Universal motifs and the diversity of autocatalytic systems

A Self-Sustaining Supramolecular (Auto)Photocatalysis via the Synthesis of N-Vinylacetamides

Efforts to enhance photocatalysts prioritize improving their accessibility and practicality in photocatalytic applications. Supramolecular (auto)photocatalysis, which exploits transient self-assembled complexes, facilitates visible light-driven reactions, with autocatalytic systems promoting sustainable and atom-economical processes. In this study, the photocatalyst Mes-Acr-MeClO4, typically active under blue light, formed a dark red charge-transfer (CT) complex with N-bromoacetamide (NBA) in the presence of K2CO3 in DCE, enabling green-light photocatalysis. This self-assembled CT complex initiated an auto-photocatalytic process via two-photon absorption, generating an N-centered radical that drove anti-Markovnikov, syn-periplanar addition to phenylacetylene, achieving exclusive Z-selective formation of (Z)-N-(2-bromo-2-phenylvinyl)acetamide. Interestingly, the product itself functioned as a potent green-LED photocatalyst (λem = 518 nm, τ = 10 ns), driving its own synthesis with added terminal alkynes. With 100% atom economy, this work highlights a system chemistry approach, showcasing a highly efficient, self-sustaining catalytic process that advances green and sustainable synthetic strategies. This protocol emphasizes sustainability with an outstanding E-factor of 11.15, reflecting minimal waste production (11.15 kg per 1 kg of product) and demonstrating a strong commitment to green chemistry principles.

A stepwise emergence of evolution in the RNA world

Building on experimental evidence and replicator theories, I propose a 3-stage scenario for a transition from autocatalysis into template-based replication of RNA, providing a pathway for the origin of life. In stage 1, self-reproduction occurs via autocatalysis using oligomer substrates, replicator viability relies on substrate-specificity, and heritable variations are mediated by structural interactions. In stage 2, autocatalysis coexists with the templated ligation of external substrates. This dual mode of reproduction combined with limited diffusion avoids the error catastrophe. In stage 3, template-based replication takes over and uses substrates of decreasing size, made possible by enhanced catalytic properties and compartmentalization. Structural complexity, catalytic efficiency, metabolic efficiency, and cellularization all evolve gradually and interdependently, ultimately leading to evolutionary processes similar to extant biology. Impact statement This perspective proposes a testable stepwise scenario for the emergence of evolution in an RNA origin of life. It shows how evolution could appear in a gradual manner, thanks to catalytic feedback among random mixtures of molecules. It highlights possible couplings between the different facets of molecular self-organization, which could bootstrap life.

Thermodynamic consistency of autocatalytic cycles

Autocatalysis is seen as a potential key player in the origin of life, and perhaps more generally in the emergence of Darwinian dynamics. Building on recent formalizations of this phenomenon, we tackle the computational challenge of exhaustively detecting minimal autocatalytic cycles (autocatalytic cores) in reaction networks and further evaluate the impact of thermodynamic constraints on their realization under mass action kinetics. We first characterize the complexity of the detection problem by proving its NP-completeness. This justifies the use of constraint solvers to list all cores in a given reaction network, and also to group them into compatible sets, composed of cores whose stoichiometric requirements are not contradictory. Crucially, we show that the introduction of thermodynamic realism does constrain the composition of these sets. Compatibility relationships among autocatalytic cores can indeed be disrupted when the reaction kinetics obey thermodynamic consistency throughout the network. On the contrary, these constraints have no impact on the realizability of isolated cores, unless upper or lower bounds are imposed on the concentrations of the reactants. Overall, by better characterizing the conditions of autocatalysis in complex reaction systems, this work brings us a step closer to assessing the contribution of this collective chemical behavior to the emergence of natural selection in the primordial soup.

Multi-Layer Autocatalytic Feedback Enables Integral Control Amidst Resource Competition and Across Scales

Integral feedback control strategies have proven effective in regulating protein expression in unpredictable cellular environments. These strategies, grounded in model-based designs and control theory, have advanced synthetic biology applications. Autocatalytic integral feedback controllers, utilizing positive autoregulation for integral action, are one class of simplest architectures to design integrators. This class of controllers offers unique features, such as robustness against dilution effects and cellular growth, as well as the potential for synthetic realizations across different biological scales, owing to their similarity to self-regenerative behaviors widely observed in nature. Despite this, their potential has not yet been fully exploited. One key reason, we discuss, is that their effectiveness is often hindered by resource competition and context-dependent couplings. This study addresses these challenges using a multilayer feedback strategy. Our designs enabled population-level integral feedback and multicellular integrators, where the control function emerges as a property of coordinated interactions distributed across different cell populations coexisting in a multicellular consortium. We provide a generalized mathematical framework for modeling resource competition in complex genetic networks, supporting the design of intracellular control circuits. The use of our proposed multilayer autocatalytic controllers is examined in two typical control tasks that pose significant relevance to synthetic biology applications: concentration regulation and ratiometric control. We define a ratiometric control task and solve it using a variant of our controller. The effectiveness of our controller motifs is demonstrated through a range of application examples, from precise regulation of gene expression and gene ratios in embedded designs to population growth and coculture composition control in multicellular designs within engineered microbial ecosystems. These findings offer a versatile approach to achieving robust adaptation and homeostasis from subcellular to multicellular scales.

