Chasing the tail: The emergence of autocatalytic networks

Serpentinization as the source of energy, electrons, organics, catalysts, nutrients and pH gradients for the origin of LUCA and life

Serpentinization in hydrothermal vents is central to some autotrophic theories for the origin of life because it generates compartments, reductants, catalysts and gradients. During the process of serpentinization, water circulates through hydrothermal systems in the crust where it oxidizes Fe (II) in ultramafic minerals to generate Fe (III) minerals and H2. Molecular hydrogen can, in turn, serve as a freely diffusible source of electrons for the reduction of CO2 to organic compounds, provided that suitable catalysts are present. Using catalysts that are naturally synthesized in hydrothermal vents during serpentinization H2 reduces CO2 to formate, acetate, pyruvate, and methane. These compounds represent the backbone of microbial carbon and energy metabolism in acetogens and methanogens, strictly anaerobic chemolithoautotrophs that use the acetyl-CoA pathway of CO2 fixation and that inhabit serpentinizing environments today. Serpentinization generates reduced carbon, nitrogen and - as newer findings suggest - reduced phosphorous compounds that were likely conducive to the origins process. In addition, it gives rise to inorganic microcompartments and proton gradients of the right polarity and of sufficient magnitude to support chemiosmotic ATP synthesis by the rotor-stator ATP synthase. This would help to explain why the principle of chemiosmotic energy harnessing is more conserved (older) than the machinery to generate ion gradients via pumping coupled to exergonic chemical reactions, which in the case of acetogens and methanogens involve H2-dependent CO2 reduction. Serpentinizing systems exist in terrestrial and deep ocean environments. On the early Earth they were probably more abundant than today. There is evidence that serpentinization once occurred on Mars and is likely still occurring on Saturn's icy moon Enceladus, providing a perspective on serpentinization as a source of reductants, catalysts and chemical disequilibrium for life on other worlds.

Cascade autohydrolysis of Alzheimer's Aβ peptides

Protein/peptide self-assembly into amyloid structures associates with major neurodegenerative disorders such as Alzheimer's disease (AD). Soluble assemblies (oligomers) of the Aβ peptide and their aggregates are perceived as neurotoxic species in AD. While screening for synthetic cleavage agents that could break down such aberrant assemblies through hydrolysis, we observed that the assemblies of Aβ oligopeptides, containing the nucleation sequence Aβ14-24 (H14QKLVFFAEDV24), could act as cleavage agents by themselves. Autohydrolysis showed a common fragment fingerprint among various mutated Aβ14-24 oligopeptides, Aβ12-25-Gly and Aβ1-28, and full-length Aβ1-40/42, under physiologically relevant conditions. Primary endoproteolytic autocleavage at the Gln15-Lys16, Lys16-Leu17 and Phe19-Phe20 positions was followed by subsequent exopeptidase self-processing of the fragments. Control experiments with homologous d-amino acid enantiomers Aβ12-25-Gly and Aβ16-25-Gly showed the same autocleavage pattern under similar reaction conditions. The autohydrolytic cascade reaction (ACR) was resilient to a broad range of conditions (20-37 °C, 10-150 μM peptide concentration at pH 7.0-7.8). Evidently, assemblies of the primary autocleavage fragments acted as structural/compositional templates (autocatalysts) for self-propagating autohydrolytic processing at the Aβ16-21 nucleation site, showing the potential for cross-catalytic seeding of the ACR in larger Aβ isoforms (Aβ1-28 and Aβ1-40/42). This result may shed new light on Aβ behaviour in solution and might be useful in the development of intervention strategies to decompose or inhibit neurotoxic Aβ assemblies in AD.

Onset model of mutually catalytic self-replicative systems formed by an assembly of polynucleotides

Self-replicability is a unique attribute observed in all living organisms, and the question of how the life was physically initiated could be equivalent to the question of how self-replicating informative polymers were formed in the abiotic material world. It has been suggested that the present DNA and proteins world was preceded by an RNA world in which genetic information of RNA molecules was replicated by the mutual catalytic function of RNA molecules. However, the important question of how the transition occurred from a material world to the very early pre-RNA world remains unsolved both experimentally and theoretically. We present an onset model of mutually catalytic self-replicative systems formed in an assembly of polynucleotides. A quantitative expression of the critical condition for the onset of growing fluctuation towards self-replication in this model is obtained by analytical and numerical calculations.

