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An Iterated loop matching approach to the prediction of RNA secondary structures with pseudoknots
, 2004
"... Motivation: Pseudoknots have generally been excluded from the prediction of RNA secondary structures due to its difficulty in modeling. Although, several dynamic programming algorithms exist for the prediction of pseudoknots using thermodynamic approaches, they are neither reliable nor efficient. On ..."
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Cited by 53 (2 self)
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Motivation: Pseudoknots have generally been excluded from the prediction of RNA secondary structures due to its difficulty in modeling. Although, several dynamic programming algorithms exist for the prediction of pseudoknots using thermodynamic approaches, they are neither reliable nor efficient. On the other hand, comparative methods are more reliable, but are often done in an ad hoc manner and require expert intervention. Maximum weighted matching, an algorithm for pseudoknot prediction with comparative analysis, suffers from lowprediction accuracy in many cases.
Thermodynamic analysis of interacting nucleic acid strands
 SIAM Rev
, 2007
"... Abstract. Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary stru ..."
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Cited by 31 (4 self)
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Abstract. Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for singlestranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium basepairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality.
Paradigms for computational nucleic acid design
 Nucleic Acids Res
"... The design of DNA and RNA sequences is critical for many endeavors, from DNA nanotechnology, to PCRbased applications, to DNA hybridization arrays. Results in the literature rely on a wide variety of design criteria adapted to the particular requirements of each application. Using an extensivelyst ..."
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Cited by 26 (3 self)
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The design of DNA and RNA sequences is critical for many endeavors, from DNA nanotechnology, to PCRbased applications, to DNA hybridization arrays. Results in the literature rely on a wide variety of design criteria adapted to the particular requirements of each application. Using an extensivelystudied thermodynamic model, we perform a detailed study of several criteria for designing sequences intended to adopt a target secondary structure. We conclude that superior design methods should explicitly implement both a positive design paradigm (optimize affinity for the target structure) and a negative design paradigm (optimize specificity for the target structure). The commonly used approaches of sequence symmetry minimization and minimum free energy satisfaction primarily implement negative design and can be strengthened by introducing a positive design component. Surprisingly, our findings hold for a wide range of secondary structures and are robust to modest perturbation of the thermodynamic parameters used for evaluating sequence quality, suggesting the feasibility and ongoing utility of a unified approach to nucleic acid design as parameter sets are further refined. Finally, we observe that designing for thermodynamic stability does not determine folding kinetics, emphasizing the opportunity for extending design criteria to target kinetic features of the energy landscape.
P.: A discipline of dynamic programming over sequence data
 Science of Computer Programming
, 2004
"... Abstract. Dynamic programming is a classical programming technique, applicable in a wide variety of domains such as stochastic systems analysis, operations research, combinatorics of discrete structures, flow problems, parsing of ambiguous languages, and biosequence analysis. Little methodology has ..."
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Cited by 26 (12 self)
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Abstract. Dynamic programming is a classical programming technique, applicable in a wide variety of domains such as stochastic systems analysis, operations research, combinatorics of discrete structures, flow problems, parsing of ambiguous languages, and biosequence analysis. Little methodology has hitherto been available to guide the design of such algorithms. The matrix recurrences that typically describe a dynamic programming algorithm are difficult to construct, errorprone to implement, and, in nontrivial applications, almost impossible to debug completely. This article introduces a discipline designed to alleviate this problem. We describe an algebraic style of dynamic programming over sequence data. We define its formal framework, based on a combination of grammars and algebras, and including a formalization of Bellman’s Principle. We suggest a language used for algorithm design on a convenient level of abstraction. We outline three ways of implementing this language, including an embedding in a lazy functional language. The workings of the
Kinefold web server for RNA/DNA folding path and structure prediction including pseudoknots and knots
 Nucleic Acids Res
, 2005
"... The Kinefold web server provides a web interface for stochastic folding simulations of nucleic acids on second to minute molecular time scales. Renaturation or cotranscriptional folding paths are simulated at the level of helix formation and dissociation in agreement with the seminal experimental r ..."
