Eigen M. Self-organization of matter and the evolution of biological macromolecules. Naturwissenschaften 1971;58:465--523.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....tends to be maximized when the gene pool is at the edge of genetic disorder. These results are quite reminiscent of the error threshold from molecular evolution the critical mutation rate at which evolutionary adaptations are destroyed more quickly than natural selection can produce them [13, 14]. It is still an open question to what extent our results might be a reflection of an error threshold, for our results are obtained in a significantly more complicated context than that in which the error threshold has been demonstrated, and our bifurcation of diversity dynamics occurs whether or ....

Eigen, M. 1971. Self-organization of matter and the evolution of biological macromolecules. Naturwissenschaften 58, 465--523.

....the fundamental driving force of selection seems to be one of the principal archievments of Darwin s work [10] 1.2 Self Organization The self organization of matter associated with the origin of life must have started from random events in a sense of non existing of fundamental organization. [12]. In his famous paper, which stimulated much research in this field, Manfred Eigen sets out the development of a theory about self organization. He addresses the question of self organizing matter into replicating individuals . Glansdorff and Prigogine [29] created a thermodynamic theory of open ....

....This equation describes the selection process. Adding errors while replicating allows to describe evolutionary processes such as mutation or recombination [53, 58, 60, 56] 68] 72] Many works have been performed on this subject and on special cases, such as the development of the hyper cycle [12], 15] 17] 3.2 Reaction Networks There are n replicating species in all dynamical systems treated in this work. For each species k=1, n X k represent the genom and T k denotes the geneproducts, necessary for replication (e.g. the DNA (RNA) polymerases) Because it is impossible to ....

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M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Die Naturwissenschaften, 10:465--523, 1971.

....models based on chemical reaction kinetics and stochastic processes. The simplest successful experimental approach to study evolution was implemtented by Sol Spiegelman [57] in his test tube assay of RNA replication and mutation. His work was complemented by the seminal paper of Manfred Eigen [6] who presented a theory of molecular evolution based on chemical kinetics. Within this frame the concept of molecular quasispecies was developed [8, 9] Evolutionary optimization and adaptation to the environment are not bound to the existence of cellular life. They occur also in vitro provided ....

.... master shape G[m] defines the fitness landscape f G[m] v) oe 1 iff v 2 v 1 iff v 2 v n v At first the error threshold for the maintenance of phenotypes will be derived by means of a phenomenological approach based on the kinetic differential equation for replication and mutation [6], then we shall apply a stochastic replicationdeletion process in the derivation. 3.1. Genotypic and phenotypic error thresholds Error thresholds in replication mutation equations were studied extensively in systems lacking selective neutrality [6, 8, 9] The frequencies of genotypes x i are ....

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M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58:465--523, 1971.

....by modular construction and the build upon latest version strategy seems to be nature s way of coping with the unpredictable. INNOVATION IN BIOLOGY Lastly, we are left with the problem of radical innovation. The mechanism of evolution is built upon chemical kinetics of replication and mutation [6, 8]. Various scenarios have been derived by applying di erent types of replication. Independent replication led to Darwinian behavior based on competition and resulted in the concept of the molecular quasispecies [8, 7] If replicating molecules become mutually dependent on each other, population ....

M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58:465-523, 1971.

....makes them accessible to an anlysis by the conventional methods of physics and chemistry. Two great scholars initiated studies on evolution in vitro: Sol Spiegelman [67, 85] did the rst optimization experiments on molecules based on Darwin s principle of variation and selection and Manfred Eigen [21] presented an access to the phenomena of evolution by means of chemical reaction kinetics. Spiegelman s work started from an in vitro replication assays for RNA molecules that used a virus speci c RNA replicase isolated form Escherichia coli bacteria infected by the bacteriophage Q . Replication ....

.... of evolution it has also provided the basis for a novel kind of biotechnology as predicted already in the eighties [25, 54] Manfred Eigen s theory of molecular evolution is dealing with the kinetics of replication, mutation, and selection in populations of asexually reproducing species [21]. The novelty in this approach is the view of correct replication and mutation being parallel reactions involving the same template. The notion of sequence space turned out to be illustrative and useful in the context of evolution as it relates biophysics of evolution to information theory and the ....

[Article contains additional citation context not shown here]

M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58:465-523, 1971.

....that leads to adaptation and improvement of fitness, in the absence of cellular life. A theoretical frame for handling evolution of molecules has been developed almost simultaneously through combining the concepts of population genetics with the knowledge of molecular and structural biology [11]. The mechanistic way how autocatalysis shapes transitions from the evolution of molecules towards higher functional units is essentially comprised by the role of catalysis in autocatalytic kinetic networks [15] Extensive theoretical and computational studies of RNA evolution in vitro by the ....

