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MATH:7450 (22M:305) Topics in Topology: Scientific and Engineering Applications of Algebraic Topology Nov 22, 2013: Topological methods for exploring low-density states in biomolecular folding pathways . Fall 2013 course offered through the

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  1. MATH:7450 (22M:305) Topics in Topology: Scientific and Engineering Applications of Algebraic Topology Nov 22, 2013: Topological methods for exploring low-density states in biomolecular folding pathways. Fall 2013 course offered through the University of Iowa Division of Continuing Education Isabel K. Darcy, Department of Mathematics Applied Mathematical and Computational Sciences, University of Iowa http://www.math.uiowa.edu/~idarcy/AppliedTopology.html

  2. You can join live lecture Wednesday and Friday either by going to or joining via regular classroom. NOTE: to ask questions, you need to joing via regular classroom.

  3. IMA Annual Program Year Workshop, December 9-13, 2013 Topological Structures in Computational Biology http://www.ima.umn.edu/2013-2014/W12.9-13.13/ Tuesday December 10, 2013 11:30am-12:20pm PekLum (Ayasdi, Inc.) Friday December 13, 2013 9:00am-9:50am Monica Nicolau (Stanford University)

  4. http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.htmlhttp://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

  5. Data Set: Example: Point cloud data representing a hand. Function f : Data Set  R Example: x-coordinate f : (x, y, z)  x http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

  6. Put data into overlapping bins. Example: f-1(ai, bi) (()()()()()) Function f : Data Set  R Ex 1: x-coordinate f : (x, y, z)  x http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

  7. D) Cluster each bin & create network. Vertex = a cluster of a bin. Edge = nonempty intersection between clusters http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

  8. D) Cluster each bin & create network. Vertex = a cluster of a bin. Edge = nonempty intersection between clusters http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

  9. D) Cluster each bin & create network. Vertex = a cluster of a bin. Edge = nonempty intersection between clusters http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

  10. A) Data Set Example: Point cloud data representing a hand. B) Function f : Data Set  R Example: x-coordinate f : (x, y, z)  x Put data into overlapping bins. Example: f-1(ai, bi) Cluster each bin & create network. Vertex = a cluster of a bin. Edge = nonempty intersection between clusters http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

  11. Chose filter http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

  12. Chose filter http://www.nature.com/srep/2013/130207/srep01236/full/srep01236.html

  13. http://scitation.aip.org/content/aip/journal/jcp/130/14/10.1063/1.3103496http://scitation.aip.org/content/aip/journal/jcp/130/14/10.1063/1.3103496

  14. Data: Contact maps from 2,800 Serial Replica Exchange Molecular Dynamics (SREMD) simulations of the GCAA tetraloopon the Folding@home distributed computing platform. • 760 trajectories with a complete unfolding event • 550 trajectories with a complete refolding event. Goal: To determine secondary structure pathways between folded and unfolded state

  15. Problem: Many more folded and unfolded conformations than intermediate conformations How to distinguish intermediate conformations from noise? Solution Choose f: space of conformations  R f(conformation) = density

  16. 550 trajectories with a complete refolding event 2952 configurations

  17. Distance = Hamming distance

  18. 550 trajectories with a complete refolding event 2952 configurations

  19. 760 trajectories with a complete refolding event 4330 configurations

  20. An eQTL biological data visualization challenge and approaches from the visualization community, Bartlett et al. BMC Bioinformatics 2012, 13(Suppl 8):S8 Mapper applied to SNP data: http://www.biomedcentral.com/1471-2105/13/S8/S8

  21. Monday December 09, 2013 9:00am-9:50am Visualizing and Exploring Molecular Simulation Data via Energy Landscape Metaphor YusuWang (The Ohio State University)

  22. Motivation: Let S = set of conformations of the survivin protein Energy landscape E: S  R E(conformation) = energy of the conformation http://pubs.acs.org/doi/pdf/10.1021/jp911085d https://parasol.tamu.edu/foldingserver/FAQ_Technique.php

  23. Data from: 20,000 conformations obtained via replica exchange molecular dynamics. The backbone = 46 alpha-carbon atoms = 1035 dimensional vector of pairwise distances describing the protein shape. Intrinsic dimensionality of the conformational manifold has been estimated at around 20.

  24. http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf contour tree level set = f-1(r) = { x in M | f(x) = r } A contour = a connected component of a level set. Let Cq = the contour in M that is collapsed to q Let TopoComp(edge) = UCq q in edge

  25. Given f: Md R, Find g: R2 R such that f and g share same contour tree (2) the area of TopoComp(edge) of g is the same as the volumes of the corresponding TopoComp(edge) of f for each edge in the contour tree. Expands upon Weber’s Topological Landscapes, 2007

  26. http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

  27. http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

  28. http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

  29. Figure 8: (a) Slice-and-dice and (b) Voronoitreemaplayouts of terrains in Figure 6. http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

  30. http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

  31. http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

  32. http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

  33. http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

  34. http://www.cse.ohio-state.edu/~yusu/papers/Eurovis10.pdf

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