Autocatalytic Reaction Networks Research Articles

Stationary distributions of systems with discreteness-induced transitions

We provide a theoretical analysis of some autocatalytic reaction networks exhibiting the phenomenon of discreteness-induced transitions. The family of networks that we address includes the celebrated Togashi and Kaneko model. We prove positive recurrence, finiteness of all moments and geometric ergodicity of the models in the family. For some parameter values, we find the analytic expression for the stationary distribution and discuss the effect of volume scaling on the stationary behaviour of the chain. We find the exact critical value of the volume for which discreteness-induced transitions disappear.

Availability-Driven Design of Hairpin Fuels and Small Interfering Strands for Leakage Reduction in Autocatalytic Networks.

DNA-based circuits and computational tools offer great potential for advanced biomedical and technological applications. However, leakage, which is the production of an output in the absence of an input, widely exists in DNA network. As a new approach to leakage reduction, this study utilizes availability to reduce leakage in an entropy-driven autocatalytic DNA reaction networks. Here, we report the performance improvements resulting from direct tailoring of fuel strand availability through two novel approaches: (1) the addition of interfering domains to fuel strands, and (2) the introduction of separate small interfering strands. The best performing fuel designs resulted in increased performance ratios of up to 22%. Employing small interfering strands (5-12 nucleotides (nt)) improved the performance ratios by up to 21%. Furthermore, the stability of the network using either leakage reduction method matched well with computed availability and experimental results showing Spearman correlation coefficients of -0.84 for modified fuel strands and -0.92 for small interfering strands.

Mathematical Analysis of a Prototypical Autocatalytic Reaction Network.

Network autocatalysis, which is autocatalysis whereby a catalyst is not directly produced in a catalytic cycle, is likely to be more common in chemistry than direct autocatalysis is. Nevertheless, the kinetics of autocatalytic networks often does not exactly follow simple quadratic or cubic rate laws and largely depends on the structure of the network. In this article, we analyzed one of the simplest and most chemically plausible autocatalytic networks where a catalytic cycle is coupled to an ancillary reaction that produces the catalyst. We analytically analyzed deviations in the kinetics of this network from its exponential growth and numerically studied the competition between two networks for common substrates. Our results showed that when quasi-steady-state approximation is applicable for at least one of the components, the deviation from the exponential growth is small. Numerical simulations showed that competition between networks results in the mutual exclusion of autocatalysts; however, the presence of a substantial noncatalytic conversion of substrates will create broad regions where autocatalysts can coexist. Thus, we should avoid the accumulation of intermediates and the noncatalytic conversion of the substrate when designing experimental systems that need autocatalysis as a source of positive feedback or as a source of evolutionary pressure.

Exponential Molecular Amplification by H2 O2 -Mediated Autocatalytic Deprotection of Boronic Ester Probes to Redox Cyclers.

Herein, a new molecular autocatalytic reaction scheme based on a H2 O2 -mediated deprotection of a boronate ester probe into a redox cycling compound is described, generating an exponential signal gain in the presence of O2 and a reducing agent or enzyme. For such a purpose, new chemosensing probes built around a naphthoquinone/naphthohydroquinone redox-active core, masked by a self-immolative boronic ester protecting group, were designed. With these probes, typical autocatalytic kinetic traces with characteristic lags and exponential phases were obtained by using either UV/Visible or fluorescence optical detection, or by using electrochemical monitoring. Detection of concentrations as low as 0.5 μm H2 O2 and 0.5 nm of a naphthoquinone derivative were achieved in a relatively short time (<1 h). From kinetic analysis of the two cross-activated catalytic loops associated with the autocatalysis, the key parameters governing the autocatalytic reaction network were determined, indirectly showing that the analytical performances are currently limited by the slow nonspecific self-deprotection of boronate probes. Collectively, the present results demonstrate the potential of this new exponential molecular amplification strategy, which, owing to its generic nature and modularity, is quite promising for coupling to a wide range of bioassays involving H2 O2 or redox cycling compounds, or for use as a new building block in the development of more complex chemical reaction networks.