....reaction scheme I k I l (M) # 2I k I l , 2) i.e. one polymer species I k is copied by another polymer species I l of the same type, thereby consuming building material (M) which is assumed to be present in excess. Although postulated and analyzed already in the nineteen seventies [11,14], no direct experimental implementation of this system was possible since the known biopolymers with the required properties were either (obligatory) templates, like RNA molecules, or protein based replicases. But recently an RNA replicating ribozyme was obtained by means of artificial evolution ....

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M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58:465--523, 1971.

....of mixing operators. In fact, it is strictly invariant not just form invariant, as there is no renormalization necessary of any parameter or variable and we have f # # = # # )f # = f # , where, here, # # represents the phenotype and # the genotype. A concrete example is that of the Eigen model [42, 43], where the fitness landscape is degenerate for all genotypes except one, the master sequence. At the level of selection only, given that there are only two phenotypes, there is a reduction in the size of the configuration space from to 2, i.e. a reduction in the number of degrees of freedom ....

....has intuitive value by restoring a notion of hill climbing even in cases where the requirements for having a (static) fitness landscape are violated. The requirement that fitness be a Lyapunov function of equation (1) is very restrictive. To see this we consider again Eigen s quasispecies model [42] described by equation (11) In the absence of mutation M xy is the identity matrix. Now, consider a population consisting exclusively of individuals that maximize f x . In the presence of mutation the average fitness of the population will decrease due to the introduction of disadvantageous ....

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Eigen, M. Selforganization of matter and the evolution of biological macromolecules. Die Naturwissenschaften, 10:465--523, 1971.

....state forms the basis on which it can be decided whether the population is able to adapt to, or track, the changes in the tness landscape. Our mathematical formalism applies to GAs as well as to biological self replicating systems, since the analyzed GA model and Eigen s quasispecies model [6, 7, 8] in the molecular evolution theory (see [9] for a recent review) are very similar. Hence, all introduced concepts for GAs are valid and relevant in analogous form for molecular evolutionary systems. In the following section, we will introduce the model to be analyzed and show the correspondence ....

....But in the next section, the heuristics are expected to play a minor role for our general conclusion on an inertia of ssGAs against time variations. At this point, we want to review shortly the correspondence of our GA model with the quasispecies model, extensively studied by Eigen and coworkers [6, 7, 8] in the context of molecular evolution theory (see also [13] in this book) The quasispecies model describes a system of self replicating entities i (e.g. RNA , DNA strands) with replication rates f i and an imperfect copying procedure such that mutations occur. For simplicity reasons, the ....

M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58, p. 465, 1971.

....a certain temperature. We need, however, a supply of Gibbs energy because it is a perishable commodity, turning into heat if not used for work. As soon as we postulate replication in a chemical system, it becomes a model, although very much incomplete, of life. The pioneering work of Manfred Eigen [16, 17], who investigated the kinetics of this type of systems, gave an impetus to the whole new area Manfred Eigen was concerned mainly with linear sequences for two reasons: the linear model is the simplest for simulation and it is the closest to natural linear chains such as proteins, DNA, and texts. ....

.... Systems of matter, in order to be eligible for selective self organization, have to inherit physical properties which allow for metabolism, i.e. the turnover of energy rich reactants to energy deficient products, and for ( noisy ) self reproduction. These prerequisites are indispensable. [16]. The mind, located in the brain, 2 of the body by weight, consumes 20 of energy. We do not know how this energy is used, but it is obvious that only a small part of all daily content of the brain leaves any trace in it, while a part of the earlier stored material disappears. Two hypotheses on ....

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Eigen15. M. Eigen, Selforganization of Matter and the Evolution of Biological Macromolecules, Die Naturwissenschaften, 58, 465-522 (1971).

....does not fall below the limit Gamma1 F = 1=2N . 2. 2 MOLECULAR QUASISPECIES An extension of conventional population genetics which considers evolution as chemical reactions in genotype space was proposed by Manfred Eigen in his seminal paper on the theory of the evolution of molecules [21]. His concept can be understood, in essence, as an application of chemical reaction kinetics to molecular evolution. A main issue of Eigen s approach was to derive the mechanism by which biological information is created. Populations migrate through sequence space as metastable but structured ....

