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 ....

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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 ....

[Article contains additional citation context not shown here]

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.

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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.

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

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

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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.

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

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