| Mathews, D., Sabina, J., Zuker, M. & Turner, D., Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. J. Mol. Biol. 288 (5), 911-940, 1999. |
....and u is the total number of unpaired bases in the loop. Significant e#ort has been expended to determine many of these energy contributions experimentally [21, 23] Other contributions are estimated based on extrapolations from known data or existing databases of naturally occurring structures [17]. More sophisticated models also associate energy contributions with coaxially stacked pairs and other structural features, but we will ignore these here for the sake of simplicity. 3 RNA secondary structure prediction If 10 of protein fold researchers switched to RNA, the problem could be ....
....algorithm, due to Lyngs et al. 16] has running time O(n ) We note that the algorithm exploits the simplified loop energy contributions of the standard thermodynamic model mentioned earlier. Implementations of this algorithm are available on the world wide web as part of the mfold [17] and the Vienna [13] packages. Mathews et al. 17] report that on a large data set of RNA molecules of length up to 700, the algorithm reports 73 of known base pairs. On longer molecules, the prediction accuracy is poorer. Thus, there is certainly room for improvement in the current mfe approach ....
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D.H. Mathews, J. Sabina, M. Zuker, and D.H. Turner, "Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure", J. Molecular Biology, 288, 1999, 911--940.
....of matching parentheses, see Figure 1. As a consequence of their simple graph theoretical form, RNA secondary structures can be predicted from the sequence information by means of a dynamic programming algorithm [10] that makes use of a extensive set of experimental determined energy parameters [11]. Data reported here have been obtained using the Vienna RNA Package [12] For a given chain length n, there are # di#erent RNA sequences, where the alphabet size is # = 2 for GC sequences and # = 4 for natural RNA sequences. An exact enumeration of all possible secondary structure graphs, ....
D.H. Mathews, J. Sabina, M. Zucker, and H. Turner. Expanded sequence dependence of thermodynamic parameters provides robust prediction of RNA secondary structure. J. Mol. Biol., 288:911--940, 1999.
....as loops of zero size. The energy of the secondary structure is the sum of the energy contributions of all loops. Due to the additivity of energy contributions, the minimum free energy can be calculated recursively by dynamic programming [144] The energy parameters were determined experimentally [93], and depend on loop type, loop size and partly on its sequence. For pseudo knots only the H type variant was measured [67] and so this is another obstacle for including this pattern in secondary structures of nucleic acids. Zucker and co workers were the first to formulate the algorithm for the ....
D. Mathews, J. Sabina, M. Zucker, and H. Turner. Expanded sequence dependence of thermodynamic parameters provides robust prediction of RNA secondary structure. J. Mol. Biol., 288:911--940, 1999.
....into nested loops hairpin turns, helices, bulges, two sided internal loops and multi branched internal loops. These loop structures are illustrated in Figure 2. Zuker, et.al [13, 21] has developed algorithms which achieve substantial success in RNA secondary structure prediction. Recent studies [15] show, on average, that 73 of known base pairs on domains of fewer than 700 nucleotides are correctly predicted by these methods. Measurements Hairpin loop Bulge Multibranched loop Stacked pairs Internal loop External base Figure 2: Illustration of substructures in an example RNA structure. ....
D.H. Mathews, J. Sabina, M. Zuker, and D.H. Turner. Expanded sequence dependence of thermodynamic parameters provides robust prediction of RNA secondary structure. J. Mol. Biol., 288:911-940, 1999.
....such pairs demarcate the RNA strand into nested loops hairpin turns, helices, bulges, two sided internal loops and multisided internal loops. Zuker, et.al [2] has developed algorithms which achieve substantial success (on average, 73 of known base pairs on domains of fewer than 700 nucleotides [3]) in RNA secondary structure prediction. Measurements in Turner s laboratory [1] of energy involved in various nucleotide interactions form the basis of the energy function employed. Dynamic programming is used to optimize the secondary structure under the observed energy functions. The ....
D.H. Mathews, J. Sabina, M. Zuker, and D.H. Turner. Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. Journal of Molecular Biology, 288:911-940, 1999.
....that we can calculate the energy of a structure as a sum of independent contributions from each of the loops of the structure. Experimentally determining and estimating the energies of loops in RNA structures has been ongoing work at the Turner Group and the most recent parameters are published in [99]. Based on this model Zuker and Stiegler [167] and Nussinov and Jacobson [112] propose a recursive algorithm for finding the minimum energy of a structure for an RNA sequence s. A structure of this minimum energy can then be determined by backtracking the computations that yielded this energy. ....
.... to be able to compare competing structures of low energies, not to mention the fact that the structure of minimum free energy on average only contains 73 of the base pairs of the true secondary structure while a near optimal structure often exists containing more of the true base pairs, cf. [99]. Zuker [164] proposes a base pair oriented method for finding suboptimal structures. Just as we can calculate the energy of an optimal structure of the subsequence s[i. j] of an RNA sequence s with the restriction that the structure contains i j, we can calculate the energy of an optimal ....