....of error classes) by the number of mutations which are required to produce them as mutants of the master sequence. In case of point mutations the distance between sequences is the Hamming distance. 6 In precise terms, the quasispecies is defined as the stable stationary solution of equation (3) [21, 24], the mutant distribution described by the largest eigenvector of the matrix W = fW ij = Q ij Delta a j ; i; j = 1; ng [51, 73, 96, 100] Its diagonal elements are approximations for fitness values, Ik : fk Wkk = ak Delta Qkk ) In reality, such a stationary solution exist only if the ....

[Article contains additional citation context not shown here]

Eigen, M., "Selforganization of Matter and the Evolution of Biological Macromolecules". Naturwissenschaften 58 (1971):465--523.

....the fundamental driving force of selection seems to be one of the principal achievements of Darwin s work [6] 1.2 Self Organization The self organization of matter associated with the origin of life must have started from random events in a sense of non existing of fundamental organization. [8]. In his famous paper, which stimulated much research in this field, Manfred Eigen sets out the development of a theory about self organization. He addresses the question of self organizing matter into replicating individuals . In the last decades, a number of physical and chemical systems that ....

....on the rate constants f i , but also on the initial conditions. In both cases a generalized gradient could be found; hence, complicated dynamical behaviour like oscillations, quasiperiodicity and chaotic dynamics are impossible. CHAPTER 1. INTRODUCTION 18 1.6. 2 Symbiosis: The Hypercycle Eigen [8] estimated that nucleic acids viewed as information carriers could not accumulate a stable information content of more than about 200 bits, corresponding to the formation of polymers not longer than approximately 100 base pairs. Since even the simplest bacteria have genomes that are several orders ....

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M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Die Naturwissenschaften, 10:465--523, 1971.

....(GC 30 ) 18] For structures with u and p way below the critical values we find many components and a characteristically decreasing size distribution of these components, see figure 9, as predicted by random graph theory. 5.5. Diffusion on Neutral Networks Eigen s theory of molecular evolution [7], formulated later as the theory of the molecular quasispecies [9, 8] describes the evolution of a population of haploid individuals on the sequence space. Each sequence replicates independently of all other members of the population with a sequence dependent replication rate A v and a single ....

M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Die Naturwissenschaften, 10:465--523, 1971.

....as for artificial selection in biotechnology. We predict that there is no need to systematically search huge portions of the sequence space, nor does one need specially designed initial conditions. These properties provide further support for the widespread applicability of molecular evolution [91, 92, 4]. 100 References 6. References [1] Charles Darwin. The Origin of Species. reprinted in Penguin Classics, 1859. 2] Sewall Wright. The roles of mutation, inbreeding, crossbreeeding and selection in evolution. In D. F. Jones, editor, int. Proceedings of the Sixth International Congress on ....

Manfred Eigen. Selforganization of matter and the evolution of biological macromolecules. Die Naturwissenschaften, 10:465--523, 1971.

....y (6.2) The first class of landscapes in which mutation based dynamics has been investigated were single peak landscapes. In a single peak landscape one particular configuration has the maximum fitness while all other configurations have inferior fitness values. Eigen, Schuster, and collaborators [40, 42, 187, 41] completely analyzed the errorprone replication of haploid organisms (or, equivalently, biopolymer sequences) on a single peak landscape. They discovered the genotypic error threshold phenomenon, i.e. the existence of some critical error rate at which the population becomes unstable and drifts ....

M. Eigen, Selforganization of matter and the evolution of biological macromolecules, Die Naturwissenschaften, 10 (1971), pp. 465--523.

....does not fall below the limit Gamma1 F = 1=2N . 2. 2 MOLECULAR QUASISPECIES An extension of conventional population genetics which considers evolution as chemical reactions in genotype space was proposed by Manfred Eigen in his seminal paper on the theory of the evolution of molecules [20]. His concept can be understood, in essence, as an application of chemical reaction kinetics to molecular evolution. A main issue of Eigen s approach was to derive the mechanism by which biological information is created. Populations migrate through sequence space as metastable but structured ....

....of error classes) by the number of mutations which are required to produce them as mutants of the master sequence. In case of point mutations the distance between sequences is the Hamming distance. 6 In precise terms, the quasispecies is defined as the stable stationary solution of equation (3) [20, 23], the mutant distribution described by the largest eigenvector of the matrix W = fW ij = Q ij Delta a j ; i; j = 1; ng [48, 67, 86, 90] Its diagonal elements are approximations for fitness values, Ik : fk Wkk = ak Delta Qkk ) In reality, such a stationary solution exist only if the ....

[Article contains additional citation context not shown here]

Eigen, M., "Selforganization of Matter and the Evolution of Biological Macromolecules". Naturwissenschaften 58 (1971):465--523.