Semigroup models for biochemical reaction networks

The catalytic reaction system (CRS) formalism by Hordijk and Steel is a versatile method to model autocatalytic biochemical reaction networks. It is particularly suited, and has been widely used, to study self-sustainment and self-generation properties. Its distinguishing feature is the explicit assignment of a catalytic function to chemicals that are part of the system. In this work, it is shown that the subsequent and simultaneous catalytic functions give rise to an algebraic structure of a semigroup with the additional compatible operation of idempotent addition and a partial order. The aim of this article is to demonstrate that such semigroup models are a natural setup to describe and analyze self-sustaining CRS. The basic algebraic properties of the models are established and the notion of the function of any set of chemicals on the whole CRS is made precise. This leads to a natural discrete dynamical system on the power set of chemicals, which is obtained by iteratively considering the self-action on a set of chemicals by its own function. The fixed points of this dynamical system are proven to correspond to self-sustaining sets of chemicals, which are functionally closed. Finally, as the main application, a theorem on the maximal self-sustaining set and a structure theorem on the set of functionally closed self-sustaining sets of chemicals are proven.

An algebraic characterization of self-generating chemical reaction networks using semigroup models

The ability of a chemical reaction network to generate itself by catalyzed reactions from constantly present environmental food sources is considered a fundamental property in origin-of-life research. Based on Kaufmann's autocatalytic sets, Hordijk and Steel have constructed the versatile formalism of catalytic reaction systems (CRS) to model and to analyze such self-generating networks, which they named reflexively autocatalytic and food-generated. Recently, it was established that the subsequent and simultaenous catalytic functions of the chemicals of a CRS give rise to an algebraic structure, termed a semigroup model. The semigroup model allows to naturally consider the function of any subset of chemicals on the whole CRS. This gives rise to a generative dynamics by iteratively applying the function of a subset to the externally supplied food set. The fixed point of this dynamics yields the maximal self-generating set of chemicals. Moreover, the set of all functionally closed self-generating sets of chemicals is discussed and a structure theorem for this set is proven. It is also shown that a CRS which contains self-generating sets of chemicals cannot have a nilpotent semigroup model and thus a useful link to the combinatorial theory of finite semigroups is established. The main technical tool introduced and utilized in this work is the representation of the semigroup elements as decorated rooted trees, allowing to translate the generation of chemicals from a given set of resources into the semigroup language.

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.

Autocatalytic Sets Arising in a Combinatorial Model of Chemical Evolution

The idea that chemical evolution led to the origin of life is not new, but still leaves open the question of how exactly it could have led to a coherent and self-reproducing collective of molecules. One possible answer to this question was proposed in the form of the emergence of an autocatalytic set: a collection of molecules that mutually catalyze each other's formation and that is self-sustaining given some basic "food" source. Building on previous work, here we investigate in more detail when and how autocatalytic sets can arise in a simple model of chemical evolution based on the idea of combinatorial innovation with random catalysis assignments. We derive theoretical results, and compare them with computer simulations. These results could suggest a possible step towards the (or an) origin of life.

A Dynamic Autocatalytic Network Model of Therapeutic Change

Psychotherapy involves the modification of a client's worldview to reduce distress and enhance well-being. We take a human dynamical systems approach to modeling this process, using Reflexively Autocatalytic foodset-derived (RAF) networks. RAFs have been used to model the self-organization of adaptive networks associated with the origin and early evolution of both biological life, as well as the evolution and development of the kind of cognitive structure necessary for cultural evolution. The RAF approach is applicable in these seemingly disparate cases because it provides a theoretical framework for formally describing under what conditions systems composed of elements that interact and 'catalyze' the formation of new elements collectively become integrated wholes. In our application, the elements are mental representations, and the whole is a conceptual network. The initial components-referred to as foodset items-are mental representations that are innate, or were acquired through social learning or individual learning (of pre-existing information). The new elements-referred to as foodset-derived items-are mental representations that result from creative thought (resulting in new information). In clinical psychology, a client's distress may be due to, or exacerbated by, one or more beliefs that diminish self-esteem. Such beliefs may be formed and sustained through distorted thinking, and the tendency to interpret ambiguous events as confirmation of these beliefs. We view psychotherapy as a creative collaborative process between therapist and client, in which the output is not an artwork or invention but a more well-adapted worldview and approach to life on the part of the client. In this paper, we model a hypothetical albeit representative example of the formation and dissolution of such beliefs over the course of a therapist-client interaction using RAF networks. We show how the therapist is able to elicit this worldview from the client and create a conceptualization of the client's concerns. We then formally demonstrate four distinct ways in which the therapist is able to facilitate change in the client's worldview: (1) challenging the client's negative interpretations of events, (2) providing direct evidence that runs contrary to and counteracts the client's distressing beliefs, (3) using self-disclosure to provide examples of strategies one can use to diffuse a negative conclusion, and (4) reinforcing the client's attempts to assimilate such strategies into their own ways of thinking. We then discuss the implications of such an approach to expanding our knowledge of the development of mental health concerns and the trajectory of the therapeutic change.

