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Volumn 280, Issue 5368, 1998, Pages 1451-1455

Continuity in evolution: On the nature of transitions

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CELL POPULATION; EVOLUTION; PHENOTYPE; PRIORITY JOURNAL; PROTEIN FOLDING; PROTEIN SECONDARY STRUCTURE; RNA SEQUENCE; SEQUENCE HOMOLOGY;

EID: 0032577365     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.280.5368.1451     Document Type: Article
Times cited : (351)

References (39)
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    • note
    • Let i, j, k, and I denote positions of bases in the linear sequence and (i, j) denote a base pair. The secondary structure of an RNA sequence is defined as the set P of allowed base pairs (here Watson-Crick pairs plus GU) that minimize free energy, subject to a no-knot condition requiring that if (i, J) and (k, l) are both in P, then i < k < j implies i < l < j (that is, base pairs do not cross). The secondary structure is computed with our implementation (10) of a dynamic programming algorithm, originally from (21), which is widely used in laboratories to assist in the prediction of secondary structures. The procedure is based on empirical energy parameters (22).
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    • The same phenomenon has been observed in optimization problems of a quite different nature, such as the evolution of particle-based computation in cellular automata with the use of genetic algorithms (23).
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    • The shape α itself occurs in every sequence neighborhood of the a sample (omitted from Fig. 2). This reflexivity of the nearness relation is the topological way of expressing neutrality.
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    • Coarse-grained shapes are derived from secondary structures by ignoring the size of stacks and loops, keeping only their relative arrangement. Our tRNA boundary sample (see legend to Fig. 2A) contained 5882 coarse-grained shapes. A pool of 11,000 random sequences yielded 1578 distinct coarse-grained shapes, 90.4% of which were found in the tRNA boundary.
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    • An example for a discontinuous transition of type i is the formation of a multiloop (a loop issuing more than two stacking regions). Generally, the free energy gain upon formation of a stack must offset the free energy loss from the loop caused by it. A stack closing a multiloop must, therefore, come into existence with some minimum length (typically more than 5 base pairs) in a single step. Likewise, the discontinuity of generalized shifts (type ii) has thermodynamic and structural origins. Shifting a stack by sequentially shifting its base pairs in random order would cause severe sterical conflicts, besides violating the formal no-knot condition. As a consequence, the shifting of a stack requires that all base pairs move synchronously.
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    • Most, but not all, phenotypes on the path are highly populated. A path inferred from the fossil record almost certainly misses the low populated ones.
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    • note
    • Financial support was provided by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung (Projects P-10578 and P-11065), by HASA Laxenburg, Austria, by the Commission of the European Union (Contract Study PSS*0884), and by the integrative core research at the Santa Fe Institute.


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