The Nature of Organization in Living Systems

Living systems are thermodynamically open but closed in their organization. In other words, even though their material components turn over constantly, a material-independent property persists, which we call organization. Moreover, organization comes from within organisms themselves, which requires us to explain how this self-organization is established and maintained. In this paper we propose a mathematical and conceptual framework to understand the kinds of organized systems that living systems are, aiming to explain how self-organization emerges from more basic elemental processes. Additionally, we map our own notions to existing traditions in theoretical biology and philosophy, aiming to bring the main formal ideas into conceptual congruence.

Viedma deracemization mechanisms in self-assembly processes

Simulations on an ODE-based model shows that there are many common points between Viedma deracemization and chiral self-assemblies of achiral building blocks towards chiral nanoparticles. Both systems occur in a closed system with energy exchange but no matter exchange with the surroundings and show parallel reversible growth mechanisms which coexist with an irreversible cluster breaking (grinding). The various mechanisms of growth give rise to the formation of polymerization/depolymerization cycles while the consecutive transformation of achiral monomer into chiral cluster results into an indirect enantioselective autocatalysis. Deracemization occurs by the destabilization of the racemic non-equilibrium stationary state likely because of the excess of entropy production generated by the coupling of the reversible cluster growth mechanisms with grinding. Results show that the SMSB bias from the racemic composition occurs already at the oligomeric level of polymerization. Our model goes beyond the scope of the effect of grinding by the stirring of solutions which is thoroughly reported in supramolecular chirality. For instance, some unique characteristics, as those of a SMSB in closed systems, the simultaneous presence of different coupled reversible growth mechanisms, the activation by a depolymerization agent and the reincorporation of oligomers to the polymer growth reactions, could be adapted to replicator selectivity and to the emergence of biological homochirality scenarios.

Maintaining an autocatalytic reaction system in a protocell: Nonenzymatic RNA templating and the link between replication and metabolism

The first protocells must have been driven by a reaction system in which autocatalysis is maintained inside the cell while food molecules outside the cell are unreactive. We show that if there is a second-order autocatalytic mechanism, then an active state can be stable inside the cell with a high catalyst concentration while the environment remains stable in an unreactive state with no catalyst. Addition of a small amount of catalyst to the environment does not cause the initiation of the autocatalytic cycle outside the cell. In contrast, for a first-order mechanism, addition of a small amount of catalyst initiates the reaction outside the cell unless there is continual removal of the catalyst from the environment. Hence, a second-order reaction mechanism maintains the difference between the inside and outside of a protocell much better than a first-order mechanism. The formose reaction, although a prebiotically plausible autocatalytic system, is first order and therefore is unlikely as a means of support for the first protocells. We give other theoretical examples of first- and second-order reaction networks but note there are few known real-world chemical systems that fit these schemes. However, we show that nonenzymatic RNA templating constitutes a second-order autocatalytic system with the necessary properties to support a protocell. Templating is maintained inside the cell but is not initiated outside the cell. If the reaction is driven by an external supply of activated nucleotides, then templating is itself a metabolic cycle. It is not necessary to have an additional separate metabolic cycle before templating reactions can occur. In this view, templating reactions, which are usually considered as the origin of replication and heredity, are also the origin of metabolism.

Nonequilibrium properties of autocatalytic networks

Autocatalysis, the ability of a chemical system to make more of itself, is a crucial feature in metabolism and is speculated to have played a decisive role in the origin of life. Nevertheless, how autocatalytic systems behave far from equilibrium remains unexplored. In this work, we elaborate on recent advances regarding the stoichiometric characterization of autocatalytic networks, particularly their absence of mass-like conservation laws, to study how this topological feature influences their nonequilibrium behavior. Building upon the peculiar topology of autocatalytic networks, we derive a decomposition of the chemical fluxes, which highlights the existence of productive modes in their dynamics. These modes produce the autocatalysts in net excess and require the presence of external fuel/waste species to operate. Relying solely on topology, the flux decomposition holds under broad conditions and, in particular, does not require steady state or elementary reactions. Additionally, we show that once externally controlled, the nonconservative forces brought by the external species do not act on these productive modes. This must be considered when one is interested in the thermodynamics of open autocatalytic networks. Specifically, we show that an additional term must be added to the semigrand free energy. Finally, from the thermodynamic potential, we derive the thermodynamic cost associated with the production of autocatalysts.

