Barrier heights between ground states in a model of RNA secondary structure

Secondary structure formation is an important factor influencing the behaviour of many types of naturally occurring RNA molecules. RNA secondary structure also provides an example of a disordered system showing frustration and a rugged energy landscape with many alternative ground states. We use a numerical method to estimate energy barrier heights between a set of alternative ground-state structures of a given sequence. Both the mean barrier height and the maximum barrier height for a given sequence scale with a sequence length N approximately as . The matrix h of barriers is exactly ultrametric, which means that structures form an exactly hierarchical set of clusters based on barrier heights. The matrix of distances d between structures is correlated with h, but with large fluctuations. Hence, the d matrix is approximately ultrametric, but the clustering of structures based on distances is not perfectly hierarchical. Certain base pairs are observed to be present in every ground-state structure. These `frozen' pairs divide the molecule up into mutually inaccessible pieces. All of the separate pieces contribute to determining the distance between structures, but only the largest piece will contribute to the barrier height. The length of the largest piece varies between sequences, and scales in proportion to N on average. We compare these results with studies of other disordered systems, and discuss the consequences for the folding of naturally occurring RNAs.

[1]  R. Nussinov,et al.  Fast algorithm for predicting the secondary structure of single-stranded RNA. , 1980, Proceedings of the National Academy of Sciences of the United States of America.

[2]  A. P. Young,et al.  Low-temperature behavior of the infinite-range Ising spin-glass: Exact statistical mechanics for small samples , 1982 .

[3]  A. P. Young,et al.  Lack of Ergodicity in the Infinite-Range Ising Spin-Glass , 1982 .

[4]  Richard G. Palmer,et al.  Broken ergodicity in spin glasses , 1983 .

[5]  I. Morgenstern.  Numerical simulations of spin glasses , 1983 .

[6]  A P Young,et al.  Statics and dynamics of the infinite-range Ising spin glass model , 1983 .

[7]  S. Kirkpatrick,et al.  Configuration space analysis of travelling salesman problems , 1985 .

[8]  D. Turner,et al.  Improved free-energy parameters for predictions of RNA duplex stability. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Temple F. Smith,et al.  Rapid dynamic programming algorithms for RNA secondary structure , 1986 .

[10]  G. Toulouse,et al.  Ultrametricity for physicists , 1986 .

[11]  D. Sherrington,et al.  Graph bipartitioning and statistical mechanics , 1987 .

[12]  Bernardo A. Huberman,et al.  Complexity and ultradiffusion , 1987 .

[13]  Transition to anomalous relaxation: Localization in a hierarchical potential. , 1988, Physical review letters.

[14]  Dynamics on ultrametric spaces with random transfer rates. , 1989 .

[15]  A. Young,et al.  Ultrametricity in the infinite-range Ising spin glass , 1989 .

[16]  B. Gu,et al.  Calculation of the angular correlation and the lifetime of positron surface states on metal surfaces , 1989 .

[17]  N. Parga,et al.  Ultrametricity, frustration and the graph colouring problem , 1989 .

[18]  Eugene I. Shakhnovich,et al.  Enumeration of all compact conformations of copolymers with random sequence of links , 1990 .

[19]  Fernández,et al.  Activation-energy landscape for metastable RNA folding. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[20]  Glassy kinetic barriers between conformational substates in RNA. , 1990, Physical review letters.

[21]  J. McCaskill.  The equilibrium partition function and base pair binding probabilities for RNA secondary structure , 1990, Biopolymers.

[22]  D. Turner,et al.  A comparison of optimal and suboptimal RNA secondary structures predicted by free energy minimization with structures determined by phylogenetic comparison. , 1991, Nucleic acids research.

[23]  A Model of Directed Walks with Random Self-Interactions , 1992 .

[24]  Structural and ultrametric properties of (L-alanine)20 , 1993, cond-mat/9303022.

[25]  Paul Higgs,et al.  RNA secondary structure: a comparison of real and random sequences , 1993 .

[26]  Walter Fontana,et al.  Fast folding and comparison of RNA secondary structures , 1994 .

[27]  P. Higgs.  Thermodynamic properties of transfer RNA: a computational study , 1995 .

[28]  D. Yee,et al.  Principles of protein folding — A perspective from simple exact models , 1995, Protein science : a publication of the Protein Society.

[29]  Newman,et al.  Broken ergodicity and the geometry of rugged landscapes. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  A R Panchenko,et al.  Foldons, protein structural modules, and exons. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[31]  Ground-state structure in a highly disordered spin-glass model , 1995, adap-org/9505005.

[32]  Higgs.  Overlaps between RNA secondary structures. , 1996, Physical review letters.

[33]  Paul Higgs,et al.  Evidence for kinetic effects in the folding of large RNA molecules , 1996 .

[34]  Robustness and efficiency in inverse protein folding , 1997 .