Autocatalytic Systems Research Articles

Traveling waves in quadratic autocatalytic systems with complexing agent

The quadratic autocatalytic reaction forms a key step in a number of chemical reaction systems, and traveling waves are observed in such systems. In this study, we investigate the effect of complexation reactions on traveling waves in the quadratic autocatalytic reaction system. More precisely, under the assumption that the complexation reaction is fast relative to the autocatalytic reaction, we show that the governing system is reduced to a two-component reaction-diffusion system with density-dependent diffusivity. Further, the numerical evidence suggests that for some parameter values, a traveling wave solution of this reduced two-component system is nonlinearly selected. This is contrast to that associated with the quadratic autocatalytic reaction (without complexation reactions).

The structure of autocatalytic networks, with application to early biochemistry.

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

Universal motifs and the diversity of autocatalytic systems

Autocatalysis is essential for the origin of life and chemical evolution. However, the lack of a unified framework so far prevents a systematic study of autocatalysis. Here, we derive, from basic principles, general stoichiometric conditions for catalysis and autocatalysis in chemical reaction networks. This allows for a classification of minimal autocatalytic motifs called cores. While all known autocatalytic systems indeed contain minimal motifs, the classification also reveals hitherto unidentified motifs. We further examine conditions for kinetic viability of such networks, which depends on the autocatalytic motifs they contain and is notably increased by internal catalytic cycles. Finally, we show how this framework extends the range of conceivable autocatalytic systems, by applying our stoichiometric and kinetic analysis to autocatalysis emerging from coupled compartments. The unified approach to autocatalysis presented in this work lays a foundation toward the building of a systems-level theory of chemical evolution.

Stability and robustness of asymptotic autocatalytic systems

Here, we address the consequences of the extension in the space of a simple model of a system that is closed to efficient causation: the (M,R)-system model. To do so, we use a diffusion term to describe the collective motion of the nutrients’ concentration across the compartmentalized space that defines the organism. We show that the non-trivial stable steady state remains despite such generalization, as long as the system is small enough to deal with the transport of the precursors to feed the entire protocell and dispose of a sufficient concentration of it in its surroundings. Such consideration explains the emergence of a bifurcation with two parameters that we characterize. Finally, we show that the robustness of the system under catastrophic losses of catalysts also remains, preserving the original’s model character.

Autocatalysis: Kinetics, Mechanisms and Design

AbstractThe importance of autocatalysis spans from practical applications such as in chemically amplified photoresists, to autocatalysis playing a fundamental role in evolution as well as a plausible key role in the origin of life. The phenomenon of autocatalysis is characterized by its kinetic signature rather than by its mechanistic aspects. The molecules that form autocatalytic systems and the mechanisms underlying autocatalytic reactions are very diverse. This chemical diversity, combined with the strong involvement of chemical kinetics, creates a formidable barrier for entrance to the field. Understanding these challenges, we wrote this Review with three main goals in mind: (i) To provide a basic introduction to the kinetics of autocatalytic systems and its relation to the role of autocatalysis in evolution, (ii) To provide a comprehensive overview, including tables, of synthetic chemical autocatalytic systems, and (iii) To provide an in‐depth analysis of the concept of autocatalytic reaction networks, their design, and perspectives for their development.

A Dynamic Study of Biochemical Self-Replication

As it is well understood, in biological systems, small regulatory motifs are present at all scales, thus looking at simple negative feedback loops give us some information of how autocatalytic systems may be affected by regulation. For a single template self-replication, we consider a plausible mechanism, which we reduce to a 2-variable dimensionless set of ordinary differential equations, (ODE). The stability analysis of the steady states allows us to obtain exact relations to describe two-parameter bifurcation diagrams. We include a negative feedback to the reactants input to study the effect of regulation in biochemical self-replication. Surprisingly, the simpler regulation has the largest impact on the parameter space.

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

Here we show how a simple inorganic salt can spontaneously form autocatalytic sets of replicating inorganic molecules that work via molecular recognition based on the {PMo12} ≡ [PMo12O40]3- Keggin ion, and {Mo36} ≡ [H3Mo57M6(NO)6O183(H2O)18]22- cluster. These small clusters are able to catalyze their own formation via an autocatalytic network, which subsequently template the assembly of gigantic molybdenum-blue wheel {Mo154} ≡ [Mo154O462H14(H2O)70]14-, {Mo132} ≡ [MoVI72MoV60O372(CH3COO)30(H2O)72]42- ball-shaped species containing 154 and 132 molybdenum atoms, and a {PMo12}⊂{Mo124Ce4} ≡ [H16MoVI100MoV24Ce4O376(H2O)56 (PMoVI10MoV2O40)(C6H12N2O4S2)4]5- nanostructure. Kinetic investigations revealed key traits of autocatalytic systems including molecular recognition and kinetic saturation. A stochastic model confirms the presence of an autocatalytic network involving molecular recognition and assembly processes, where the larger clusters are the only products stabilized by the cycle, isolated due to a critical transition in the network.