Design principles, growth laws, and competition of minimal autocatalysts

The difficulty of designing simple autocatalysts that grow exponentially in the absence of enzymes, external drives or ingenious internal mechanisms severely constrains scenarios for the emergence of evolution by natural selection in chemical and physical systems. Here, we systematically analyze these difficulties in the simplest and most generic autocatalyst: a dimeric molecule that duplicates by templated ligation. We show that despite its simplicity, such an autocatalyst can achieve exponential growth autonomously. We also show, however, that it is possible to design as simple sub-exponential autocatalysts that have an advantage over exponential autocatalysts when competing for a common resource. We reach these conclusions by developing a theoretical framework based on kinetic barrier diagrams. Besides challenging commonly accepted assumptions in the field of the origin of life, our results provide a blueprint for the experimental realization of elementary autocatalysts exhibiting a form of natural selection, whether on a molecular or colloidal scale.

Autocatalytic Sets and Assembly Theory: A Toy Model Perspective

Assembly Theory provides a promising framework to explain the complexity of systems such as molecular structures and the origins of life, with broad applicability across various disciplines. In this study, we explore and consolidate different aspects of Assembly Theory by introducing a simplified Toy Model to simulate the autocatalytic formation of complex structures. This model abstracts the molecular formation process, focusing on the probabilistic control of catalysis rather than the intricate interactions found in organic chemistry. We establish a connection between probabilistic catalysis events and key principles of Assembly Theory, particularly the probability of a possible construction path in the formation of a complex object, and examine how the assembly of complex objects is impacted by the presence of autocatalysis. Our findings suggest that this presence of autocatalysis tends to favor longer consecutive construction sequences in environments with a low probability of catalysis, while this bias diminishes in environments with higher catalysis probabilities, highlighting the significant influence of environmental factors on the assembly of complex structures.

Beyond fitness: The information imparted in population states by selection throughout lifecycles

We approach the questions, what part of evolutionary change results from selection, and what is the adaptive information flow into a population undergoing selection, as a problem of quantifying the divergence of typical trajectories realized under selection from the expected dynamics of their counterparts under a null stochastic-process model representing the absence of selection. This approach starts with a formulation of adaptation in terms of information and from that identifies selection from the genetic parameters that generate information flow; it is the reverse of a historical approach that defines selection in terms of fitness, and then identifies adaptive characters as those amplified in relative frequency by fitness. Adaptive information is a relative entropy on distributions of histories computed directly from the generators of stochastic evolutionary population processes, which in large population limits can be approximated by its leading exponential dependence as a large-deviation function. We study a particular class of generators that represent the genetic dependence of explicit transitions around reproductive cycles in terms of stoichiometry, familiar from chemical reaction networks. Following Smith (2023), which showed that partitioning evolutionary events among genetically distinct realizations of lifecycles yields a more consistent causal analysis through the Price equation than the construction from units of selection and fitness, here we show that it likewise yields more complete evolutionary information measures.

Primitive purine biosynthesis connects ancient geochemistry to modern metabolism

An unresolved question in the origin and evolution of life is whether a continuous path from geochemical precursors to the majority of molecules in the biosphere can be reconstructed from modern-day biochemistry. Here we identified a feasible path by simulating the evolution of biosphere-scale metabolism, using only known biochemical reactions and models of primitive coenzymes. We find that purine synthesis constitutes a bottleneck for metabolic expansion, which can be alleviated by non-autocatalytic phosphoryl coupling agents. Early phases of the expansion are enriched with enzymes that are metal dependent and structurally symmetric, supporting models of early biochemical evolution. This expansion trajectory suggests distinct hypotheses regarding the tempo, mode and timing of metabolic pathway evolution, including a late appearance of methane metabolisms and oxygenic photosynthesis consistent with the geochemical record. The concordance between biological and geological analyses suggests that this trajectory provides a plausible evolutionary history for the vast majority of core 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.

Universal Transitions between Growth and Dormancy via Intermediate Complex Formation

A simple cell model consisting of a catalytic reaction network with intermediate complex formation is numerically studied. As nutrients are depleted, the transition from the exponential growth phase to the growth-arrested dormant phase occurs along with hysteresis and a lag time for growth recovery. This transition is caused by the accumulation of intermediate complexes, leading to the jamming of reactions and the diversification of components. These properties are generic in random reaction networks, as supported by dynamical systems analyses of corresponding mean-field models.