....concentration space; when a variant dies out, the corresponding variable disappears. The number of variables (m) matches the number of currently existing genotype classes. As a well known example we mention the selection mutation equation for asexually reproducing individuals introduced by Eigen [13]: dx i dt = x i i k i Q ii Gamma d i Gamma Phi(x) j X j 6=i k j Q ji x j ; i = 1; 2; m (2) Replication and degradation rate constants are denoted by k i and d i , respectively, replication accuracies and mutation frequencies are contained in the (bistochastic) matrix Q : ....

.... to the existence of cellular life: molecules capable of reproduction and mutation fulfil the prerequisites for Darwin s principle and behave like asexually replicating individuals (as far as selection and adaptation to environmental conditions are concerned) About the same time Manfred Eigen [13] developed a theoretical frame for molecular evolution which had its roots in chemical reaction kinetics. In vitro evolution of RNA molecules circumvents the three problems indicated above: i) generation times can be reduced to a few seconds under favorable conditions and evolutionary phenomena ....

[Article contains additional citation context not shown here]

M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58:465--523, 1971.

....models based on chemical reaction kinetics and stochastic processes. The simplest successful experimental approach to study evolution was implemtented by Sol Spiegelman [57] in his test tube assay of RNA replication and mutation. His work was complemented by the seminal paper of Manfred Eigen [6] who presented a theory of molecular evolution based on chemical kinetics. Within this frame the concept of molecular quasispecies was developed [8, 9] Evolutionary optimization and adaptation to the environment are not bound to the existence of Reidys, Forst, Schuster: Replication on Neutral ....

.... f G[m] v) ae oe 1 iff v 2 v Theta G[m] 1 iff v 2 v Theta Q n ff n v Theta G[m] At first the error threshold for the maintenance of phenotypes will be derived by means of a phenomenological approach based on the kinetic differential equation for replication and mutation [6], then we shall apply a stochastic replicationdeletion process in the derivation. 3.1. Genotypic and phenotypic error thresholds Error thresholds in replication mutation equations were studied extensively in systems lacking selective neutrality [6, 8, 9] The frequencies of genotypes x i are ....

[Article contains additional citation context not shown here]

M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58:465--523, 1971.

....organizations. Achieving this challenge will be a big step toward discerning the boundaries of life as it could be. The central dogma of molecular biology and an essentially universal genetic code are examples of strongly conserved organizational themes of living organisms. As an example, Eigen [7] gave a strong argument that autocatalytic sets without genetic underpinning have a problem in principle with evolvability. No proof of this conclusion has been given, but examples to date of autocatalytic sets without replicable elements have failed to exhibit convincing evolution. This may serve ....

....where the dynamics of functions rather than states is studied. Genetic models of evolution start with a discrete state space in the form of heteropolymers of defined sequence, but in which the transmission of information (reading the symbols) is probabilistic. The quasispecies theory of Eigen [7] already demonstrates how information can then be generated from physical dynamics, selection being achievable through differences in rate coefficients for the production and destruction of such polymers. Chemical kinetics also provides a convincing theory to explain the relatively discrete logic ....

Eigen, M. 1971. Self-organization of matter and evolution of biological macromolecules. Naturwissenschaften 58: 465-523.

....makes them accessible to an anlysis by the conventional methods of physics and chemistry. Two great scholars initiated studies on evolution in vitro: Sol Spiegelman [67, 85] did the first optimization experiments on molecules based on Darwin s principle of variation and selection and Manfred Eigen [21] presented an access to the phenomena of evolution by means of chemical reaction kinetics. Spiegelman s work started from an in vitro replication assays for RNA molecules that used a virus specific RNA replicase isolated form Escherichia coli bacteria infected by the bacteriophage Qfi. Replication ....

.... of evolution it has also provided the basis for a novel kind of biotechnology as predicted already in the eighties [25, 54] Manfred Eigen s theory of molecular evolution is dealing with the kinetics of replication, mutation, and selection in populations of asexually reproducing species [21]. The novelty in this approach is the view of correct replication and mutation being parallel reactions involving the same template. The notion of sequence space turned out to be illustrative and useful in the context of evolution as it relates biophysics of evolution to information theory and the ....

[Article contains additional citation context not shown here]

M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58:465--523, 1971.

....representations and stochastic dynamics are discussed. Keywords: catalytic network, association, architecture, molecular evolution, dynamics, sigma pi units 1 Introduction Catalytic networks are a mechanism for self organisation that has first been described in the area of molecular evolution (Eigen, 1971). Catalytic networks are applied here as a model of association, very similar to McClelland Rumelhart s (1981) interactive activation model of letter and word perception. Why would one want to have another model of association Problems in current neural models are for example that the usual ....