Stationary Distributions and Condensation in Autocatalytic Reaction Networks

We investigate a broad family of non weakly reversible stochastically modeled reaction networks (CRN), by looking at their steady-state distributions. Most known results on stationary distributions assume weak reversibility and zero deficiency. We first give explicitly product-form steady-state distributions for a class of non weakly reversible autocatalytic CRN of arbitrary deficiency. Examples of interest in statistical mechanics (inclusion process), life sciences and robotics (collective decision making in ant and robot swarms) are provided. The product-form nature of the steady-state then enables the study of condensation in particle systems that are generalizations of the inclusion process.

ChemInform Abstract: Absolute Asymmetric Synthesis in Enantioselective Autocatalytic Reaction Networks: Theoretical Games, Speculations on Chemical Evolution and Perhaps a Synthetic Option

AbstractReview: [73 refs.

Absolute asymmetric synthesis in enantioselective autocatalytic reaction networks: theoretical games, speculations on chemical evolution and perhaps a synthetic option.

The Soai reaction and the Viedma deracemization of racemic conglomerate crystal mixtures are experimental pieces of evidence of the ability of enantioselective autocatalytic coupled networks to yield absolute asymmetric synthesis. Thermodynamically open systems or systems with non-uniform energy distributions may lead to chiral final states and, in systems able to come into thermodynamic equilibrium with their surroundings, to kinetically controlled absolute asymmetric synthesis. The understanding of network parameters and of the thermodynamic scenarios that may lead to spontaneous mirror symmetry breaking (SMSB) could assist in the development of new methods for asymmetric synthesis and enantioselective polymerizations (e.g., replicators), and to frame reasonable speculations on the origin of biological homochirality.

Hierarchical Control Based Virtual Coordinated Synchronization of Chemical Auto Catalytic Reaction Networks

This paper suggests the concept of hierarchical control based virtual coordinated synchronization of chemical auto catalytic reaction networks. Under the new framework, the virtual coordinated variable is introduced, which is the average of the ensemble of the corresponding auto catalytic reaction networks, and on account of that, synchronization becomes possible. Unlike the already existing results, the average of the virtual coordinated variable is injected into the every auto catalytic reaction networks. And for the virtual coordinated construction has a lot of flexibility, so the suggested scheme can be easily extended to the multi-purposes control of the auto catalytic reaction networks.

Noise-induced metastability in biochemical networks

Intracellular biochemical reactions exhibit a rich dynamical phenomenology which cannot be explained within the framework of mean-field rate equations and additive noise. Here, we show that the presence of metastable states and radically different time scales are general features of a broad class of autocatalytic reaction networks, and that this fact may be exploited to gain analytical results. The latter point is demonstrated by a treatment of the paradigmatic Togashi-Kaneko reaction, which has resisted theoretical analysis for the last decade.

On bifurcation of Prion disease: A Chemical Reaction Network approach

Fatal neurodegenerative diseases such as bovine spongiform encephalopathy in cattle, scrapie in sheep, and Creutzfeldt-Jakob disease in humans are caused by prions. A prion is a protein encoded by a normal cellular gene. The cellular form of the prion, namely PrPC, is benign but can be reconfigured into a disease-causing form (named scrapie), PrPSc, by a conformational change from α—helix to β—sheets. Prions replicate by this conformational change; that is, PrPSc interacts with PrPC producing a new molecule of PrPSc. This kind of replication is modeled in this contribution as an autocatalytic Chemical Reaction Network (CRN). The Mass Action Kinetic (MAK) ODEs support three distinct dynamical scenarios: multiple steady states, sustained oscillations and a degenerate steady state. We perform equilibria analysis of each dynamical scenario.