Modeling Discontinuous Cultural Evolution: The Impact of Cross-Domain Transfer

This paper uses autocatalytic networks to model discontinuous cultural transitions involving cross-domain transfer, using as an illustrative example, artworks inspired by the oldest-known uncontested example of figurative art: the carving of the Hohlenstein-Stadel Löwenmensch, or lion-human. Autocatalytic networks provide a general modeling setting in which nodes are not just passive transmitters of activation; they actively galvanize, or "catalyze" the synthesis of novel ("foodset-derived") nodes from existing ones (the "foodset.") This makes them uniquely suited to model how new structure grows out of earlier structure, i.e., cumulative, generative network growth. They have been used to model the origin and early evolution of biological life, and the emergence of cognitive structures capable of undergoing cultural evolution. We conducted a study in which six individual creators and one group generated music, prose, poetry, and visual art inspired by the Hohlenstein-Stadel Löwenmensch, and answered questions about the process. The data revealed four through-lines by which they expressed the Löwenmensch in an alternative art form: (1) lion-human hybrid, (2) subtracting from the whole to reveal the form within, (3) deterioration, and (4) waiting to be found with a story to tell. Autocatalytic networks were used to model how these four spontaneously derived through-lines form a cultural lineage from Löwenmensch to artist to audience. We used the resulting data from three creators to model the cross-domain transfer from inspirational source (sculpted figurine) to creative product (music, poetry, prose, visual art). These four spontaneously-generated threads of cultural continuity formed the backbone of this Löwenmensch-inspired cultural lineage, enabling culture to evolve even in the face of discontinuity at the level conventional categories or domains. We know of no other theory of cultural evolution that accommodates cross-domain transfer or other forms of discontinuity. The approach paves the way for a broad scientific framework for the origins of evolutionary processes.

Undefining life's biochemistry: implications for abiogenesis

In the mid-twentieth century, multiple Nobel Prizes rewarded discoveries of a seemingly universal set of molecules and interactions that collectively defined the chemical basis for life. Twenty-first-century science knows that every detail of this Central Dogma of Molecular Biology can vary through either biological evolution, human engineering (synthetic biology) or both. Clearly the material, molecular basis of replicating, evolving entities can be different. There is far less clarity yet for what constitutes this set of possibilities. One approach to better understand the limits and scope of moving beyond life's central dogma comes from those who study life's origins. RNA, proteins and the genetic code that binds them each look like products of natural selection. This raises the question of what step(s) preceded these particular components? Answers here will clarify whether any discrete point in time or biochemical evolution will objectively merit the label of life's origin, or whether life unfolds seamlessly from the non-living universe.

