Autocatalytic Networks Research Articles

Exploring the programmability of autocatalytic chemical reaction networks

Networks of chemical reactions exhibit emergent properties under out-of-equilibrium conditions. Recent advances in systems chemistry demonstrate that networks with sufficient chemical complexity can be harnessed to emulate properties important for neuromorphic computing. In all examples, autocatalysis appears an essential element for facilitating the nonlinear integration of the input and self-regulatory abilities in the output. How this chemical analogue of a positive feedback mechanism can be controlled in a programmable manner is, however, unexplored. Here, we develop a strategy that uses metal ions (Ca2+, La3+, and Nd3+) to control the rate of a trypsin-catalysed autocatalytic reaction network. We demonstrate that this type of control allows for tuning the kinetics in the network, thereby changing the nature of the positive feedback. The simulations and experiments reveal that an input with one or more metal ions allow for temporal and history-dependent outputs that can be mapped onto a variety of mathematical functions.

Coupling DNA Origami Filament Growth to an Autocatalytic Production of Fuel

AbstractIn this study, the hierarchical assembly of DNA origami filaments (DOF) initiated by an autocatalytic DNA reaction network (DRN) is investigated. The so‐formed filaments are subsequently disassembled by toehold‐mediated strand displacement mechanisms. Using fluorescence resonance energy transfer, the kinetics of DOF growth after direct addition of fuel and compared it to the polymerization process triggered by the release of fuel from the DRN is monitored. Optimization of design and experimental conditions enabled to fine‐tune the kinetics of the two processes, ensuring that the release of fuel from the DRN outpaced the consumption of fuel by the downstream polymerization reaction. This resulted in a sustained and controlled DOF growth leading to micrometer‐long filament structures. Finally, although the presence of a toehold in the fuel strand reduced the efficiency of monomer association in the polymerization process, a 10‐fold excess of the anti‐fuel strand is efficient in dissociating the filament structures, permitting a potential reset for new reactions. The study shows that the kinetics of DNA origami filaments growth can be finely manipulated by a cascade of upstream reactions, suggesting alternative approaches for the creation of programmable DNA‐based nanomaterials that can sense and respond to more complex and distant events.

CatReNet: interactive analysis of (auto-) catalytic reaction networks.

Catalytic reaction networks serve as fundamental models for understanding biochemical systems. CatReNet is a novel software designed to facilitate interactive analysis of such networks. It offers fast and exact algorithms for computing various types of self-sustaining autocatalytic subnetworks, including so-called CAFs (constructively autocatalytic food-generated networks), RAFs (reflexively autocatalytic food-generated networks), and pseudo-RAFs. It provides dynamic visualizations to aid exploration and understanding. This open-source Java application runs on Linux, MacOS, and Windows. It is available at https://github.com/husonlab/catrenet under a GPL3 license.

Structural constraints limit the regime of optimal flux in autocatalytic reaction networks

Autocatalytic chemical networks play a predominant role in a large number of natural systems such as in metabolic pathways and in ecological networks. Despite recent efforts, the precise impact of thermodynamic constraints on these networks remains elusive. In this work, we present a theoretical framework that allows specific bounds on the thermodynamic affinity and on the concentrations of autocatalysts in mass-action autocatalytic networks. These bounds can be obtained solely from the stoichiometry of the underlying chemical reaction network, and are independent from the numerical values of kinetic parameters. This property holds in the specific regime where all the fluxes of the network are tightly coupled and maximal. Our method is applicable to large networks, and can be used to complement constraints-based modeling methods of metabolic networks, which typically do not provide predictions about thermodynamic properties or concentration ranges of metabolites.

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.

Demonstrating Prebiotic Peptide Evolution by Nitrogen Isotope Discrimination in an Autocatalytic Chemical Reaction Network

Demonstrating Prebiotic Peptide Evolution by Nitrogen Isotope Discrimination in an Autocatalytic Chemical Reaction Network

Opinion: The Key Steps in the Origin of Life to the Formation of the Eukaryotic Cell.