Multiplicity, travelling waves and spatial patterns in coupled autocatalytic reaction systems

In an autocatalytic reaction, one of the products catalyzes its own formation. In this work, we analyze a system of two species, each participating in two autocatalytic reactions. Each species participates in the autocatalysis of the other. We first analyze how the kinetics of the reactions determines the non-linear characteristics of the lumped system, such as multiple steady-states. Two cases are considered depending on the kinetics of the two reactions. In the first case, both reactions are quadratic in nature, while in the second, reactions are cubic. Singularity theory and bifurcation theory are employed to comprehensively understand the multiplicity features of the steady states and to classify the bifurcation behavior of the lumped system. The analysis here forms the basis to determine operating conditions under which a pure enantiomer can be produced. The occurrence of spontaneous spatio-temporal features like travelling waves and Turing patterns under specific conditions has been established.

Selection from a pool of self-assembling lipid replicators

Replication and compartmentalization are fundamental to living systems and may have played important roles in life’s origins. Selection in compartmentalized autocatalytic systems might provide a way for evolution to occur and for life to arise from non-living systems. Herein we report selection in a system of self-reproducing lipids where a predominant species can emerge from a pool of competitors. The lipid replicators are metastable and their out-of-equilibrium population can be sustained by feeding the system with starting materials. Phase separation is crucial for selective surfactant formation as well as autocatalytic kinetics; indeed, no selection is observed when all reacting species are dissolved in the same phase. Selectivity is attributed to a kinetically controlled process where the rate of monomer formation determines which replicator building blocks are the fittest. This work reveals how kinetics of a phase-separated autocatalytic reaction may be used to control the population of out-of-equilibrium replicators in time.

Chemical Basis of Biological Homochirality during the Abiotic Evolution Stages on Earth

Spontaneous mirror symmetry breaking (SMSB), a phenomenon leading to non-equilibrium stationary states (NESS) that exhibits biases away from the racemic composition is discussed here in the framework of dissipative reaction networks. Such networks may lead to a metastable racemic non-equilibrium stationary state that transforms into one of two degenerate but stable enantiomeric NESSs. In such a bifurcation scenario, the type of the reaction network, as well the boundary conditions, are similar to those characterizing the currently accepted stages of emergence of replicators and autocatalytic systems. Simple asymmetric inductions by physical chiral forces during previous stages of chemical evolution, for example in astrophysical scenarios, must involve unavoidable racemization processes during the time scales associated with the different stages of chemical evolution. However, residual enantiomeric excesses of such asymmetric inductions suffice to drive the SMSB stochastic distribution of chiral signs into a deterministic distribution. According to these features, we propose that a basic model of the chiral machinery of proto-life would emerge during the formation of proto-cell systems by the convergence of the former enantioselective scenarios.

Towardsa General Definition of Life.

A new definition of life is proposed and discussed in the present article. It is formulated by modifying and extending NASA's working definition of life, which postulates that life is a "self-sustaining chemical system capable of Darwinian evolution". The new definition includes a thermodynamical aspect of life as a far from equilibrium system and considers the flow of information from the environment to the living system. In our derivation of the definition of life we have assumed the hypothesis, that during the emergence of life evolution had to first involve autocatalytic systems that only subsequently acquired the capacity of genetic heredity. The new proposed definition of life is independent of the mode of evolution, regardless of whether Lamarckian or Darwinian evolution operated at the origins of life and throughout evolutionary history. The new definition of life presented herein is formulated in a minimal manner and it is general enough that it does not distinguish between individual (metabolic) network and the collective (ecological) one. The newly proposed definition of life may be of interest for astrobiology, research into the origins of life or for efforts to produce synthetic or artificial life, and it furthermore may also have implications in the cognitive and computer sciences.

In the Beginning was a Mutualism - On the Origin of Translation.

The origin of translation is critical for understanding the evolution of life, including the origins of life. The canonical genetic code is one of the most dominant aspects of life on this planet, while the origin of heredity is one of the key evolutionary transitions in living world. Why the translation apparatus evolved is one of the enduring mysteries of molecular biology. Assuming the hypothesis, that during the emergence of life evolution had to first involve autocatalytic systems which only subsequently acquired the capacity of genetic heredity, we propose and discuss possible mechanisms, basic aspects of the emergence and subsequent molecular evolution of translation and ribosomes, as well as enzymes as we know them today. It is possible, in this sense, to view the ribosome as a digital-to-analogue information converter. The proposed mechanism is based on the abilities and tendencies of short RNA and polypeptides to fold and to catalyse biochemical reactions. The proposed mechanism is in concordance with the hypothesis of a possible chemical co-evolution of RNA and proteins in the origin of the genetic code or even more generally at the early evolution of life on Earth. The possible abundance and availability of monomers at prebiotic conditions are considered in the mechanism. The hypothesis that early polypeptides were folding on the RNA scaffold is also considered and mutualism in molecular evolutionary development of RNA and peptides is favoured.

Autocatalytic confusion clarified

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

Noise-induced symmetry breaking far from equilibrium and the emergence of biological homochirality.