An Autocatalytic Network Model of Conceptual Change

In reflexively autocatalytic foodset (RAF)-generated networks, nodes are not only passive transmitters of activation, but they also actively galvanize, or "catalyze" the synthesis of novel ("foodset-derived") nodes from existing ones (the "foodset"). Thus, RAFs are uniquely suited to modeling how new structure grows out of currently available structure, and analyzing phase transitions in potentially very large networks. RAFs have been used to model the origins of evolutionary processes, both biological (the origin of life) and cultural (the origin of cumulative innovation), and may potentially provide an overarching framework that integrates evolutionary and developmental approaches to cognition. Applied to cognition, the foodset consists of information obtained through social learning or individual learning of pre-existing information, and foodset-derived items arise through mental operations resulting in new information. Thus, mental representations are not only propagators of spreading activation, but they also trigger the derivation of new mental representations. To illustrate the application of RAF networks in cognitive science, we develop a step-by-step process model of conceptual change (i.e., the process by which a child becomes an active participant in cultural evolution), focusing on childrens' mental models of the shape of the Earth. Using results from (Vosniadou & Brewer, 1992), we model different trajectories from the flat Earth model to the spherical Earth model, as well as the impact of other factors, such as pretend play, on cognitive development. As RAFs increase in size and number, they begin to merge, bridging previously compartmentalized knowledge, and get subsumed by a giant RAF (the maxRAF) that constrains and enables the scaffolding of new conceptual structure. At this point, the cognitive network becomes self-sustaining and self-organizing. The child can reliably frame new knowledge and experiences in terms of previous ones, and engage in recursive representational redescription and abstract thought. We suggest that individual differences in the reactivity of mental representations, that is, their proclivity to trigger conceptual change, culminate in different cognitive networks and concomitant learning trajectories.

When Is a Reaction Network a Metabolism? Criteria for Simple Metabolisms That Support Growth and Division of Protocells

With the aim of better understanding the nature of metabolism in the first cells and the relationship between the origin of life and the origin of metabolism, we propose three criteria that a chemical reaction system must satisfy in order to constitute a metabolism that would be capable of sustaining growth and division of a protocell. (1) Biomolecules produced by the reaction system must be maintained at high concentration inside the cell while they remain at low or zero concentration outside. (2) The total solute concentration inside the cell must be higher than outside, so there is a positive osmotic pressure that drives cell growth. (3) The metabolic rate (i.e., the rate of mass throughput) must be higher inside the cell than outside. We give examples of small-molecule reaction systems that satisfy these criteria, and others which do not, firstly considering fixed-volume compartments, and secondly, lipid vesicles that can grow and divide. If the criteria are satisfied, and if a supply of lipid is available outside the cell, then continued growth of membrane surface area occurs alongside the increase in volume of the cell. If the metabolism synthesizes more lipid inside the cell, then the membrane surface area can increase proportionately faster than the cell volume, in which case cell division is possible. The three criteria can be satisfied if the reaction system is bistable, because different concentrations can exist inside and out while the rate constants of all the reactions are the same. If the reaction system is monostable, the criteria can only be satisfied if there is a reason why the rate constants are different inside and out (for example, the decay rates of biomolecules are faster outside, or the formation rates of biomolecules are slower outside). If this difference between inside and outside does not exist, a monostable reaction system cannot sustain cell growth and division. We show that a reaction system for template-directed RNA polymerization can satisfy the requirements for a metabolism, even if the small-molecule reactions that make the single nucleotides do not.

Modeling a Cognitive Transition at the Origin of Cultural Evolution Using Autocatalytic Networks

Autocatalytic networks have been used to model the emergence of self-organizing structure capable of sustaining life and undergoing biological evolution. Here, we model the emergence of cognitive structure capable of undergoing cultural evolution. Mental representations (MRs) of knowledge and experiences play the role of catalytic molecules, and interactions among them (e.g., the forging of new associations) play the role of reactions and result in representational redescription. The approach tags MRs with their source, that is, whether they were acquired through social learning, individual learning (of pre-existing information), or creative thought (resulting in the generation of new information). This makes it possible to model how cognitive structure emerges and to trace lineages of cumulative culture step by step. We develop a formal representation of the cultural transition from Oldowan to Acheulean tool technology using Reflexively Autocatalytic and Food set generated (RAF) networks. Unlike more primitive Oldowan stone tools, the Acheulean hand axe required not only the capacity to envision and bring into being something that did not yet exist, but hierarchically structured thought and action, and the generation of new MRs: the concepts EDGING, THINNING, SHAPING, and a meta-concept, HAND AXE. We show how this constituted a key transition toward the emergence of semantic networks that were self-organizing, self-sustaining, and autocatalytic, and we discuss how such networks replicated through social interaction. The model provides a promising approach to unraveling one of the greatest anthropological mysteries: that of why development of the Acheulean hand axe was followed by over a million years of cultural stasis.

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.

