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September 25, 2009
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September 25, 2009
Abstract
The perspective of this paper is to compare mathematical models for the evolutionary dynamics of genomes and languages. The quasispecies equation describes the evolution of genetic sequences under the influence of mutation and selection. A central result is an error threshold which specifies the minimum replication accuracy required for maintaining genetic information of a certain length. The language equation describes the evolution of communication, including the cultural evolution of grammar and the biological evolution of universal grammar. A central result is a coherence threshold which specifies certain conditions that universal grammar has to fulfill in order to induce coherent communication in a population.
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September 25, 2009
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The population dynamics of macromolecules that reproduce by means of template-directed ligation of two fragments are shown to be represented by a replicator equation with a special non-linear response function. This result is obtained through detailed consideration of the mechanism of ligation autocatalysis. In contrast to treatments which involve simplification to a parabolic growth law and the expectation of global coexistence of all species, we find that strong selection can take place in such systems, even when there is slow uncatalysed synthesis of replicators. Also, systems of this type are subject to invasion by new species that have a selective advantage. An expression is derived for the survival threshold in terms of species parameters and it is shown that this threshold depends on the total concentration of all species in the system. For a plausible distribution of species parameters, the number of surviving species coexisting above the threshold increases monotonically with increasing concentration. Illustrative numerical simulations are presented.
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September 25, 2009
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A conjecture of Eigen and Schuster (1979) concerning the competitive exclusion of disjoint hypercycles is finally proved.
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September 25, 2009
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A chemical autonomous agent is defined as a reproducing molecular system that carries out a thermodynamic work cycle, reminiscent of the earliest prebiotic replicators that harnessed free energy. The efficiency with which free energy is utilized to promote replication is a measure of the selective fitness of such a system. Simulations of the operation of a typical autonomous agent over a wide range of possible parameter settings reveals a fitness landscape with a well-defined maximum and a variety of features that are amenable to interpretation in terms of evolutionary concepts.
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Adenosine triphosphate (ATP) is a key compound in the energy metabolism of cells and is required to drive vital biochemical reactions. In heterotrophic organisms ATP production is coupled to the degradation of energy-rich organic material taken up from the environment. In the transfer of the environmental energy to cellular processes heterotrophs face a tradeoff, since the conversion of the environmental energy into ATP cannot be both maximally fast and efficient. Here we show how tradeoffs between rate and yield of ATP production arise firstly from thermodynamical principles, and secondly for the ATP production by respiration and fermentation. Using methods derived from game theory and population dynamics we investigate the evolutionary consequences for both tradeoffs. We show that spatially structured environments enable the evolution of efficient pathways with high yield. The strategies of ATP production realized in a population, however, depend on the quantitative properties of the tradeoffs.
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September 25, 2009
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In this paper we demonstrate how ideas from thermodynamics as well as evolutionary biology can be combined to form powerful optimization strategies. These strategies however introduce new parameters to an already parameter dependent optimization task. By testing the introduced strategies with numerous optimization parameter settings for three model problems we develop a semi-automatic parameter adaption which allows an easy control of the free search parameters for potential users.
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September 25, 2009
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Biological evolution is a multilevel process and should be studied as such. A first, important step in studying evolution in this way has been the work of Peter Schuster and co-workers on RNA evolution. For RNA the genotype-phenotype mapping can be calculated explicitly. The resulting evolutionary dynamics is dominated by neutral paths, and the potential of major change by a single point mutation. Examining whole genomes, of which about 60 are now available, we see that gene content of genomes is changing relatively rapidly: gene duplication, gene loss and gene generation is ubiquitous. In fact, it seems that point-mutations play a relatively minor role, relative to changes in gene regulation and gene content in adaptive evolution. Large scale micro-array studies, in which the expression of every gene can be measured simultaneously, give a first glimpse of the `division of labor´ between duplicated genes. A preliminary analysis suggests that differential expression is often the primary event which allows duplicated genes to be maintained in a genome, but alternate routes also exist, most notably on the one hand the mere need of a lot of product, and on the other hand differentiation within multi-protein complexes consisting of homologous genes. I will discuss these results in terms of multilevel evolution. in particular in terms of information integration and the alternatives of `individual based´ versus `population based´ diversity.
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September 25, 2009
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In biotechnics microsystems have been introduced primarily for analytical purpose in the past few years. Recently miniaturised microtiterplates, so called nanotiterplates, as efficient tools in screening have been discussed. In a case study we demonstrate the application of cell-free translation or transcription/translation and nucleic acid amplification in such nanotiterplates. The results show the potential range of applications of nanotiterplates for biotechnology even for biochemical systems, which have not been discussed as miniaturisable in screening.
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September 25, 2009
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A realization of the ladder operators for the 1D Morse potential is presented. These operators satisfy the SU(2) group. The case of anisotropic 3D Morse potential is also discussed if it can be regarded as three 1D Morse potential. The average values of some observables in the coherent states are also calculated.
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