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Computational RNA secondary structure design: empirical complexity and improved methods.

Aguirre-Hernández R, Hoos HH, Condon A - BMC Bioinformatics (2007)

Bottom Line: Such understanding provides the basis for improving the performance of one of the best algorithms for this problem, RNA-SSD, and for characterising its limitations.We also found that the algorithms are in general faster when constraints are placed only on paired bases in the structure.Our analysis helps to better understand the strengths and limitations of both the RNA-SSD and RNAinverse algorithms, and suggests ways in which the performance of these algorithms can be further improved.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of Applied Mathematics, University of British Columbia, Vancouver, BC, Canada. rosalia@cs.ubc.ca <rosalia@cs.ubc.ca>

ABSTRACT

Background: We investigate the empirical complexity of the RNA secondary structure design problem, that is, the scaling of the typical difficulty of the design task for various classes of RNA structures as the size of the target structure is increased. The purpose of this work is to understand better the factors that make RNA structures hard to design for existing, high-performance algorithms. Such understanding provides the basis for improving the performance of one of the best algorithms for this problem, RNA-SSD, and for characterising its limitations.

Results: To gain insights into the practical complexity of the problem, we present a scaling analysis on random and biologically motivated structures using an improved version of the RNA-SSD algorithm, and also the RNAinverse algorithm from the Vienna package. Since primary structure constraints are relevant for designing RNA structures, we also investigate the correlation between the number and the location of the primary structure constraints when designing structures and the performance of the RNA-SSD algorithm. The scaling analysis on random and biologically motivated structures supports the hypothesis that the running time of both algorithms scales polynomially with the size of the structure. We also found that the algorithms are in general faster when constraints are placed only on paired bases in the structure. Furthermore, we prove that, according to the standard thermodynamic model, for some structures that the RNA-SSD algorithm was unable to design, there exists no sequence whose minimum free energy structure is the target structure.

Conclusion: Our analysis helps to better understand the strengths and limitations of both the RNA-SSD and RNAinverse algorithms, and suggests ways in which the performance of these algorithms can be further improved.

Show MeSH
Impact of constrained bases on the difficulty of secondary structure design using RNA-SSD. Correlation between the fraction of bases constrained in a particular structure (x-axis) and the median expected run time for designing the structure with RNA-SSD (y-axis). We report the fraction of constrained bases after propagation for constraints on randomly chosen base positions. This fraction, for both randomly chosen bases and stems, corresponds to the median fraction of bases constrained in a set of 50 constraints that were generated by fixing a given percentage of bases or stems. There are two curves in each graph, one for designing structures with base constraints located in random positions and the other for constraints located in stems. (a) VS ribozyme from Neurospora mitochondria; (b) Group II intron ribozyme D135 from Saccharomyces.
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Figure 9: Impact of constrained bases on the difficulty of secondary structure design using RNA-SSD. Correlation between the fraction of bases constrained in a particular structure (x-axis) and the median expected run time for designing the structure with RNA-SSD (y-axis). We report the fraction of constrained bases after propagation for constraints on randomly chosen base positions. This fraction, for both randomly chosen bases and stems, corresponds to the median fraction of bases constrained in a set of 50 constraints that were generated by fixing a given percentage of bases or stems. There are two curves in each graph, one for designing structures with base constraints located in random positions and the other for constraints located in stems. (a) VS ribozyme from Neurospora mitochondria; (b) Group II intron ribozyme D135 from Saccharomyces.

Mentions: Figure 9 shows how the hardness of the design problem depends on the fraction of constrained bases for randomly located base constraints and for constrained stems. As can be seen from these results, there are some cases in which base constraints of either type render a secondary design problem easier, while in other cases, we observe a substantial increase in hardness as a critical number of bases is constrained.


Computational RNA secondary structure design: empirical complexity and improved methods.

Aguirre-Hernández R, Hoos HH, Condon A - BMC Bioinformatics (2007)

Impact of constrained bases on the difficulty of secondary structure design using RNA-SSD. Correlation between the fraction of bases constrained in a particular structure (x-axis) and the median expected run time for designing the structure with RNA-SSD (y-axis). We report the fraction of constrained bases after propagation for constraints on randomly chosen base positions. This fraction, for both randomly chosen bases and stems, corresponds to the median fraction of bases constrained in a set of 50 constraints that were generated by fixing a given percentage of bases or stems. There are two curves in each graph, one for designing structures with base constraints located in random positions and the other for constraints located in stems. (a) VS ribozyme from Neurospora mitochondria; (b) Group II intron ribozyme D135 from Saccharomyces.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC1808480&req=5

Figure 9: Impact of constrained bases on the difficulty of secondary structure design using RNA-SSD. Correlation between the fraction of bases constrained in a particular structure (x-axis) and the median expected run time for designing the structure with RNA-SSD (y-axis). We report the fraction of constrained bases after propagation for constraints on randomly chosen base positions. This fraction, for both randomly chosen bases and stems, corresponds to the median fraction of bases constrained in a set of 50 constraints that were generated by fixing a given percentage of bases or stems. There are two curves in each graph, one for designing structures with base constraints located in random positions and the other for constraints located in stems. (a) VS ribozyme from Neurospora mitochondria; (b) Group II intron ribozyme D135 from Saccharomyces.
Mentions: Figure 9 shows how the hardness of the design problem depends on the fraction of constrained bases for randomly located base constraints and for constrained stems. As can be seen from these results, there are some cases in which base constraints of either type render a secondary design problem easier, while in other cases, we observe a substantial increase in hardness as a critical number of bases is constrained.

Bottom Line: Such understanding provides the basis for improving the performance of one of the best algorithms for this problem, RNA-SSD, and for characterising its limitations.We also found that the algorithms are in general faster when constraints are placed only on paired bases in the structure.Our analysis helps to better understand the strengths and limitations of both the RNA-SSD and RNAinverse algorithms, and suggests ways in which the performance of these algorithms can be further improved.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of Applied Mathematics, University of British Columbia, Vancouver, BC, Canada. rosalia@cs.ubc.ca <rosalia@cs.ubc.ca>

ABSTRACT

Background: We investigate the empirical complexity of the RNA secondary structure design problem, that is, the scaling of the typical difficulty of the design task for various classes of RNA structures as the size of the target structure is increased. The purpose of this work is to understand better the factors that make RNA structures hard to design for existing, high-performance algorithms. Such understanding provides the basis for improving the performance of one of the best algorithms for this problem, RNA-SSD, and for characterising its limitations.

Results: To gain insights into the practical complexity of the problem, we present a scaling analysis on random and biologically motivated structures using an improved version of the RNA-SSD algorithm, and also the RNAinverse algorithm from the Vienna package. Since primary structure constraints are relevant for designing RNA structures, we also investigate the correlation between the number and the location of the primary structure constraints when designing structures and the performance of the RNA-SSD algorithm. The scaling analysis on random and biologically motivated structures supports the hypothesis that the running time of both algorithms scales polynomially with the size of the structure. We also found that the algorithms are in general faster when constraints are placed only on paired bases in the structure. Furthermore, we prove that, according to the standard thermodynamic model, for some structures that the RNA-SSD algorithm was unable to design, there exists no sequence whose minimum free energy structure is the target structure.

Conclusion: Our analysis helps to better understand the strengths and limitations of both the RNA-SSD and RNAinverse algorithms, and suggests ways in which the performance of these algorithms can be further improved.

Show MeSH