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Plasticity, evolvability, and modularity in RNA
 J EXP ZOOL
, 2000
"... RNA folding from sequences into secondary structures is a simple yet powerful, biophysically grounded model of a genotype–phenotype map in which concepts like plasticity, evolvability, epistasis, and modularity can not only be precisely defined and statistically measured but also reveal simultaneou ..."
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Cited by 102 (3 self)
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RNA folding from sequences into secondary structures is a simple yet powerful, biophysically grounded model of a genotype–phenotype map in which concepts like plasticity, evolvability, epistasis, and modularity can not only be precisely defined and statistically measured but also reveal simultaneous and profoundly nonindependent effects of natural selection. Molecular plasticity is viewed here as the capacity of an RNA sequence to assume a variety of energetically favorable shapes by equilibrating among them at constant temperature. Through simulations based on experimental designs, we study the dynamics of a population of RNA molecules that evolve toward a predefined target shape in a constant environment. Each shape in the plastic repertoire of a sequence contributes to the overall fitness of the sequence in proportion to the time the sequence spends in that shape. Plasticity is costly, since the more shapes a sequence can assume, the less time it spends in any one of them. Unsurprisingly, selection leads to a reduction of plasticity (environmental canalization). The most striking observation, however, is the simultaneous slowdown and eventual halting of the evolutionary process. The reduction of plasticity entails genetic canalization, that is, a dramatic loss of variability (and hence a loss of evolvability) to the point of lockin. The causal bridge between environmental canalization and genetic canalization
The topology of the possible: Formal spaces underlying patterns of evolutionary change
, 2000
"... The current implementation of the NeoDarwinian model of evolution typically assumes that the set of possible phenotypes is organized into a highly symmetric and regular space equipped with a notion of distance, for example, a Euclidean vector space. Recent computational work on a biophysical genoty ..."
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Cited by 73 (25 self)
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The current implementation of the NeoDarwinian model of evolution typically assumes that the set of possible phenotypes is organized into a highly symmetric and regular space equipped with a notion of distance, for example, a Euclidean vector space. Recent computational work on a biophysical genotypephenotype model based on the folding of RNA sequences into secondary structures suggests a rather different picture. If phenotypes are organized according to genetic accessibility, the resulting space lacks a metric and is formalized by an unfamiliar structure, known as a pretopology. Patterns of phenotypic evolution  such as punctuation, irreversibility, modularity  result naturally from the properties of this space. The classical framework, however, addresses these patterns by exclusively invoking natural selection on suitably imposed fitness landscapes. We propose to extend the explanatory level for phenotypic evolution from fitness considerations alone to include the topological st...
Molecular Insights into Evolution of Phenotypes
, 2000
"... re analyzed for RNA secondary structures. Optimization of molecular properties in populations is modeled in silico through replication and mutation in a flow reactor. The approach towards a predefined structure is monitored and reconstructed in terms of an uninterrupted series of phenotypes from ..."
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Cited by 27 (11 self)
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re analyzed for RNA secondary structures. Optimization of molecular properties in populations is modeled in silico through replication and mutation in a flow reactor. The approach towards a predefined structure is monitored and reconstructed in terms of an uninterrupted series of phenotypes from initial stucture to target, called relay series. We give a novel definition of continuity in evolution which identifies discontinuities as major changes in molecular phenotypes. Evolutionary Dynamics  Exploring the Interplay of Accident, Selection, Neutrality, and Function Edited by J. P. Crutchfield and P. Schuster, Oxford Univ. Press 1 2 Evolution of Phenotypes 1 GENOTYPES AND PHENOTYPES Evolutionary optimization in asexually multiplying populations follows Darwin 's principle and is determined by the interplay of two processes which exert counteracting influences on genetic heterogeneity: (i) Mutations increase di
Modelling ’evodevo’ with RNA
 Bioessays
, 2002
"... Introduction Phenotype refers to the physica , organizationa and behaviora expression of an organismduani its ifetime. Genotype refers to a heritab e repository of information that instruYl the produlTj" of moecu es whose interactions, in conjujlzTE with the environment, generate and maintain t ..."