The path from life's origin to the emergence of the eukaryotic cell was long and complex, and as such it is rarely treated in one publication. Here, we offer a sketch of this path, recognizing that there are points of disagreement and that many transitions are still shrouded in mystery. We assume life developed within microchambers of an alkaline hydrothermal vent system. Initial simple reactions were built into more sophisticated reflexively autocatalytic food-generated networks (RAFs), laying the foundation for life's anastomosing metabolism, and eventually for the origin of RNA, which functioned as a genetic repository and as a catalyst (ribozymes). Eventually, protein synthesis developed, leading to life's biology becoming dominated by enzymes and not ribozymes. Subsequent enzymatic innovation included ATP synthase, which generates ATP, fueled by the proton gradient between the alkaline vent flux and the acidic sea. This gradient was later internalized via the evolution of the electron transport chain, a preadaptation for the subsequent emergence of the vent creatures from their microchamber cradles. Differences between bacteria and archaea suggests cellularization evolved at least twice. Later, the bacterial development of oxidative phosphorylation and the archaeal development of proteins to stabilize its DNA laid the foundation for the merger that led to the formation of eukaryotic cells.

Theoretical perspective on synthetic man‐made life: Learning from the origin of life

AbstractCreating a man‐made life in the laboratory is one of life science’s most intriguing yet challenging problems. Advances in synthetic biology and related theories, particularly those related to the origin of life, have laid the groundwork for further exploration and understanding in this field of artificial life or man‐made life. But there remains a wealth of quantitative mathematical models and tools that have yet to be applied to this area. In this paper, we review the two main approaches often employed in the field of man‐made life: the top‐down approach that reduces the complexity of extant and existing living systems and the bottom‐up approach that integrates well‐defined components, by introducing the theoretical basis, recent advances, and their limitations. We then argue for another possible approach, namely “bottom‐up from the origin of life”: Starting with the establishment of autocatalytic chemical reaction networks that employ physical boundaries as the initial compartments, then designing directed evolutionary systems, with the expectation that independent compartments will eventually emerge so that the system becomes free‐living. This approach is actually analogous to the process of how life originated. With this paper, we aim to stimulate the interest of synthetic biologists and experimentalists to consider a more theoretical perspective, and to promote the communication between the origin of life community and the synthetic man‐made life community.

Autocatalysis and CO2: Carbon Capture and Utilization (CCU) Meets Natural Processes

AbstractAutocatalytic reactions were proposed to play a key role at the beginning of life starting from the first reduction of CO2 to formate, acetate and C1−C4 hydrocarbons. In carbon capture and utilization (CCU) processes, the same reactions were demonstrated to be autocatalytic and, in some cases, promoted by catalysts of the same composition. Through evolution, CO2 reduction then turned into complex autocatalytic networks such as photosynthesis, where CCU chemists found inspiration for the development of more advanced systems for the synthesis of value‐added chemicals. Less evolved systems than photosynthesis, however, may be easier to emulate and provide valuable inspiration into CO2 reduction chemistry for CCU. Other synthetic systems were also demonstrated to be autocatalytic demonstrating that CO2 reactions and autocatalysis are closely connected. In this concept article, the relationship between natural, artificial and bio‐inspired autocatalytic CO2 reduction processes is summarized and discussed. The accomplishments resulting from the integration of autocatalysis and CCU strategies, along with their inherent benefits and future prospectives are also outlined.

Oscillatory dynamics in a reaction network based on imine hydrolysis.

We have built an autocatalytic reaction network, based on the hydrolysis of certain imines, which exhibits bistability in an open system. The positive feedback originates from the interplay of fast acid-base equilibria, leading to hydroxide ion production, and pH-dependent hydrolysis rates. The addition of a first-order removal of the autocatalyst can result in sustained pH oscillations close to physiological conditions. The unit-amplitude pH oscillations are accompanied by the stoichiometric conversion of imine into amine back and forth. A systematic parameter search is carried out to characterize the rich observable dynamics and identify the evolving bifurcations.

