The Mathematical Biocomplexity Laboratory studies information in biological systems and networks using topology. In the presence of mutations, biological systems create redundancy, preserving key information. For instance, RNA folding creates neutral networks formed by sequences of one fixed structure. We develop a topological framework for networks.

Highlights

People

Principal Investigators

Fenix Huang

Research Assistant Professor

Christian Reidys

Director and Professor, Mathematical Biocomplexity

Publications

2015


Barrett C, Huang FW, Reidys CM. Evidence of higher order patterns in information transmission between nucleotide sequences and folded molecular shapes of RNA. New York City, New York, USA; 2015. 9th EAI International Conference on Bio-inspired Information and Communications Technologies (former.  

Barrett C, Huang FW, Reidys CM. Sequence-structure relations of biopolymers. arXiv preprint arXiv:1511.03141. 2015;Submitted.  

Chen RXF, Reidys CM. A Zagier-Stanley result and various distances of permutations via plane permutations. http://arxiv.org/abs/1502.07674v3. 2015;Submitted.  

Chen RXF, Reidys CM. Linear sequential dynamical systems and the M\"{o} bius functions of partially ordered sets. arXiv preprint arXiv:1510.04930. 2015;Submitted.  

Chen RXF, Reidys CM. On the local genus distribution of graph embeddings. Journal of Combinatorial Mathematics and Combinatorial Computing. 2015;In Press.  

Chen RXF, Reidys CM. On various formulas counting one-face maps. arXiv preprint arXiv:1510.05038. 2015;Submitted.  

Fu B, Han H, Reidys C. On the RNA-RNA interaction structures of fixed topological genus. Math. Biosc.. 2015;62:88–104.  

Huang FWD, Reidys CM. A topological framework for signed permutations. arXiv preprint arXiv:1410.4706. 2015;Submitted.  

Huang FWD, Reidys CM. Shapes of topological RNA structures. Math Biosci. 2015;270, Part A:57–65.  http://www.sciencedirect.com/science/article/pii/S0025556415002102

2014


Fu B, Reidys C. Shapes of interacting RNA complexes. J. Comp. Biol.. 2014;21(9):649–664.  

Han H, Li T, Reidys C. Combinatorics of γ-structures. J. Comp. Biol.. 2014;21(8):591–608.  

Li TJX, Reidys CM. A combinatorial interpretation of the K*g(n) coefficients. arXiv preprint arXiv:1406.3162. 2014.  

Reidys C, Jin E. The evolution of the random reversal graph. Appl. Math. Comp.. 2014;227:347â?358.  

2013


Andersen J, Chekhov L, Penner R, Reidys C, Sulkowski P. Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces. Nucl. Phys. B. 2013;866(3):414–443.  

Han H, Reidys C. A bijection between unicellular and bicellular maps. arXiv:1301.7177. 2013.  

Han HSW, Reidys CM. A Bijection for Tricellular Maps. ISRN Discrete Mathematics. 2013;2013.  

Huang F, Nebel M, C R. Generation of RNA pseudoknot structures with topological genus filtration. Math. Biosc.. 2013;245(2):216–225.  

Li T, Reidys C. The genus filtration of γ -structures. Math. Biosc.. 2013;241(1):24–33.  

Qin J, Reidys C. On topological RNA interaction structures. J. Comp. Biol.. 2013;20(7):495–513.  

2012


Andersen J, Huang F, Penner R, Reidys C. Topology of RNA-RNA interaction structures. J. Comp. Biol.. 2012;19(7):928–943.  

Han H, Reidys C. The 5'-3' distance of RNA secondary structures. J. Comp. Biol.. 2012;19(7):867–878.  

Han H, Reidys C. A phase transition in energy-filtered RNA secondary structures structures. J. Comp. Biol.. 2012;19(10):1105–1119.  

Hofacker I, Reidys C, Stadler P. Symmetric Circular Matchings and RNA Folding. Discr. Math.. 2012;312(1):100–112.  