Effect of Alkali- and Alkaline-Earth-Metal Promoters on Silica-Supported Co-Fe Alloy for Autocatalytic CO2 Fixation

Hydrothermal vents harbor numerous microbial communities rich in reduced carbon species such as formate, acetate, and hydrocarbons. Such essential chemicals for life are produced by H2 -dependent CO2 reduction, where serpentinization provides continuous H2 and thermal energy. Here, we show that silica-supported bimetallic Co-Fe alloys, naturally occurring minerals around serpentinite, can convert CO2 and H2 O to key metabolic intermediates of the acetyl coenzyme A pathway such as formate (up to 72 mM), acetate, and pyruvate under mild hydrothermal vent conditions. Long-chain hydrocarbons up to C6 including propene are also detected, just as in the Lost City hydrothermal field. The effects of promoters on structural properties and catalytic functionalities of the Co-Fe alloy are systematically investigated by incorporating a series of alkali and alkaline earth metals including Na, Mg, K, and Ca. Alkali and alkaline earth metals resulted in higher formate concentrations when dissolved in water and increased reaction pH, while alkaline earth metals also favored the formation of insoluble hydroxides and carbonates similar to the constituent minerals of the chimneys at the Lost City hydrothermal fields.

Small-molecule autocatalysis drives compartment growth, competition and reproduction

Sustained autocatalysis coupled to compartment growth and division is a key step in the origin of life, but an experimental demonstration of this phenomenon in an artificial system has previously proven elusive. We show that autocatalytic reactions within compartments-when autocatalysis, and reactant and solvent exchange outpace product exchange-drive osmosis and diffusion, resulting in compartment growth. We demonstrate, using the formose reaction compartmentalized in aqueous droplets in an emulsion, that compartment volume can more than double. Competition for a common reactant (formaldehyde) causes variation in droplet growth rate based on the composition of the surrounding droplets. These growth rate variations are partially transmitted after selective division of the largest droplets by shearing, which converts growth-rate differences into differences in droplet frequency. This shows how a combination of properties of living systems (growth, division, variation, competition, rudimentary heredity and selection) can arise from simple physical-chemical processes and may have paved the way for the emergence of evolution by natural selection.

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.

On the Emergence of Autonomous Chemical Systems through Dissipation Kinetics

This work addresses the kinetic requirements for compensating the entropic cost of self-organization and natural selection, thereby revealing a fundamental principle in biology. Metabolic and evolutionary features of life cannot therefore be separated from an origin of life perspective. Growth, self-organization, evolution and dissipation processes need to be metabolically coupled and fueled by low-entropy energy harvested from the environment. The evolutionary process requires a reproduction cycle involving out-of-equilibrium intermediates and kinetic barriers that prevent the reproductive cycle from proceeding in reverse. Model analysis leads to the unexpectedly simple relationship that the system should be fed energy with a potential exceeding a value related to the ratio of the generation time to the transition state lifetime, thereby enabling a process mimicking natural selection to take place. Reproducing life's main features, in particular its Darwinian behavior, therefore requires satisfying constraints that relate to time and energy. Irreversible reaction cycles made only of unstable entities reproduce some of these essential features, thereby offering a physical/chemical basis for the possible emergence of autonomy. Such Emerging Autonomous Systems (EASs) are found to be capable of maintaining and reproducing their kind through the transmission of a stable kinetic state, thereby offering a physical/chemical basis for what could be deemed an epigenetic process.

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.

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.

Beyond fitness: the nature of selection acting through the constructive steps of lifecycles

We address the problem of defining selection and extracting the adaptive part of evolutionary change, originally formalized by Fisher and Price. Conventionally, selection and adaptation are defined through fitness attributed to genes or genotypes chosen as units of selection. The construction through fitness is known to suffer ambiguities and omissions as a theory of change due to selection. We construct an alternative framing in which units of selection and fitness are replaced as the main abstractions by formal lifecycle models and reproduction rates through genetically distinct lifecycle realizations. Graphical representations of lifecycles express relations among reproductive stages that cannot be assigned to any one unit of selection. The lifecycle partition refines the statistics of overall reproductive success and resolves modes of selection that fitness either excludes or distorts through additive projections. We derive the Price equation in the basis of lifecycle realizations and compare it to the conventional Price equation for additive fitness of organisms. We show how the lifecycle approach recovers fitnesses acting concurrently at multiple levels, or contrasts forms of competition within and between levels that are invisible to additive fitness. Defining selection through lifecycles recasts population genetics from an object-focused to a construction- and process-focused representation.

