Hypercycle Model Research Articles

Functional Shift-Induced Degenerate Transcritical Neimark–Sacker Bifurcation in a Discrete Hypercycle

In this paper, we investigate the impact of functional shifts in a time-discrete cross-catalytic system. We use the hypercycle model considering that one of the species shifts from a cooperator to a degrader. At the bifurcation caused by this functional shift, an invariant curve collapses to a point [Formula: see text] while, simultaneously, two fixed points collide with [Formula: see text] in a transcritical bifurcation. Moreover, all points of a line containing [Formula: see text] become fixed points at the bifurcation and only at the bifurcation in a degenerate scenario. We provide a complete analytical description of this degenerate bifurcation. As a result of our study, we prove the existence of the invariant curve arising from the transition to cooperation.

Enterprise target cost control algorithm based on hypercycle model

Considering that the current cost control algorithm has the problems of poor control effect and high cost of manpower and material resources in enterprise cost control, a target cost control algorithm based on Hypercycle model is proposed. By analyzing the relationship between capital, price, technology and target cost control, this paper analyzes the influence of uncertain factors on target cost, and constructs a cost control super cycle model to realize enterprise cost control. Examples show that the algorithm can effectively improve the cost effect of enterprises, and has the practicability of reducing enterprise costs and improving enterprise profits.

Intellectual Property Information Service in Colleges and Universities Under the Background of Innovation Driven

This paper studies the intellectual property information service in Colleges and Universities under the background of innovation driven. Firstly, this paper expounds the concept and characteristics of intellectual property management in knowledge intensive manufacturing industry. On this basis, this paper compares and analyzes the current situation of intellectual property in knowledge intensive manufacturing industry at home and abroad from the aspects of intellectual property development, operation, protection and coordination, and finds out the achievements and shortcomings of intellectual property management in knowledge intensive manufacturing industry in China. This paper analyzes the hypercycle model of knowledge transfer and the collaborative evolution mechanism of knowledge transfer in knowledge intensive manufacturing industry by using the relevant theories of linkage and hypercycle. On this basis, the linkage relationship between knowledge transfer and intellectual property management in knowledge intensive manufacturing industry is analyzed. Based on the specific domestic intellectual property environment, this paper constructs the intellectual property management system of China's knowledge intensive manufacturing industry from three dimensions: intellectual property development, intellectual property protection and intellectual property operation.

Modelling Functional Shifts in Two-Species Hypercycles

Research on hypercycles focuses on cooperative interactions among replicating species, including the emergence of catalytic parasites and catalytic shortcircuits. Further interactions may be expected to arise in cooperative systems. For instance, molecular replicators are subject to mutational processes and ecological species to behavioural shifts due to environmental and ecological changes. Such changes could involve switches from cooperative to antagonistic interactions, in what we call a functional shift. In this article, we investigate a model for a two-member hypercycle model, considering that one species performs a functional shift. First, we introduce the model dynamics without functional shifts to illustrate the dynamics only considering obligate and facultative cooperation. Then, two more cases maintaining cross-catalysis are considered: (i) a model describing the dynamics of ribozymes where a fraction of the population of one replicator degrades the other molecular species while the other fraction still receives catalytic aid; and (ii) a system in which a given fraction of the population predates on the cooperating species while the rest of the population still receives aid. We have characterised the key bifurcation parameters determining extinction, survival, and coexistence of species. We show that predation, regardless of the fraction that benefits from it, does not significantly change dynamics with respect to the degradative case (i), thus conserving dynamics and bifurcations. Their biological significance is interpreted, and their potential implications for the dynamics of early replicators and ecological species are outlined.

