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Published on: September 30, 2016
Algebraic and combinatorial properties of common RNA pseudoknot classes with applications
Markus E Nebel1, Frank Weinberg
1Computer Science Department, University of Kaiserslautern, Gottlieb Daimler Str. 48, Kaiserslautern 67663, Germany. nebel@informatik.uni-kl.de
Summary
Predicting RNA structures with pseudoknots is complex. This study unifies algebraic views of RNA structure classes, enabling linear time recognition algorithms and solving open enumeration problems for pseudoknot classes.
Area of Science:
- Computational Biology
- Bioinformatics
- Structural Biology
Background:
- RNA structure prediction with pseudoknots is an NP-complete problem.
- Existing algorithms focus on specific subclasses of RNA structures.
- A unified approach is needed to address the complexity of pseudoknots.
Purpose of the Study:
- To introduce a unifying algebraic framework for various RNA structure classes.
- To develop linear time recognition algorithms for these classes.
- To derive the asymptotic size of these classes and solve enumeration problems.
Main Methods:
- Developed a unifying algebraic description for RNA structure classes.
- Created linear time recognition algorithms based on the algebraic framework.
- Translated algebraic descriptions into multiple context-free grammars.
- Established a correspondence between multiple context-free grammars and generating functions.
Main Results:
- Introduced a general algebraic view applicable to most RNA structure subclasses.
- Developed linear time algorithms for recognizing membership in these classes.
- Derived precise asymptotic sizes for RNA structure classes, including the Rivas & Eddy class of pseudoknots.
Conclusions:
- The unifying algebraic approach simplifies the analysis of RNA structure classes.
- Linear time recognition algorithms are now available for various pseudoknot subclasses.
- This work provides solutions to long-standing problems in RNA structure enumeration.
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