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Cited by 25 (0 self)
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Introduction Phenotype refers to the physica , organizationa and behaviora expression of an organismduani its ifetime. Genotype refers to a heritab e repository of information that instruYl the produlTj" of moecu es whose interactions, in conjujlzTE with the environment, generate and maintain the phenotype. The processes inking genotype to phenotype are known as deve opment. They intervene in the genesis of phenotypic nove ty from genetic mu tation. EvouGYYYxl trajectories therefore depend on deve opment. In tu(( evouG""""l processes shape deve opment, creating a feedback known as "evodevo" 1,2 . The main thruj of this review is to show that some key aspects of this feedback are present even in the microcosm of RNA fo ding. In a narrow sense, the re ation between RNA sequY"jl and their shapes is treated as a prob em in biophysics. Yet, in a wider sense, RNA fo ding can be regarded as a minima mode of a genotypephenotype re ation . The RNA mode is not a representation of organis
Quasiindependence, homology and the unity of type: A topological theory of characters
 J. THEOR. BIOL
, 2002
"... ..."
Recombination Spaces, Metrics, and Pretopologies
 Z. PHYS. CHEM
, 2002
"... The topological features of genotype spaces given a genetic operator have a substantial impact on the course of evolution. We explore the structure of the recombination spaces arising from four different unequal crossover models in the context of pretopological spaces. We show that all four models a ..."
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Cited by 11 (7 self)
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The topological features of genotype spaces given a genetic operator have a substantial impact on the course of evolution. We explore the structure of the recombination spaces arising from four different unequal crossover models in the context of pretopological spaces. We show that all four models are incompatible with metric distance measures due to a lack of symmetry.
A Topological Approach to Chemical Organizations
, 2006
"... Large chemical reaction networks often exhibit distinctive features which can be interpreted as higherlevel structures. Prime examples are metabolic pathways in a biochemical context. In this contribution we review mathematical approaches that exploit the stoichiometric structure, which can be seen ..."
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Cited by 9 (4 self)
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Large chemical reaction networks often exhibit distinctive features which can be interpreted as higherlevel structures. Prime examples are metabolic pathways in a biochemical context. In this contribution we review mathematical approaches that exploit the stoichiometric structure, which can be seen as a particular directed hypergraph, to derive an algebraic picture of chemical organizations. We then give an alternative interpretation in terms of setvalued setfunctions the encapsulate the production rules of the individual reactions. From the mathematical point of view, these functions define generalized topological spaces on the set of chemical species. We show that organizationtheoretic concepts also appear in a natural way in the topological language. This abstract representation in turn suggest to explore the chemical meaning of wellestablished topological concepts. As an example, we consider connectedness in some details.
Spectral Landscape Theory
 Evolutionary Dynamics—Exploring the Interplay of Selection, Neutrality, Accident, and Function
, 1999
"... INTRODUCTION Evolutionary change is caused by the spontaneously generated genetic variation and its subsequent fixation by drift and/or selection. Consequently, the main focus of evolutionary theory has been to understand the genetic structure and dynamics of populations, see e.g. [101]. In recent ..."
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Cited by 7 (3 self)
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INTRODUCTION Evolutionary change is caused by the spontaneously generated genetic variation and its subsequent fixation by drift and/or selection. Consequently, the main focus of evolutionary theory has been to understand the genetic structure and dynamics of populations, see e.g. [101]. In recent years, however, alternative approaches have gained increasing prominence in evolutionary theory. This development has been stimulated to some extent by the application of evolutionary models to designing evolutionary algorithms such as Genetic Al Evolutionary Dynamics edited by J.P. Crutchfield and P. Schuster, 1999 2 Spectral Landscape Theory gorithms, Evolution Strategies, and Genetic Programming, as well as by the theory of Complex Adaptive Systems [69, 79, 38]. The generic structure of an evolutionary model is x 0 = S (x; w) ffi T (x;<F
Approximate Graph Products
, 2008
"... The problem of recognizing approximate graph products arises in theoretical biology. This paper presents an algorithm that recognizes a large class of approximate graph products. The main part of this contribution is concerned with a new, local prime factorization algorithm that factorizes all stron ..."
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Cited by 7 (4 self)
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The problem of recognizing approximate graph products arises in theoretical biology. This paper presents an algorithm that recognizes a large class of approximate graph products. The main part of this contribution is concerned with a new, local prime factorization algorithm that factorizes all strong products on an extensive class of graphs that contains, in particular, all products of trianglefree graphs on at least three vertices. The local approach is linear for graph with fixed maximal degree.