Models of Prebiotic Evolution

The models of prebiotic evolution studied by the author are characterized: (1) the quasispecies model, (2) the hypercycle model, and (3) the syser model. The quasispecies model was proposed by Manfred Eigen. This model describes the evolution of a population of RNA macromolecules that can encode hereditary information. During the reproduction of RNA molecules, the inherited information is copied. Errors in the copying process lead to RNA mutations. The evolution of such a population leads to the selection of a quasispecies. The quasispecies is such a distribution of RNA chains that include both the “best RNA” (that is reproducing at maximal speed) and similar RNA chains that differ slightly from this best RNA by mutational substitutions. The hypercycle model was proposed in the late 1970s by Manfred Eigen and Peter Schuster. The hypercycle includes both RNA chains and amino acid chains, which perform certain catalytic functions. Both types of chains form a system of cooperatively interacting macromolecules. The syser model was proposed by Vadim Ratner and Vladimir Shamin. The term syser is abbreviation of “system of self-reproduction.” A syser includes the polynucleotide chain, replication enzyme, translation enzyme, and other enzymes/proteins. Also noted is the stochastic-correlator model, which, like the syser model, characterizes a certain approach to real biological cells. The syser model and the stochastic correlator model are compared. This study characterizes all of the noted models. A brief mathematical description of the models and the main results of computer simulations corresponding to the models are presented.

The comparative analysis of prebiological evolution models

Several models of prebiological systems are described and analyzed. The following models are characterized: a quasispecies model, a hypercycle model, a syser model (the term "syser" is an abbreviation of SYstem of SElf-Reproduction), a stochastic corrector model, a model of the origin of a primordial genome through spontaneous symmetry breaking. The quasispecies model analyzes the Darwinian evolution of information chains; this evolution is similar to the evolution of RNA molecules. Rather general estimates of the speed and efficiency of evolutionary processes can be obtained in the framework of the quasispecies model. We briefly describe the method for obtaining these estimates and the corresponding results. The hypercycle model considers the interaction of RNA chains and enzymes. The syser model characterizes a rather general scheme of the self-reproducing system, which is similar to the self-reproducing systems of biological cells. Syser includes a polynucleotide sequence, a replication enzyme, a translation enzyme, and other enzymes; these macromolecules are located inside the protocell. The stochastic corrector model describes the process of using a relatively small number of molecules of competing and cooperating replicators in protocells. The model of the origin of a primordial genome through spontaneous symmetry breaking characterizes an interesting and important process of the appearance of genotypes in protocells. This model was proposed and investigated by Takeuchi, Hogeweg, and Kaneko in 2017; we call it further “the THK model.” The current article characterizes and compares all these models.

Some mechanistic requirements for major transitions.

Major transitions in nature and human society are accompanied by a substantial change towards higher complexity in the core of the evolving system. New features are established, novel hierarchies emerge, new regulatory mechanisms are required and so on. An obvious way to achieve higher complexity is integration of autonomous elements into new organized systems whereby the previously independent units give up their autonomy at least in part. In this contribution, we reconsider the more than 40 years old hypercycle model and analyse it by the tools of stochastic chemical kinetics. An open system is implemented in the form of a flow reactor. The formation of new dynamically organized units through integration of competitors is identified with transcritical bifurcations. In the stochastic model, the fully organized state is quasi-stationary whereas the unorganized state corresponds to a population with natural selection. The stability of the organized state depends strongly on the number of individual subspecies, n, that have to be integrated: two and three classes of individuals, [Formula: see text] and [Formula: see text], readily form quasi-stationary states. The four-membered deterministic dynamical system, [Formula: see text], is stable but in the stochastic approach self-enhancing fluctuations drive it into extinction. In systems with five and more classes of individuals, [Formula: see text], the state of cooperation is unstable and the solutions of the deterministic ODEs exhibit large amplitude oscillations. In the stochastic system self-enhancing fluctuations lead to extinction as observed with [Formula: see text] Interestingly, cooperative systems in nature are commonly two-membered as shown by numerous examples of binary symbiosis. A few cases of symbiosis of three partners, called three-way symbiosis, have been found and were analysed within the past decade. Four-way symbiosis is rather rare but was reported to occur in fungus-growing ants. The model reported here can be used to illustrate the interplay between competition and cooperation whereby we obtain a hint on the role that resources play in major transitions. Abundance of resources seems to be an indispensable prerequisite of radical innovation that apparently needs substantial investments. Economists often claim that scarcity is driving innovation. Our model sheds some light on this apparent contradiction. In a nutshell, the answer is: scarcity drives optimization and increase in efficiency but abundance is required for radical novelty and the development of new features.This article is part of the themed issue 'The major synthetic evolutionary transitions'.