The Origin of Large Molecules in Primordial Autocatalytic Reaction Networks

Large molecules such as proteins and nucleic acids are crucial for life, yet their primordial origin remains a major puzzle. The production of large molecules, as we know it today, requires good catalysts, and the only good catalysts we know that can accomplish this task consist of large molecules. Thus the origin of large molecules is a chicken and egg problem in chemistry. Here we present a mechanism, based on autocatalytic sets (ACSs), that is a possible solution to this problem. We discuss a mathematical model describing the population dynamics of molecules in a stylized but prebiotically plausible chemistry. Large molecules can be produced in this chemistry by the coalescing of smaller ones, with the smallest molecules, the ‘food set’, being buffered. Some of the reactions can be catalyzed by molecules within the chemistry with varying catalytic strengths. Normally the concentrations of large molecules in such a scenario are very small, diminishing exponentially with their size. ACSs, if present in the catalytic network, can focus the resources of the system into a sparse set of molecules. ACSs can produce a bistability in the population dynamics and, in particular, steady states wherein the ACS molecules dominate the population. However to reach these steady states from initial conditions that contain only the food set typically requires very large catalytic strengths, growing exponentially with the size of the catalyst molecule. We present a solution to this problem by studying ‘nested ACSs’, a structure in which a small ACS is connected to a larger one and reinforces it. We show that when the network contains a cascade of nested ACSs with the catalytic strengths of molecules increasing gradually with their size (e.g., as a power law), a sparse subset of molecules including some very large molecules can come to dominate the system.

A stochastic model of autocatalytic reaction networks

Autocatalytic cycles are rather widespread in nature and in several theoretical models of catalytic reaction networks their emergence is hypothesized to be inevitable when the network is or becomes sufficiently complex. Nevertheless, the emergence of autocatalytic cycles has been never observed in wet laboratory experiments. Here, we present a novel model of catalytic reaction networks with the explicit goal of filling the gap between theoretical predictions and experimental findings. The model is based on previous study of Kauffman, with new features in the introduction of a stochastic algorithm to describe the dynamics and in the possibility to increase the number of elements and reactions according to the dynamical evolution of the system. Furthermore, the introduction of a temporal threshold allows the detection of cycles even in our context of a stochastic model with asynchronous update. In this study, we describe the model and present results concerning the effect on the overall dynamics of varying (a) the average residence time of the elements in the reactor, (b) both the composition of the firing disk and the concentration of the molecules belonging to it, (c) the composition of the incoming flux.

1F1548 Weber則にしたがう自己触媒反応ネットワークモデルの設計(数理生物学1,第49回日本生物物理学会年会)

1F1548 Weber則にしたがう自己触媒反応ネットワークモデルの設計(数理生物学1,第49回日本生物物理学会年会)

Spontaneous Emergence of Homochirality via Coherently Coupled Antagonistic and Reversible Reaction Cycles

Asymmetric synthesis aims at obtaining enantio-enriched products in stereoselective reactions under a chiral influence. We demonstrate both mathematically and numerically that, even under nominally achiral conditions, fully homochiral steady states can be obtained in open reactive systems by spontaneous mirror-symmetry breaking in the homogenous solution phase when the autocatalytic reaction network is closed in the form of coherently coupled antagonistic reversible reaction cycles which, paradoxically, allow for complete recycling of the reactant. We show that the fully reversible Frank mechanism for spontaneous mirror-symmetry breaking is closely related to the Lotka-Volterra system, which models predator-prey relations in ecosystems. Amplification of total enantiomeric excess and the principle of microscopic reversibility are not in conflict for all conceivable reactions. A viable and widely applicable reaction protocol is introduced and discussed, and it permits the theoretical implications to be applied to practical laboratory examples. Implications for the possible origin of biological homochirality on early earth are discussed.

Punctuated chirality.

Most biomolecules occur in mirror, or chiral, images of each other. However, life is homochiral: proteins contain almost exclusively L-amino acids, while only D-sugars appear in RNA and DNA. The mechanism behind this fundamental asymmetry of life remains an open problem. Coupling the spatiotemporal evolution of a general autocatalytic polymerization reaction network to external environmental effects, we show through a detailed statistical analysis that high intensity and long duration events may drive achiral initial conditions towards chirality. We argue that life's homochirality resulted from sequential chiral symmetry breaking triggered by environmental events, thus extending the theory of punctuated equilibrium to the prebiotic realm. Applying our arguments to other potentially life-bearing planetary platforms, we predict that a statistically representative sampling will be racemic on average.