Prevalence of multistability and nonstationarity in driven chemical networks

External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical reaction networks? Here, we analyze transitions giving rise to complex behavior in random reaction networks subject to external driving forces. In the absence of driving, we characterize the uniqueness of the steady state and identify the percolation of a giant connected component in these networks as the number of reactions increases. When subject to chemical driving (influx and outflux of chemical species), the steady state can undergo bifurcations, leading to multistability or oscillatory dynamics. By quantifying the prevalence of these bifurcations, we show how chemical driving and network sparsity tend to promote the emergence of these complex dynamics and increased rates of entropy production. We show that catalysis also plays an important role in the emergence of complexity, strongly correlating with the prevalence of bifurcations. Our results suggest that coupling a minimal number of chemical signatures with external driving can lead to features present in biochemical processes and abiogenesis.

Error-suppression mechanism of PCR by blocker strands

The polymerase chain reaction (PCR) is a central technique in biotechnology. Its ability to amplify a specific target region of a DNA sequence has led to prominent applications, including virus tests, DNA sequencing, genotyping, and genome cloning. These applications rely on the specificity of the primer hybridization and therefore require effective suppression of hybridization errors. A simple and effective method to achieve that is to add blocker strands, also called clamps, to the PCR mixture. These strands bind to the unwanted target sequence, thereby blocking the primer mishybridization. Because of its simplicity, this method is applicable to a broad nucleic-acid-based biotechnology. However, the precise mechanism by which blocker strands suppress PCR errors remains to be understood, limiting the applicability of this technique. Here, we combine experiments and theoretical modeling to reveal this mechanism. We find that the blocker strands both energetically destabilize the mishybridized complex and sculpt a kinetic barrier to suppress mishybridization. This combination of energetic and kinetic biasing extends the viable range of annealing temperatures, which reduces design constraint of the primer sequence and extends the applicability of PCR.

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.

An interdisciplinary effort to understand chemical organizations at the origin of life

This backstory features the perspectives of three group leaders of a Franco-Indian collaboration on the origin of life, involving efforts to engineer evolvable chemical systems. The researchers explain how they overcame the difficulties to bring empiricist and theorist cultures together and the importance of such synergy for the future of origin of life research.

Dynamic scaling of stochastic thermodynamic observables for chemical reactions at and away from equilibrium

Physical kinetic roughening processes are well-known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the chemical reaction mechanisms available synthetically and occurring naturally? Here, we formulate an approach to the dynamic scaling of stochastic fluctuations in thermodynamic observables at and away from equilibrium. Both analytical expressions and numerical simulations confirm our dynamic scaling ansatz with associated scaling exponents, function, and law. A survey of common chemical mechanisms reveals classes that organize according to the molecularity of the reactions involved, the nature of the reaction vessel and external reservoirs, (non)equilibrium conditions, and the extent of autocatalysis in the reaction network. Varying experimental parameters, such as temperature, can cause coupled reactions capable of chemical feedback to transition between these classes. While path observables, such as the dynamical activity, have scaling exponents that are time-independent, the variance in the entropy production and flow can have time-dependent scaling exponents and self-averaging properties as a result of temporal correlations that emerge during thermodynamically irreversible processes. Altogether, these results establish dynamic universality classes in the nonequilibrium fluctuations of thermodynamic observables for well-mixed chemical reactions.

Network Analysis Reveals Spatial Clustering and Annotation of Complex Chemical Spaces: Application to Astrochemistry

How are molecules linked to each other in complex systems? In a proof-of-concept study, we have developed the method mol2net (https://zenodo.org/record/7025094) to generate and analyze the molecular network of complex astrochemical data (from high-resolution Orbitrap MS¹ analysis of H₂O:CH₃OH:NH₃ interstellar ice analogs) in a data-driven and unsupervised manner, without any prior knowledge about chemical reactions. The molecular network is clustered according to the initial NH₃ content and unlocked HCN, NH₃, and H₂O as spatially resolved key transformations. In comparison with the PubChem database, four subsets were annotated: (i) saturated C-backbone molecules without N, (ii) saturated N-backbone molecules, (iii) unsaturated C-backbone molecules without N, and (iv) unsaturated N-backbone molecules. These findings were validated with previous results (e.g., identifying the two major graph components as previously described N-poor and N-rich molecular groups) but with additional information about subclustering, key transformations, and molecular structures, and thus, the structural characterization of large complex organic molecules in interstellar ice analogs has been significantly refined.

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 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.