....in general) that exhibit a high population number due to catalytic support are called an autocatalytic set. The changes of the population in time are called population dynamics. In chemistry the population dynamics is very well understood, and described mathematically by deterministic models. M. Eigen (1971) has based his theory of the self organisation of matter on this kind of dynamics. The cooperating molecules form a replicating unit, and as such can compete with other replicating units. In some cases these units can coexist, in other cases only one unit can win and others die out. This is a ....

Eigen, M. (1971). Selforganization of Matter and the Evolution of Biological Macromolecules. Die Naturwissenschaften 58, 465-523.

....reveal some properties of the process that in some cases are striking at the first glance. These findings may not only be helpful for better understanding natural intelligence but also be beneficial for global longterm planning and other groping in the dark situations. 2. ORGANIC EVOLUTION Eigen [1] once modeled the replication of RNA matrices in the primordial soup by means of the following set of nonlinear ordinary differential equations. Let x i be the concentration of species i 2 [1; n = 4 N ] with N denoting the number of nucleotide bases (there are 4 different types of them) that ....

M. Eigen, Self-organization of matter and the evolution of biological macromolecules, Naturwissenschaften 58, 1971, pp. 465-523.

....The position of this equilibrium will depend on the selection mechanism and the genetic operators being used (figure 7.20) 7.4. 5 GA on Needle in a Haystack The simple ESP generated by running a GA on a N in H landscape has led to one of the most directly useful understandings of ESP dynamics (Eigen, 1971; Woodcock Higgs, 1995; Ochoa Harvey, 1998) The entire population of the GA is started off on the needle, as everyone knows that actually finding the needle is so technically hard that it is not interesting. Instead the question that people look at is: when does the GA population fall off the ....

....to determine the relation between persistence and the error threshold. It may be the case that to remain on a neutral network with high fitness one has to have a high enough persistence value, reflecting a low enough effective mutation rate. The traditional investigations of the error threshold (Eigen, 1971) look at the relation between the actual mutation rate and the chances of falling off a needle (and similarly a neutral network) The suggestion being looked at here is that it may actually be the effective mutation rate that is more influential in determining whether or not a given ESA will ....

Eigen, M. (1971). Self-organization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58, 465--523.

....in statistical physics is the so called error threshold. It describes the breakdown of genetic order in mutation selection models for mutation rates surpassing a certain critical value. The prototype model for the description of the error threshold is Eigen s quasispecies model in sequence space [7, 8] (which is e ectively equivalent to a coupled mutation selection model in population genetics, cf [5] originally designed for the description of prebiotic RNA evolution. One important step towards an understanding of the threshold phenomenon has been its identi cation with an equilibrium phase ....

....length, we have scaled the variables such that a well de ned limit is approached as N 1. In particular, the critical mutation rate per site in a nite system quickly converges to the limiting value c . Originally, the threshold has been viewed as a limitating factor on the sequence length [7]. This, however, should not be confusing: We switch to this latter picture simply by letting the reduced mutation rate depend 20 linearly on the sequence length, N , and obtain a critical length N c c (for suciently large sequences) Our results on the error threshold phenomenon t ....

M. Eigen, Selforganization of matter and the evolution of biological macromolecules, Naturwiss. 58 (1971) 465-523. 21

....could act as a barrier to the fixation of a favourable mutant. We derive analytic approximations for the equilibrium concentrations of the optimum genotype and for the error threshold. We also analyse the stability of the equilibria. 1 Introduction Manfred Eigen, in his quasispecies formalism (Eigen, 1971; Eigen and Schuster, 1979; Eigen et al. 1989) developed an approach to analysing the evolution of large populations of informationencoding sequences based on (deterministic) flow reactor kinetics, whereby concentrations of sequence types change according to differential rates of replication, ....

Eigen, M. (1971). Selforganization of matter and the evolution of biological macromolecules. Natuurwissenschaften, 10:465--523.

....state forms the basis on which it can be decided whether the population is able to adapt to, or track, the changes in the fitness landscape. Our mathematical formalism applies to GAs as well as to biological self replicating systems, since the analyzed GA model and Eigen s quasispecies model [6, 7, 8] in the molecular evolution theory (see [9] for a recent review) are very similar. Hence, all introduced concepts for GAs are valid and relevant in analogous form for molecular evolutionary systems. In the following section, we will introduce the model to be analyzed and show the correspondence to ....