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Cited by 21 (1 self)
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The Kinefold web server provides a web interface for stochastic folding simulations of nucleic acids on second to minute molecular time scales. Renaturation or cotranscriptional folding paths are simulated at the level of helix formation and dissociation in agreement with the seminal experimental results. Pseudoknots and topologically ‘entangled ’ helices (i.e. knots) are efficiently predicted taking into account simple geometrical and topological constraints. To encourage interactivity, simulations launched as immediate jobs are automatically stopped after a few seconds and return adapted recommendations. Users can then choose to continue incomplete simulations using the batch queuing system or go back and modify suggested options in their initial query. Detailed output provide (i) a series of low free energy structures, (ii) an online animated folding path and (iii) a programmable trajectory plot focusing on a few helices of interest to each user. The service can be accessed at
Combinatorics of RNA structures with pseudoknots. Bull.Math.Biol
 Bull.Math.Biol
, 2007
"... Abstract. In this paper we derive the generating function of RNA structures with pseudoknots. We enumerate all knoncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition we enumerate pseudoknot structures over circular RNA. For 3noncrossing ..."
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Cited by 20 (15 self)
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Abstract. In this paper we derive the generating function of RNA structures with pseudoknots. We enumerate all knoncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition we enumerate pseudoknot structures over circular RNA. For 3noncrossing RNA structures and RNA secondary structures we present a novel 4term recursion formula and a 2term recursion, respectively. Furthermore we enumerate for arbitrary k all knoncrossing, restricted RNA structures i.e. knoncrossing RNA structures without 2arcs i.e. arcs of the form (i, i + 2), for 1 ≤ i ≤ n − 2. 1.
Translational Control by RNARNA Interaction Improved Computation of RNARNA Binding Thermodynamics
"... Abstract. The thermodynamics of RNARNA interaction consists of two components: the energy necessary to make a potential binding region accessible, i.e. unpaired, and the energy gained from the base pairing of the two interaction partners. We show here that both components can be efficiently compute ..."
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Cited by 14 (3 self)
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Abstract. The thermodynamics of RNARNA interaction consists of two components: the energy necessary to make a potential binding region accessible, i.e. unpaired, and the energy gained from the base pairing of the two interaction partners. We show here that both components can be efficiently computed using an improved variant of RNAup. The method is then applied to a set of bacterial small RNAs involved in translational control. In all cases of biologically active sRNA target interactions, the target sites predicted by RNAup are in perfect agreement with literature. In addition to prediction of target site location, RNAup can also be used to determine the mode of sRNA action. Using information about target site location and the accessibility change resulting from sRNA binding we can discriminate between positive and negative regulators of translation. 1
Approximating the 2interval pattern problem
 IN PROCEEDINGS OF THE 13TH ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA
, 2005
"... We address the problem of approximating the 2Interval Pattern problem over its various models and restrictions. This problem, which is motivated by RNA secondary structure prediction, asks to find a maximum cardinality subset of a 2interval set with respect to some prespecified model. For each s ..."
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Cited by 14 (6 self)
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We address the problem of approximating the 2Interval Pattern problem over its various models and restrictions. This problem, which is motivated by RNA secondary structure prediction, asks to find a maximum cardinality subset of a 2interval set with respect to some prespecified model. For each such model, we give varying approximation quality depending on the different possible restrictions imposed on the input 2interval set.
Classifying RNA Pseudoknotted Structures
, 2004
"... Computational prediction of the minimum free energy (mfe) secondary structure of an RNA molecule from its base sequence is valuable in understanding the structure and function of the molecule. Since the general problem of predicting pseudoknotted secondary structures is NPhard, several algorithms ..."
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Cited by 13 (1 self)
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Computational prediction of the minimum free energy (mfe) secondary structure of an RNA molecule from its base sequence is valuable in understanding the structure and function of the molecule. Since the general problem of predicting pseudoknotted secondary structures is NPhard, several algorithms have been proposed that find the mfe secondary structure from a restricted class of secondary structures. In this work, we order the algorithms by generality of the structure classes that they handle. We provide simple characterizations of the classes of structures handled by four algorithms, as well as linear time methods to test whether a given secondary structure is in three of these classes. We report on the percentage of biological structures from the PseudoBase and Gutell databases that are handled by these two algorithms.
Asymmetry in RNA pseudoknots: observation and theory
 Nucleic Acids Res
, 2005
"... RNA can fold into a topological structure called a pseudoknot, composed of nonnested doublestranded stems connected by singlestranded loops. Our examination of the PseudoBase database of pseudoknotted RNA structures reveals asymmetries in the stem and loop lengths and provocative composition diffe ..."
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Cited by 11 (0 self)
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RNA can fold into a topological structure called a pseudoknot, composed of nonnested doublestranded stems connected by singlestranded loops. Our examination of the PseudoBase database of pseudoknotted RNA structures reveals asymmetries in the stem and loop lengths and provocative composition differences between the loops. By taking into account differences between major and minor grooves of the RNA double helix, we explain much of the asymmetry with a simple polymer physics model and statistical mechanical theory, with only one adjustable parameter.