What Wilhelm Ostwald meant by "Autokatalyse" and its significance to origins-of-life research: Facilitating the search for chemical pathways underlying abiogenesis by reviving Ostwald's thought that reactants may also be autocatalysts: Facilitating the search for chemical pathways underlying abiogenesis by reviving Ostwald's thought that reactants may also be autocatalysts

A closer look at Wilhelm Ostwald's articles that originally proposed the concept of autocatalysis reveals that he accepted reactants, not just products, as potential autocatalysts. Therefore, that a process is catalyzed by some of its products, which is the common definition of autocatalysis, is only a proper subset of what Ostwald meant by "Autokatalyse." As a result, it is necessary to reconsider the definition of autocatalysis, which is especially important for origins-of-life research because autocatalysis provides an abiotic mechanism that yields reproduction-like dynamics. Here, we translate and briefly review the two key publications on autocatalysis by Ostwald to revive his understanding of autocatalysis, and we introduce the concepts of recessive and expansive autocatalysis. Then we discuss the twofold significance of such a revival: first, facilitating the search for candidate processes underlying the origins of life, and second, updating our view of autocatalysis in complex reaction networks and metabolism.

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'.

An open source computational workflow for the discovery of autocatalytic networks in abiotic reactions

A central question in origins of life research is how non-entailed chemical processes, which simply dissipate chemical energy because they can do so due to immediate reaction kinetics and thermodynamics, enabled the origin of highly-entailed ones, in which concatenated kinetically and thermodynamically favorable processes enhanced some processes over others. Some degree of molecular complexity likely had to be supplied by environmental processes to produce entailed self-replicating processes. The origin of entailment, therefore, must connect to fundamental chemistry that builds molecular complexity. We present here an open-source chemoinformatic workflow to model abiological chemistry to discover such entailment. This pipeline automates generation of chemical reaction networks and their analysis to discover novel compounds and autocatalytic processes. We demonstrate this pipeline's capabilities against a well-studied model system by vetting it against experimental data. This workflow can enable rapid identification of products of complex chemistries and their underlying synthetic relationships to help identify autocatalysis, and potentially self-organization, in such systems. The algorithms used in this study are open-source and reconfigurable by other user-developed workflows.

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.

Determining the "Biosignature Threshold" for Life Detection on Biotic, Abiotic, or Prebiotic Worlds

The field of prebiotic chemistry has demonstrated that complex organic chemical systems that exhibit various life-like properties can be produced abiotically in the laboratory. Understanding these chemical systems is important for astrobiology and life detection since we do not know the extent to which prebiotic chemistry might exist or have existed on other worlds. Nor do we know what signatures are diagnostic of an extant or "failed" prebiotic system. On Earth, biology has suppressed most abiotic organic chemistry and overprints geologic records of prebiotic chemistry; therefore, it is difficult to validate whether chemical signatures from future planetary missions are remnant or extant prebiotic systems. The "biosignature threshold" between whether a chemical signature is more likely to be produced by abiotic versus biotic chemistry on a given world could vary significantly, depending on the particular environment, and could change over time, especially if life were to emerge and diversify on that world. To interpret organic signatures detected during a planetary mission, we advocate for (1) gaining a more complete understanding of prebiotic/abiotic chemical possibilities in diverse planetary environments and (2) involving experimental prebiotic samples as analogues when generating comparison libraries for "life-detection" mission instruments.

History Dependence in a Chemical Reaction Network Enables Dynamic Switching

This work describes an enzymatic autocatalytic network capable of dynamic switching under out-of-equilibrium conditions. The network, wherein a molecular fuel (trypsinogen) and an inhibitor (soybean trypsin inhibitor) compete for a catalyst (trypsin), is kept from reaching equilibria using a continuous flow stirred tank reactor. A so-called 'linear inhibition sweep' is developed (i.e., a molecular analogue of linear sweep voltammetry) to intentionally perturb the competition between autocatalysis and inhibition, and used to demonstrate that a simple molecular system, comprising only three components, is already capable of a variety of essential neuromorphic behaviors (hysteresis, synchronization, resonance, and adaptation). This research provides the first steps in the development of a strategy that uses the principles in systems chemistry to transform chemical reaction networks into platforms capable of neural network computing.

