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NUPACK
The Nucleic Acid Package, is a growing software suite for the analysis and design of nucleic acid systems.〔Zadeh, J.N., C.D. Steenberg, J.S. Bois, B.R. Wolfe, A.R. Khan, M.B. Pierce, R.M. Dirks, and N.A. Pierce, NUPACK: analysis and design of nucleic acid systems. Journal of Computational Chemistry〕 Jobs can be run online on the NUPACK webserver or NUPACK source code can be downloaded and compiled locally. NUPACK algorithms are formulated in terms of nucleic acid secondary structure. In most cases, pseudoknots are excluded from the structural ensemble.
== Secondary structure model ==
The secondary structure of multiple interacting strands is defined by a list of base
pairs.〔Dirks, R.M., J.S. Bois, J.M. Schaeffer, E. Winfree, and N.A. Pierce, Thermodynamic analysis of interacting nucleic acid strands SIAM Review, 2007. 49(1): p. 65-88.〕 A polymer graph for a secondary structure can be constructed by ordering the strands around a circle, drawing the backbones in succession from 5’ to 3’ around the circumference with a nick between each strand, and drawing straight lines connecting paired bases. A secondary structure is pseudoknotted if every strand ordering corresponds to a polymer graph with crossing lines. A secondary structure is connected if no subset of the strands is free of the others. Algorithms are formulated in terms of ordered complexes, each corresponding to the structural ensemble of all connected polymer graphs with no crossing lines for a particular ordering of a set of strands. The free energy of an unpseudoknotted secondary structure is calculated using nearest-neighbor empirical parameters for RNA in 1M Na+ 〔Serra, M.J. and D.H. Turner, Predicting thermodynamic properties of RNA. Methods in Enzymology, 1995. 259: p. 242-261.〕〔Mathews, D.H., J. Sabina, M. Zuker, and D.H. Turner, Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. Journal of Molecular Biology, 1999. 288: p. 911-940.〕 or for DNA in user-specified Na+ and Mg++ concentrations;〔SantaLucia, J., J., A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics. Proceedings of the National Academy of Sciences of the United States of America, 1998. 95(4): p. 1460-1465.〕〔SantaLucia, J. and D. Hicks, The thermodynamics of DNA structural motifs. Annual Review of Biophysics and Biomolecular Structure, 2004. 33: p. 415-440.〕〔Koehler, R.T. and N. Peyret, Thermodynamic properties of DNA sequences: characteristic values for the human genome. Bioinformatics, 2005. 21(16): p. 3333-3339.〕 additional parameters are employed for the analysis of pseudoknots (single RNA strands only).〔Dirks, R.M. and N.A. Pierce, A partition function algorithm for nucleic acid secondary structure including pseudoknots. Journal of Computational Chemistry, 2003. 24: p. 1664-1677.〕〔Dirks, R.M. and N.A. Pierce, An algorithm for computing nucleic acid base-pairing probabilities including pseudoknots. Journal of Computational Chemistry, 2004. 25: p. 1295-1304.〕
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