Autocatalytic Networks Research Articles

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.

Weber’s Law for Biological Responses in Autocatalytic Networks of Chemical Reactions

Biological responses often obey Weber's law, according to which the magnitude of the response depends only on the fold change in the external input. In this study, we demonstrate that a system involving a simple autocatalytic reaction shows such a response when a chemical is slowly synthesized by the reaction from a faster influx process. We also show that an autocatalytic reaction process occurring in series or in parallel can obey Weber's law with an oscillatory adaptive response. Considering the simplicity and ubiquity of the autocatalytic process, our proposed mechanism is thought to be commonly observed in biological reactions.

A multi-agent approach using perceptron-based learning for robust operation of distributed chemical reactor networks

Controlling the individual reactors of a chemical reactor network producing different grades of a product requires intelligent reconfiguration strategies. Agent-based approaches are ideal for such distributed manufacturing processes, since they provide flexible, robust, and emergent solutions under dynamically changing process conditions. This paper proposes a multi-layered, multi-agent framework based on a decentralized online learning approach for the supervision of grade transitions in autocatalytic reactor networks. The values for the manipulated variables and the path to the target reactor are determined to give the least disturbance to the system. Case studies illustrate the performance of the approach in managing grade transition and disturbance rejection in a reactor network.

Required Levels of Catalysis for Emergence of Autocatalytic Sets in Models of Chemical Reaction Systems

The formation of a self-sustaining autocatalytic chemical network is a necessary but not sufficient condition for the origin of life. The question of whether such a network could form “by chance” within a sufficiently complex suite of molecules and reactions is one that we have investigated for a simple chemical reaction model based on polymer ligation and cleavage. In this paper, we extend this work in several further directions. In particular, we investigate in more detail the levels of catalysis required for a self-sustaining autocatalytic network to form. We study the size of chemical networks within which we might expect to find such an autocatalytic subset, and we extend the theoretical and computational analyses to models in which catalysis requires template matching.

Prebiological Evolution and the Metabolic Origins of Life

The chemoton model of cells posits three subsystems: metabolism, compartmentalization, and information. A specific model for the prebiological evolution of a reproducing system with rudimentary versions of these three interdependent subsystems is presented. This is based on the initial emergence and reproduction of autocatalytic networks in hydrothermal microcompartments containing iron sulfide. The driving force for life was catalysis of the dissipation of the intrinsic redox gradient of the planet. The codependence of life on iron and phosphate provides chemical constraints on the ordering of prebiological evolution. The initial protometabolism was based on positive feedback loops associated with in situ carbon fixation in which the initial protometabolites modified the catalytic capacity and mobility of metal-based catalysts, especially iron-sulfur centers. A number of selection mechanisms, including catalytic efficiency and specificity, hydrolytic stability, and selective solubilization, are proposed as key determinants for autocatalytic reproduction exploited in protometabolic evolution. This evolutionary process led from autocatalytic networks within preexisting compartments to discrete, reproducing, mobile vesicular protocells with the capacity to use soluble sugar phosphates and hence the opportunity to develop nucleic acids. Fidelity of information transfer in the reproduction of these increasingly complex autocatalytic networks is a key selection pressure in prebiological evolution that eventually leads to the selection of nucleic acids as a digital information subsystem and hence the emergence of fully functional chemotons capable of Darwinian evolution.

Catalysis in Reaction Networks

We define catalytic networks as chemical reaction networks with an essentially catalytic reaction pathway: one which is "on" in the presence of certain catalysts and "off" in their absence. We show that examples of catalytic networks include synthetic DNA molecular circuits that have been shown to perform signal amplification and molecular logic. Recall that a critical siphon is a subset of the species in a chemical reaction network whose absence is forward invariant and stoichiometrically compatible with a positive point. Our main theorem is that all weakly-reversible networks with critical siphons are catalytic. Consequently, we obtain new proofs for the persistence of atomic event-systems of Adleman etal., and normal networks of Gnacadja. We define autocatalytic networks, and conjecture that a weakly-reversible reaction network has critical siphons if and only if it is autocatalytic.

