RNA Shape Space Topology

2000 ◽  
Vol 6 (1) ◽  
pp. 3-23 ◽  
Author(s):  
Jan Cupal ◽  
Stephan Kopp ◽  
Peter F. Stadler

The distinction between continuous and discontinuous transitions is a long-standing problem in the theory of evolution. Because continuity is a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the probabilities with which one phenotype is accessible from another through changes at the genotypic level. The shape space of RNA secondary structures is used to illustrate this approach. We show that evolutionary trajectories are continuous if and only if they follow connected paths in phenotype space.

Genetics ◽  
1996 ◽  
Vol 144 (1) ◽  
pp. 419-426 ◽  
Author(s):  
Wolfgang Stephan

Abstract A two-locus model is presented to analyze the evolution of compensatory mutations occurring in stems of RNA secondary structures. Single mutations are assumed to be deleterious but harmless (neutral) in appropriate combinations. In proceeding under mutation pressure, natural selection and genetic drift from one fitness peak to another one, a population must therefore pass through a valley of intermediate deleterious states of individual fitness. The expected time for this transition is calculated using diffusion theory. The rate of compensatory evolution, kc, is then defined as the inverse of the expected transition time. When selection against deleterious single mutations is strong, kc, depends on the recombination fraction r between the two loci. Recombination generally reduces the rate of compensatory evolution because it breaks up favorable combinations of double mutants. For complete linkage, kc, is given by the rate at which favorable combinations of double mutantS are produced by compensatory mutation. For r > 0, kc, decreases exponentially with r. In contrast, kc, becomes independent of r for weak selection. We discuss the dynamics of evolutionary substitutions of compensatory mutants in relation to Wright'S shifting balance theory of evolution and use our results to analyze the substitution process in helices of mRNA secondary structures.


RNA ◽  
2016 ◽  
Vol 22 (11) ◽  
pp. 1739-1749 ◽  
Author(s):  
Knut I. Kristiansen ◽  
Ragnhild Weel-Sneve ◽  
James A. Booth ◽  
Magnar Bjørås

2016 ◽  
Vol 31 (3) ◽  
pp. 78-85 ◽  
Author(s):  
Qingfeng Chen ◽  
Yi-Ping Phoebe Chen ◽  
Chengqi Zhang

PLoS ONE ◽  
2011 ◽  
Vol 6 (6) ◽  
pp. e20561 ◽  
Author(s):  
Paul M. Krzyzanowski ◽  
Feodor D. Price ◽  
Enrique M. Muro ◽  
Michael A. Rudnicki ◽  
Miguel A. Andrade-Navarro

Biochimie ◽  
2011 ◽  
Vol 93 (11) ◽  
pp. 2019-2023 ◽  
Author(s):  
Sven Findeiß ◽  
Jan Engelhardt ◽  
Sonja J. Prohaska ◽  
Peter F. Stadler

2018 ◽  
Vol 13 (5) ◽  
pp. 450-460 ◽  
Author(s):  
Xingli Guo ◽  
Lin Gao ◽  
Yu Wang ◽  
David K.Y. Chiu ◽  
Bingbo Wang ◽  
...  

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