....But in the next section, the heuristics are expected to play a minor role for our general conclusion on an inertia of ssGAs against time variations. At this point, we want to review shortly the correspondence of our GA model with the quasispecies model, extensively studied by Eigen and coworkers [6, 7, 8] in the context of molecular evolution theory (see also [13] in this book) The quasispecies model describes a system of self replicating entities i (e.g. RNA , DNA strands) with replication rates f i and an imperfect copying procedure such that mutations occur. For simplicity reasons, the ....

M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58, p. 465, 1971.

....a process whereby macro conservative hypercycles may emerge through self organizing compartmentation. The crucial point of this study regards the meta interactions that take place between the genotypic atomic reactions and the phenotypic potential field. 1 Introduction The hypercycle model [1, 2] was advocated to explain that process from the stage of chemical evolution to the emergence of primitive bio molecules. M. Eigen was interested in what kind of dynamics would bring about a macro functional system under the appropriate conditions, and investigated the possibility of ....

. Eigen, M.: Self-Organization of Matter and the Evolution of Biological Macromolecules. Naturwissenschaften 58 (1971)

....U.K. h.huening ic.ac.uk Abstract In contrast to standard genetic algorithms with generational reproduction, we adopt the viewpoint of the reactor algorithm (Dittrich Banzhaf, 1998) which is similar to steady state genetic algorithms, but without ranking. This permits an analysis similar to Eigen s (1971) molecular evolution model. From this viewpoint, we consider combining segments from different populations into one genotype at every time step, which can be regarded as many parent combinations with fixed crossover points, and is comparable to cooperative evolution (Potter De Jong, 2000) We ....

....So this shares with the reactor algorithm that strings are chosen at random, and that fit results are put back into the populations at every time step. Using the reactor metaphor, we can draw on the formal analysis of catalytic networks, where similar dynamical systems have been studied (Eigen, 1971, Eigen Schuster, 1978, Bagley, Farmer Fontana, 1992) The analysis of catalytic networks is based on mass action kinetics of chemical reactions. Deterministic equations are obtained for these essentially stochastic systems by the Master equation (Gillespie, 1992, van Kampen, 1981) In ....

Eigen, M. (1971). Selforganization of Matter and the Evolution of Biological Macromolecules. Die Naturwissenschaften 58, 465-523.

....of RNA structure optimization [14, 15, 24] favor Wright s rather than Kimura s ideas. The simplest experimental model system of evolution was discovered by Sol Spiegelman [39] in his test tube assay of RNA replication and mutation. His work was complemented by the seminal paper of Manfred Eigen [5] who presented a theory of molecular evolution based on chemical kinetics. Within this theoretical frame the theory of molecular quasispecies was developed [7, 8] Evolutionary Reidys, Forst, Schuster: Replication on Neutral Networks 3 optimization and adaptation to the environment based on ....

....relative to an averaged fitness of the mutant distributions (see section 3. 1) Reidys, Forst, Schuster: Replication on Neutral Networks 12 The error threshold will be derived first by means of a phenomenological approach based on the kinetic differential equation for replication and mutation [5], then a stochastic replication deletion process will be used in the derivation. In section 4 numerical values for the threshold are compared with the results from computer simulations [18, 19] 3.1. Genotypic and phenotypic error thresholds Error thresholds in replication mutation equations have ....

[Article contains additional citation context not shown here]

M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58:465--523, 1971.

....the replication ability is set to attempt 3 offspring per lifetime. The three lines shown on the graph represent the best, average and worst levels of persistence of the objects at a given time during the run. As can be seen, the population of objects soon reaches a persistence error threshold [6] beyond which they are unable to evolve. A simple explanation of this error threshold can be gained through looking at the necessary requirements to maintain a persistence ratchet [1] A persistence ratchet is said to be in place when the replication rate is higher than the net negative mutation ....

Eigen, M.: Self-organization of matter and the evolution of biological macromolecules. Naturwissenschaften 58 (1971) 465--523

....phenomena of self organization in non living systems. Section 2 outlines the model of the reaction formation system Atomoid. Section 3 describes the reaction rules of Atomoid in detail. Section 4 shows simulation results and presents the emergence of self reproductive hypercycles. Lastly, section 5 discusses those simulation results and the prospects of Atomoid, and then concludes this paper. 2. Atomoid 2.1 Penrose s work and Atomoid L. S. Penrose s work [13] was helpful in modeling Atomoid. Penrose built a series of mechanical models illustrating self reproduction. The blocks in his ....