Analysis of autocatalytic networks in biology

Autocatalytic networks, in particular the glycolytic pathway, constitute an important part of the cell metabolism. Changes in the concentration of metabolites and catalyzing enzymes during the lifetime of the cell can lead to perturbations from its nominal operating condition. We investigate the effects of such perturbations on stability properties, e.g., the extent of regions of attraction, of a particular family of autocatalytic network models. Numerical experiments demonstrate that systems that are robust with respect to perturbations in the parameter space have an easily “verifiable” (in terms of proof complexity) region of attraction properties. Motivated by the computational complexity of optimization-based formulations, we take a compositional approach and exploit a natural decomposition of the system, induced by the underlying biological structure, into a feedback interconnection of two input–output subsystems: a small subsystem with complicating nonlinearities and a large subsystem with simple dynamics. This decomposition simplifies the analysis of large pathways by assembling region of attraction certificates based on the input–output properties of the subsystems. It enables numerical as well as analytical construction of block-diagonal Lyapunov functions for a large family of autocatalytic pathways.

Design and Evolution of an Agent Based System Applied to an Autocatalytic Network

In this paper, the design and implementation of an agent-based framework to safeguard an auto-catalytic reactor network against external disturbances is discussed. The autocatalytic reactor network producing a robust, host species is attacked by an unmeasured, un-sustained disturbance of a non-robust invading species. The invading species adversely affects host species and manifests different behavioural responses depending on its magnitude and location of injection. The agent framework is employed to detect and counteract the invasion. The agent architecture consists of the physical layer and multiple invasion detection and local operator agents. Based on the operation state of the process, the detection agent raise a variety of flags (for example, “normal operation”, “severe invasion” etc.), whereas the operator agents take control actions based on the flags raised by the detection agent. The agent knowledge in the form of rule-based heuristics designed based on process knowledge gained through simulation under open-loop. The agent knowledge base consists of several parameters which affect their behaviours. Here, we propose a methodology to optimize the parameters critical to agent design. With this method, the agent system evolves in its structure, which facilitates more accurate responses.

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)

Overview

Man-made self-organizing systems date back to antiquity; for example, elaborate water clocks found from Alexandria (Ctesibius's clepsydra) to Seoul (King Sejong's Chagyongnu) were designed to keep constant rates or strike at regular time intervals without human adjustment. More modern examples include Watt's centrifugal governor, Black's negative feedback amplifier, and Nyquist's stability test, which enabled engineered systems to stabilize themselves. These and numerous innovations in control theory and engineering optimization have contributed much to modern communications technology. But there is a need for advances in both methods and applications beyond what has been achieved in the precise settings of mechanical, electronic, and optical switching and transmission towards the self-management and control of large-scale systems with many interacting and semi-autonomous components. Natural phenomena may be a guide for us, a model for self-organized decentralized systems. Spontaneous magnetization, crystallization, lasers, and superconductivity are examples of structural self-organization in physics where cohesive behavior emerges from initial disorder. In self-assembly and auto-catalytic networks in chemistry, molecules organize themselves in well-ordered arrangements without external action, and in biology, we observe highly complex coordinated action as in the folding of proteins, homeostasis, and flocking.

An Autocatalytic Cycle Model of Asymmetric Amplification and Mirror‐Symmetry Breaking in the Soai Reaction

Do it yourself: An autocatalytic cycle network is introduced to accurately reproduce the unprecedented features of the Soai reaction such as huge asymmetric autoamplification and spontaneous mirror-symmetry breaking. In contrast to previous attempts, which were based on formal kinetics, the present mechanism involves interconnected realistic structures including dimers, trimers and tetramers and resembles stereoselective and template-directed self-replication (see picture).

Robust dynamical pattern formation from a multifunctional minimal genetic circuit

BackgroundA practical problem during the analysis of natural networks is their complexity, thus the use of synthetic circuits would allow to unveil the natural mechanisms of operation. Autocatalytic gene regulatory networks play an important role in shaping the development of multicellular organisms, whereas oscillatory circuits are used to control gene expression under variable environments such as the light-dark cycle.ResultsWe propose a new mechanism to generate developmental patterns and oscillations using a minimal number of genes. For this, we design a synthetic gene circuit with an antagonistic self-regulation to study the spatio-temporal control of protein expression. Here, we show that our minimal system can behave as a biological clock or memory, and it exhibites an inherent robustness due to a quorum sensing mechanism. We analyze this property by accounting for molecular noise in an heterogeneous population. We also show how the period of the oscillations is tunable by environmental signals, and we study the bifurcations of the system by constructing different phase diagrams.ConclusionsAs this minimal circuit is based on a single transcriptional unit, it provides a new mechanism based on post-translational interactions to generate targeted spatio-temporal behavior.