Challenging the concept of “recycling” as a mechanism for the evolution of homochirality in chemical reactions

The concept that "recycling" of reactants may be key to the spontaneous generation of a homochiral state in closed autocatalytic reaction networks has recently been introduced and has been supported by computer simulations of such reaction networks. It has been suggested that unidirectional cycles maintained away from equilibrium may avoid the inevitable establishment of a racemic state, and under such conditions the explicit reverse reactions dictated by microscopic reversibility may be all be treated as having negligible rates. We show here that because the equilibrium constants in a recycled network are interdependent, it is not valid to neglect all reverse reactions simultaneously; a very low value for the rate constant of one reverse reaction in the network dictates that another reverse reaction in the same network will exhibit a large rate constant. This conclusion is general and applies to any closed mass system where the energy input is subject to microscopic reversibility. Therefore, chemical reversibility cannot be invoked as a mechanism for the evolution of a single chiral molecular state in thermally activated reactions.

Von Neumann’s expanding model on random graphs

Within the framework of Von Neumann’s expanding model, we study the maximum growthrate achievable by an autocatalytic reaction network in which reactions involve a finite (fixed or fluctuating)number D of reagents. is calculated numerically using a variant of the Minover algorithm, and analytically viathe cavity method for disordered systems. As the ratio between the number of reactionsand that of reagents increases the system passes from a contracting () to an expanding regime (). These results extend the scenario derived in the fully connected model (D → ∞), with the important difference that, generically, larger growth rates are achievable in the expanding phasefor finite D and in more diluted networks. Moreover, the range of attainable values of shrinks as the connectivity increases.

Asymmetric Spatiotemporal Evolution of Prebiotic Homochirality

The role of asymmetry on the evolution of prebiotic homochirality is investigated in the context of autocatalytic polymerization reaction networks. A model featuring enantiometric cross-inhibition and chiral bias is used to study the diffusion equations controlling the spatiotemporal development of left and right-handed domains. Bounds on the chiral bias are obtained based on present-day constraints on the emergence of life on early Earth. The viability of biasing mechanisms such as weak neutral currents and circularly polarized UV light is discussed. The results can be applied to any hypothetical planetary platform.

Dynamics of Autocatalytic Replicator Networks Based on Higher-order Ligation Reactions

A class of autocatalytic reaction networks based on template-dependent ligation and higher-order catalysis is analysed. Apart from an irreversible ligation reaction we consider only reversible aggregation steps that provide a realistic description of molecular recognition. The overall dynamics can be understood by means of replicator equations with highly non-linear interaction functions. The dynamics depends crucially on the total concentration c0of replicating material. For small c0, in the hyperbolic growth regime, we recover the familiar dynamics of second-order replicator equations with its wealth of complex dynamics ranging from multi-stability to periodic and strange attractors as well as to heteroclinic orbits. For large c0, in the parabolic growth regime, product inhibition becomes dominating and we observe a single globally stable equilibrium tantamount to permanent coexistence. In an intermediate parameter range we sometimes observe a behavior that is reminiscent of ‘survival of the fittest’. Independently replicating species (Schlögl’s model) and the hypercycle are discussed in detail.

Remarks on autocatalysis and autopoiesis.

The notions of collective autocatalysis and of autopoiesis are clearly related; equally clearly, they are not quite the same. The purpose of this paper is to try to clarify the relationship. Specifically I suggest that autopoiesis can be at least roughly characterized as collective autocatalysis plus spatial individuation. Although some mechanism of spatial confinement or concentration is probably necessary to the effective operation of any collectively autocatalytic reaction network, autopoiesis requires, in addition, that the mechanism for maintaining this confinement should itself be a product of the reaction network--and should thus (?) be capable of separating or individuating otherwise identically organized networks. I suggest an informal heuristic test to discriminate the (merely) collectively autocatalytic from the (properly) autopoietic. Finally, in the light of this, I review a variety of published abstract or model systems, Alchemy, alpha-universes, Tierra, and SCL.