....bonding condition between and 1 is satisfied, they are bonded again, as shown in Fig. 4. Such reaction processes in Atomoid show how its features differ from other artificial models. First, the reaction 0.968071 0.419281 A 0.478281 5.714773 0.351692 2.859282 B 0.654436 0.132388 0. 512205 4.269322 0.939977 3.282287 C 0.378829 4.983282 0.288201 1.678595 0.356823 0.806595 0.703298 2.633307 D r (k ) Fig. 6 Atoms in simulation. A B C D Fig. 7 Component ratio of atoms. activation energy population 5000 threshold for absorbing photons E f = 0.7 = 6 Table 1 ....

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Eigen, M.: Self-Organization of Matter and the Evolution of Biological Macromolecules, Naturwissenschaften 58, 1971.

.... to understand what Arthur Peacocke has called the causal joint, for the connection between us and God, must be rooted in thermodynamics (Peacocke 1993, 151 60) Of course questions regarding prebiotic evolution and the primordial emergence of life must be thermodynamically based and formulated (Eigen 1971). My own experience in the religion and science dialogue is that there is widespread interest in thermodynamics among colleagues from outside of the sciences as well as among those of us who engage the questions as scientists. Thus, I believe a discussion paper on basic thermodynamics may serve ....

....(relatively simple) self replicating systems can be expected to form structures. Although to leap from there to the claim that we have a window on the fundamentals of biological origins is unwarranted, it would be satisfying at least to say that we can show that it is not an impossible occurrence (Eigen 1971). To make this step we must consider systems far from equilibrium. There the coupling of internal entropy production rates and entropy flux across the system boundary, with the principle of minimum entropy production, has been shown to produce stable states with spatial or time structures. This is ....

Eigen, Manfred. 1971. "Self-organization of Matter and the Evolution of Biological Macromolecules." Die Naturwissenschaften 58 (10):465--519.

....model of an evolutionary dynamics is the Fisher Eigen model which is based on the assumption that competing objects i = 1; n have different reproduction rates V i . These rates play now the role of the fitness. The evolutionary dynamics is given by the differential equations (Fisher, 1930; Eigen, 1971) x i = V i Gamma hV i)x i ; hV i = X i V i x i ; X i x i = 1 ; 6) where x i the fraction of individuals with the genotype i in the population. The species with values better than the social average hV i will succeed in the competition and the others will fail. Finally only the species ....

Eigen, M., 1971, The selforganization of matter and the evolution of biological macromolecules. Naturwiss. 58, 465.

....is the Boltzmann distribution lim t 1 P (x; t) e F (x) Evolutionary Algorithms using a selection scheme adopted from the natural selection of biological systems may realize a Darwin strategy with = 1 and W xy = S xy . The rst term of (1) was introduced by Fisher [9] and Eigen [8] to explain a simple model of Darwinian selection with a reproduction rate related to the mean tness of a population hF i = P F (x)P x . The combination of the strategies 0 (2) generates a new class of Evolutionary Algorithms the Mixed Strategy which shows a improvement in robustness ....

Eigen, M., The selforganization of matter and the evolution of biological macromolecules, Naturwiss. 58 (1971), 465.

....is developed for further changes of the segmentations to achieve global convergence. In contrast to standard genetic algorithms which progress from generation to generation, we adopt the viewpoint of the reactor algorithm (Dittrich Banzhaf, 1998) which permits an analysis similar to Eigen s (1971) molecular evolution model. From this viewpoint, we consider employing cross over at every time step, and present xed point analysis and phase portraits of the competitive dynamics. A problem is that second order interactions like cross over can get stuck in non optimal solutions due to ....

....In the reactor algorithm, strings are sampled at random (like parents for cross over) and t results are put back into the populations at every time step. Using the reactor metaphor, we can draw on the formal analysis of catalytic networks, where similar dynamical systems have been studied (Eigen, 1971, Eigen Schuster, 1978) This paper analyses both simple mutations and cross over as well as mixed systems, and from there a segmentation algorithm is developed that combines the best of both kinds of mutations. For the analysis, the training of neural networks is abstracted as explicitly de ....

Eigen, M. (1971). Selforganization of Matter and the Evolution of Biological Macromolecules. Die Naturwissenschaften 58, 465-523.

....RNA replication in vitro [17] has demonstarted that populations of replicating RNA molecules fulfill all criteria and show all characteristic features of Darwinian evolution. The experimental work was complemented by the development of a kinetic theory of evolution by Manfred Eigen and coworkers [18,19] which provided a proper frame for the description of molecular evolution. After the mechanisms of evolution in vitro had been explored, it was straightforward to search for possible applications in biotechnology. Indeed, techniques based on variation and selection became a powerful tool in the ....