An evolutionary process without variation and selection

Natural selection successfully explains how organisms accumulate adaptive change despite that traits acquired over a lifetime are eliminated at the end of each generation. However, in some domains that exhibit cumulative, adaptive change-e.g. cultural evolution, and earliest life-acquired traits are retained; these domains do not face the problem that Darwin's theory was designed to solve. Lack of transmission of acquired traits occurs when germ cells are protected from environmental change, due to a self-assembly code used in two distinct ways: (i) actively interpreted during development to generate a soma, and (ii) passively copied without interpretation during reproduction to generate germ cells. Early life and cultural evolution appear not to involve a self-assembly code used in these two ways. We suggest that cumulative, adaptive change in these domains is due to a lower-fidelity evolutionary process, and model it using reflexively autocatalytic and foodset-generated networks. We refer to this more primitive evolutionary process as self-other reorganization (SOR) because it involves internal self-organizing and self-maintaining processes within entities, as well as interaction between entities. SOR encompasses learning but in general operates across groups. We discuss the relationship between SOR and Lamarckism, and illustrate a special case of SOR without variation.

The Expected Number of Viable Autocatalytic Sets in Chemical Reaction Systems

The emergence of self-sustaining autocatalytic networks in chemical reaction systems has been studied as a possible mechanism for modeling how living systems first arose. It has been known for several decades that such networks will form within systems of polymers (under cleavage and ligation reactions) under a simple process of random catalysis, and this process has since been mathematically analyzed. In this paper, we provide an exact expression for the expected number of self-sustaining autocatalytic networks that will form in a general chemical reaction system, and the expected number of these networks that will also be uninhibited (by some molecule produced by the system). Using these equations, we are able to describe the patterns of catalysis and inhibition that maximize or minimize the expected number of such networks. We apply our results to derive a general theorem concerning the trade-off between catalysis and inhibition, and to provide some insight into the extent to which the expected number of self-sustaining autocatalytic networks coincides with the probability that at least one such system is present.

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.

Molecules to Microbes

How did life begin on Earth? And is there life elsewhere in the Cosmos? Challenging questions, indeed. The series of conferences established by NoR CEL in 2013 addresses these very questions. This paper comprises a summary report of oral presentations that were delivered by NoR CEL’s network members during the 2018 Athens conference and, as such, disseminates the latest research which they have put forward. More in depth material can be found by consulting the contributors referenced papers. Overall, the outcome of this conspectus on the conference demonstrates a case for the existence of “probable chemistry” during the prebiotic epoch.

A model of the transition to behavioural and cognitive modernity using reflexively autocatalytic networks

This paper proposes a model of the cognitive mechanisms underlying the transition to behavioural and cognitive modernity in the Upper Palaeolithic using autocatalytic networks. These networks have been used to model life's origins. More recently, they have been applied to the emergence of cognitive structure capable of undergoing cultural evolution. Mental representations of knowledge and experiences play the role of catalytic molecules, the interactions among them (e.g. the forging of new associations or affordances) play the role of reactions, and thought processes are modelled as chains of these interactions. We posit that one or more genetic mutations may have allowed thought to be spontaneously tailored to the situation by modulating the degree of (i) divergence (versus convergence), (ii) abstractness (versus concreteness), and (iii) context specificity. This culminated in persistent, unified autocatalytic semantic networks that bridged previously compartmentalized knowledge and experience. We explain the model using one of the oldest-known uncontested examples of figurative art: the carving of the Hohlenstein-Stadel Löwenmensch, or lion man. The approach keeps track of where in a cultural lineage each innovation appears, and models cumulative change step by step. It paves the way for a broad scientific framework for the origins of both biological and cultural evolutionary processes.

The structure of autocatalytic networks, with application to early biochemistry

Metabolism across all known living systems combines two key features. First, all of the molecules that are required are either available in the environment or can be built up from available resources via other reactions within the system. Second, the reactions proceed in a fast and synchronized fashion via catalysts that are also produced within the system. Building on early work by Stuart Kauffman, a precise mathematical model for describing such self-sustaining autocatalytic systems (RAF theory) has been developed to explore the origins and organization of living systems within a general formal framework. In this paper, we develop this theory further by establishing new relationships between classes of RAFs and related classes of networks, and developing new algorithms to investigate and visualize RAF structures in detail. We illustrate our results by showing how it reveals further details into the structure of archaeal and bacterial metabolism near the origin of life, and provide techniques to study and visualize the core aspects of primitive biochemistry.