Elementary vectors and autocatalytic sets for resource allocation in next-generation models of cellular growth

Traditional (genome-scale) metabolic models of cellular growth involve an approximate biomass “reaction”, which specifies biomass composition in terms of precursor metabolites (such as amino acids and nucleotides). On the one hand, biomass composition is often not known exactly and may vary drastically between conditions and strains. On the other hand, the predictions of computational models crucially depend on biomass. Also elementary flux modes (EFMs), which generate the flux cone, depend on the biomass reaction. To better understand cellular phenotypes across growth conditions, we introduce and analyze new classes of elementary vectors for comprehensive (next-generation) metabolic models, involving explicit synthesis reactions for all macromolecules. Elementary growth modes (EGMs) are given by stoichiometry and generate the growth cone. Unlike EFMs, they are not support-minimal, in general, but cannot be decomposed “without cancellations”. In models with additional (capacity) constraints, elementary growth vectors (EGVs) generate a growth polyhedron and depend also on growth rate. However, EGMs/EGVs do not depend on the biomass composition. In fact, they cover all possible biomass compositions and can be seen as unbiased versions of elementary flux modes/vectors (EFMs/EFVs) used in traditional models. To relate the new concepts to other branches of theory, we consider autocatalytic sets of reactions. Further, we illustrate our results in a small model of a self-fabricating cell, involving glucose and ammonium uptake, amino acid and lipid synthesis, and the expression of all enzymes and the ribosome itself. In particular, we study the variation of biomass composition as a function of growth rate. In agreement with experimental data, low nitrogen uptake correlates with high carbon (lipid) storage.

Next-generation, genome-scale metabolic models allow to study the reallocation of cellular resources upon changing environmental conditions, by not only modeling flux distributions, but also expression profiles of the catalyzing proteome. In particular, they do no longer assume a fixed biomass composition. Methods to identify optimal solutions in such comprehensive models exist, however, an unbiased understanding of all feasible allocations is missing so far. Here we develop new concepts, called elementary growth modes and vectors, that provide a generalized definition of minimal pathways, thereby extending classical elementary flux modes (used in traditional models with a fixed biomass composition). The new concepts provide an understanding of all possible flux distributions and of all possible biomass compositions. In other words, elementary growth modes and vectors are the unique functional units in any comprehensive model of cellular growth. As an example, we show that lipid accumulation upon nitrogen starvation is a consequence of resource allocation and does not require active regulation. Our work puts current approaches on a theoretical basis and allows to seamlessly transfer existing workflows (e.g. for the design of cell factories) to next-generation metabolic models.

A robust transition to homochirality in complex chemical reaction networks

Homochirality, i.e. the dominance across all living matter of one enantiomer over the other among chiral molecules, is thought to be a key step in the emergence of life. Building on ideas put forward by Frank and many others, we proposed recently one such mechanism in Laurent et al. (Laurent, 2021 Proc. Natl Acad. Sci. USA 118 , e2012741118. ( doi:10.1073/pnas.2012741118 )) based on the properties of large out of equilibrium chemical networks. We showed that in such networks, a phase transition towards a homochiral state is likely to occur as the number of chiral species in the system becomes large or as the amount of free energy injected into the system increases. This paper aims at clarifying some important points in that scenario, not covered by our previous work. We first analyse the various conventions used to measure chirality, introduce the notion of chiral symmetry of a network and study its implications regarding the relative chiral signs adopted by different groups of molecules. We then propose a generalization of Frank’s model for large chemical networks, which we characterize completely using methods of random matrices. This analysis is extended to sparse networks, which shows that the emergence of homochirality is a robust transition.

Self-reproducing catalytic micelles as nanoscopic protocell precursors

Protocells at life's origin are often conceived as bilayer-enclosed precursors of life, whose self-reproduction rests on the early advent of replicating catalytic biopolymers. This Perspective describes an alternative scenario, wherein reproducing nanoscopic lipid micelles with catalytic capabilities were forerunners of biopolymer-containing protocells. This postulate gains considerable support from experiments describing micellar catalysis and autocatalytic proliferation, and, more recently, from reports on cross-catalysis in mixed micelles that lead to life-like steady-state dynamics. Such results, along with evidence for micellar prebiotic compatibility, synergize with predictions of our chemically stringent computer-simulated model, illustrating how mutually catalytic lipid networks may enable micellar compositional reproduction that could underlie primal selection and evolution. Finally, we highlight studies on how endogenously catalysed lipid modifications could guide further protocellular complexification, including micelle to vesicle transition and monomer to biopolymer progression. These portrayals substantiate the possibility that protocellular evolution could have been seeded by pre-RNA lipid assemblies.

