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T. J. M. Schopf, Ed. Freeman, San Francisco, CA
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N. Eldredge and S. J. Gould, in Models in Paleobiology, T. J. M. Schopf, Ed. (Freeman, San Francisco, CA, 1972), pp. 82-115; S. J. Gould and N. Eldredge, Nature 366, 223 (1993); S. F. Elena, V. S. Cooper, R. E. Lenski, Science 272, 1802 (1996).
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Models in Paleobiology
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Eldredge, N.1
Gould, S.J.2
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2
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0027790582
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N. Eldredge and S. J. Gould, in Models in Paleobiology, T. J. M. Schopf, Ed. (Freeman, San Francisco, CA, 1972), pp. 82-115; S. J. Gould and N. Eldredge, Nature 366, 223 (1993); S. F. Elena, V. S. Cooper, R. E. Lenski, Science 272, 1802 (1996).
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Gould, S.J.1
Eldredge, N.2
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3
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N. Eldredge and S. J. Gould, in Models in Paleobiology, T. J. M. Schopf, Ed. (Freeman, San Francisco, CA, 1972), pp. 82-115; S. J. Gould and N. Eldredge, Nature 366, 223 (1993); S. F. Elena, V. S. Cooper, R. E. Lenski, Science 272, 1802 (1996).
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Elena, S.F.1
Cooper, V.S.2
Lenski, R.E.3
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4
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2642619573
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note
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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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5
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84974325243
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S. Spiegelman, Q. Rev. Biophys. 4, 213 (1971); G. F. Joyce, Gene 82, 83 (1989); A. D. Ellington and J. W. Szostak, Nature 346, 818 (1990); A. A. Beaudry and G. F. Joyce, Science 257, 635 (1992); D. P. Bartel and J. W. Szostak, ibid. 261, 1411 (1993).
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Q. Rev. Biophys.
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Spiegelman, S.1
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6
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0024443885
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S. Spiegelman, Q. Rev. Biophys. 4, 213 (1971); G. F. Joyce, Gene 82, 83 (1989); A. D. Ellington and J. W. Szostak, Nature 346, 818 (1990); A. A. Beaudry and G. F. Joyce, Science 257, 635 (1992); D. P. Bartel and J. W. Szostak, ibid. 261, 1411 (1993).
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Gene
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Joyce, G.F.1
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7
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0025074907
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S. Spiegelman, Q. Rev. Biophys. 4, 213 (1971); G. F. Joyce, Gene 82, 83 (1989); A. D. Ellington and J. W. Szostak, Nature 346, 818 (1990); A. A. Beaudry and G. F. Joyce, Science 257, 635 (1992); D. P. Bartel and J. W. Szostak, ibid. 261, 1411 (1993).
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Nature
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Ellington, A.D.1
Szostak, J.W.2
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8
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0026649231
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S. Spiegelman, Q. Rev. Biophys. 4, 213 (1971); G. F. Joyce, Gene 82, 83 (1989); A. D. Ellington and J. W. Szostak, Nature 346, 818 (1990); A. A. Beaudry and G. F. Joyce, Science 257, 635 (1992); D. P. Bartel and J. W. Szostak, ibid. 261, 1411 (1993).
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Science
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Beaudry, A.A.1
Joyce, G.F.2
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9
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0027488624
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S. Spiegelman, Q. Rev. Biophys. 4, 213 (1971); G. F. Joyce, Gene 82, 83 (1989); A. D. Ellington and J. W. Szostak, Nature 346, 818 (1990); A. A. Beaudry and G. F. Joyce, Science 257, 635 (1992); D. P. Bartel and J. W. Szostak, ibid. 261, 1411 (1993).
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Science
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Bartel, D.P.1
Szostak, J.W.2
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13
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2642714303
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note
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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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14
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2642683359
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The folding of RNA sequences is notoriously redundant (24)
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The folding of RNA sequences is notoriously redundant (24).
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15
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2642648825
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note
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In RNA folding, some shapes are realized much more frequently than others (11, 25). They were termed common shapes (26), and our statements, based on statistics, can be expected to hold only for these common shapes.
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16
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34249772381
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A public domain version of the Vienna RNA package
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I. L. Hofacker et al., Monatsh. Chem. 125, 167 (1994). A public domain version of the Vienna RNA package is available at www.tbi.univie.ac.at. An RNA folding server can be accessed at www.tbi. univie.ac.at/cgi-bin/RNAfold.cgi. Upon typing in an RNA sequence the following information can be obtained: the minimum free energy secondary structure, the partition function and the matrix of base pairing probabilities computed from the Boltzmann ensemble, and the complete set of suboptimal folds in the vicinity of the minimum free energy.
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(1994)
Monatsh. Chem.
, vol.125
, pp. 167
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Hofacker, I.L.1
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17
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34249772381
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An RNA folding server can be accessed
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I. L. Hofacker et al., Monatsh. Chem. 125, 167 (1994). A public domain version of the Vienna RNA package is available at www.tbi.univie.ac.at. An RNA folding server can be accessed at www.tbi. univie.ac.at/cgi-bin/RNAfold.cgi. Upon typing in an RNA sequence the following information can be obtained: the minimum free energy secondary structure, the partition function and the matrix of base pairing probabilities computed from the Boltzmann ensemble, and the complete set of suboptimal folds in the vicinity of the minimum free energy.
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18
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0028196714
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P. Schuster, W. Fontana, P. F. Stadler, I. L. Hofacker, Proc. R. Soc. London Ser. B Biol. Sci. 255, 279 (1994).
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Proc. R. Soc. London Ser. B Biol. Sci.
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Schuster, P.1
Fontana, W.2
Stadler, P.F.3
Hofacker, I.L.4
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20
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2642709389
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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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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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21
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2642715098
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note
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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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22
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2642638954
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note
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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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23
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2642640620
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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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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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24
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2642615559
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The shapes on the evolutionary path, including an "active" version of Fig. 1A, and additional information and www.tbi.univie.ac.at/~walter/RNA/punct.html
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The shapes on the evolutionary path, including an "active" version of Fig. 1A, and additional information are available at www.santafe.edu/~walter/RNA/punct.html and www.tbi.univie.ac.at/~walter/RNA/punct.html.
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25
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2642710220
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note
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The average number of replication events per time unit depends on the average replication rate constant in the population. The plateaus preceding events a and b had a duration comparable to those preceding events g and h, but during the former about 4300 replications occurred per time unit, whereas during the latter this number rose to 10,800.
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26
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2642609630
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note
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Discontinuous transitions may trigger a cascade of continuous events. On a few occasions, continuous transitions hitchhike on discontinuous ones. For example, a major rearrangement, such as a double flip, may involve the simultaneous elongation of a stack formed in the event.
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28
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0002213113
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Puglisi, J.D.2
Florentz, C.3
Giegé, R.4
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35
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0027180473
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J. Pütz, J. D. Puglisi, C. Florentz, R. Giegé, Science 252, 1696 (1991); M. Sassanfar and J. W. Szostak, Nature 364, 550 (1993); H. Komiyama, G. Miyazaki, J. Tame, K. Nagai, ibid. 373, 244 (1995).
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Sassanfar, M.1
Szostak, J.W.2
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J. Pütz, J. D. Puglisi, C. Florentz, R. Giegé, Science 252, 1696 (1991); M. Sassanfar and J. W. Szostak, Nature 364, 550 (1993); H. Komiyama, G. Miyazaki, J. Tame, K. Nagai, ibid. 373, 244 (1995).
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Komiyama, H.1
Miyazaki, G.2
Tame, J.3
Nagai, K.4
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39
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2642643106
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note
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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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