Excess Mutual Catalysis Is Required for Effective Evolvability

It is widely accepted that autocatalysis constitutes a crucial facet of effective replication and evolution (e.g., in Eigen's hypercycle model). Other models for early evolution (e.g., by Dyson, Gánti, Varela, and Kauffman) invoke catalytic networks, where cross-catalysis is more apparent. A key question is how the balance between auto- (self-) and cross- (mutual) catalysis shapes the behavior of model evolving systems. This is investigated using the graded autocatalysis replication domain (GARD) model, previously shown to capture essential features of reproduction, mutation, and evolution in compositional molecular assemblies. We have performed numerical simulations of an ensemble of GARD networks, each with a different set of lognormally distributed catalytic values. We asked what is the influence of the catalytic content of such networks on beneficial evolution. Importantly, a clear trend was observed, wherein only networks with high mutual catalysis propensity (p(mc)) allowed for an augmented diversity of composomes, quasi-stationary compositions that exhibit high replication fidelity. We have reexamined a recent analysis that showed meager selection in a single GARD instance and for a few nonstationary target compositions. In contrast, when we focused here on compotypes (clusters of composomes) as targets for selection in populations of compositional assemblies, appreciable selection response was observed for a large portion of the networks simulated. Further, stronger selection response was seen for high p(mc) values. Our simulations thus demonstrate that GARD can help analyze important facets of evolving systems, and indicate that excess mutual catalysis over self-catalysis is likely to be important for the emergence of molecular systems capable of evolutionlike behavior.

A least-constraint principle for population dynamics and reaction kinetics: Modeling entropy-controlled chemical hypercycles

In this paper, we investigate the treatment of constraints in rate equations describing the temporal evolution of biological populations or chemical reactions. We present a formulation for arbitrary holonomic and linear nonholonomic constraints which ensures the positivity of the dynamical variables and which is an analog of Gauss' principle of least constraint in classical mechanics. The approach is illustrated for the replication of molecular species in the Schuster-Eigen hypercycle model, imposing the conservation of the total number of molecules and the entropy production as constraints. The latter is used to model the behavior of an isolated system tending toward equilibrium and, for comparison, a stationary nonequilibrium state of an open system, which is characterized by undamped oscillations.

An intellectual development production hyper-cycle model – new JIT fundamentals and applications in Toyota

Study on an intellectual hyper-cycle model for development production strategy in automobile industry by utilising the author's new JIT fundamentals with TMS, TDS, TPS and Science TQM, is the traditional just in time (JIT) system for not only manufacturing, but also for customer relations, business and sales, merchandise planning and engineering design, production engineering, administration and management for enhancing business process innovation and introduction of new concepts and procedures. The author believes that proposal and effectiveness of an intellectual development production hyper-cycle model (IDP-HM) by structured 'dual model – advanced TDS and advanced TPS' has been demonstrated as described herein based on the author's experience in Toyota.

Ghosts in high dimensional non-linear dynamical systems: The example of the hypercycle

Ghost-induced delayed transitions are analyzed in high dimensional non-linear dynamical systems by means of the hypercycle model. The hypercycle is a network of catalytically-coupled self-replicating RNA-like macromolecules, and has been suggested to be involved in the transition from non-living to living matter in the context of earlier prebiotic evolution. It is demonstrated that, in the vicinity of the saddle-node bifurcation for symmetric hypercycles, the persistence time before extinction, T ϵ , tends to infinity as n → ∞ (being n the number of units of the hypercycle), thus suggesting that the increase in the number of hypercycle units involves a longer resilient time before extinction because of the ghost. Furthermore, by means of numerical analysis the dynamics of three large hypercycle networks is also studied, focusing in their extinction dynamics associated to the ghosts. Such networks allow to explore the properties of the ghosts living in high dimensional phase space with n = 5, n = 10 and n = 15 dimensions. These hypercyclic networks, in agreement with other works, are shown to exhibit self-maintained oscillations governed by stable limit cycles. The bifurcation scenarios for these hypercycles are analyzed, as well as the effect of the phase space dimensionality in the delayed transition phenomena and in the scaling properties of the ghosts near bifurcation threshold.