Natural Selection beyond Life? A Workshop Report

Natural selection is commonly seen not just as an explanation for adaptive evolution, but as the inevitable consequence of “heritable variation in fitness among individuals”. Although it remains embedded in biological concepts, such a formalisation makes it tempting to explore whether this precondition may be met not only in life as we know it, but also in other physical systems. This would imply that these systems are subject to natural selection and may perhaps be investigated in a biological framework, where properties are typically examined in light of their putative functions. Here we relate the major questions that were debated during a three-day workshop devoted to discussing whether natural selection may take place in non-living physical systems. We start this report with a brief overview of research fields dealing with “life-like” or “proto-biotic” systems, where mimicking evolution by natural selection in test tubes stands as a major objective. We contend the challenge may be as much conceptual as technical. Taking the problem from a physical angle, we then discuss the framework of dissipative structures. Although life is viewed in this context as a particular case within a larger ensemble of physical phenomena, this approach does not provide general principles from which natural selection can be derived. Turning back to evolutionary biology, we ask to what extent the most general formulations of the necessary conditions or signatures of natural selection may be applicable beyond biology. In our view, such a cross-disciplinary jump is impeded by reliance on individuality as a central yet implicit and loosely defined concept. Overall, these discussions thus lead us to conjecture that understanding, in physico-chemical terms, how individuality emerges and how it can be recognised, will be essential in the search for instances of evolution by natural selection outside of living systems.

Specific Versus Non-specific Response in Exponential Molecular Amplification from Cross-Catalysis: Modeling the Influence of Background Amplifications on the Analytical Performances

Molecule based signal amplifications relying on an autocatalytic process may represent an ideal strategy for the development of ultrasensitive analytical or bioanalytical assays, the main reason being the exponential nature of the amplification. However, to take full advantage of such amplification rates, high stability of the starting co-reactants is required in order to avoid any undesirable background amplification. Here, on the basis of a simple kinetic model of cross-catalysis including a certain degree of intrinsic instability of co-reactants, we highlight the key parameters governing the analytical response of the system and discuss the analytical performances that are expected from a given kinetic set. In particular, we show how the detection limit is directly related to the relative instability of reactants within each catalytic loop. The model is validated with an experimental dataset and is intended to serve as a guide in the design and optimization of autocatalytic molecular-based amplification systems with improved analytical performances.

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.

Reciprocally-Coupled Gating: Strange Loops in Bioenergetics, Genetics, and Catalysis

Bioenergetics, genetic coding, and catalysis are all difficult to imagine emerging without pre-existing historical context. That context is often posed as a "Chicken and Egg" problem; its resolution is concisely described by de Grasse Tyson: "The egg was laid by a bird that was not a chicken". The concision and generality of that answer furnish no details-only an appropriate framework from which to examine detailed paradigms that might illuminate paradoxes underlying these three life-defining biomolecular processes. We examine experimental aspects here of five examples that all conform to the same paradigm. In each example, a paradox is resolved by coupling "if, and only if" conditions for reciprocal transitions between levels, such that the consequent of the first test is the antecedent for the second. Each condition thus restricts fluxes through, or "gates" the other. Reciprocally-coupled gating, in which two gated processes constrain one another, is self-referential, hence maps onto the formal structure of "strange loops". That mapping uncovers two different kinds of forces that may help unite the axioms underlying three phenomena that distinguish biology from chemistry. As a physical analog for Gödel's logic, biomolecular strange-loops provide a natural metaphor around which to organize a large body of experimental data, linking biology to information, free energy, and the second law of thermodynamics.

Emergence of homochirality in large molecular systems

The selection of a single molecular handedness, or homochirality across all living matter, is a mystery in the origin of life. Frank's seminal model showed in the '50s how chiral symmetry breaking can occur in nonequilibrium chemical networks. However, an important shortcoming in this classic model is that it considers a small number of species, while there is no reason for the prebiotic system, in which homochirality first appeared, to have had such a simple composition. Furthermore, this model does not provide information on what could have been the size of the molecules involved in this homochiral prebiotic system. Here, we show that large molecular systems are likely to undergo a phase transition toward a homochiral state, as a consequence of the fact that they contain a large number of chiral species. Using chemoinformatics tools, we quantify how abundant chiral species are in the chemical universe of all possible molecules of a given length. Then, we propose that Frank's model should be extended to include a large number of species, in order to possess the transition toward homochirality, as confirmed by numerical simulations. Finally, using random matrix theory, we prove that large nonequilibrium reaction networks possess a generic and robust phase transition toward a homochiral state.

Thresholds in Origin of Life Scenarios

Thresholds are widespread in origin of life scenarios, from the emergence of chirality, to the appearance of vesicles, of autocatalysis, all the way up to Darwinian evolution. Here, we analyze the “error threshold,” which poses a condition for sustaining polymer replication, and generalize the threshold approach to other properties of prebiotic systems. Thresholds provide theoretical predictions, prescribe experimental tests, and integrate interdisciplinary knowledge. The coupling between systems and their environment determines how thresholds can be crossed, leading to different categories of prebiotic transitions. Articulating multiple thresholds reveals evolutionary properties in prebiotic scenarios. Overall, thresholds indicate how to assess, revise, and compare origin of life scenarios.