M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58:465--523, 1971.

....of PES thus makes extensive use of differential topology. The analysis of discrete landscapes, on the other hand, requires different techniques. For instance, the critical points of a PES, characterized by rU( R) 0, have no obvious discrete counterpart. It has been known since Eigen s [8, 9] pioneering work on the molecular quasispecies that the dynamics of evolutionary adaptation (optimization) on a landscape depends crucially on the detailed structure of the landscapes itself. Extensive computer simulations [10, 11] have made it very clear that a complete understanding of the ....

.... equation that does not correctly describe some important effects even in the limit of large populations (see [85] for an instructive example) Evolutionary dynamics on rugged landscapes without neutrality, such as the spinglass like models discussed in section 2, are considered for instance in [8, 12, 82]. For small mutation rates p a population is likely to get stuck in local optima for very long times. Populations form localized quasi species around a master sequence . There is a critical mutation rate p et at which diffusion outweighs selection and the 14 P.F. Stadler: Fitness ....

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M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Die Naturwissenschaften, 10:465--523, 1971.

....to test the hypothesis under study, we present the experimental results obtained, and we discuss the insight gained. 2 Quasispecies And Error Thresholds The concept of a quasi species was developed in the context of polynucleotide replication, and in particular studies of early RNA evolution [3], 4] 5] A protein space, 12] or more generally a sequence space, can be modelled as the space of all possible sequences of length drawn from a finite alphabet of size A. Each sequence has a fitness value which specifies its replication rate, or expected number of offspring per unit time. ....

M. Eigen. Self-organization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58:465--523, 1971.

....phenomena of self organization in non living systems. Section 2 outlines the model of the reaction formation system Atomoid. Section 3 describes the reaction rules of Atomoid in detail. Section 4 shows simulation results and presents the emergence of self reproductive hypercycles. Lastly, section 5 discusses those simulation results and the prospects of Atomoid, and then concludes this paper. 2. Atomoid 2.1 Penrose s work and Atomoid L. S. Penrose s work [13] was helpful in modeling Atomoid. Penrose built a series of mechanical models illustrating self reproduction. The blocks in his ....

....the bonding condition between b and g 1 is satisfied, they are bonded again, as shown in Fig. 4. Such reaction processes in Atomoid show how its features differ from other artificial models. First, the reaction 0.968071 0.419281 A 0.478281 5.714773 0.351692 2.859282 B 0.654436 0.132388 0. 512205 4.269322 0.939977 3.282287 C 0.378829 4.983282 0.288201 1.678595 0.356823 0.806595 0.703298 2.633307 D q r (k ) Fig. 6 Atoms in simulation. A B C D Fig. 7 Component ratio of atoms. activation energy population 5000 threshold for absorbing photons DE f = 0.7 y = p 6 Table 1 Parameters of ....

[Article contains additional citation context not shown here]

Eigen, M.: Self-Organization of Matter and the Evolution of Biological Macromolecules, Naturwissenschaften 58, 1971.

....the population should strongly influence the dynamics of evolution: broader populations feel in general smoother landscapes, and hence optimization should easier. Usually the broadness of 20 P.F. Stadler: Linear Operators and Landscapes the population is controlled via the mutation rate [3,33] which at the same time controls the exploration rate. Further investigations are necessary in order to separate the effects of enhanced exploration and implicit smoothing of the underlying landscape caused by an increased mutation rate. It should be kept in mind that the results presented here ....

Eigen M. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58, 465-523 (1971)

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Eigen M. Self-organization of matter and the evolution of biological macromolecules. Naturwissenschaften 1971;58:465--523.

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Eigen, M. (1971) Self-organization of matter and evolution of biological macromolecules, Naturwissenschaften 58, 465--526

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Eigen, M. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 1971, 58, 465--523.

No context found.

Eigen, M. (1971). Self-organization of matter and evolution of biological macromolecules. Naturwissenschaften, 58, 465--523.

No context found.

M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58:465-523, 1971.

No context found.

M. Eigen, "Self-organization of matter and the evolution of biological macromolecules," Naturwissenschaften, Vol.58, pp.465-523, 1971.

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M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Die Naturwissenschaften, 10:465--523, 1971.

No context found.

Eigen M. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58, 465--523 (1971).

No context found.

Eigen M. 1971. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58:465--523.

No context found.

M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 10:465--523, 1971.

No context found.

Eigen, M. (1971). Selforganization of Matter and the Evolution of Biologocal Macromolecules. Naturwissenschaften 58, 465--523.

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