The structure of autocatalytic networks, with application to early biochemistry

Self-generating autocatalytic networks: structural results, algorithms and their relevance to early biochemistry

The concept of an autocatalytic network of reactions that can form and persist, starting from just an available food source, has been formalized by the notion of a reflexively autocatalytic and food-generated (RAF) set. The theory and algorithmic results concerning RAFs have been applied to a range of settings, from metabolic questions arising at the origin of life, to ecological networks, and cognitive models in cultural evolution. In this article, we present new structural and algorithmic results concerning RAF sets, by studying more complex modes of catalysis that allow certain reactions to require multiple catalysts (or to not require catalysis at all), and discuss the differing ways catalysis has been viewed in the literature. We also focus on the structure and analysis of minimal RAFs and derive structural results and polynomial-time algorithms. We then apply these new methods to a large metabolic network to gain insights into possible biochemical scenarios near the origin of life.

Interior Operators and Their Relationship to Autocatalytic Networks

The emergence of an autocatalytic network from an available set of elements is a fundamental step in early evolutionary processes, such as the origin of metabolism. Given the set of elements, the reactions between them (chemical or otherwise), and with various elements catalysing certain reactions, a Reflexively Autocatalytic F-generated (RAF) set is a subset R[Formula: see text] of reactions that is self-generating from a given food set, and with each reaction in R[Formula: see text] being catalysed from within R[Formula: see text]. RAF theory has been applied to various phenomena in theoretical biology, and a key feature of the approach is that it is possible to efficiently identify and classify RAFs within large systems. This is possible because RAFs can be described as the (nonempty) subsets of the reactions that are the fixed points of an (efficiently computable) interior map that operates on subsets of reactions. Although the main generic results concerning RAFs can be derived using just this property, we show that for systems with at least 12 reactions there are generic results concerning RAFs that cannot be proven using the interior operator property alone.Kindly check and confirm the edit made in the title.I confirm that the edit is fine.

Assessment of Stoichiometric Autocatalysis across Element Groups

Autocatalysis has been proposed to play critical roles during abiogenesis. These proposals are at odds with a limited number of known examples of abiotic (and, in particular, inorganic) autocatalytic systems that might reasonably function in a prebiotic environment. In this study, we broadly assess the occurrence of stoichiometries that can support autocatalytic chemical systems through comproportionation. If the product of a comproportionation reaction can be coupled with an auxiliary oxidation or reduction pathway that furnishes a reactant, then a Comproportionation-based Autocatalytic Cycle (CompAC) can exist. Using this strategy, we surveyed the literature published in the past two centuries for reactions that can be organized into CompACs that consume some chemical species as food to synthesize more autocatalysts. 226 CompACs and 44 Broad-sense CompACs were documented, and we found that each of the 18 groups, lanthanoid series, and actinoid series in the periodic table has at least two CompACs. Our findings demonstrate that stoichiometric relationships underpinning abiotic autocatalysis could broadly exist across a range of geochemical and cosmochemical conditions, some of which are substantially different from the modern Earth. Meanwhile, the observation of some autocatalytic systems requires effective spatial or temporal separation between the food chemicals while allowing comproportionation and auxiliary reactions to proceed, which may explain why naturally occurring autocatalytic systems are not frequently observed. The collated CompACs and the conditions in which they might plausibly support complex, "life-like" chemical dynamics can directly aid an expansive assessment of life's origins and provide a compendium of alternative hypotheses concerning false-positive biosignatures.

The hierarchical organization of autocatalytic reaction networks and its relevance to the origin of life

Prior work on abiogenesis, the emergence of life from non-life, suggests that it requires chemical reaction networks that contain self-amplifying motifs, namely, autocatalytic cores. However, little is known about how the presence of multiple autocatalytic cores might allow for the gradual accretion of complexity on the path to life. To explore this problem, we develop the concept of a seed-dependent autocatalytic system (SDAS), which is a subnetwork that can autocatalytically self-maintain given a flux of food, but cannot be initiated by food alone. Rather, initiation of SDASs requires the transient introduction of chemical "seeds." We show that, depending on the topological relationship of SDASs in a chemical reaction network, a food-driven system can accrete complexity in a historically contingent manner, governed by rare seeding events. We develop new algorithms for detecting and analyzing SDASs in chemical reaction databases and describe parallels between multi-SDAS networks and biological ecosystems. Applying our algorithms to both an abiotic reaction network and a biochemical one, each driven by a set of simple food chemicals, we detect SDASs that are organized as trophic tiers, of which the higher tier can be seeded by relatively simple chemicals if the lower tier is already activated. This indicates that sequential activation of trophically organized SDASs by seed chemicals that are not much more complex than what already exist could be a mechanism of gradual complexification from relatively simple abiotic reactions to more complex life-like systems. Interestingly, in both reaction networks, higher-tier SDASs include chemicals that might alter emergent features of chemical systems and could serve as early targets of selection. Our analysis provides computational tools for analyzing very large chemical/biochemical reaction networks and suggests new approaches to studying abiogenesis in the lab.

Small-molecule autocatalytic networks are universal metabolic fossils

Life and the genetic code are self-referential and so are autocatalytic networks made of simpler, small molecules. Several origins of life theories postulate autocatalytic chemical networks preceding the primordial genetic code, yet demonstration with biochemical systems is lacking. Here, small-molecule reflexively autocatalytic food-generated networks (RAFs) ranging in size from 3 to 619 reactions were found in all of 6683 prokaryotic metabolic networks searched. The average maximum RAF size is 275 reactions for a rich organic medium and 93 for a medium with a single organic cofactor, NAD. In the rich medium, all universally essential metabolites are produced with the exception of glycerol-1-p (archaeal lipid precursor), phenylalanine, histidine and arginine. The 300 most common reactions, present in at least 2732 RAFs, are mostly involved in amino acid biosynthesis and the metabolism of carbon, 2-oxocarboxylic acid and purines. ATP and NAD are central in generating network complexity, and because ATP is also one of the monomers of RNA, autocatalytic networks producing redox and energy currencies are a strong candidate niche of the origin of a primordial information-processing system. The wide distribution of small-molecule autocatalytic networks indicates that molecular reproduction may be much more prevalent in the Universe than hitherto predicted. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

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.