RNA secondary structure folding algorithms predict the existence of connected networks of RNA sequences with identical secondary structures. Fitness landscapes that are based on the mapping between RNA sequence and RNA secondary structure hence have many neutral paths. A neutral walk on these fitness landscapes gives access to a virtually unlimited number of secondary structures that are a single point mutation from the neutral path. This shows that neutral evolution explores phenotype space and can play a role in adaptation. Introduction Ever since Sewall Wright introduced the metaphor of an "adaptive landscape" (Wright, 1932) the view on adaptive evolution has been dominated by that of an uphill walk of a population on a mountainous fitness landscape in which it can get stuck on suboptimal peaks. The neutralist perspective that evolution at the molecular level is dominated by non-adaptive, neutral changes (Kimura, 1983) has hardly changed this picture. A notable exception is Maynard...

Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness among phenotypes, independently of their similarity. Because of neutrality, phenotypes denote equivalence classes of genotypes. The definition of neighborhood relations among phenotypes relies, therefore, on the statistics of neighborhood relations among equivalence classes of genotypes in genotype space. The folding of RNA sequences (genotypes) into secondary structures (phenotypes) is an ideal case to implement these concepts. We study the extent to which the folding of RNA sequences induces a "statistical topology" on the set of minimum free energy secondary structures. The resulting nearness relation suggests a notion of "continuous" structure transformation. We can, then, rationalize major transitions in evolutionary trajectories at the level of RNA structures by identifying those tra...

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 non-independent 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 the...

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

Adleman's [Adl94] successful solution of a seven-vertex instance of the NP-complete Hamiltonian Path problem by recombinant DNA technology initiated the field of biological computing. We propose a very different model of molecular computing based on the biochemistry of RNA editing and RNA translation. In our model, individual molecules become fully capable general purpose computers. 1 Introduction Our goal in this paper is to show how chemically plausible modifications of well-understood biological systems can be used to construct general purpose processors out of individual molecules. To this end, we summarize basic biochemistry in Section 3, in order to make the technological proposals of Sections 4 and 5 understandable. Scientific understanding of the molecular basis for cell biology has grown enormously in recent years. The cell is now understood as a computational system: its program resides in DNA , and its state in the distribution of chemical compounds and electrical charges. ...

Theoretical concepts and experiments dealing with evolution of molecules in vitro reached a state that allows for direct applications to the design of biomolecules with predefined properties. RNA evolution in vitro represents a basis for the development of a new and comprehensive model of evolution focusing on the phenotype and its fitness relevant properties. Relations between genotypes and phenotypes are described by mappings from genotype space onto a space of phenotypes, which are many-to-one and thus give ample room for neutrality as expressed by existence of extended neutral networks in genotype space. The RNA model reduces genotype-phenotype relations to mappings from sequences into secondary structures of minimal free energies and allows for derivation of otherwise inaccessible quantitative results. Continuity and discontinuity in evolution are defined through a new notion of accessibility in phenotype space that provides a basis for straightforward interpretation of computer simulations on RNA optimization and reveal the constructive role of random genomic drift in the search for phenotypes of higher fitness. The effects of population size on the course of evolutionary optimization can be predicted quantitatively by means of a simple stochastic model based on a birth-and-death process with immigration.

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The aptamer database is designed to contain comprehensive sequence information on aptamers and unnatural ribozymes that have been generated by in vitro selection methods. Such data are not normally collected in `natural ' sequence databases, such as GenBank. Besides serving as a storehouse of sequences that may have diagnostic or therapeutic utility, the database serves as a valuable resource for theoretical biologists who describe and explore ®tness landscapes. The database is updated monthly and is publicly available at

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Early papers on biological computing focussed on combinatorial and algorithmic issues, and worked with intentionally oversimplified chemical models. In this paper, we reintroduce complexity to the chemical model by considering the effect problem size has on the initial concentrations of reactants, and the effect this has in turn on the rate of production and quantity of final reaction products. We give a sobering preliminary analyses of Adleman's technique for solving Hamiltonian path. Even on the simplest problems, the annealling phase of Adleman's technique requires time\Omega\Gamma n 2 ) rather than the O(log n) complexity given by a computationally inspired but chemically naive analysis. On more difficult problems, not only does the rate of production of witnessing molecules drop exponentially in problem size, the final yield also drops exponentially. These issues are not objections to biological computing per se, but rather difficulties to be overcome in its development as a v...