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.

Molecular shape as a key source of prebiotic information

One of the most striking features of a living system is the self-sustaining functional inner organization, which is only possible when a source of internal references is available from which the system is able to self-organize components and processes. Internal references are intrinsically related to biological information, which is typically understood as genetic information. However, the organization in living systems supports a diversity of intricate processes that enable life to endure, adapt and reproduce because of this organization. In a biological context, information refers to a complex relationship between internal architecture and system functionality. Nongenetic processes, such as conformational recognition, are not considered biological information, although they exert important control over cell processes. In this contribution, we discuss the informational nature in the recognition of molecular shape in living systems. Thus, we highlight supramolecular matching as having a theoretical key role in the origin of life. Based on recent data, we demonstrate that the transfer of molecular conformation is a very likely dynamic of prebiotic information, which is closely related to the origin of biological homochirality and biogenic systems. In light of the current hypothesis, we also revisit the central dogma of molecular biology to assess the consistency of the proposal presented here. We conclude that both spatial (molecular shape) and sequential (genetic) information must be represented in this biological paradigm.

Complexity results for autocatalytic network models

A key step in the origin of life is the emergence of a primitive metabolism. This requires the formation of a subset of chemical reactions that is both self-sustaining and collectively autocatalytic. A generic approach to study such processes ('RAF theory') has provided a precise and computationally effective way to address these questions, both on simulated data and in laboratory studies. In this paper, we solve some questions posed in more recent papers concerning the computational complexity of some key questions in RAF theory. In particular, although there is a fast algorithm to determine whether or not a catalytic reaction network contains a subset that is both self-sustaining and autocatalytic (and, if so, find one), determining whether or not sets exist that satisfy certain additional constraints turns out to be NP-hard.

Molecules to Microbes

How did life begin on Earth? And is there life elsewhere in the Cosmos? Challenging questions, indeed. The series of conferences established by NoR CEL in 2013, addresses these very same questions. The basis for this paper is the summary report of oral presentations that were delivered by NoR CEL’s network members during the 2018 Athens conference and, as such, disseminates the latest research which they have put forward. More in depth material can be found by consulting the contributors referenced papers. Overall, the outcome of this conspectus on the conference demonstrates a case for the existence of “probable chemistry” during the prebiotic epoch.

On the emergence of cognition: from catalytic closure to neuroglial closure

In an analogous manner as occurred during the development of a connected metabolism that at some point reached characteristics associated with what is called "life"-due mainly to a catalytic closure phenomenon when chemicals started to autocatalyze themselves forming a closed web of chemical reactions-it is here proposed that cognition and consciousness (or features associated with them) arose as a consequence of another type of closure within the nervous system, the brain especially. Proper brain function requires an efficient web of connections and once certain complexity is attained due to the number and coordinated activities of the brain cell networks, the emergent properties of cognition and consciousness take place. Seeking to identify main features of the nervous system organization for optimal function, it is here proposed that while catalytic closure yielded life, neuroglial closure produced cognition/consciousness.

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.

From inert matter to the global society life as multi-level networks of processes

A few billion years have passed since the first life forms appeared. Since then, life has continued to forge complex associations between the different emergent levels of interconnection it forms. The advances of recent decades in molecular chemistry and theoretical biology, which have embraced complex systems approaches, now make it possible to conceptualize the questions of the origins of life and its increasing complexity from three complementary notions of closure: processes closure, autocatalytic closure and constraints closure. Developed in the wake of the second-order cybernetics, this triple closure approach, that relies on graph theory and complex networks science, sketch a paradigm where it is possible to go up the physical levels of organization of matter, from physics to biology and society, without resorting to strong reductionism. The phenomenon of life is conceived as the contingent complexification of the organization of matter, until the emergence of life forms, defined as a network of auto-catalytic process networks, organized in a multi-level manner. This approach of living systems, initiated by Maturana & Varela and Kauffman, inevitably leads to a reflection on the nature of cognition; and in the face of the deep changes that affected humanity as a complex systems, on the nature of cultural evolution. Faced with the major challenges that humanity will have to address in the decades to come, this new paradigm invites us to change our conception of causality by shifting our attention from state change to process change and to abandon a widespread notion of 'local' causality in favour of complex systems thinking. It also highlights the importance of a better understanding of the influence of social networks, recommendation systems and artificial intelligence on our future collective dynamics and social cognition processes. This article is part of the theme issue 'Unifying the essential concepts of biological networks: biological insights and philosophical foundations'.