Autocatalytic flow chemistry

Autocatalysis is a crucial process of nonequilibrium self-organization in nature and is assumed to play a role in the origin of life. The essential dynamical phenomena of an autocatalytic reaction network are bistability and the development of propagating front when combined with diffusion. The presence of bulk fluid motion may widen the range of emerging behavior in those systems. Many aspects of the dynamics of autocatalytic reactions in a continuous flow have already been studied, especially the shape and dynamics of the chemical front and the influence of the chemical reactions on hydrodynamic instabilities. This paper aims to provide experimental evidence of bistability and related dynamical phenomena, such as excitability and oscillations in autocatalytic reactions performed in a tubular flow reactor, where the flow is laminar and advection is the dominating transport process. We show that the linear residence time ramp may result in the simultaneous appearance of different dynamic states along the length of the pipe. Therefore, long tubular reactors offer a unique opportunity to quickly explore the dynamics of reaction networks. These findings enhance our understanding of nonlinear flow chemistry and its role in natural pattern formation.

Multispecies autocatalytic RNA reaction networks in coacervates

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

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.

Dynamics of hydroxide-ion-driven reversible autocatalytic networks.

In living systems adaptive regulation requires the presence of nonlinear responses in the underlying chemical networks. Positive feedbacks, for example, can lead to autocatalytic bursts that provide switches between two stable states or to oscillatory dynamics. The stereostructure stabilized by hydrogen bonds provides an enzyme its selectivity, rendering pH regulation essential for its functioning. For effective control, triggers by small concentration changes play roles where the strength of feedback is important. Here we show that the interaction of acid-base equilibria with simple reactions with pH-dependent rate can lead to the emergence of a positive feedback in hydroxide ion concentration during the hydrolysis of some Schiff bases in the physiological pH range. The underlying reaction network can also support bistability in an open system.

Chemical reaction network decomposition technique for stability analysis

This paper develops the concept of decomposition for chemical reaction networks, based on which a network decomposition technique is proposed to capture the stability of large-scale networks characterized by a high number of species, high dimension, high deficiency, and/or non-weakly reversible structure. We present some sufficient conditions to capture the stability of a network when it can be decomposed into a complex balanced subnetwork and a few 1-dimensional subnetworks (and/or a few two-species subnetworks) with shared species between different subnetworks. The results cover encouraging applications on autocatalytic networks with some frequently-encountered biochemical reactions examples of interest, such as the autophosphorylation of PAK1 and Aurora B kinase, or autocatalytic cycles originating from metabolism.

Lyapunov Function PDEs to the Stability of Some Complex Balancing Derivative and Compound Networks

This article contributes to extending the validity of Lyapunov function partial differential equations (PDEs) whose solution is conjectured to be able to behave as a Lyapunov function in stability analysis to more mass-action chemical reaction networks. First, we have proved that the Lyapunov function PDEs method is valid in capturing the asymptotic stability of the networks compounded of a complex balanced network and any species-dependent two-species autocatalytic network if some moderate conditions are included. Then, by defining a new class of networks, called complex balanced produced networks, we also show the asymptotic stability of this class of networks, and also to their compound with any species-independent one-dimensional network and with any species-dependent two-species autocatalytic network under some conditions by using the same method. A notable point is that these classes of networks are nonweakly reversible, of any dimension, and of any deficiency. Finally, we apply our results to some practical biochemical reaction networks, including birth-death processes, motifs related networks, etc., to illustrate validity.

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.

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 .

Modeling dynamics of chemical reaction networks using electrical analogs: Application to autocatalytic reactions

Modeling complex chemical reaction networks has inspired a considerable body of research and a variety of approaches to modeling nonlinear pathways are being developed. Here, a general methodology is formulated to convert an arbitrary reaction network into its equivalent electrical analog. The topological equivalence of the electrical analog is mathematically established for unimolecular reactions using Kirchhoff's laws. The modular approach is generalized to bimolecular and nonlinear autocatalytic reactions. It is then applied to simulate the dynamics of nonlinear autocatalytic networks without making simplifying assumptions, such as use of the quasi-steady state/Bodenstein approximation or the absence of nonlinear steps in the intermediates. This is among the few papers that quantify the dynamics of a nonlinear chemical reaction network by generating and simulating an electrical network analog. As a realistic biological application, the early phase of the spread of COVID-19 is modeled as an autocatalytic process and the predicted dynamics are in good agreement with experimental data. The rate-limiting step of viral transmission is identified, leading to novel mechanistic insights.

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'.