The origin of homochirality, the observed single-handedness of biological amino acids and sugars, has long been attributed to autocatalysis, a frequently assumed precursor for early life self-replication. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross-inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here we present a theory for a stochastic individual-level model of autocatalytic prebiotic self-replicators that are maintained out of thermal equilibrium. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states. Moreover, we show that this noise-induced bistability is robust with respect to diffusion of molecules of opposite chirality, and systems of diffusively coupled autocatalytic chemical reactions synchronize their final homochiral states when the self-replication is the dominant production mechanism for the chiral molecules. We conclude that nonequilibrium autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.

Stability of traveling waves for autocatalytic reaction systems with strong decay

This paper is concerned with the spatial decay and stability of travelling wave solutions for a reaction diffusion system $u_{t}=d u_{xx}-uv$, $v_{t}=v_{xx}+uv-Kv^{q}$ with $q>1$. By applying Centre Manifold Theorem and detailed asymptotic analysis, we get the precise spatial decaying rate of the travelling waves with noncritical speeds. Further by applying spectral analysis, Evans function method and some numerical simulation, we proved the spectral stability and the linear exponential stability of the waves with noncritical speeds in some weighted spaces.

On a quest of reverse translation

Explaining the emergence of life is perhaps central and the most challenging question in modern science. Within this area of research, the emergence and evolution of the genetic code is supposed to be a critical transition in the evolution of modern organisms. The canonical genetic code is one of the most dominant aspects of life on this planet, and thus studying its origin is critical to understanding the evolution of life, including life’s emergence. In this sense it is possible to view the ribosome as a digital-to-analogue information converter. Why the translation apparatus evolved, is one of the enduring mysteries of molecular biology. Assuming the hypothesis that during the emergence of life evolution had to first involve autocatalytic systems, which only subsequently acquired the capacity of genetic heredity, in the present article we discuss some aspects and causes of the possible emergence of digital, discrete information arising from analogue information realized in the intra- and inter-molecular interactions throughout molecular evolution. How such reverse translation was achieved at a molecular level is still unclear. The results of such debates and investigations might shift current biological paradigms and might also have a momentous significance for modern philosophy in understanding our place in the universe.

Computational Study of Traveling Wave Solutions of Isothermal Chemical Systems

AbstractThis article studies propagating traveling waves in a class of reaction-diffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two different cases will be studied. The first is autocatalytic chemical reaction of order m without decay. The second is chemical reaction of order m with a decay of order n, where m and n are positive integers and m>n≥1. A typical system in autocatalysis is A+2B→3B and B→C involving two chemical species, a reactant A and an auto-catalyst B and C an inert chemical species.The numerical computation gives more accurate estimates on minimum speed of traveling waves for autocatalytic reaction without decay, providing useful insight in the study of stability of traveling waves.For autocatalytic reaction of order m = 2 with linear decay n = 1, which has a particular important role in chemical waves, it is shown numerically that there exist multiple traveling waves with 1, 2 and 3 peaks with certain choices of parameters.

Existence of traveling waves of auto-catalytic systems with decay

This article establishes the existence of traveling waves of a class of reaction–diffusion systems which model the pre-mixed isothermal autocatalytic chemical reaction of order m (m>1) between two chemical species, a reactant and an auto-catalyst, and a linear decay. Moreover, our result shows that the set of speed is contained in a bounded interval for any fixed initial value at x=−∞. This is in strong contrast to either the reaction–diffusion systems of autocatalytic chemical reaction of the order m without decay, or to the systems which have the same order of decay, which were shown by various authors (e.g. [8,13,17,26]) that the set of traveling wave speeds contains [c⁎,∞) for some c⁎>0.The same systems also appear in a mathematical model of microbial growth and competition in a flow reactor; see [2,24].

Noise-Induced Mechanism for Biological Homochirality of Early Life Self-Replicators.

The observed single-handedness of biological amino acids and sugars has long been attributed to autocatalysis. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here, we present a theory for a stochastic individual-level model of autocatalysis due to early life self-replicators. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states, in both well-mixed and spatially extended systems. We conclude that autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.

An Autocatalytic System of Photooxidation‐Driven Substitution Reactions on a FeII4L6 Cage Framework

AbstractThe functions of life are accomplished by systems exhibiting nonlinear kinetics: autocatalysis, in particular, is integral to the signal amplification that allows for biological information processing. Novel synthetic autocatalytic systems provide a foundation for the design of artificial chemical networks capable of carrying out complex functions. Here we report a set of FeII4L6 cages containing BODIPY chromophores having tuneable photosensitizing properties. Electron‐rich anilines were observed to displace electron‐deficient anilines at the dynamic‐covalent imine bonds of these cages. When iodoaniline residues were incorporated, heavy‐atom effects led to enhanced 1O2 production. The incorporation of (methylthio)aniline residues into a cage allowed for the design of an autocatalytic system: oxidation of the methylthio groups into sulfoxides make them electron‐deficient and allows their displacement by iodoanilines, generating a better photocatalyst and accelerating the reaction.