some others are self-replicating, that is, different parts replicate each other and the system self-replicates as a whole (as in the formose reaction, in which sugar is replicated from formaldehyde); 2) side reactions do not always inhibit such systems; 3) randomly chosen chemical universes (namely random artificial chemistries) often contain one or more such systems; 4) it is possible to construct a self-replicating system in which the entropy of some parts spontaneously decreases, in a manner similar to that discussed by Schrödinger; and 5) complex self-replicating molecules can emerge spontaneously and relatively easily from simple chemical reaction systems through a sequence of transitions. Together, these results start to explain the origins of prebiotic evolution.

Population Dynamics of Autocatalytic Sets in a Compartmentalized Spatial World

Autocatalytic sets are self-sustaining and collectively catalytic chemical reaction networks which are believed to have played an important role in the origin of life. Simulation studies have shown that autocatalytic sets are, in principle, evolvable if multiple autocatalytic subsets can exist in different combinations within compartments, i.e., so-called protocells. However, these previous studies have so far not explicitly modeled the emergence and dynamics of autocatalytic sets in populations of compartments in a spatial environment. Here, we use a recently developed software tool to simulate exactly this scenario, as an important first step towards more realistic simulations and experiments on autocatalytic sets in protocells.

The origin and early evolution of life in chemical composition space

Life can be viewed as a localized chemical system that sits in the basin of attraction of a metastable dynamical attractor state that remains out of equilibrium with the environment. To explore the implications of this conception, I introduce an abstract coordinate system, chemical composition (CC Space), which summarizes the degree to which chemical systems are out of equilibrium with the bulk environment. A system's chemical disequilibrium (CD) is defined to be proportional to the Euclidean distance between the composition of a small region of physical space, a pixel, and the origin of CC space. Such a model implies that new living states arise through chance changes in local chemical concentration ("mutations") that cause chemical systems to move in CC space and enter the basin of attraction of a life state. The attractor of a life state comprises an autocatalytic set of chemicals whose essential ("keystone") species are produced at a higher rate than they are lost to the environment by diffusion, such that spatial growth of the life state is expected. This framework suggests that new life states are most likely to form at the interface between different physical phases, where the rate of diffusion of keystone species is tied to the low-diffusion regime, whereas food and waste products are subject to the more diffusive regime. Once life nucleates, for example on a mineral surface, it will tend to grow and generate variants as a result of additional mutations that find alternative life states. By jumping from life state to life state, systems can eventually occupy areas of CC space that are too far out of equilibrium with the environment to ever arise in a single mutational step. Furthermore, I propose that variation in the capacity of different surface associated life states to persist and compete may systematically favor states that have higher chemical disequilibrium. The model also suggests a simple and predictable path from surface-associated life to cell-like individuation. This dynamical systems theoretical framework provides an integrated view of the origin and early evolution of life and supports novel empirical approaches.

Existing Self-Replicators Can Direct the Emergence of New Ones

The study of the interplay between different self-replicating molecules constitutes an important new phase in the synthesis of life and in unravelling the origin of life. Here we show how existing replicators can direct the nature of a newly formed replicator. Starting from the same building block, 6-ring replicators formed when the mixture was exposed to pre-existing 6-membered replicators, while pre-formed 8-membered replicators funneled the building block into 8-ring replicators. Not only ring size, but also the mode of assembly of the rings into stacks was inherited from the pre-existing replicators. These results show that the nature of self-replicating molecules can be strongly influenced by the interplay between different self-replicators, overriding preferences innate to the structure of the building block.

Exploiting limited valence patchy particles to understand autocatalytic kinetics

Autocatalysis, i.e., the speeding up of a reaction through the very same molecule which is produced, is common in chemistry, biophysics, and material science. Rate-equation-based approaches are often used to model the time dependence of products, but the key physical mechanisms behind the reaction cannot be properly recognized. Here, we develop a patchy particle model inspired by a bicomponent reactive mixture and endowed with adjustable autocatalytic ability. Such a coarse-grained model captures all general features of an autocatalytic aggregation process that takes place under controlled and realistic conditions, including crowded environments. Simulation reveals that a full understanding of the kinetics involves an unexpected effect that eludes the chemistry of the reaction, and which is crucially related to the presence of an activation barrier. The resulting analytical description can be exported to real systems, as confirmed by experimental data on epoxy-amine polymerizations, solving a long-standing issue in their mechanistic description.