Computational prediction of nucleic acid secondary structure: Methods, applications, and challenges
Theoretical Computer Science
biRNA: fast RNA-RNA binding sites prediction
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Towards domain-based sequence design for DNA strand displacement reactions
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Strand algebras for DNA computing
Natural Computing: an international journal
Fast parallel DNA-based algorithms for molecular computation: discrete logarithm
The Journal of Supercomputing
Localized hybridization circuits
DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
A framework for modeling DNA based molecular systems
DNA'06 Proceedings of the 12th international conference on DNA Computing
Time and space efficient RNA-RNA interaction prediction via sparse folding
RECOMB'10 Proceedings of the 14th Annual international conference on Research in Computational Molecular Biology
On the Local Form and Transitions of Pre-symmetry Sets
Journal of Mathematical Imaging and Vision
Enumeration approach to computing chemical equilibria
Theoretical Computer Science
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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 single-stranded 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 base-pairing 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.