Bifurcations and phase transitions in spatially extended two-member hypercycles

Mounting theoretical and experimental evidence indicates that the success of molecular replicators is strongly tied to the local nature of their interactions. Local dispersal in a given spatial domain, particularly on surfaces, might strongly enhance the growth and selection of fit molecules and their resistance to parasites. In this work the spatial dynamics of a simple hypercycle model consisting of two molecular species is analysed. In order to characterize it, both mean field models and stochastic, spatially explicit approaches are considered. The mean field approach predicts the presence of a saddle-node bifurcation separating a phase involving stable hypercycles from extinction, consistently with spatially explicit models, where an absorbing first-order phase transition is shown to exist and diffusion is explicitly introduced. The saddle-node bifurcation is shown to leave a ghost in the phase plane. A metapopulation-based model is also developed in order to account for the observed phases when both diffusion and reaction are considered. The role of information and diffusion as well as the relevance of these phases and the underlying spatial structures are discussed, and their potential implications for the evolution of early replicators are outlined.

Economic production as chemistry

Inspired by the hypercycle model of the origins of chemical life on earth, this paper develops an autocatalytic model of the co‐evolution of economic production and economic firms, represented as skills. The production and distribution of goods by firms are only half of what is accomplished in markets. Firms are produced and transformed, via learning, through goods passing through them. Through means of both agent‐based and analytic modeling, this article establishes three principles of social organization that provide sufficient foundations for the unconscious evolution of technological complexity: structured topology, altruistic learning and stigmergy.

Spatial models of prebiotic evolution: soup before pizza?

The problem of information integration and resistance to the invasion of parasitic mutants in prebiotic replicator systems is a notorious issue of research on the origin of life. Almost all theoretical studies published so far have demonstrated that some kind of spatial structure is indispensable for the persistence and/or the parasite resistance of any feasible replicator system. Based on a detailed critical survey of spatial models on prebiotic information integration, we suggest a possible scenario for replicator system evolution leading to the emergence of the first protocells capable of independent life. We show that even the spatial versions of the hypercycle model are vulnerable to selfish parasites in heterogeneous habitats. Contrary, the metabolic system remains persistent and coexistent with its parasites both on heterogeneous surfaces and in chaotically mixing flowing media. Persistent metabolic parasites can be converted to metabolic cooperators, or they can gradually obtain replicase activity. Our simulations show that, once replicase activity emerged, a gradual and simultaneous evolutionary improvement of replicase functionality (speed and fidelity) and template efficiency is possible only on a surface that constrains the mobility of macromolecule replicators. Based on the results of the models reviewed, we suggest that open chaotic flows ('soup') and surface dynamics ('pizza') both played key roles in the sequence of evolutionary events ultimately concluding in the appearance of the first living cell on Earth.

3D hypercycles have no stable spatial structure

Two-dimensional (2D) hypercycles have been shown to generate spiral patterns, which may protect the hypercycle from parasites that would be fatal to the hypercycle in a homogeneous spatial distribution. We perform numerical experiments on a partial differential equations hypercycle model and show that scroll rings are formed and are not stable: They contract by a power law and disappear within finite time. Similar results are obtained with a 3D cellular automaton hypercycle model. For the 3D hypercycle the final state is homogeneously oscillating, except with initial conditions creating plane waves or 2D spirals. This indicates that the mechanism which may protect the 2D hypercycle from parasites is not applicable to 3D hypercycles. The contraction of the scroll rings is analogous to what has been observed and calculated for other phenomena and models, of which one is the Belousov-Zhabotinsky reaction, described by several mathematical models.