Huang F, Reidys C. On the combinatorics of sparsification. Algor. Molec. Biol.. 2012;7:28.  

Reidys CM, Huang FW, Andersen JE, Penner RC, Stadler PF, Nebel ME. Addendum: topology and prediction of RNA pseudoknots. Bioinformatics. 2012;28(2):300.  http://www.ncbi.nlm.nih.gov/pubmed/22106334

2011


Jin E, Reidys C. Random induced subgraphs of Cayley graphs induced by transpositions. Discr. Math.. 2011;311(21):2496–2511.  

Li A, Marz M, Qin J, Reidys C. RNA-RNA interaction prediction based on multiple sequence alignments. Bioinformatics. 2011;27(4):456–463.  http://bioinformatics.oxfordjournals.org/content/27/4/456.full.pdf

Li T, Reidys C. Combinatorial analysis of interacting RNA molecules. Math. Biosc.. 2011;233(1):47–58.  

Li T, Reidys C. Combinatorics of RNA-RNA interaction. J. Math. Biol.. 2011;3:1–28.  

Nebel M, Reidys C, Wang R. Loops in canonical RNApseudoknot structures. J. Comp. Biol.. 2011;18(12):1793–1806.  

Reidys C, Huang F, Andersen J and, Stadler P, Nebel ME. Topology and prediction of RNA pseudoknots. Bioinformatics. 2011;27(8):1076–1085.  http://bioinformatics.oxfordjournals.org/content/27/8/1076.full.pdf

2010


Gao J, Li L, Reidys C. Inverse Folding of RNA Pseudoknot Structures. Algor. Molec. Biol.. 2010;5:R27.  

Huang F, Qin J, Reidys C, Stadler P. Target prediction and a statistical sampling algorithm for RNA-RNA interaction. Bioinformatics. 2010;26(2):175–181.  http://bioinformatics.oxfordjournals.org/content/26/2/175.full.pdf

Huang F, Reidys C. On the uniform generation of modular diagrams. Electr. J. Combin.. 2010;17:R175.  

Reidys C, Wang R, Zhao A. Modular, k-noncrossing diagrams. Electr. J. Combin.. 2010;17(1):R76.  

Wang R, Reidys C. Shapes of RNA pseudoknot structures interaction. J. Comp. Biol.. 2010;17(11):1575–1590.  

2009


Chen W, Qin J, Reidys C. Crossings and Nestings of tangled-diagrams. Electr. J. Combin.. 2009;15:R86.  

Chen W, Qin J, Reidys C, Zeilberger D. Efficient Counting and Asymptotics of k-noncrossing tangled-diagrams. Electr. J. Combin.. 2009;16:R37.  

Han H, Reidys C. Stacks in canonical RNA pseudoknot structures. Math. Biosc.. 2009;219:7–14.  

Huang F, Li L, Reidys C. Sequence-structure relations of pseudoknot RNA. BMC Bioinformatics. 2009;10(Suppl 1):S39.  http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2648775/pdf/1471-2105-10-S1-S39.pdf

Huang F, Peng W, Reidys C. Folding 3-noncrossing RNA pseudoknot structures. J. Comp. Biol.. 2009;11(16):1549–1575.  

Huang F, Qin J, Reidys C, Stadler P. Partition function and base pairing probabilities for RNA-RNA interaction prediction. Bioinformatics. 2009;25(20):2646–2654.  http://bioinformatics.oxfordjournals.org/content/25/20/2646.full.pdf

Jin E, Reidys C. Combinatorial design of pseudoknot RNA. Adv. Appl. Math.. 2009;42:135–151.  

Jin E, Reidys C. On the decomposition of k-noncrossing RNA Structures. Adv. Appl. Math.. 2009;44(1):53–70.  

Jin E, Reidys C. RNA Pseudoknots Structures with Arc-length >=3 and Stack-length >= 2. Discr. Appl. Math.. 2009;158(1):25–36.  

Reidys C. Large Components of Random induced subgraphs of n-cubes. Discr. Math.. 2009;309:3113–3124.  