Coupled catabolism and anabolism in autocatalytic RNA sets

The ability to process molecules available in the environment into useable building blocks characterizes catabolism in contemporary cells and was probably critical for the initiation of life. Here we show that a catabolic process in collectively autocatalytic sets of RNAs allows diversified substrates to be assimilated. We modify fragments of the Azoarcus group I intron and find that the system is able to restore the original native fragments by a multi-step reaction pathway. This allows in turn the formation of catalysts by an anabolic process, eventually leading to the accumulation of ribozymes. These results demonstrate that rudimentary self-reproducing RNA systems based on recombination possess an inherent capacity to assimilate an expanded repertoire of chemical resources and suggest that coupled catabolism and anabolism could have arisen at a very early stage in primordial living systems.

Molecules to Microbes

How did life begin on Earth? And is there life elsewhere in the Cosmos? Challenging questions, indeed. The series of conferences established by NoR CEL in 2013, addresses these very same questions. The basis for this paper is the summary report of oral presentations that were delivered by NoR CEL’s network members during the 2018 Athens conference and, as such, disseminates the latest research which they have put forward. More in depth material can be found by consulting the contributors referenced papers. Overall, the outcome of this conspectus on the conference demonstrates a case for the existence of “probable chemistry” during the prebiotic epoch.

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.

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.

Autocatalytic Networks at the Basis of Life's Origin and Organization

Life is more than the sum of its constituent molecules. Living systems depend on a particular chemical organization, i.e., the ways in which their constituent molecules interact and cooperate with each other through catalyzed chemical reactions. Several abstract models of minimal life, based on this idea of chemical organization and also in the context of the origin of life, were developed independently in the 1960s and 1970s. These models include hypercycles, chemotons, autopoietic systems, (M,R)-systems, and autocatalytic sets. We briefly compare these various models, and then focus more specifically on the concept of autocatalytic sets and their mathematical formalization, RAF theory. We argue that autocatalytic sets are a necessary (although not sufficient) condition for life-like behavior. We then elaborate on the suggestion that simple inorganic molecules like metals and minerals may have been the earliest catalysts in the formation of prebiotic autocatalytic sets, and how RAF theory may also be applied to systems beyond chemistry, such as ecology, economics, and cognition.

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 last universal common ancestor between ancient Earth chemistry and the onset of genetics

All known life forms trace back to a last universal common ancestor (LUCA) that witnessed the onset of Darwinian evolution. One can ask questions about LUCA in various ways, the most common way being to look for traits that are common to all cells, like ribosomes or the genetic code. With the availability of genomes, we can, however, also ask what genes are ancient by virtue of their phylogeny rather than by virtue of being universal. That approach, undertaken recently, leads to a different view of LUCA than we have had in the past, one that fits well with the harsh geochemical setting of early Earth and resembles the biology of prokaryotes that today inhabit the Earth's crust.

The Influence of Modularity, Seeding, and Product Inhibition on Peptide Autocatalytic Network Dynamics

Chemical networks often exhibit emergent, systems-level properties that cannot be simply derived from the linear sum of the individual components. The design and analysis of increasingly complex chemical networks thus constitute a major area of research in Systems Chemistry. In particular, much research is focused on the emergence of functional properties in prebiotic chemical networks relevant to the origin and early evolution of life. Here, we apply a formal framework known as RAF theory to study the dynamics of a complex network of mutually catalytic peptides. We investigate in detail the influence of network modularity, initial template seeding, and product inhibition on the network dynamics. We show that these results can be useful for designing new experiments, and further argue how they are relevant to origin of life studies.

Niche emergence as an autocatalytic process in the evolution of ecosystems

The utilisation of the ecospace and the change in diversity through time has been suggested to be due to the effect of niche partitioning, as a global long-term pattern in the fossil record. However, niche partitioning, as a way to coexist, could be a limited means to share the environmental resources and condition during evolutionary time. In fact, a physical limit impedes a high partitioning without a high restriction of the niche's variables. Here, we propose that niche emergence, rather than niche partitioning, is what mostly drives ecological diversity. In particular, we view ecosystems in terms of autocatalytic sets: catalytically closed and self-sustaining reaction (or interaction) networks. We provide some examples of such ecological autocatalytic networks, how this can give rise to an expanding process of niche emergence (both in time and space), and how these networks have evolved over time (so-called evoRAFs). Furthermore, we use the autocatalytic set formalism to show that it can be expected to observe a power-law in the size distribution of extinction events in ecosystems. In short, we elaborate on our earlier argument that new species create new niches, and that biodiversity is therefore an autocatalytic process.

