Georgia Institute of Technology

Introduction

• M.S. Waterman and T.F. Smith. RNA Secondary Structure: A Complete Mathematical Analysis. Math Biosci, 42(3-4): 257-266, 1987.
• R. Nussinov, G. Pieczenik, J.R. Griggs and D.J. Kleitman. Algorithms for Loop Matchings. SIAM J Appl Math, 35(1): 68-82, 1978.

Sampling

• C. Y. Chan and Y. Ding. Boltzmann ensemble features of RNA secondary structures: a comparative analysis of biological RNA sequences and random shuffles. J Math Biol, 56(1-2):93-105, 2008.
• Y. Ding and C. E. Lawrence. A statistical sampling algorithm for RNA secondary structure prediction. Nucleic Acids Res, 31(24):7280-7301, 2003.
• Y. Ding, C. Y. Chan, and C. E. Lawrence. RNA secondary structure prediction by centroids in a Boltzmann weighted ensemble. RNA, 11: 1157-1166, 2005.

Metrics

• J. Allali and M.-F. Sagot. A New Distance for High Level RNA Secondary Structure Comparison. IEEE/ACM Trans Comput Biol Bioinform, 2(1): 3-14, 2005.
• V. Moulton, M. Zuker, M. Steel, R. Pointon, and David Penny. Metrics on RNA Secondary Structures. J Comput Biol, 7(1): 277-292, 2000.
• P. Bille. A survey on tree edit distance and related problems. Theoret Comput Sci, 337(1-3): 217-239, 2005.

Kinetics

• X. Tang, B. Kirkpatrick, S. Thomas, G. Song and N.M. Amato. Using Motion Planning to Study RNA Folding Kinetics. J Comput Biol, 12(6):862-881, 2005.
• S. R. Morgan and P. G. Higgs. Evidence for Kinetic Effects in the Folding of Large RNA Molecules. J Chem Phys, 105(11): 7152-7157, 1996.
• C. Flamm and I. L. Hofacker. Beyond energy minimization: approaches to the kinetic folding of RNA. Monatsh Chem, 139(4): 447-457, 2008.
• C. Flamm, W. Fontana, I. L. Hofacker, and Peter Schuster. RNA folding at elementary step resolution. RNA, 6: 325-338, 2000.
• H. Isambert and E. D. Siggia. Modeling RNA folding paths with pseudoknots: Application to hepatitis delta virus ribozyme. PNAS, 97(12): 6515-6520, 2000.
• M. Tacker, P. Stadler, E. Bornberg-Bauer, I. Hofacker, and P. Schuster. Algorithm independent properties of RNA secondary structure predictions. Eur Biophys J, 25(2): 115-130, 1996.

Combinatorics

• W. Schmitt and M. S. Waterman, Linear trees and RNA secondary structure. Discrete Appl Math, 51(3): 317-3232, 1994.
• I. Hofacker, P. Schuster, and P. Stadler. Combinatorics of RNA secondary structures. Discrete Appl Math, 88(1-3): 207-237, 1998.

Suboptimal structures

R. Giegerich, B. Voss, and M. Rehmsmeier. Abstract shapes of RNA. Nucleic Acids Res, 32(16): 4843-4851, 2004.

B. Voss, R. Giegerich, and M. Rehmsmeier. Complete probabilistic analysis of RNA shapes. BMC Biology, 4(5): Epub, 2006.

S. Wuchty, W. Fontana, I. L. Hofacker, and P. Schuster. Complete suboptimal folding of RNA and the stability of secondary structures. Biopolymers, 49(2): 145-65, 1999.

SHAPE

• K. E. Deigan, T. W. Li, D. H. Mathews, and K. M. Weeks. Accurate SHAPE-directed RNA structure determination. PNAS, 106(1): 97-102, 2009.
• J. T. Low and K. M. Weeks. SHAPE-directed RNA secondary structure prediction. Methods, 52(2): 105-158, 2010.
• W. Kladwang, C. C. VanLang, P. Codero, and R. Das. Understanding the Errors of SHAPE-Directed RNA Structure Modeling. Biochemistry, 50(37): 8049–8056, 2011.
• S. Quarrier, J. S. Martin, L. Davis-Neulander, A. Beauregard, and A. Laederach. Evaluation of the information content of RNA structure mapping data for secondary structure prediction. RNA, 16: 1108-1117, 2010.
• S. Washietl, I. L. Hofacker, P. F. Stadler, and M. Kellis. RNA folding with soft constraints: reconciliation of probing data and thermodynamic secondary structure prediction. RNA, 40(10): 4261-4272, 2012.
• S. Aviran, C. Trapnell, J. B. Lucks, S. A. Mortimer, S. Luo, G. P. Schroth, J. A. Doudna, A. P. Arkin, and L. Pachter. Modeling and automation of sequencing-based characterization of RNA structure. PNAS, 108(27): 11069-11074, 2011.

Stochastic models

• G. Ben Arous and J. Cerny. Dynamics of trap models. In Mathematical Statistical Physics Lecture Notes, Vol LXXXIII Les Houches Summer School, Elsevier, 2006.
• I. Shmulevich, E. R. Dougherty, S. Kim, and W. Zhang. Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics, 18(2): 261-274, 2002.
• A. Datta, A. Choudhary, M. L. Bittner, and E. R. Dougherty. External Control in Markovian Genetic Regulatory Networks. Machine Learning, 52(1-2): 169-181, 2003.
• S. Bornholdt. Boolean network models of cellular regulation: prospects and limitations. J. R. Soc. Interface, 5: S85-S94, 2008.
• P. D'haeseleer, S. Liang, and R. Somogyi. Genetic network inference: from co-expression clustering to reverse engineering. Bioinformatics, 16(8): 707-726, 2000.
• E. M. Airoldi. Getting started in probabilistic graphical models. PLoS Comput Biol, 3(12): e252, 2007.
• N. Friedman. Inferring cellular networks using probabilistic graphical models. Science, 303(5659): 799-805, 2004.
• E. Segal, M. Shapira, A. Regev, D. Pe'er, D. Botstein, D. Koller, and N. Friedman. Module networks: identifying regulatory modules and their condition-specific regulators from gene expression data. Nature Genetics 34: 166 - 176, 2003.