W C, Han H, Reidys C. Random k-noncrossing RNA structures. Pnas. 2009;106(52):22061–22066.  

2008


Han H, Reidys C. Pseudoknot RNA structures with arc-length >= 4. J. Comp. Biol.. 2008;15:1195–1208.  

Huang F, Reidys C. Statistics of canonical RNA Pseudoknot Structures. J. Theoret. Biol.. 2008;253:570–578.  

Jin E, J Q, Reidys C. Combinatorics of RNA structures with pseudoknots. Bull. Math. Biol.. 2008;70:46–67.  

Jin E, Qin J, Reidys C. Neutral networks of sequence to shape maps. J. Theoret. Biol.. 2008;250:484–497.  

Jin E, Reidys C. Central and Local Limit Theorems for RNA Structures. J. Theoret. Biol.. 2008;250:547–559.  

Ma G, Reidys C. Canonical RNA pseudoknot structures. J. Comp. Biol.. 2008;15:1257–1273.  

2007


Reidys C. Combinatorics of Sequential Dynamical Systems. Discr. Math.. 2007;308:514–528.  

2006


Reidys C. Sequential Dynamical Systems over Words. Ann. Combin.. 2006;10:481–498.  

2005


Reidys C. Certain Morphisms of Sequential Dynamical Systems. Discr. Math.. 2005;296:245–257.  

2004


Reidys C. Distance-2-Matchings of Random Graphs. Ann. Combin.. 2004;8:93–101.  

2003


Reidys C. Covering Maps over n-Cubes. Ann. Combin.. 2003;6:419–426.  

Reidys C. Distances in Random Induced Subgraphs of generalized n- Cubes. Combin. Prob. and Comput.. 2003;11:599–605.  

2002


Reidys C, Stadler P. Combinatorial Landscapes. SIAM Rev.. 2002;44:3–54.  

2001


Mortveit H, Reidys C. Towards a calculus of biological networks. Z. Phys. Chem.. 2001;216:1–13.  

Reidys C, Forst C, Schuster P. Replication and mutation on neutral networks. Bull. Math. Biol.. 2001;63:57–94.  http://ac.els-cdn.com/S0092824000902064/1-s2.0-S0092824000902064-main.pdf?_tid=83fcaa50-9f53-11e5-894a-00000aacb360&acdnat=1449761855_9b1a4c9de98e54fe0b4b040fdd24cf39

Reidys C, Stadler P. Neutrality in fitness landscapes. Appl. Math. Comp.. 2001;117:321–350.  

Reidys CM. On acyclic orientations and sequential dynamical systems. Advances in Applied Mathematics. 2001;27(4):790–804.  

2000


Mortveit H, Reidys C. Discrete, sequential dynamical systems. Discr. Math.. 2000;226:281–295.  

Reidys C. Random Subgraphs of Cayley Graphs over p-Groups. Europ. J. of Combin.. 2000;21:1057–1066.  

Reidys C. Random Structures. Ann. Combin.. 2000;4:375–382.  

1998


Reidys C. Acyclic Orientations of Random Graphs. Adv. Appl. Math.. 1998;21:181–192.  

1997


Reidys C. Random induced subgraphs of generalized n-cubes. Adv. Appl. Math.. 1997;19:360–377.  

Reidys C, Stadler P, Schuster P. Generic Properties of Combinatory Maps and Neutral Networks of RNA Secondary Structures. Bull. Math. Biol.. 1997;59:339–397.  

1996


Gruner W, Strothmann D, Reidys C, et al. Analysis of RNA Sequence Structure Maps by Exhaustive Enumeration I. Neutral Networks. Chem. Month.. 1996;(127):355–374.  

Gruner W, Strothmann D, Reidys C, et al. Analysis of RNA Sequence Structure Maps by Exhaustive Enumeration II. Neutral Networks. Chem. Month.. 1996;(127):375–389.  

Reidys C, Stadler P. Bio-molecular Shapes and Algebraic Structures. Comp. Chem.. 1996;20(85-94).