Autocatalytic confusion clarified

There is frequent confusion about the terms autocatalytic reaction, autocatalytic cycle, and autocatalytic set. As the use of the same adjective implies, these three systems do indeed share common properties, in particular their potential for exponential growth. However, the ways in which they achieve this potential are different, giving rise to different internal network structures and dynamics. Therefore, care should be taken which term is used in which context. Here, we explain and discuss the similarities and differences between the three systems in detail, in an effort to avoid any further confusion. We then also discuss the relevance of these autocatalytic systems for possible origin of life scenarios, with an emphasis on how autocatalytic sets may have played an important role in this.

Autocatalytic networks in cognition and the origin of culture

It has been proposed that cultural evolution was made possible by a cognitive transition brought about by onset of the capacity for self-triggered recall and rehearsal. Here we develop a novel idea that models of collectively autocatalytic networks, developed for understanding the origin and organization of life, may also help explain the origin of the kind of cognitive structure that makes cultural evolution possible. In this setting, mental representations (for example, memories, concepts, ideas) play the role of 'molecules', and 'reactions' involve the evoking of one representation by another through remindings and associations. In the 'episodic mind', representations are so coarse-grained (encode too few properties) that such reactions must be 'catalyzed' by external stimuli. As cranial capacity increased, representations became more fine-grained (encoded more features), which facilitated recursive catalysis and culminated in free-association and streams of thought. At this point, the mind could combine representations and adapt them to specific needs and situations, and thereby contribute to cultural evolution. In this paper, we propose and study a simple and explicit cognitive model that gives rise naturally to autocatalytic networks, and thereby provides a possible mechanism for the transition from a pre-cultural episodic mind to a mimetic mind.

Self-Referential Encoding on Modules of Anticodon Pairs-Roots of the Biological Flow System

The proposal that the genetic code was formed on the basis of (proto)tRNA Dimer-Directed Protein Synthesis is reviewed and updated. The tRNAs paired through the anticodon loops are an indication on the process. Dimers are considered mimics of the ribosomes-structures that hold tRNAs together and facilitate the transferase reaction, and of the translation process-anticodons are at the same time codons for each other. The primitive protein synthesis system gets stabilized when the product peptides are stable and apt to bind the producers therewith establishing a self-stimulating production cycle. The chronology of amino acid encoding starts with Glycine and Serine, indicating the metabolic support of the Glycine-Serine C1-assimilation pathway, which is also consistent with evidence on origins of bioenergetics mechanisms. Since it is not possible to reach for substrates simpler than C1 and compounds in the identified pathway are apt for generating the other central metabolic routes, it is considered that protein synthesis is the beginning and center of a succession of sink-effective mechanisms that drive the formation and evolution of the metabolic flow system. Plasticity and diversification of proteins construct the cellular system following the orientation given by the flow and implementing it. Nucleic acid monomers participate in bioenergetics and the polymers are conservative memory systems for the synthesis of proteins. Protoplasmic fission is the final sink-effective mechanism, part of cell reproduction, guaranteeing that proteins don't accumulate to saturation, which would trigger inhibition.

Autocatalytic Sets and RNA Secondary Structure

The dominant paradigm in origin of life research is that of an RNA world. However, despite experimental progress towards the spontaneous formation of RNA, the RNA world hypothesis still has its problems. Here, we introduce a novel computational model of chemical reaction networks based on RNA secondary structure and analyze the existence of autocatalytic sub-networks in random instances of this model, by combining two well-established computational tools. Our main results are that (i) autocatalytic sets are highly likely to exist, even for very small reaction networks and short RNA sequences, and (ii) sequence diversity seems to be a more important factor in the formation of autocatalytic sets than sequence length. These findings could shed new light on the probability of the spontaneous emergence of an RNA world as a network of mutually collaborative ribozymes.