The Origin of Synergistic Symbiosis

A dominant theme in the history of life has been the evolutionary innovations of cooperative symbioses: the first genomes near the origin of life, integrated prokaryotic cells, the complex symbiotic communities that evolved into modern eukaryotic cells, lichens, mycorrhizae, and so on. In this paper, a mode l of cooperative symbiosis that shows a threshold condition for the evolution of cooperation is analyzed. The threshold is not easily passed, but cooperative evolution proceeds rapidly once a symbiosis overcomes the threshold. In the model presented here, each species has genetic variability for a symbiotic trait. The trait imposes a reproductive cost on its bearer but enhances the reproduction of its partner species. For example, in the origin of genetic systems, the trait may cause biochemical synergism for the rate of replication of primitive RNA strands as in Eigen and Schuster's hypercycle model. Models of growth are contrasted with synergism, which are most appropriate for the evolution of genetic systems and for mutualisms such as lichens, with the strategic and psychological applications of the Prisoner's Dilemma model.

Group selection of early replicators and the origin of life

A major problem of the origin of life has been that of information integration. As Eigen (1971) has shown, a mutant distribution of RNAs replicating without the aid of a replicase cannot integrate sufficient information for the functioning of a higher-level unit utilizing several types of encoded enzymes. He proposed the hypercycle model to bridge this gap in prebiology. It can be shown by a nonlinear game model, incorporating mutation of a hypercycle, that the selection properties of hypercycles make them inefficient information integrators as they cannot compete favourably with all kinds of less efficient information carriers or mutationally coupled hypercycles. The stochastic corrector model is presented as an alternative resolution of Eigen's paradox. It assumes that replicative templates are competing within replicative compartments, whose selective values depend on the internal template composition via a catalytic acid in replication and "metabolism". The dynamics of template replication are analyzed by numerical simulation of master equations. Due to the stochasticity in replication and compartment fission the best compartment types recur. An Eigen equation at the compartment level is set up and calculated. Even selfish template mutants cannot destroy the system though they make it less efficient. The genetic information of templates is evaluated at both levels, and the higher (compartment) level successfully constrains the lower (template) one. Compartmentation together with stochastic effects is sufficient to integrate information dispersed in competitive replicators. Compartment selection is considered to be group selection of replicators. Implications for the origin of life are discussed.

The evolution of meiosis and sexual reproduction

It has been argued that because intermediate states would not be advantageous, it is impossible for natural selection to account for the evolution of meiosis and sexual reproduction. The argument is invalid because a reasonable hypothesis is presented. The hypothesis is developed from a consideration of unicellular eukaryotes and prokaryotes and is that the ancestral eukaryote had a form of parasexual cycle with ‘somatic’ or ‘mitotic’ recombination. Later mitosis, then meiosis evolved. In multicellular organisms genetic recombination then usually became restricted to meiosis. Several predictions are made that could be tested in the near future. A conclusion is that we have been misled by treating meiosis and genetic recombination as more or less synonomous. The question of the ultimate origin of recombination is more obscure but it is pointed out that recombination could give the most immediate advantage early in the origin of life, particularly with a hypercycle model. It could result in the combination of advantageous quasi-species (short nucleotidc sequences) into one genome, and it could eliminate ineffective combinations. There are discussions of the scientific role of hypotheses for the origin of complex biological features and on the biological success of cooperative units of DNA.

Hypercycles, parasites and packages

The hypercycle model considers a functional rather than spatial coupling of primitive tRNA molecules the essential phenomenon at the origin of life. We will critically discuss this model with special regard to the problems of selecting for functionally improved mutant molecules. To overcome these difficulties compartmentalization must become effective much earlier than suggested by the hypercycle model. Consequently, we sketch some features relevant for the genetics of primitive compartments.

A solvable selfreproductive hypercycle model for the selection of biological molecules.

By introducing a modified enzyme coupling in Eigen's hypercycle equations we have produced an exactly solvable selfreproductive hypercycle model. The model shows explicitly how collections of different macromolecular information carriers may coexist, through internal couplings, in the presence of constraints. We show how the "selective value" concept is manifested in the model and give simple criteria for selection among competing hypercycles.