Effect of Asymmetric Manipulations in Autocatalytic Networks

In this paper, we show that heterogeneous networks can be configured and reconfigured to operate in flexible spatial patterns. The concept is demonstrated by using a square grid of continuous stirred tank reactors with nearest neighbor interactions and hosting multiple cubic autocatalytic species. Asymmetry is introduced in the system by allowing for different feed flow rates in the reactors. A heterogeneous system offers expanded phase space, improved stability, and coexistence characteristics. The advantages of asymmetry are studied using bifurcation diagrams, continuation studies, and dynamics.

Lack of evolvability in self-sustaining autocatalytic networks constraints metabolism-first scenarios for the origin of life

A basic property of life is its capacity to experience Darwinian evolution. The replicator concept is at the core of genetics-first theories of the origin of life, which suggest that self-replicating oligonucleotides or their similar ancestors may have been the first "living" systems and may have led to the evolution of an RNA world. But problems with the nonenzymatic synthesis of biopolymers and the origin of template replication have spurred the alternative metabolism-first scenario, where self-reproducing and evolving proto-metabolic networks are assumed to have predated self-replicating genes. Recent theoretical work shows that "compositional genomes" (i.e., the counts of different molecular species in an assembly) are able to propagate compositional information and can provide a setup on which natural selection acts. Accordingly, if we stick to the notion of replicator as an entity that passes on its structure largely intact in successive replications, those macromolecular aggregates could be dubbed "ensemble replicators" (composomes) and quite different from the more familiar genes and memes. In sharp contrast with template-dependent replication dynamics, we demonstrate here that replication of compositional information is so inaccurate that fitter compositional genomes cannot be maintained by selection and, therefore, the system lacks evolvability (i.e., it cannot substantially depart from the asymptotic steady-state solution already built-in in the dynamical equations). We conclude that this fundamental limitation of ensemble replicators cautions against metabolism-first theories of the origin of life, although ancient metabolic systems could have provided a stable habitat within which polymer replicators later evolved.

Coenzyme autocatalytic network on the surface of oil microspheres as a model for the origin of life.

Coenzymes are often considered as remnants of primordial metabolism, but not as hereditary molecules. I suggest that coenzyme-like molecules (CLMs) performed hereditary functions before the emergence of nucleic acids. Autocatalytic CLMs modified (encoded) surface properties of hydrocarbon microspheres, to which they were anchored, and these changes enhanced autocatalysis and propagation of CLMs. Heredity started from a single kind of self-reproducing CLM, and then evolved into more complex coenzyme autocatalytic networks containing multiple kinds of CLMs. Polymerization of CLMs on the surface of microspheres and development of template-based synthesis is a potential evolutionary path towards the emergence of nucleic acids.

Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes

In the present work we propose an alternative approach to model autocatalytic networks, called piecewise-deterministic Markov processes. These were originally introduced by Davis in 1984. Such a model allows for random transitions between the active and inactive state of a gene, whereas subsequent transcription and translation processes are modeled in a deterministic manner. We consider three types of autoregulated networks, each based on a positive feedback loop. It is shown that if the densities of the stationary distributions exist, they are the solutions of a system of equations for a one-dimensional correlated random walk. These stationary distributions are determined analytically. Further, the distributions are analyzed for different simulation periods and different initial concentration values by numerical means. We show that, depending on the network structure, beside a binary response also a graded response is observable.

An autocatalytic network for ribozyme self-construction

The emergence of a primordial RNA world would have required the formation of RNA polymers of sufficient length to possess catalytic activities, which are difficult to obtain by spontaneous polymerization. An analysis of an autocatalytic assembly pathway that can self-construct a functioning ribozyme from smaller oligonucleotide building blocks describes a potential route for RNA extension.

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.