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D. H. Mathews, J. Sabina, M. Zuker, and D. H. Turner. Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. Journal of Molecular Biology, 288:911--940,
....on the mathematical structure of the free energy functions, and the second step is to determine the proper parameters of the free energy functions. Performing experiments to estimate the energies of the various types of loops in RNA structures is ongoing work. Recent results are published in [134]. Using a loop dependent free energy function, Zuker and Stiegler in [213] and Nussinov and Jacobsen in [154] present a recursive algorithm that finds the minimum free energy of a secondary structure of an RNA sequence S of length n in time O(n ) An optimal structure of S, i.e. a secondary ....
....about a reasonable cuto# size without increasing the asymptotic running time. Free energy minimization methods to predict the secondary structure of an RNA molecule based on its primary structure are useful, but unfortunately they seldom predict the true secondary structure. Mathews et al. in [134] report that on average only 73 percent of the base pairs in the true secondary structure are found in a secondary structure predicted by free energy minimization methods, while a secondary structure that contains more true base pairs is usually found among the structures with energy close to the ....
D. H. Mathews, J. Sabina, M. Zuker, and D. H. Turner. Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. Journal of Molecular Biology, 288:911--940, 1999.
....states, the result is a free energy that can be split into an enthalpic and an entropic term. G = H T S (3) The standard set of energy parameters is measured for T = 37 C, but can be extrapolated using the temperature dependence of the free energy. The most recent compilation can be found in [89]. 32 The Vienna RNA Package consists of several algorithms. As the most basic, RNAfold takes an input sequence and calculates its minimum free energy structure, on request also the partition function and the base pair probability matrix. It returns the mfe structure in bracket notation, together ....
....kcal mole) The used program takes into account coaxial stacking by reevaluating the energy of structures by means of a more complex multiloop energy function (for n 6) GML = a b 6 1:75RT ln(n=6) c k G Stacking (4) a = 10.1;b = 0.3; c = 0. 3 kcal mole; parameters compiled in [89]) G stacking includes the favourable free energy of coaxial stacking and terminal mismatch or dangling end stacking as described above. Coaxial stacking leads to a relevant improvement of the accuracy of secondary structure prediction. For molecules with multi branched loops, like tRNAs, the ....
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D. H. Mathews, J. Sabina, M. Zuker, and D. Turner. Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. JMB, 288:911-940, 1999.
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Mathews, D., Sabina, J., Zuker, M. & Turner, D., Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. J. Mol. Biol. 288 (5), 911-940, 1999.
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Mathews, D., Sabina, J., Zuker, M. and Turner, D., Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. Journal of Molecular Biology, 288:911-940, 1999.
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Mathews, D.H., Sabina, J., Zucker, M., and Turner, H., Expanded sequence dependence of thermodynamic parameters provides robust prediction of RNA secondary structure, J. Mol. Biol., 288:911--940, 1999.
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Mathews, D. H., Sabina, J., Zuker, M. & Turner, D. H. (1999). Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. J. Mol. Biol., 288, 911--940.
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Mathews, D., Sabina, J., Zuker, M., Turner, H.: Expanded sequence dependence of thermodynamic parameters provides robust prediction of RNA secondary structure. J. Mol. Biol. 288 (1999) 911--940
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D. Mathews, J. Sabina, M. Zuker, and H. Turner. Expanded sequence dependence of thermodynamic parameters provides robust prediction of RNA secondary structure. J. Mol. Biol., 288:911--940, 1999.
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D. H. Mathews, S. Jerey, Z. Michael, and D. H. Turner. Expanded sequence dependence of thermodynamic parameters improves prediction of rna secondary structure. J.Mol.Biol., 288:911-940, 1999.
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D. Mathews, J. Sabina, M. Zucker, and H. Turner. Expanded sequence dependence of thermodynamic parameters provides robust prediction of RNA secondary structure. J. Mol. Biol., 288:911--940, 1999.
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D. H. Mathews, J. Sabina, M. Zuker, D. H. Turner, Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure, J. Mol. Biol. 288 (1999) 911--940.
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D. Mathews, J. Sabina, M. Zuker, and H. Turner. Expanded sequence dependence of thermodynamic parameters provides robust prediction of RNA secondary structure. J. Mol. Biol., 288:911--940, 1999.
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Mathews, D. H., J. Sabina, M. Zuker and D.H. Turner (1999). Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure, J. Mol. Biol., 288:911--940.
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Mathews,D.H., Sabina,J., Zuker,M. and Turner,D.H. (1999) Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. J. Mol. Biol., ###, 911940.
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Matthews,D.H., Sabina,J., Zuker,M. and Turner,D.H. (1999) Expanded sequence dependence on thermodynamic parameters improves prediction of RNA secondary structure. J. Mol. Biol., ###, 911940.
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Mathews, D., J. Sabina, M. Zucker, and H. Turner: 1999, `Expanded Sequence Dependence of Thermodynamic Parameters Provides Robust Prediction of RNA Secondary Structure'. J. Mol. Biol. 288, 911--940.
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Mathews, D., J. Sabina, M. Zucker, and H. Turner: 1999, `Expanded Sequence Dependence of Thermodynamic Parameters Provides Robust Prediction of RNA Secondary Structure'. J. Mol. Biol. 288, 911--940.
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D. H. Mathews, J. Sabina, M. Zuker, and D. H. Turner. Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. d. Mol. Biol., 288(5):91140, May 21 1999.
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D.H. Mathews, J. Sabina, M. Zuker, and D.H. Turner. Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. Journal of Molecular Biology, 288:911--940, 1999.
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