Abstract
There are many examples of RNA molecules in which the secondary structure has been strongly conserved during evolution, but the base sequence is much less conserved, e.g., transfer RNA, ribosomal RNA, and ribonuclease P. A model of compensatory neutral mutations is used here to describe the evolution of the base sequence in RNA helices. There are two loci (i.e., the two sides of the pair) with four alleles at each locus (corresponding to A, C., G, U). Watson-Crick base pairs (AU, CG, GC, and UA) are each assigned a fitness 1, whilst all other pairs are treated as mismatches and assigned fitness 1-s. A population of N diploid individuals is considered with a mutation rate of u per base. For biologically reasonable parameter values, the frequency of mismatches is always small but the frequency of the four matching pairs can vary over a wide range. Using a diffusion model, the stationary distribution for the frequency x of any of the four matching pairs is calculated. The shape depends on the combination of variables β = 8Nu2/9s. For small β, the distribution diverges at the two extremes, x = 0 and x = 1-z, where z is the mean frequency of mismatches. The population typically consists almost entirely of one of the four types of matching pairs, but occasionally makes shifts between the four possible states. The mean rate at which these shifts occur is calculated here. The effect of recombination between the two loci is to decrease the probability density at intermediate x, and to increase the weight at the extremes. The rate of transition between the four states is slowed by recombination (as originally shown by Kimura in a two-allele model with irreversible mutation). A very small recombination rate r ∼ u2/s is sufficient to increase the mean time between transitions dramatically. In addition to its application to RNA, this model is also relevant to the’ shifting balance’ theory describing the drift of populations between alternative equilibria separated by low fitness valleys. Equilibrium values for the frequencies of the different allele combinations in an infinite population are also calculated. It is shown that for low recombination rates the equilibrium is symmetric, but there is a critical recombination rate above which alternative asymmetric equilibria become stable.
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References
Barton, N., 1989. The divergence of a polygenic system subject to stabilizing selection, mutation and drift. Genet. Res. Camb. 54: 59–77.
Barton, N. & S. Rouhani, 1993. Adaptation and the shifting balance. Genet. Res. Camb. 61: 57–74.
Brown, J.W., 1997. The Ribonuclease P database. Nucl. Acids Res. 25: 263–264. Database available at http://jwbrown.mbio.ncsu.edu/RNaseP/home.html
Crow, J.F. & M. Kimura, 1970. An Introduction to Population Genetics Theory. Harper and Row, New York.
Damberger, S.H. & R.R. Gutell, 1994. A comparative database of Group I intron structures. Nucl. Acids Res. 22: 3508–3510. Data base available at http://www.pundit.colorado.edu:8080/RNA.
Eigen, M., B.F. Lindemann, M. Tietze, R. Winkler-Oswatitsch, A. Dress, & A. von Haeseler, 1989. How old is the genetic code? Statistical geometry in sequence space provides an answer. Science 244: 672–679.
Eigen, M., J. McCaskill & P. Schuster, 1989. The molecular quasispecies. Adv. Chem. Phys. 75: 149–263.
Forst, C.V., C. Reidys & J. Weber, 1995. Neutral networks as mod el landscapes for RNA secondary structure folding landscapes. Proceedings of the Third European Conference on Artificial Life. Lecture Notes in Artificial Intelligence, 929: 128–147.
Gutell, R.R., 1994. Collection of small subunit ribosomal RNA structures. Nucl. Acids Res. 22: 3502–3507. Database available at http://www.pundit.colorado.edu:8080/RNA.
Hastings, A., 1985. Four simultaneously stable polymorphic equilibria in two-locus two-allele selection models. Genetics 109: 255–261.
Higgs, P.G., 1995. Thermodynamic properties of transfer RNA: a computational study. J. Chem. Soc. Faraday Transactions 91: 2531–2540.
Huynen, M., P.F. Stadler & W. Fontana, 1996. Smoothness within ruggedness: the role of neutrality in adaptation. Proc. Nat. Acad. Sci. USA, 93: 397–401.
Karlin, S., 1975. General two-locus selection models: some objec tives, results and interpretations. Theor. Pop. Biol. 7: 364–398.
Kimura, M., 1985. The role of compensatory neutral mutations in molecular evolution. J. Genet. 64: 7–19.
Michalakis, Y., & M. Slatkin, 1996. Interaction of selection and recombination in the fixation of negative-epistatic genes. Genet. Res. Camb. 67: 257–269.
Morgan, S.R., & P.G. Higgs, 1996. Evidence for Kinetic Effects in the Folding of Large RNA Molecules. J. Chem. Phys. 105: 7152–7157.
Muse, S., 1995. Evolutionary analysis of DNA sequences subject to constraints on secondary structure. Genetics 139: 1429–1439.
Phillips, P.C., 1996. Waiting for a compensatory mutation: phase zero of the shifting balance process. Genet. Res. Camb. 67: 271–283.
Rousset, F., M. Pelandakis & M. Solignac, 1991. Evolution of compensatory substitutions through GU intermediate state in Drosophila rRNA. Proc. Nat. Acad. Sci. USA 88: 10032–10036.
Rzhetsky, A., 1995. Estimating substitution rates in ribosomal RNA genes. Genetics 141: 771–783.
Sprinzl, M., C. Steegborn, F. Hubel & S. Steinberg, 1996. Com pilation of transfer RNA sequences and sequences of transfer RNA genes. Nucl. Acids Res. 24: 68–72. Database available at http://www.embl-heidelberg.de/pub/databases/trna
Steinberg, S., A. Misch & M. Sprinzl, 1993. Compilation of tRNA sequences. Nucl. Acids Res. 21: 301. Database available at http://www.embl-heidelberg.de/pub/databases/trna
Stephan, W., 1996. The rate of compensatory evolution. Genetics 144: 419–426.
Tillier, E.R.M., & R.A. Collins, 1995. Neighbour joining and maxi mum likelihood with RNA sequences: addressing the interdepen dence of sites. Mol. Biol. Evol. 12: 7–15.
Van de Peer, Y., J. Jansen, P. De Rijk, & R. De Wachter, 1997. Database on structure of small ribosomal subunit RNA. Nucl. Acids Res. 24: 114–116. Database available at http://rrna.uia.ac.be/ssu/index.html
Wiehe, T., E. Baake & P. Schuster, 1995. Error propagation in reproduction of diploid organisms. J. Theor. Biol. 177: 1–15.
Woese, C.R. & N.R. Pace, 1993. Probing RNA structure, function and history by comparative analysis, pp. 91–117 in The RNA World, edited by R.F. Gesteland & J.F. Atkins. Cold Spring Harbor Laboratory Press.
Wright, S., 1977. Evolution and the Genetics of Populations, Vol. 3. University of Chicago Press.
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Higgs, P.G. (1998). Compensatory neutral mutations and the evolution of RNA. In: Woodruff, R.C., Thompson, J.N. (eds) Mutation and Evolution. Contemporary Issues in Genetics and Evolution, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5210-5_9
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DOI: https://doi.org/10.1007/978-94-011-5210-5_9
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